prepare version 3.6.3

Cosmetic bug ("safer" way to get same thing).

.clang-format

@@ -0,0 +1 @@
+BasedOnStyle:  Google

.gitignore

@@ -1,14 +1,62 @@
-*.o
-*.lo
-Makefile
-*.la
-.libs/
-SRC/.libs/
-UTIL/.libs/
+.hgignore
+
+# Generated by `autoreconf`
+Makefile.in
+aclocal.m4
+configure
 autom4te.cache/
+build-aux/
+m4/libtool.m4
+m4/lt*.m4
+
+# Generated by `./configure`
+Makefile
 config.log
 config.status
 libtool
+.deps/
+arpack.pc
+
+# Generated by `make`
+*.o
+*.mod
+*.lo
+*.la
+.libs/
+
+# CMake build directories
+BUILD
+Build
+build
+
+# Generated by `make check`
+*.log
+*.trs
+TESTS/dnsimp
+TESTS/bug_1315_double
+TESTS/bug_1315_single
+TESTS/bug_1323
+TESTS/bug_58_double
+TESTS/bug_79_double_complex
+TESTS/icb_arpack_c
+TESTS/icb_arpack_cpp
+TESTS/bug_142
+TESTS/bug_142_gen
+EXAMPLES/BAND/[sd][sn]bdr[123456]
+EXAMPLES/BAND/[cz]nbdr[1234]
+EXAMPLES/COMPLEX/[cz]ndrv[1234]
+EXAMPLES/NONSYM/[sd]ndrv[123456]
+EXAMPLES/SIMPLE/[sd]ssimp
+EXAMPLES/SIMPLE/[sdcz]nsimp
+EXAMPLES/SVD/[sd]svd
+EXAMPLES/SYM/[sd]sdrv[123456]
+PARPACK/EXAMPLES/MPI/p[sd]ndrv[13]
+PARPACK/EXAMPLES/MPI/p[sd]sdrv1
+PARPACK/EXAMPLES/MPI/p[cz]ndrv1
+PARPACK/TESTS/MPI/icb_parpack_c
+PARPACK/TESTS/MPI/icb_parpack_cpp
+PARPACK/TESTS/MPI/issue46
+
 *.lib
 *.def
 *.dll
@@ -18,5 +66,3 @@ libtool
 *.suo
 VISUAL_STUDIO/Release MKL/
 VISUAL_STUDIO/bin/
-TESTS/dnsimp
-

.hgignore

@@ -0,0 +1,34 @@
+syntax: glob
+
+.gitignore
+
+Makefile
+
+*.o
+*.lo
+*.la
+.libs/
+SRC/.libs/
+UTIL/.libs/
+arpack.pc
+autom4te.cache/
+config.log
+config.status
+libtool
+*.lib
+*.def
+*.dll
+*.bak
+*.exp
+*.u2d
+*.suo
+VISUAL_STUDIO/Release MKL/
+VISUAL_STUDIO/bin/
+TESTS/dnsimp
+PARPACK/EXAMPLES/MPI/pcndrv1
+PARPACK/EXAMPLES/MPI/pdndrv1
+PARPACK/EXAMPLES/MPI/pdndrv3
+PARPACK/EXAMPLES/MPI/pdsdrv1
+PARPACK/EXAMPLES/MPI/psndrv3
+PARPACK/EXAMPLES/MPI/pssdrv1
+PARPACK/EXAMPLES/MPI/pzndrv1

.travis.yml

@@ -0,0 +1,32 @@
+sudo: false
+
+language: c
+
+compiler:
+  - gcc
+
+addons:
+  apt:
+    packages:
+      - gfortran
+      - gcc
+      - g++
+      - openmpi-bin
+      - libopenmpi-dev
+      - cmake
+      - automake
+      - autoconf
+      - libblas-dev
+      - liblapack-dev
+
+jobs:
+  include:
+    - script: mkdir -p build && cd build && cmake -D EXAMPLES=ON -D MPI=OFF -D ICB=OFF               .. && make VERBOSE=1 && make test;
+    - script: mkdir -p build && cd build && cmake -D EXAMPLES=ON -D MPI=ON  -D ICB=OFF               .. && make VERBOSE=1 && make test;
+    - script: mkdir -p build && cd build && cmake -D EXAMPLES=ON -D MPI=OFF -D ICB=ON                .. && make VERBOSE=1 && make test;
+    - script: mkdir -p build && cd build && cmake -D EXAMPLES=ON -D MPI=ON  -D ICB=ON                .. && make VERBOSE=1 && make test;
+    - script: mkdir -p build && cd build && cmake -D EXAMPLES=ON -D MPI=ON  -D ICB=ON -DCOVERALLS=ON .. && make VERBOSE=1 && make test;
+    - script: ./bootstrap && ./configure                                                                && make VERBOSE=1 && make check && make distcheck;
+    - script: ./bootstrap && ./configure --enable-mpi                                                   && make VERBOSE=1 && make check && make distcheck;
+    - script: ./bootstrap && ./configure              --enable-icb                                      && make VERBOSE=1 && make check && make distcheck;
+    - script: ./bootstrap && ./configure --enable-mpi --enable-icb                                      && make VERBOSE=1 && make check && make distcheck;

CHANGES

@@ -1,12 +1,224 @@
+arpack-ng - 3.6.3
+
+[ Franck Houssen ]
+ * Add Fortran common initialization (block data).
+
+ [ Marco Caliari ]
+ * Give up forcing the initial residual to be in the range of the operator OP after a restart (Closes: #142).
+
+ -- Sylvestre Ledru <sylvestre@debian.org> Wed, 19 Sep 2018 09:59:59 +0200
+
+arpack-ng - 3.6.2
+
+ * Remove all trailing whitespaces
+
+ [ Franck Houssen ]
+ * Install: move headers into a dedicated directory (local/include/arpack).
+   (Closes #126)
+ * Add configuration summary.
+ * Improve the flag detection. Hopefully fix the ppc64el and other archs
+   issues in Debian
+
+ -- Sylvestre Ledru <sylvestre@debian.org> Sat, 23 Jun 2018 14:56:54 +0200
+
+arpack-ng - 3.6.1
+
+ [ Ruslan Kabatsayev ]
+ * Fix a regression on i386 and other archs (Closes #123)
+
+ -- Sylvestre Ledru <sylvestre@debian.org> Thu Jun 7 21:41:16 2018 +0200
+
+arpack-ng - 3.6.0
+
+ [ Franck Houssen ]
+ * Add support for ISO_C_BINDING (Fortran 2003) for ARPACK, PARPACK (Fortran <-> C/C++).
+   ARPACK:  example of   C/Fortran binding can be found in the         TESTS/icb_arpack_c.c          file.
+   ARPACK:  example of C++/Fortran binding can be found in the         TESTS/icb_arpack_cpp.cpp      file.
+   PARPACK: example of   C/Fortran binding can be found in the PARPACK/TESTS/MPI/icb_parpack_c.c     file.
+   PARPACK: example of C++/Fortran binding can be found in the PARPACK/TESTS/MPI/icb_parpack_cpp.cpp file.
+   DEBUG:   add support for debug.
+   STAT:    add support for statistics (timers, nb operations, ...).
+ * Provide tarball generation using cmake (cpack).
+ * Provide find_package for (cmake) users to find arpack-ng.
+
+ [ Denis Davydov ]
+ * Rename pslamch to pslamch10 to avoid symbol collision with Scalapack 2.0.2 in MPI context.
+
+ [ Kyle Guinn ]
+ * Autoconf cleanup; move generated files to the build-aux subdirectory.
+
+ [ Marco Caliari ]
+ * Force the initial residual to be in the range of the operator OP in the standard case, too (Closes: #79).
+
+ [ Sylvestre Ledru ]
+ * Add coverage information to improve testing: https://coveralls.io/github/opencollab/arpack-ng
+
+ [ Darcy Beurle]
+ * Add C++11 interface through arpack.hpp and parpack.hpp
+ * Rewrite C++ examples / tests demonstrating new C++11 interface
+ * Pre-C++11 interface available through arpack.h and parpack.h
+
+ -- Sylvestre Ledru <sylvestre@debian.org> Mon, 30 Oct 2017 14:21:48 +0200
+
+arpack-ng - 3.5.0
+
+ [ Julien Schueller ]
+ * Improve cmake build system: disable C++ detection, set default build type.
+
+ [ Marco Atzeri]
+ * Use AC_PROG_FC instead of AC_PROG_F77 for proper inizialization
+   for the usage of AC_FC_LINE_LENGTH. Noted on Cygwin.
+
+ [ Denis Davydov ]
+ * Improve cmake build system: add make install and fix shared libraries.
+
+ [ Zhang Z ]
+ * fix usages of DLACPY to not alias inputs
+   (patch from https://software.intel.com/en-us/articles/how-to-resolve-arpack-issues-with-intel-mkl-110-update-3)
+
+ [ Iskakov Sergei ]
+ *  Fix possible deadlock when PARPACK call uses communicator with a larger
+    number of CPUs than previous call
+
+ [ Kyle Guinn ]
+ * Portability improvements to the autotools build system.
+ * Let cmake guess the default installation directories.  Can be
+   overridden by changing CMAKE_INSTALL_LIBDIR and CMAKE_INSTALL_BINDIR.
+ * Shared libraries built by cmake now have their SONAME set identical to
+   those built by autotools.
+
+ [ Marco Caliari ]
+ * Avoid purification stage in [d,s]neupd.f if it requires division
+    by zero (Closes: #58)
+
+ -- Sylvestre Ledru <sylvestre@debian.org>  Mon, 15 May 2017 14:21:48 +0200
+
+arpack-ng - 3.4.0
+
+  [ Milan Bouchet-Valat ]
+  * Allow adding suffixes to symbols and library names to build ILP64 version
+    based on ILP64 BLAS/LAPACK with suffixes. This avoids conflicts when loading
+    libraries with different integer sizes in the same program.
+
+  [ Martin Reuter ]
+  * Add the support of cmake build system
+
+ -- Sylvestre Ledru <sylvestre@debian.org>  Sat, 02 Jul 2016 21:51:52 +0200
+
+arpack-ng - 3.3.0
+
+ [ Denis Davydov ]
+ * Rename pdlamch to pdlamch10 to avoid symbol collision with Scalapack 2.0.2 in MPI context.
+
+ [ Kyle Guinn ]
+ * General improvements on the build system
+ * libparpack links against libarpack (instead of doing a static link)
+
+ [ Guillaume Horel ]
+ * reverts using {d,s}lahqr from lapack 2
+ * use dlahqr from lapack 3 instead of dlaqrb (credit to Marco Caliari)
+
+ -- Sylvestre Ledru <sylvestre@debian.org>  Mon, 12 October 2015 08:40:51 +0200
+
+arpack-ng - 3.2.0
+
+ * Switch to github - https://github.com/opencollab/arpack-ng/
+
+ * Fix dsneupd select/calculate wrong eigenpairs if rvec = true
+   by using dlahqr and slahqr from lapack2 (Closes: #3)
+
+ -- Sylvestre Ledru <sylvestre@debian.org>  Sat, 14 Nov 2014 16:25:36 +0200
+
+arpack-ng - 3.1.5
+
+ * Build all examples and run them as tests
+
+ * Fix the version of arpack-ng itself
+
+ * Switch to automake 1.14.1
+
+ [ Ruediger Meier ]
+ * Do not install test binaries (Closes: #1348)
+
+ [ Nikita Styopin ]
+ * Fix the diagonal matrix example (dndrv5) (Closes: #1397)
+
+ -- Sylvestre Ledru <sylvestre@debian.org>  Sat, 15 Feb 2014 14:24:42 +0200
+
+arpack-ng - 3.1.4
+
+ * libparpack2: missing dependency on MPI:
+   http://bugs.debian.org/cgi-bin/bugreport.cgi?bug=718790
+
+ * Replace LAPACK second function with ARPACK's own arscnd in PARPACK
+
+ * Fix issue #1259 in DSEUPD and SSEUPD
+   The Ritz vector purification step assumes workl(iq) still contains the
+   original Q matrix. This is however overwritten by the call to xGEQR2
+   earlier.
+   .
+   This patch fixes the issue by making a copy of the last row of the
+   eigenvector matrix, after it is recomputed after QR by xORM2R. The work
+   space WORKL(IW+NCV:IW+2*NCV) is not used later in the routine, and can
+   be used for this.
+
+ * Use configure supplied blas and lapack in the pkg-config.
+   Thanks to Ward Poelmans (Closes: #1320)
+
+ * Switch to automake 1.14 + libtool 2.4.2.
+   Thanks to Ward Poelmans (Closes: #1321)
+
+ * dseupd routine may lead to a segmentation fault
+   Thanks to Edouard Canot (Closes: #1323)
+
+ * dsaupd and 'BE' option returns wrong eigenvalues for a SPD matrix
+   Thanks to Edouard Canot (Closes: #1329)
+
+ -- Sylvestre Ledru <sylvestre.ledru@scilab-enterprises.com>  Mon, 07 Oct 2013 14:24:42 +0200
+
+arpack-ng - 3.1.3
+
+  [ Jordi Gutiérrez Hermoso ]
+  * Replace depcomp symlink with actual file.
+  * Update libtool usage. Thanks to John W. Eaton <jwe@octave.org>.
+  * Replace arpack.pc with proper autotooled arpack.pc.in
+  * Add debug.h to TESTS/Makefile.am sources
+
+  * "make dist" is functionnal
+  * Also build the library "libparpacksrcblacs" (PARPACK/UTIL/BLACS/)
+
+ -- Sylvestre Ledru <sylvestre.ledru@scilab-enterprises.com>  Tue, 02 Apr 2013 10:53:08 +0200
+
+arpack-ng - 3.1.2
+
+   * Wrong call to pdlamch was causing segfaults
+     Thanks to Kyrre Sjøbæk for finding the bug and the fix.
+   * Get rid of the mpif.h occurrences in the source code (Closes: #782)
+   * Compile also PARPACK / MPI example (Closes: #783)
+   * Configure detected built-in LAPACK and BLAS, but refused to use them
+     (Closes: #784)
+   * Fixed division by zero in smlnum by usind p[d,s]lamch instead of the
+     serial. Thanks to Umberto De Giovannini.
+
+ -- Sylvestre Ledru <sylvestre.ledru@scilab-enterprises.com>  Fri, 22 Jun 2012 22:05:41 +0200
+
+arpack-ng - 3.1.1
+
+   * Option --enable-maintainer-mode added to the configure
+   * --disable-mpi disables the build of parpack (Closes: #714)
+   * Switch to automake 1.11.3
+
+ -- Sylvestre Ledru <sylvestre.ledru@scilab-enterprises.com>  Mon, 21 May 2012 09:08:41 +0200
+
 arpack-ng - 3.1.0
 
    * Many bug fixes in the parpack lib. It is an old patch from upstream.
      Thanks to Viral Shah for pinging us on this subject.
      See the PARPACK_CHANGES file for the details.
-   * Change the bug report from arpack@caam.rice.edu to 
+   * Change the bug report from arpack@caam.rice.edu to
      http://forge.scilab.org/index.php/p/arpack-ng/issues/
    * Provide a M4 macro (detect_arpack_bug.m4) to check if the underlying
-     arpack is buggy (ie not arpack-ng). This allows developper applications
+     arpack is buggy (ie not arpack-ng). This allows developer applications
      to perform the check in their autotools build system (configure).
    * Fixed a lack of appropriate bounds check in DNAUP2. Thanks to Pauli Virtanen
      for the patch (Closes: #632)
@@ -45,8 +257,8 @@ arpack-ng - 3.0
      second_NONE works with all fortrans compilers (used by default with Scilab)
 
      sneupd.f, cneupd.f: modified for scilab add a check on nconv value (Scilab bug fix)
-     dnaupd.f: modified  NEV Integer: INPUT/OUTPUT before only INPUT (Scilab bug fix) 
- 
+     dnaupd.f: modified  NEV Integer: INPUT/OUTPUT before only INPUT (Scilab bug fix)
+
    * Patches from Octave: (Thanks to John W. EATON)
      dneupd.f: Restore value of nconv
      dseupd.f: Restore value of nconv

CMakeLists.txt

@@ -0,0 +1,648 @@
+cmake_minimum_required(VERSION 2.8.6)
+
+if (NOT DEFINED CMAKE_BUILD_TYPE)
+   set (CMAKE_BUILD_TYPE Release CACHE STRING "Build type")
+endif ()
+
+project(arpack C Fortran)
+
+set(CMAKE_MODULE_PATH ${CMAKE_MODULE_PATH} ${PROJECT_SOURCE_DIR}/cmake)
+
+# Adopted from https://github.com/feymark/arpack.git
+
+if (POLICY CMP0042)
+  # enable MACOSX_RPATH by default
+  cmake_policy (SET CMP0042 NEW)
+endif ()
+
+option(MPI "Enable parallel support" OFF)
+option(ICB "Enable support for *[ae]upd_c with ISO_C_BINDING" OFF)
+#option(SYSTEM_BLAS "Use system BLAS" ON)
+#option(SYSTEM_LAPACK "Use system LAPACK" ON)
+option(EXAMPLES "Compile ARPACK examples" OFF)
+set(LIBSUFFIX ""
+    CACHE STRING "suffix to add to ARPACK libraries names")
+set(SYMBOLSUFFIX ""
+    CACHE STRING "suffix to add to ARPACK, BLAS and LAPACK function names")
+option(INTERFACE64 "use the 64-bit integer interface (ILP64) for ARPACK, BLAS and LAPACK")
+
+set(CMAKE_LIBRARY_OUTPUT_DIRECTORY ${CMAKE_BINARY_DIR}/lib)
+
+if (COVERALLS)
+    include(Coveralls)
+    set(CMAKE_Fortran_FLAGS "${CMAKE_Fortran_FLAGS} -g -O0 -fprofile-arcs -ftest-coverage")
+    set(EXTRA_LDLAGS "${EXTRA_LDLAGS}-lgcov")
+endif()
+
+function(prefixlist list_name prefix)
+    set(${list_name}_TMP)
+    foreach(l ${${list_name}})
+      list(APPEND ${list_name}_TMP ${prefix}${l} )
+    endforeach()
+    set(${list_name} "${${list_name}_TMP}" PARENT_SCOPE)
+endfunction(prefixlist)
+
+function(examples list_name)
+    foreach(l ${${list_name}})
+        get_filename_component(lwe ${l} NAME_WE)
+        add_executable(${lwe} ${arpackexample_DIR}/${l} ${examples_EXTRA_SRCS})
+        target_link_libraries(${lwe} arpack ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES} ${EXTRA_LDLAGS})
+        add_test(NAME "${lwe}_ex" COMMAND ${lwe} WORKING_DIRECTORY ${arpackexample_DIR})
+    endforeach()
+endfunction(examples)
+
+function(pexamples list_name)
+    foreach(l ${${list_name}})
+        get_filename_component(lwe ${l} NAME_WE)
+        add_executable(${lwe} ${parpackexample_DIR}/${l} )
+        target_link_libraries(${lwe} parpack arpack  ${MPI_Fortran_LIBRARIES})
+    endforeach()
+endfunction(pexamples)
+
+# Enable language(s) before any find_package (in particular before MPI find_package).
+if (ICB)
+    enable_language(C CXX) # For testing binding with c/c++.
+
+    set(CMAKE_CXX_STANDARD 11) # OK, since cmake-3.1 only.
+
+    file(WRITE ${CMAKE_BINARY_DIR}${CMAKE_FILES_DIRECTORY}/CMakeTmp/PROG_ICB.f90
+         "
+          PROGRAM PROG_ICB
+          USE iso_c_binding
+          IMPLICIT NONE
+          INTEGER(C_INT) :: a
+          a = 1
+          END PROGRAM PROG_ICB
+         ")
+    try_compile(COMPILE_ICB ${CMAKE_BINARY_DIR} ${CMAKE_BINARY_DIR}${CMAKE_FILES_DIRECTORY}/CMakeTmp/PROG_ICB.f90)
+    if(NOT ${COMPILE_ICB})
+      message(FATAL_ERROR "-- Fortran compiler does not support iso_c_binding.")
+    else()
+      message("-- Fortran compiler does support iso_c_binding.")
+    endif()
+else()
+    # ICB saves you from old-fashion-boring-cumbersome-fortran/C crap...
+
+    if ("${CMAKE_Fortran_COMPILER_ID}" MATCHES "GNU")
+      set(CMAKE_Fortran_FLAGS "${CMAKE_Fortran_FLAGS} -cpp -ffixed-line-length-none")
+    elseif ("${CMAKE_Fortran_COMPILER_ID}" MATCHES "Intel")
+      set(CMAKE_Fortran_FLAGS "${CMAKE_Fortran_FLAGS} -fpp -extend-source")
+    else ()
+      message(WARNING "build script does not know how to enable your Fortran compiler's preprocessor and support for lines longer than 72 characters: set them manually via FFLAGS.")
+    endif ()
+
+    set(SCALARFUNS naitr napps naup2 naupd nconv neigh neupd ngets statn saitr sapps saup2 saupd sconv seigt seupd sgets stats getv0 sortc sortr sesrt stqrb)
+    set(COMPLEXFUNS, naitr napps naup2 naupd neigh neupd ngets statn getv0 sortc)
+
+    set(BLASFUNS1 axpy copy gemv geqr2 lacpy lae2 lahqr lanhs larnv lartg lascl laset lasrt scal trevc trmm trsen gbmv gbtrf gbtrs gttrf gttrs pttrf pttrs)
+    set(BLASFUNS2 dot ger labad laev2 lamch lanst lanv2 lapy2 larf larfg lasr nrm2 orm2r rot steqr swap)
+    set(BLASFUNS3 dotc geru unm2r)
+    set(BLASFUNS4 COPY LABAD LAMCH LANHS LANV2 LARFG ROT GEMV)
+    set(BLASFUNS5 scnrm2 dznrm2 csscal zdscal)
+
+    if (SYMBOLSUFFIX)
+        foreach (f IN LISTS SCALARFUNS BLASFUNS1 BLASFUNS2)
+            set(CMAKE_Fortran_FLAGS "${CMAKE_Fortran_FLAGS} -Ds${f}=s${f}${SYMBOLSUFFIX} -Dd${f}=d${f}${SYMBOLSUFFIX}")
+        endforeach ()
+
+        foreach (f IN LISTS COMPLEXFUNS BLASFUNS1 BLASFUNS3)
+            set(CMAKE_Fortran_FLAGS "${CMAKE_Fortran_FLAGS} -Dc${f}=c${f}${SYMBOLSUFFIX} -Dz${f}=z${f}${SYMBOLSUFFIX}")
+        endforeach ()
+
+        foreach (f IN LISTS BLASFUNS4)
+            set(CMAKE_Fortran_FLAGS "${CMAKE_Fortran_FLAGS} -DS${f}=S${f}${SYMBOLSUFFIX} -DD${f}=D${f}${SYMBOLSUFFIX}")
+        endforeach ()
+
+        foreach (f IN LISTS BLASFUNS5)
+            set(CMAKE_Fortran_FLAGS "${CMAKE_Fortran_FLAGS} -D${f}=${f}${SYMBOLSUFFIX}")
+        endforeach ()
+    endif ()
+
+    set(CFUNS sgemm snaupd sneupd dnaupd dneupd cheev)
+    foreach (f IN LISTS CFUNS)
+        set(CMAKE_C_FLAGS "${CMAKE_C_FLAGS} -D${f}=${f}${SYMBOLSUFFIX}")
+        list(APPEND CFUNS_SUFFIXED ${f}${SYMBOLSUFFIX})
+    endforeach ()
+
+    include(FortranCInterface)
+    FortranCInterface_HEADER(FCMangle.h SYMBOLS ${CFUNS_SUFFIXED})
+
+    set(CMAKE_C_FLAGS "${CMAKE_C_FLAGS} -DINCLUDE_FCMANGLE")
+
+    FortranCInterface_VERIFY()
+endif ()
+
+#if (SYSTEM_BLAS)
+    find_package(BLAS REQUIRED)
+#endif()
+#if (BLAS_LIBRARIES)
+#    set(SYSTEM_BLAS ON)
+#endif()
+
+if (MPI)
+    include(FindMPI)
+    find_package(MPI REQUIRED)
+    include_directories(${MPI_Fortran_INCLUDE_PATH})
+    set(CMAKE_Fortran_FLAGS "${CMAKE_Fortran_FLAGS} ${MPI_Fortran_COMPILE_FLAG}")
+
+    if(ICB)
+        include_directories(${MPI_C_INCLUDE_PATH})
+        include_directories(${MPI_CXX_INCLUDE_PATH})
+        check_symbol_exists(MPI_Comm_c2f "${MPI_C_INCLUDE_PATH}/mpi.h" MPI_Comm_c2f_FOUND)
+        if(NOT ${MPI_Comm_c2f_FOUND})
+          message(FATAL_ERROR "symbol MPI_Comm_c2f does not exist")
+        endif()
+    endif()
+endif()
+
+#if (SYSTEM_LAPACK)
+    find_package(LAPACK REQUIRED)
+#endif()
+#if (BLAS_LIBRARIES)
+#    set(SYSTEM_LAPACK ON)
+#endif()
+
+if (MPI)
+    set(parpackutil_DIR ${arpack_SOURCE_DIR}/PARPACK/UTIL/)
+    set(parpacksrc_DIR ${arpack_SOURCE_DIR}/PARPACK/SRC/)
+endif()
+
+#if (NOT SYSTEM_BLAS)
+#    file(GLOB arpackblas_STAT_SRCS blas/*.f)
+#endif()
+#if (NOT SYSTEM_LAPACK)
+#    file(GLOB arpacklapack_STAT_SRCS lapack/*.f)
+#endif()
+#file(GLOB arpackutil_STAT_SRCS util/*.f)
+file(GLOB arpacksrc_STAT_SRCS dbgini.f staini.f ${arpack_SOURCE_DIR}/SRC/*.f)
+
+set(arpacksrc_ICB "")
+set(parpacksrc_ICB "")
+if(ICB)
+  file(GLOB arpacksrc_ICB SRC/icba*.f90 debug_icb.f90 stat_icb.f90)
+  file(GLOB parpacksrc_ICB PARPACK/SRC/MPI/icbp*.f90 debug_icb.f90 stat_icb.f90)
+endif()
+
+set(arpackutil_STAT_SRCS
+    ${arpack_SOURCE_DIR}/UTIL/icnteq.f
+    ${arpack_SOURCE_DIR}/UTIL/icopy.f
+    ${arpack_SOURCE_DIR}/UTIL/iset.f
+    ${arpack_SOURCE_DIR}/UTIL/iswap.f
+    ${arpack_SOURCE_DIR}/UTIL/ivout.f
+    ${arpack_SOURCE_DIR}/UTIL/second_NONE.f
+    ${arpack_SOURCE_DIR}/UTIL/svout.f
+    ${arpack_SOURCE_DIR}/UTIL/smout.f
+    ${arpack_SOURCE_DIR}/UTIL/dvout.f
+    ${arpack_SOURCE_DIR}/UTIL/dmout.f
+    ${arpack_SOURCE_DIR}/UTIL/cvout.f
+    ${arpack_SOURCE_DIR}/UTIL/cmout.f
+    ${arpack_SOURCE_DIR}/UTIL/zvout.f
+    ${arpack_SOURCE_DIR}/UTIL/zmout.f )
+
+
+if (MPI)
+    file(GLOB parpackutil_STAT_SRCS PARPACK/UTIL/MPI/*.f)
+    file(GLOB parpacksrc_STAT_SRCS dbgini.f staini.f PARPACK/SRC/MPI/*.f)
+endif()
+
+# use -DBUILD_SHARED_LIBS=ON|OFF to control static/shared
+add_library(arpack ${arpackutil_STAT_SRCS} ${arpacksrc_STAT_SRCS} ${arpacksrc_ICB})
+
+if(ICB)
+  install(FILES arpack.h DESTINATION include/arpack)
+  install(FILES arpack.hpp DESTINATION include/arpack)
+  if (MPI)
+    install(FILES parpack.h DESTINATION include/arpack)
+    install(FILES parpack.hpp DESTINATION include/arpack)
+  endif()
+endif()
+
+install(FILES debug.h DESTINATION include/arpack)
+if(ICB)
+  install(FILES debug_c.h DESTINATION include/arpack)
+  install(FILES debug_c.hpp DESTINATION include/arpack)
+endif()
+
+install(FILES stat.h DESTINATION include/arpack)
+if(ICB)
+  install(FILES stat_c.h DESTINATION include/arpack)
+  install(FILES stat_c.hpp DESTINATION include/arpack)
+endif()
+
+target_link_libraries(arpack ${BLAS_LIBRARIES})
+target_link_libraries(arpack ${LAPACK_LIBRARIES} ${EXTRA_LDLAGS})
+set_target_properties(arpack PROPERTIES OUTPUT_NAME arpack${LIBSUFFIX})
+set_target_properties(arpack PROPERTIES VERSION 2.0.0)
+set_target_properties(arpack PROPERTIES SOVERSION 2)
+
+if (MPI)
+    # use -DBUILD_SHARED_LIBS=ON|OFF to control static/shared
+    add_library(parpack ${parpacksrc_STAT_SRCS} ${parpackutil_STAT_SRCS} ${parpacksrc_ICB})
+
+    if (ICB)
+        target_include_directories(parpack PUBLIC ${MPI_C_INCLUDE_DIRS})
+        target_include_directories(parpack PUBLIC ${MPI_CXX_INCLUDE_DIRS})
+        target_link_libraries(parpack ${MPI_C_LIBRARIES})
+        target_link_libraries(parpack ${MPI_CXX_LIBRARIES})
+    endif()
+    target_include_directories(parpack PUBLIC ${MPI_Fortran_INCLUDE_DIRS})
+    target_link_libraries(parpack ${MPI_Fortran_LIBRARIES})
+    target_link_libraries(parpack arpack)
+    set_target_properties(parpack PROPERTIES OUTPUT_NAME parpack${LIBSUFFIX})
+    set_target_properties(parpack PROPERTIES VERSION 2.0.0)
+    set_target_properties(parpack PROPERTIES SOVERSION 2)
+endif ()
+
+if (INTERFACE64)
+    if ("${CMAKE_Fortran_COMPILER_ID}" MATCHES "GNU")
+      set(CMAKE_Fortran_FLAGS "${CMAKE_Fortran_FLAGS} -fdefault-integer-8")
+    elseif ("${CMAKE_Fortran_COMPILER_ID}" MATCHES "Intel")
+      set(CMAKE_Fortran_FLAGS "${CMAKE_Fortran_FLAGS} -i8")
+    else ()
+      message(WARNING "build script does not know how to make your Fortran compiler use 64-bit integers: set it manually via FFLAGS.")
+    endif ()
+
+    set(CMAKE_C_FLAGS "${CMAKE_C_FLAGS} -DBLASINT=int64_t")
+endif ()
+
+set(CMAKE_INCLUDE_CURRENT_DIR ON)
+
+############################
+# EXAMPLES
+############################
+if (EXAMPLES)
+    ############################
+    # EXAMPLES/BAND
+    ############################
+    set(arpackexample_DIR ${arpack_SOURCE_DIR}/EXAMPLES/BAND/)
+    set(CMAKE_RUNTIME_OUTPUT_DIRECTORY ${CMAKE_BINARY_DIR}/Examples/band/)
+
+    set(examples_EXTRA_SRCS ${arpackexample_DIR}/cnband.f)
+    set(examples_STAT_SRCS
+        cnbdr1.f
+        cnbdr2.f
+        cnbdr3.f
+        cnbdr4.f)
+    examples(examples_STAT_SRCS)
+
+    set(examples_EXTRA_SRCS ${arpackexample_DIR}/dnband.f)
+    set(examples_STAT_SRCS
+        dnbdr1.f
+        dnbdr2.f
+        dnbdr3.f
+        dnbdr4.f
+        dnbdr5.f
+        dnbdr6.f)
+    examples(examples_STAT_SRCS)
+
+    set(examples_EXTRA_SRCS ${arpackexample_DIR}/dsband.f)
+    set(examples_STAT_SRCS
+        dsbdr1.f
+        dsbdr2.f
+        dsbdr3.f
+        dsbdr4.f
+        dsbdr5.f
+        dsbdr6.f)
+    examples(examples_STAT_SRCS)
+
+    set(examples_EXTRA_SRCS ${arpackexample_DIR}/snband.f)
+    set(examples_STAT_SRCS
+        snbdr1.f
+        snbdr2.f
+        snbdr3.f
+        snbdr4.f
+        snbdr5.f
+        snbdr6.f)
+    examples(examples_STAT_SRCS)
+
+    set(examples_EXTRA_SRCS ${arpackexample_DIR}/ssband.f)
+    set(examples_STAT_SRCS
+        ssbdr1.f
+        ssbdr2.f
+        ssbdr3.f
+        ssbdr4.f
+        ssbdr5.f
+        ssbdr6.f)
+    examples(examples_STAT_SRCS)
+
+    set(examples_EXTRA_SRCS ${arpackexample_DIR}/znband.f)
+    set(examples_STAT_SRCS
+        znbdr1.f
+        znbdr2.f
+        znbdr3.f
+        znbdr4.f)
+    examples(examples_STAT_SRCS)
+    set(examples_EXTRA_SRCS)
+
+    ############################
+    # EXAMPLES/COMPLEX
+    ############################
+    set(arpackexample_DIR ${arpack_SOURCE_DIR}/EXAMPLES/COMPLEX/)
+    set(CMAKE_RUNTIME_OUTPUT_DIRECTORY ${CMAKE_BINARY_DIR}/Examples/complex/)
+
+    set(examples_STAT_SRCS
+        cndrv1.f
+        cndrv2.f
+        cndrv3.f
+        cndrv4.f
+        zndrv1.f
+        zndrv2.f
+        zndrv3.f
+        zndrv4.f)
+    examples(examples_STAT_SRCS)
+
+    ############################
+    # examples/nonsym
+    ############################
+    set(arpackexample_DIR ${arpack_SOURCE_DIR}/EXAMPLES/NONSYM/)
+    set(CMAKE_RUNTIME_OUTPUT_DIRECTORY ${CMAKE_BINARY_DIR}/Examples/nonsym/)
+
+    set(examples_STAT_SRCS
+        dndrv1.f
+        dndrv2.f
+        dndrv3.f
+        dndrv4.f
+        dndrv5.f
+        dndrv6.f
+        sndrv1.f
+        sndrv2.f
+        sndrv3.f
+        sndrv4.f
+        sndrv5.f
+        sndrv6.f)
+    examples(examples_STAT_SRCS)
+
+    ############################
+    # examples/SIMPLE
+    ############################
+    set(arpackexample_DIR ${arpack_SOURCE_DIR}/EXAMPLES/SIMPLE/)
+    set(CMAKE_RUNTIME_OUTPUT_DIRECTORY ${CMAKE_BINARY_DIR}/Examples/simple/)
+
+    set(examples_STAT_SRCS
+        cnsimp.f
+        dnsimp.f
+        dssimp.f
+        snsimp.f
+        sssimp.f
+        znsimp.f)
+
+    examples(examples_STAT_SRCS)
+
+    ############################
+    # examples/svd
+    ############################
+    set(arpackexample_DIR ${arpack_SOURCE_DIR}/EXAMPLES/SVD/)
+    set(CMAKE_RUNTIME_OUTPUT_DIRECTORY ${CMAKE_BINARY_DIR}/Examples/svd/)
+
+    set(examples_STAT_SRCS
+        ssvd.f)
+
+    examples(examples_STAT_SRCS)
+
+    ############################
+    # examples/sym
+    ############################
+    set(arpackexample_DIR ${arpack_SOURCE_DIR}/EXAMPLES/SYM/)
+    set(CMAKE_RUNTIME_OUTPUT_DIRECTORY ${CMAKE_BINARY_DIR}/Examples/sym/)
+
+    set(examples_STAT_SRCS
+        dsdrv1.f
+        dsdrv2.f
+        dsdrv3.f
+        dsdrv4.f
+        dsdrv5.f
+        dsdrv6.f
+        ssdrv1.f
+        ssdrv2.f
+        ssdrv3.f
+        ssdrv4.f
+        ssdrv5.f
+        ssdrv6.f)
+
+    examples(examples_STAT_SRCS)
+
+    ############################
+    # parpack/examples
+    ############################
+    if (MPI)
+        set(parpackexample_DIR ${arpack_SOURCE_DIR}/PARPACK/EXAMPLES/MPI/)
+        set(CMAKE_RUNTIME_OUTPUT_DIRECTORY ${CMAKE_BINARY_DIR}/Examples/parpack)
+
+        set(pexamples_STAT_SRCS
+            pcndrv1.f
+            pdndrv1.f
+            pdndrv3.f
+            pdsdrv1.f
+            psndrv1.f
+            psndrv3.f
+            pssdrv1.f
+            pzndrv1.f)
+
+        pexamples(pexamples_STAT_SRCS)
+    endif()
+endif()
+
+
+############################
+# TEST
+############################
+
+enable_testing()
+
+set(CMAKE_CTEST_COMMAND ctest -V)
+
+set(CMAKE_RUNTIME_OUTPUT_DIRECTORY ${CMAKE_BINARY_DIR}/Tests)
+
+add_executable(dnsimp_test TESTS/dnsimp.f TESTS/mmio.f TESTS/debug.h)
+set_target_properties( dnsimp_test PROPERTIES OUTPUT_NAME  dnsimp )
+target_link_libraries(dnsimp_test arpack ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES} ${EXTRA_LDLAGS})
+add_custom_command(TARGET dnsimp_test POST_BUILD
+  COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/TESTS/testA.mtx testA.mtx
+)
+add_test(dnsimp_tst Tests/dnsimp)
+
+if (NOT ICB)
+    add_executable(bug_1315_single TESTS/bug_1315_single.c)
+    target_link_libraries(bug_1315_single arpack ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES} ${EXTRA_LDLAGS})
+    add_test(bug_1315_single_tst Tests/bug_1315_single)
+
+    add_executable(bug_1315_double TESTS/bug_1315_double.c)
+    target_link_libraries(bug_1315_double arpack ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES} ${EXTRA_LDLAGS})
+    add_test(bug_1315_double_tst Tests/bug_1315_double)
+endif()
+
+add_executable(bug_1323 TESTS/bug_1323.f)
+target_link_libraries(bug_1323 arpack ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES} ${EXTRA_LDLAGS})
+add_test(bug_1323_tst Tests/bug_1323)
+
+add_executable(bug_58_double TESTS/bug_58_double.f)
+target_link_libraries(bug_58_double arpack ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES} ${EXTRA_LDLAGS})
+add_test(bug_58_double_tst Tests/bug_58_double)
+
+add_executable(bug_79_double_complex TESTS/bug_79_double_complex.f)
+target_link_libraries(bug_79_double_complex arpack ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES} ${EXTRA_LDLAGS})
+add_test(bug_79_double_complex_tst Tests/bug_79_double_complex)
+
+add_executable(bug_142 TESTS/bug_142.f)
+target_link_libraries(bug_142 arpack ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES} ${EXTRA_LDLAGS})
+add_test(bug_142_tst Tests/bug_142)
+
+add_executable(bug_142_gen TESTS/bug_142_gen.f)
+target_link_libraries(bug_142_gen arpack ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES} ${EXTRA_LDLAGS})
+add_test(bug_142_gen_tst Tests/bug_142_gen)
+
+if(MPI)
+  add_executable(issue46 PARPACK/TESTS/MPI/issue46.f)
+  target_link_libraries(issue46 parpack arpack ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES} ${EXTRA_LDLAGS})
+  add_test(issue46_tst Tests/issue46)
+endif()
+
+if(ICB)
+  add_executable(icb_arpack_c TESTS/icb_arpack_c.c)
+  target_include_directories(icb_arpack_c PUBLIC ${PROJECT_SOURCE_DIR}) # Get arpack.h
+  target_link_libraries(icb_arpack_c arpack ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES} ${EXTRA_LDLAGS})
+  add_test(icb_arpack_c_tst Tests/icb_arpack_c)
+
+  add_executable(icb_arpack_cpp TESTS/icb_arpack_cpp.cpp)
+  target_include_directories(icb_arpack_cpp PUBLIC ${PROJECT_SOURCE_DIR}) # Get arpack.hpp
+  target_link_libraries(icb_arpack_cpp arpack ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES} ${EXTRA_LDLAGS})
+  add_test(icb_arpack_cpp_tst Tests/icb_arpack_cpp)
+
+  if (MPI)
+    add_executable(icb_parpack_c PARPACK/TESTS/MPI/icb_parpack_c.c)
+    target_include_directories(icb_parpack_c PUBLIC ${PROJECT_SOURCE_DIR} ${MPI_C_INCLUDE_DIRS}) # Get parpack.h mpi.h
+    target_link_libraries(icb_parpack_c parpack arpack ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES} ${EXTRA_LDLAGS} ${MPI_C_LIBRARIES})
+    add_test(icb_parpack_c_tst mpirun -n 2 Tests/icb_parpack_c)
+
+    add_executable(icb_parpack_cpp PARPACK/TESTS/MPI/icb_parpack_cpp.cpp)
+    target_include_directories(icb_parpack_cpp PUBLIC ${PROJECT_SOURCE_DIR} ${MPI_CXX_INCLUDE_DIRS}) # Get parpack.hpp mpi.h
+    target_link_libraries(icb_parpack_cpp parpack arpack ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES} ${EXTRA_LDLAGS} ${MPI_CXX_LIBRARIES})
+    add_test(icb_parpack_cpp_tst mpirun -n 2 Tests/icb_parpack_cpp)
+  endif()
+endif()
+
+############################
+# install
+############################
+# 'make install' to the correct location
+include(GNUInstallDirs)
+
+# Convert variable names to those expected by the .pc file.
+set(prefix ${CMAKE_INSTALL_PREFIX})
+set(exec_prefix \${prefix})
+set(libdir \${exec_prefix}/${CMAKE_INSTALL_LIBDIR})
+set(PACKAGE_NAME ${PROJECT_NAME})
+# TODO: Fill these in with something appropriate.
+#set(PACKAGE_VERSION)
+#set(PACKAGE_URL)
+#set(LAPACK_LIBS)
+#set(BLAS_LIBS)
+configure_file(arpack.pc.in arpack${LIBSUFFIX}.pc @ONLY)
+
+#install(FILES ${CMAKE_CURRENT_BINARY_DIR}/arpack${LIBSUFFIX}.pc
+#    DESTINATION ${CMAKE_INSTALL_LIBDIR}/pkgconfig)
+
+install(TARGETS arpack
+    ARCHIVE DESTINATION ${CMAKE_INSTALL_LIBDIR}
+    LIBRARY DESTINATION ${CMAKE_INSTALL_LIBDIR}
+    RUNTIME DESTINATION ${CMAKE_INSTALL_BINDIR})
+
+if (MPI)
+  install(TARGETS parpack
+      ARCHIVE DESTINATION ${CMAKE_INSTALL_LIBDIR}
+      LIBRARY DESTINATION ${CMAKE_INSTALL_LIBDIR}
+      RUNTIME DESTINATION ${CMAKE_INSTALL_BINDIR})
+endif ()
+
+# Provide find_package for arpack-ng to users.
+configure_file(arpack-ng-config.cmake.in "${PROJECT_BINARY_DIR}/arpack-ng-config.cmake" @ONLY)
+install(FILES "${PROJECT_BINARY_DIR}/arpack-ng-config.cmake" DESTINATION "${CMAKE_INSTALL_PREFIX}/lib/cmake") # find_package(arpack-ng)
+set(arpack_ng_MAJOR_VERSION 3)
+set(arpack_ng_MINOR_VERSION 6)
+set(arpack_ng_PATCH_VERSION 0)
+set(arpack_ng_VERSION ${arpack_ng_MAJOR_VERSION}.${arpack_ng_MINOR_VERSION}.${arpack_ng_PATCH_VERSION})
+configure_file(arpack-ng-config-version.cmake.in "${PROJECT_BINARY_DIR}/arpack-ng-config-version.cmake" @ONLY)
+install(FILES "${PROJECT_BINARY_DIR}/arpack-ng-config-version.cmake" DESTINATION "${CMAKE_INSTALL_PREFIX}/lib/cmake")
+
+# Packaging: ease arpack-ng distribution (precompiled binaries and sources tarballs).
+set(CPACK_VERSION_MAJOR "${arpack_ng_MAJOR_VERSION}")
+set(CPACK_VERSION_MINOR "${arpack_ng_MINOR_VERSION}")
+set(CPACK_VERSION_PATCH "${arpack_ng_PATCH_VERSION}")
+set(CPACK_SOURCE_IGNORE_FILES "/BUILD/" "/Build/" "/build/" "/local/") # Do not ship (eventual) build or install directories in tarballs.
+set(CPACK_SOURCE_PACKAGE_FILE_NAME "arpack-ng-${CPACK_VERSION_MAJOR}.${CPACK_VERSION_MINOR}.${CPACK_VERSION_PATCH}")
+include(CPack)
+
+
+# We don't want this to run on every build.
+option(COVERALLS "Generate coveralls data" OFF)
+
+
+if (COVERALLS)
+    set(COVERAGE_SRCS awesome.c code.c files.c)
+
+    # Create the coveralls target.
+    coveralls_setup(
+        "${arpackutil_STAT_SRCS} ${arpacksrc_STAT_SRCS} ${arpacksrc_ICB}" # The source files.
+        ON                 # If we should upload.
+        "${PROJECT_SOURCE_DIR}/cmake/") # (Optional) Alternate project cmake module path.
+endif()
+
+function(libsummary title include libraries)
+    message("   -- ${title}:")
+    foreach(inc ${include})
+        message("      -- compile: ${inc}")
+    endforeach()
+    foreach(lib ${libraries})
+        message("      -- link:    ${lib}")
+    endforeach()
+endfunction(libsummary)
+
+function(cprsummary title compiler debug_flags minsizerel_flags release_flags relwithdebinfo_flags more_flags)
+    message("   -- ${title}:      ${compiler}")
+    if("${CMAKE_BUILD_TYPE}" STREQUAL "Debug" OR "${CMAKE_BUILD_TYPE}" STREQUAL "DEBUG")
+        message("   -- ${title}FLAGS: ${debug_flags} ${more_flags}")
+    endif()
+    if("${CMAKE_BUILD_TYPE}" STREQUAL "MinSizeRel" OR "${CMAKE_BUILD_TYPE}" STREQUAL "MINSIZEREL")
+        message("   -- ${title}FLAGS: ${minsizerel_flags} ${more_flags}")
+    endif()
+    if("${CMAKE_BUILD_TYPE}" STREQUAL "Release" OR "${CMAKE_BUILD_TYPE}" STREQUAL "RELEASE")
+        message("   -- ${title}FLAGS: ${release_flags} ${more_flags}")
+    endif()
+    if("${CMAKE_BUILD_TYPE}" STREQUAL "RelWithDebInfo" OR "${CMAKE_BUILD_TYPE}" STREQUAL "RELWITHDEBINFO")
+        message("   -- ${title}FLAGS: ${relwithdebinfo_flags} ${more_flags}")
+    endif()
+endfunction(cprsummary)
+
+message("-- Configuration summary for arpack-ng-${arpack_ng_VERSION}:")
+message("   -- prefix: ${CMAKE_INSTALL_PREFIX}")
+message("   -- MPI: ${MPI}")
+message("   -- ICB: ${ICB}")
+cprsummary("FC" "${CMAKE_Fortran_COMPILER}"
+                "${CMAKE_Fortran_FLAGS_DEBUG}"
+                "${CMAKE_Fortran_FLAGS_MINSIZEREL}"
+                "${CMAKE_Fortran_FLAGS_RELEASE}"
+                "${CMAKE_Fortran_FLAGS_RELWITHDEBINFO}"
+                "${CMAKE_Fortran_FLAGS}")
+if (ICB)
+    cprsummary("CC" "${CMAKE_C_COMPILER}"
+                    "${CMAKE_C_FLAGS_DEBUG}"
+                    "${CMAKE_C_FLAGS_MINSIZEREL}"
+                    "${CMAKE_C_FLAGS_RELEASE}"
+                    "${CMAKE_C_FLAGS_RELWITHDEBINFO}"
+                    "${CMAKE_C_FLAGS}")
+    cprsummary("CXX" "${CMAKE_CXX_COMPILER}"
+                     "${CMAKE_CXX_FLAGS_DEBUG}"
+                     "${CMAKE_CXX_FLAGS_MINSIZEREL}"
+                     "${CMAKE_CXX_FLAGS_RELEASE}"
+                     "${CMAKE_CXX_FLAGS_RELWITHDEBINFO}"
+                     "${CMAKE_CXX_FLAGS}")
+endif()
+if (MPI)
+    libsummary("MPIFC" "${MPI_Fortran_INCLUDE_PATH}" "${MPI_Fortran_LIBRARIES}")
+    if (ICB)
+        libsummary("MPICC" "${MPI_C_INCLUDE_PATH}" "${MPI_C_LIBRARIES}")
+        libsummary("MPICXX" "${MPI_CXX_INCLUDE_PATH}" "${MPI_CXX_LIBRARIES}")
+    endif()
+endif()
+libsummary("BLAS" "" "${BLAS_LIBRARIES}")
+libsummary("LAPACK" "" "${LAPACK_LIBRARIES}")

COPYING

@@ -3,7 +3,7 @@ BSD Software License
 
 Pertains to ARPACK and P_ARPACK
 
-Copyright (c) 1996-2008 Rice University.  
+Copyright (c) 1996-2008 Rice University.
 Developed by D.C. Sorensen, R.B. Lehoucq, C. Yang, and K. Maschhoff.
 All rights reserved.
 
@@ -21,26 +21,25 @@ modification, are permitted provided that the following conditions are
 met:
 
 - Redistributions of source code must retain the above copyright
-  notice, this list of conditions and the following disclaimer. 
-  
+  notice, this list of conditions and the following disclaimer.
+
 - Redistributions in binary form must reproduce the above copyright
   notice, this list of conditions and the following disclaimer listed
   in this license in the documentation and/or other materials
   provided with the distribution.
-  
+
 - Neither the name of the copyright holders nor the names of its
   contributors may be used to endorse or promote products derived from
   this software without specific prior written permission.
-  
+
 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT  
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT 
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
 OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
 LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
-THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT  
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
-OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 
-
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

DOCUMENTS/debug.doc

@@ -219,7 +219,7 @@ c     %---------------------------------%
               of the Hessenberg matrix and their the corresponding 
               error bounds, KEV, NP.
 
- mnapps > 0: *Print information about where deflation occured.
+ mnapps > 0: *Print information about where deflation occurred.
  mnapps > 1: *Print sigmak, betak, order of the final Hessenberg matrix,
               and the final compressed upper Hessenberg matrix.
  mnapps > 2: *Print implicit application of shift number, real and imaginary 
@@ -303,7 +303,7 @@ c     %---------------------------------%
               of the Hessenberg matrix and their the corresponding 
               error bounds, KEV, NP.
 
- mcapps > 0: *Print information about where deflation occured.
+ mcapps > 0: *Print information about where deflation occurred.
  mcapps > 1: *Print sigmak, betak, order of the final Hessenberg matrix,
               and the final compressed upper Hessenberg matrix.
  mcapps > 2: *Print implicit application of shift number, the shift.

EXAMPLES/BAND/Makefile.am

@@ -0,0 +1,58 @@
+LDADD = $(top_builddir)/SRC/libarpack$(LIBSUFFIX).la $(LAPACK_LIBS) $(BLAS_LIBS)
+
+SSBDR = ssbdr1 ssbdr2 ssbdr3 ssbdr4 ssbdr5 ssbdr6
+DSBDR = dsbdr1 dsbdr2 dsbdr3 dsbdr4 dsbdr5 dsbdr6
+SNBDR = snbdr1 snbdr2 snbdr3 snbdr4 snbdr5 snbdr6
+DNBDR = dnbdr1 dnbdr2 dnbdr3 dnbdr4 dnbdr5 dnbdr6
+CNBDR = cnbdr1 cnbdr2 cnbdr3 cnbdr4
+ZNBDR = znbdr1 znbdr2 znbdr3 znbdr4
+BAND = $(SSBDR) $(DSBDR) $(SNBDR) $(DNBDR) $(CNBDR) $(ZNBDR)
+
+check_PROGRAMS = $(BAND)
+TESTS = $(check_PROGRAMS)
+
+EXTRA_DIST = README
+
+# Simple symmetric problem using BAND solver (single precision)
+ssbdr1_SOURCES = ssbdr1.f ssband.f
+ssbdr2_SOURCES = ssbdr2.f ssband.f
+ssbdr3_SOURCES = ssbdr3.f ssband.f
+ssbdr4_SOURCES = ssbdr4.f ssband.f
+ssbdr5_SOURCES = ssbdr5.f ssband.f
+ssbdr6_SOURCES = ssbdr6.f ssband.f
+
+# Simple symmetric problem using BAND solver (double precision)
+dsbdr1_SOURCES = dsbdr1.f dsband.f
+dsbdr2_SOURCES = dsbdr2.f dsband.f
+dsbdr3_SOURCES = dsbdr3.f dsband.f
+dsbdr4_SOURCES = dsbdr4.f dsband.f
+dsbdr5_SOURCES = dsbdr5.f dsband.f
+dsbdr6_SOURCES = dsbdr6.f dsband.f
+
+# Simple nonsymmetric problem using BAND solver (single precision)
+snbdr1_SOURCES = snbdr1.f snband.f
+snbdr2_SOURCES = snbdr2.f snband.f
+snbdr3_SOURCES = snbdr3.f snband.f
+snbdr4_SOURCES = snbdr4.f snband.f
+snbdr5_SOURCES = snbdr5.f snband.f
+snbdr6_SOURCES = snbdr6.f snband.f
+
+# Simple nonsymmetric problem using BAND solver (double precision)
+dnbdr1_SOURCES = dnbdr1.f dnband.f
+dnbdr2_SOURCES = dnbdr2.f dnband.f
+dnbdr3_SOURCES = dnbdr3.f dnband.f
+dnbdr4_SOURCES = dnbdr4.f dnband.f
+dnbdr5_SOURCES = dnbdr5.f dnband.f
+dnbdr6_SOURCES = dnbdr6.f dnband.f
+
+# Complex problem using BAND solver (single precision complex)
+cnbdr1_SOURCES = cnbdr1.f cnband.f
+cnbdr2_SOURCES = cnbdr2.f cnband.f
+cnbdr3_SOURCES = cnbdr3.f cnband.f
+cnbdr4_SOURCES = cnbdr4.f cnband.f
+
+# Complex problem using BAND solver (double precision complex)
+znbdr1_SOURCES = znbdr1.f znband.f
+znbdr2_SOURCES = znbdr2.f znband.f
+znbdr3_SOURCES = znbdr3.f znband.f
+znbdr4_SOURCES = znbdr4.f znband.f

EXAMPLES/BAND/cnband.f

@@ -3,27 +3,27 @@ c
 c \Name: cnband
 c
 c \Description:
-c  This subroutine returns the converged approximations to eigenvalues 
-c  of A*z = lambda*B*z and (optionally): 
-c 
-c      (1) The corresponding approximate eigenvectors; 
-c 
-c      (2) An orthonormal basis for the associated approximate 
-c          invariant subspace; 
-c 
-c      (3) Both.  
+c  This subroutine returns the converged approximations to eigenvalues
+c  of A*z = lambda*B*z and (optionally):
+c
+c      (1) The corresponding approximate eigenvectors;
+c
+c      (2) An orthonormal basis for the associated approximate
+c          invariant subspace;
+c
+c      (3) Both.
 c
 c  Matrices A and B are stored in LAPACK-style banded form.
 c
-c  There is negligible additional cost to obtain eigenvectors.  An orthonormal 
+c  There is negligible additional cost to obtain eigenvectors.  An orthonormal
 c  basis is always computed.  There is an additional storage cost of n*nev
-c  if both are requested (in this case a separate array Z must be supplied). 
+c  if both are requested (in this case a separate array Z must be supplied).
 c
 c  The approximate eigenvalues and eigenvectors of  A*z = lambda*B*z
-c  are commonly called Ritz values and Ritz vectors respectively.  They are 
-c  referred to as such in the comments that follow.  The computed orthonormal 
-c  basis for the invariant subspace corresponding to these Ritz values is 
-c  referred to as a Schur basis. 
+c  are commonly called Ritz values and Ritz vectors respectively.  They are
+c  referred to as such in the comments that follow.  The computed orthonormal
+c  basis for the invariant subspace corresponding to these Ritz values is
+c  referred to as a Schur basis.
 c
 c  cnband can be called with one of the following modes:
 c
@@ -41,14 +41,14 @@ c  Choice of different modes can be specified in IPARAM(7) defined below.
 c
 c \Usage
 c   call cnband
-c      ( RVEC, HOWMNY, SELECT, D , Z, LDZ, SIGMA, WORKEV, N, AB, 
-c        MB, LDA, FAC, KL, KU, WHICH, BMAT, NEV, TOL, RESID, NCV, 
+c      ( RVEC, HOWMNY, SELECT, D , Z, LDZ, SIGMA, WORKEV, N, AB,
+c        MB, LDA, FAC, KL, KU, WHICH, BMAT, NEV, TOL, RESID, NCV,
 c        V, LDV, IPARAM, WORKD, WORKL, LWORKL, RWORK, IWORK, INFO )
 c
 c \Arguments
-c  RVEC    LOGICAL  (INPUT) 
+c  RVEC    LOGICAL  (INPUT)
 c          Specifies whether a basis for the invariant subspace corresponding
-c          to the converged Ritz value approximations for the eigenproblem 
+c          to the converged Ritz value approximations for the eigenproblem
 c          A*z = lambda*B*z is computed.
 c
 c             RVEC = .FALSE.     Compute Ritz values only.
@@ -56,8 +56,8 @@ c
 c             RVEC = .TRUE.      Compute Ritz vectors or Schur vectors.
 c                                See Remarks below.
 c
-c  HOWMNY  Character*1  (INPUT) 
-c          Specifies the form of the invariant subspace to be computed 
+c  HOWMNY  Character*1  (INPUT)
+c          Specifies the form of the invariant subspace to be computed
 c          corresponding to the converged Ritz values.
 c          = 'A': Compute NEV Ritz vectors;
 c          = 'P': Compute NEV Schur vectors;
@@ -67,7 +67,7 @@ c
 c  SELECT  Logical array of dimension NCV.  (INPUT)
 c          If HOWMNY = 'S', SELECT specifies the Ritz vectors to be
 c          computed. To select the real Ritz vector corresponding to a
-c          Ritz value D(j), SELECT(j) must be set to .TRUE.. 
+c          Ritz value D(j), SELECT(j) must be set to .TRUE..
 c          If HOWMNY = 'A' or 'P', SELECT need not be initialized
 c          but it is used as internal workspace.
 c
@@ -76,16 +76,16 @@ c          On exit, D contains the  Ritz  approximations
 c          to the eigenvalues lambda for A*z = lambda*B*z.
 c
 c  Z       Complex  N by NEV array     (OUTPUT)
-c          On exit, if RVEC = .TRUE. and HOWMNY = 'A', then the columns of 
-c          Z represents approximate eigenvectors (Ritz vectors) corresponding 
+c          On exit, if RVEC = .TRUE. and HOWMNY = 'A', then the columns of
+c          Z represents approximate eigenvectors (Ritz vectors) corresponding
 c          to the NCONV=IPARAM(5) Ritz values for eigensystem
 c          A*z = lambda*B*z.
 c
 c          If RVEC = .FALSE. or HOWMNY = 'P', then Z is NOT REFERENCED.
 c
-c          NOTE: If if RVEC = .TRUE. and a Schur basis is not required, 
-c          the array Z may be set equal to first NEV columns of the 
-c          array V.  
+c          NOTE: If if RVEC = .TRUE. and a Schur basis is not required,
+c          the array Z may be set equal to first NEV columns of the
+c          array V.
 c
 c  LDZ     Integer.  (INPUT)
 c          The leading dimension of the array Z.  If Ritz vectors are
@@ -97,7 +97,7 @@ c          If IPARAM(7) = 3 then SIGMA represents the shift.
 c          Not referenced if IPARAM(7) = 1 or 2.
 c
 c  WORKEV  Complex  work array of dimension NCV.  (WORKSPACE)
-c 
+c
 c  N       Integer.  (INPUT)
 c          Dimension of the eigenproblem.
 c
@@ -110,7 +110,7 @@ c          AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
 c
 c  MB      Complex  array of dimension LDA by N. (INPUT)
 c          The matrix M in band storage, in rows KL+1 to
-c          2*KL+KU+1; rows 1 to KL of the array need not be set. 
+c          2*KL+KU+1; rows 1 to KL of the array need not be set.
 c          The j-th column of M is stored in the j-th column of the
 c          array MB as follows:
 c          MB(kl+ku+1+i-j,j) = M(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
@@ -134,7 +134,7 @@ c
 c  WHICH   Character*2.  (INPUT)
 c          When mode 1,2 are used, WHICH can be set to any one of
 c          the following.
-c  
+c
 c            'LM' -> want the NEV eigenvalues of largest magnitude.
 c            'SM' -> want the NEV eigenvalues of smallest magnitude.
 c            'LR' -> want the NEV eigenvalues of largest real part.
@@ -142,8 +142,8 @@ c            'SR' -> want the NEV eigenvalues of smallest real part.
 c            'LI' -> want the NEV eigenvalues of largest imaginary part.
 c            'SI' -> want the NEV eigenvalues of smallest imaginary part.
 c
-c          When mode 3 is used, WHICH should be set to 'LM' only. 
-c          
+c          When mode 3 is used, WHICH should be set to 'LM' only.
+c
 c  BMAT    Character*1.  (INPUT)
 c          BMAT specifies the type of the matrix B that defines the
 c          semi-inner product for the operator OP.
@@ -152,13 +152,13 @@ c          BMAT = 'G' -> generalized eigenvalue problem A*x = lambda*M*x
 
 c  NEV     Integer. (INPUT)
 c          Number of eigenvalues of to be computed.
-c   
+c
 c  TOL     Real  scalar.  (INPUT)
 c          Stopping criteria: the relative accuracy of the Ritz value
 c          is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I))
 c          where ABS(RITZ(I)) is the magnitude when RITZ(I) is complex.
 c          DEFAULT = slamch('EPS')  (machine precision as computed
-c                    by the LAPACK auxilliary subroutine slamch).
+c                    by the LAPACK auxiliary subroutine slamch).
 c
 c  RESID   Complex  array of length N.  (INPUT/OUTPUT)
 c          On INPUT:
@@ -171,12 +171,12 @@ c
 c  NCV     Integer.  (INPUT)
 c          Number of columns of the matrix V. NCV must satisfy the two
 c          inequalities 2 <= NCV-NEV and NCV <= N.
-c          This will indicate how many Arnoldi vectors are generated 
-c          at each iteration.  After the startup phase in which NEV 
-c          Arnoldi vectors are generated, the algorithm generates 
-c          approximately NCV-NEV Arnoldi vectors at each subsequent update 
-c          iteration. Most of the cost in generating each Arnoldi vector is 
-c          in the matrix-vector operation OP*x. 
+c          This will indicate how many Arnoldi vectors are generated
+c          at each iteration.  After the startup phase in which NEV
+c          Arnoldi vectors are generated, the algorithm generates
+c          approximately NCV-NEV Arnoldi vectors at each subsequent update
+c          iteration. Most of the cost in generating each Arnoldi vector is
+c          in the matrix-vector operation OP*x.
 c
 c  V       Complex  array N by NCV.  (OUTPUT)
 c          Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns
@@ -184,8 +184,8 @@ c                       contain approximate Schur vectors that span the
 c                       desired invariant subspace.
 c
 c          NOTE: If the array Z has been set equal to first NEV+1 columns
-c          of the array V and RVEC=.TRUE. and HOWMNY= 'A', then 
-c          the first NCONV=IPARAM(5) columns of V will contain Ritz vectors 
+c          of the array V and RVEC=.TRUE. and HOWMNY= 'A', then
+c          the first NCONV=IPARAM(5) columns of V will contain Ritz vectors
 c          of the eigensystem A*z = lambda*B*z.
 c
 c  LDV     Integer.  (INPUT)
@@ -193,7 +193,7 @@ c          Leading dimension of V exactly as declared in the calling
 c          program.  LDV must be great than or equal to N.
 c
 c  IPARAM  Integer array of length 11.  (INPUT/OUTPUT)
-c          IPARAM(1) = ISHIFT: 
+c          IPARAM(1) = ISHIFT:
 c          The shifts selected at each iteration are used to restart
 c          the Arnoldi iteration in an implicit fashion.
 c          It is set to 1 in this subroutine.  The user do not need
@@ -223,12 +223,12 @@ c          Not referenced. Implicit restarting is ALWAYS used.
 c
 c          IPARAM(7) = MODE
 c          On INPUT determines what type of eigenproblem is being solved.
-c          Must be 1,2 or 3; See under \Description of cnband for the 
+c          Must be 1,2 or 3; See under \Description of cnband for the
 c          three modes available.
 c
 c WORKD    Complex  work array of length at least 3*n. (WORKSPACE)
 c
-c WORKL    Complex  work array of length LWORKL. (WORKSPACE) 
+c WORKL    Complex  work array of length LWORKL. (WORKSPACE)
 c
 c LWORKL   Integer.  (INPUT)
 c          LWORKL must be at least 3*NCV**2 + 5*NCV.
@@ -237,9 +237,9 @@ c RWORK    Real  array of length N (WORKSPACE)
 c          Workspace used in cnaupd.
 c
 c IWORK    Integer array of dimension at least N. (WORKSPACE)
-c          Used to mode 2,3. Store the pivot information in the 
+c          Used to mode 2,3. Store the pivot information in the
 c          factorization of M or (A-SIGMA*M).
-c            
+c
 c INFO     Integer.  (INPUT/OUTPUT)
 c          Error flag on output.
 c          =  0: Normal exit.
@@ -300,21 +300,21 @@ c
 c-----------------------------------------------------------------------
 c
       subroutine cnband(rvec, howmny, select, d , z, ldz, sigma,
-     &                 workev, n, ab, mb, lda, fac, kl, ku, which, 
-     &                 bmat, nev, tol, resid, ncv, v, ldv, iparam, 
+     &                 workev, n, ab, mb, lda, fac, kl, ku, which,
+     &                 bmat, nev, tol, resid, ncv, v, ldv, iparam,
      &                 workd, workl, lworkl, rwork, iwork, info )
 c
 c     %------------------%
 c     | Scalar Arguments |
 c     %------------------%
-c 
+c
       Character        which*2, bmat, howmny
       Logical          rvec
       Integer          n, lda, kl, ku, nev, ncv, ldv,
-     &                 ldz, lworkl, info  
-      Complex          
-     &                 sigma 
-      Real 
+     &                 ldz, lworkl, info
+      Complex
+     &                 sigma
+      Real
      &                 tol
 c
 c     %-----------------%
@@ -323,11 +323,11 @@ c     %-----------------%
 c
       Integer          iparam(*), iwork(*)
       Logical          select(*)
-      Complex          
+      Complex
      &                 d(*), resid(*), v(ldv,*), z(ldz,*),
-     &                 ab(lda,*), mb(lda,*), fac(lda,*), 
+     &                 ab(lda,*), mb(lda,*), fac(lda,*),
      &                 workd(*), workl(*), workev(*)
-      Real 
+      Real
      &                 rwork(*)
 c
 c     %--------------%
@@ -346,7 +346,7 @@ c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Complex          
+      Complex
      &                  one, zero
       parameter        (one  = (1.0E+0, 0.0E+0) ,
      &                  zero = (0.0E+0, 0.0E+0) )
@@ -355,14 +355,14 @@ c     %-----------------------------%
 c     | LAPACK & BLAS routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                 scnrm2
       external         ccopy, cgbmv, cgbtrf, cgbtrs, scnrm2, clacpy
 c
 c     %-----------------------%
 c     | Executable Statements |
 c     %-----------------------%
-c     
+c
       mode = iparam(7)
 c
 c     %------------------------%
@@ -398,9 +398,9 @@ c         | to factor M.                                  |
 c         %-----------------------------------------------%
 c
           call clacpy ('A', ibot, n, mb, lda, fac, lda )
-          call cgbtrf(n, n, kl, ku, fac, lda, iwork, ierr) 
+          call cgbtrf(n, n, kl, ku, fac, lda, iwork, ierr)
           if (ierr .ne. 0) then
-              print*, ' ' 
+              print*, ' '
               print*,'_band:  error in _gbtrf'
               print*, ' '
               go to 9000
@@ -426,7 +426,7 @@ c            | Construct (A - sigma*M)   |
 c            %---------------------------%
 c
              do 30 j = 1,n
-                do 20 i = itop, ibot 
+                do 20 i = itop, ibot
                    fac(i,j) = ab(i,j) - sigma*mb(i,j)
   20            continue
   30         continue
@@ -451,7 +451,7 @@ c     %--------------------------------------------%
 c     |  M A I N   L O O P (reverse communication) |
 c     %--------------------------------------------%
 c
-  40  continue 
+  40  continue
 c
       call cnaupd ( ido, bmat, n, which, nev, tol, resid, ncv,
      &              v, ldv, iparam, ipntr, workd, workl, lworkl,
@@ -466,8 +466,8 @@ c           %----------------------------%
 c           | Perform  y <--- OP*x = A*x |
 c           %----------------------------%
 c
-            call cgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call cgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
          else if ( mode .eq. 2 ) then
@@ -476,11 +476,11 @@ c           %-----------------------------------%
 c           | Perform  y <--- OP*x = inv[M]*A*x |
 c           %-----------------------------------%
 c
-            call cgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                  lda, workd(ipntr(1)), 1, zero, 
+            call cgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                  lda, workd(ipntr(1)), 1, zero,
      &                  workd(ipntr(2)), 1)
 c
-            call cgbtrs ('Notranspose', n, kl, ku, 1, fac, lda, 
+            call cgbtrs ('Notranspose', n, kl, ku, 1, fac, lda,
      &                    iwork, workd(ipntr(2)), n, ierr)
             if (ierr .ne. 0) then
                print*, ' '
@@ -493,21 +493,21 @@ c
 c
 c           %-----------------------------------------%
 c           | Perform y <-- OP*x                      |
-c           |           = inv[A-SIGMA*M]*M* x 
+c           |           = inv[A-SIGMA*M]*M* x
 c           | to force the starting vector into the   |
 c           | range of OP.                            |
 c           %-----------------------------------------%
 c
-            call cgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call cgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
-            call cgbtrs ('Notranspose', n, kl, ku, 1, fac, lda, 
+            call cgbtrs ('Notranspose', n, kl, ku, 1, fac, lda,
      &                   iwork, workd(ipntr(2)), n, ierr)
             if (ierr .ne. 0) then
-               print*, ' ' 
+               print*, ' '
                print*, '_band: error in _gbtrs.'
-               print*, ' ' 
+               print*, ' '
                go to 9000
             end if
 c
@@ -521,8 +521,8 @@ c           %----------------------------%
 c           | Perform  y <--- OP*x = A*x |
 c           %----------------------------%
 c
-            call cgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call cgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
          else if ( mode .eq. 2 ) then
@@ -531,16 +531,16 @@ c           %-----------------------------------%
 c           | Perform  y <--- OP*x = inv[M]*A*x |
 c           %-----------------------------------%
 c
-            call cgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                  lda, workd(ipntr(1)), 1, zero, 
+            call cgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                  lda, workd(ipntr(1)), 1, zero,
      &                  workd(ipntr(2)), 1)
 c
-            call cgbtrs ('Notranspose', n, kl, ku, 1, fac, lda, 
+            call cgbtrs ('Notranspose', n, kl, ku, 1, fac, lda,
      &                    iwork, workd(ipntr(2)), ldv, ierr)
             if (ierr .ne. 0) then
                print*, ' '
                print*, '_band: error in sbgtrs.'
-               print*, ' ' 
+               print*, ' '
                go to 9000
             end if
 c
@@ -563,19 +563,19 @@ c
                end if
 c
             else
-c  
+c
 c              %--------------------------------------%
 c              | Perform  y <-- inv(A-sigma*M)*(M*x). |
 c              | (M*x) has been computed and stored   |
-c              | in workd(ipntr(3)).                  |           
+c              | in workd(ipntr(3)).                  |
 c              %--------------------------------------%
 c
                call ccopy(n, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-               call cgbtrs ('Notranspose', n, kl, ku, 1, fac, lda, 
+               call cgbtrs ('Notranspose', n, kl, ku, 1, fac, lda,
      &                      iwork, workd(ipntr(2)), n, ierr)
-               if (ierr .ne. 0) then 
+               if (ierr .ne. 0) then
                   print*, ' '
-                  print*, '_band: error in _gbtrs.' 
+                  print*, '_band: error in _gbtrs.'
                   print*, ' '
                   go to 9000
                end if
@@ -590,14 +590,14 @@ c        %--------------------%
 c        | Perform y <-- M*x  |
 c        %--------------------%
 c
-          call cgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), 
-     &                lda, workd(ipntr(1)), 1, zero, 
+          call cgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1),
+     &                lda, workd(ipntr(1)), 1, zero,
      &                workd(ipntr(2)), 1)
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
-c        |   Either we have convergence, or there is | 
+c        |   Either we have convergence, or there is |
 c        |   error.                                  |
 c        %-------------------------------------------%
 c
@@ -613,7 +613,7 @@ c
             print *, ' Check the documentation of _naupd '
             print *, ' '
 c
-         else 
+         else
 c
             call cneupd (rvec, howmny , select, d, z, ldz, sigma,
      &                   workev, bmat, n, which, nev, tol,
@@ -621,17 +621,17 @@ c
      &                   workl, lworkl, rwork, info)
 c
             if ( info .ne. 0) then
-c 
+c
 c              %------------------------------------%
 c              | Check the documentation of cneupd. |
 c              %------------------------------------%
 c
-               print *, ' ' 
+               print *, ' '
                print *, ' Error with _neupd = ', info
                print *, ' Check the documentation of _neupd '
-               print *, ' ' 
-c 
-            endif 
+               print *, ' '
+c
+            endif
 c
          end if
 c
@@ -643,7 +643,7 @@ c     %----------------------------------------%
 c     | L O O P  B A C K to call cnaupd again. |
 c     %----------------------------------------%
 c
-      go to 40 
+      go to 40
 c
  9000 continue
 c

EXAMPLES/BAND/cnbdr1.f

@@ -49,13 +49,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -64,12 +64,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Complex  
+      Complex
      &                 a(lda,maxn), m(lda,maxn), fac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn),
      &                 workev(2*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv), ax(maxn)
-      Real  
+      Real
      &                 rwork(maxn), rd(maxncv,3)
 c
 c     %---------------%
@@ -81,28 +81,28 @@ c
      &                 n, nx, lo, isub, isup, idiag, maxitr, mode,
      &                 nconv
       logical          rvec
-      Real  
+      Real
      &                 tol
-      Complex 
+      Complex
      &                 rho, h, h2, sigma
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Complex  
+      Complex
      &                 one, zero, two
-      parameter        ( one = (1.0E+0, 0.0E+0) , 
-     &                   zero = (0.0E+0, 0.0E+0) , 
+      parameter        ( one = (1.0E+0, 0.0E+0) ,
+     &                   zero = (0.0E+0, 0.0E+0) ,
      &                   two = (2.0E+0, 0.0E+0)  )
 c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  scnrm2, slapy2
-      external          scnrm2, cgbmv, caxpy, slapy2, claset 
+      external          scnrm2, cgbmv, caxpy, slapy2, claset
 c
 c     %-----------------------%
 c     | Executable Statements |
@@ -112,7 +112,7 @@ c     %-------------------------------------------------%
 c     | The number NX is the number of interior points  |
 c     | in the discretization of the 2-dimensional      |
 c     | convection-diffusion operator on the unit       |
-c     | square with zero Dirichlet boundary condition.  | 
+c     | square with zero Dirichlet boundary condition.  |
 c     | The number N(=NX*NX) is the dimension of the    |
 c     | matrix.  A standard eigenvalue problem is       |
 c     | solved (BMAT = 'I').  NEV is the number of      |
@@ -123,13 +123,13 @@ c     | the spectrum.  However, the following           |
 c     | conditions must be satisfied:                   |
 c     |                   N <= MAXN                     |
 c     |                 NEV <= MAXNEV                   |
-c     |           NEV + 2 <= NCV <= MAXNCV              | 
-c     %-------------------------------------------------% 
+c     |           NEV + 2 <= NCV <= MAXNCV              |
+c     %-------------------------------------------------%
 c
-      nx  = 10 
+      nx  = 10
       n    = nx*nx
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR1: N is greater than MAXN '
          go to 9000
@@ -154,7 +154,7 @@ c     | Arnoldi iteration.                                  |
 c     %-----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+5*ncv
-      tol  = 0.0 
+      tol  = 0.0
       info = 0
 c
 c     %---------------------------------------------------%
@@ -168,7 +168,7 @@ c
       maxitr = 300
       mode   = 1
 c
-      iparam(3) = maxitr 
+      iparam(3) = maxitr
       iparam(7) = mode
 c
 c     %----------------------------------------%
@@ -190,10 +190,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = nx 
-      ku   = nx 
+      kl   = nx
+      ku   = nx
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -203,13 +203,13 @@ c
       idiag = kl+ku+1
       do 30 j = 1, n
          a(idiag,j) = (4.0E+0, 0.0E+0)  / h2
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
-      rho = (1.0E+2, 0.0E+0) 
+c
+      rho = (1.0E+2, 0.0E+0)
       isup = kl+ku
       isub = kl+ku+2
       do 50 i = 1, nx
@@ -217,8 +217,8 @@ c
         do 40 j = lo+1, lo+nx-1
            a(isup,j+1) = -one/h2 + rho/two/h
            a(isub,j) = -one/h2 - rho/two/h
-  40    continue      
-  50  continue 
+  40    continue
+  50  continue
 c
 c     %------------------------------------%
 c     | KL-th subdiagonal and KU-th super- |
@@ -232,8 +232,8 @@ c
          do 70 j = lo+1, lo+nx
             a(isup,nx+j)  = -one / h2
             a(isub,j) = -one / h2
- 70      continue 
- 80   continue 
+ 70      continue
+ 80   continue
 c
 c     %-----------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues |
@@ -241,11 +241,11 @@ c     | and eigenvectors. Eigenvalues are returned in |
 c     | the one dimensional array D.  Eigenvectors    |
 c     | are returned in the first NCONV (=IPARAM(5))  |
 c     | columns of V.                                 |
-c     %-----------------------------------------------% 
+c     %-----------------------------------------------%
 c
-      rvec = .true. 
+      rvec = .true.
       call cnband(rvec, 'A', select, d, v, ldv, sigma,
-     &           workev, n, a, m, lda, fac, kl, ku, which, 
+     &           workev, n, a, m, lda, fac, kl, ku, which,
      &           bmat, nev, tol, resid, ncv, v, ldv, iparam,
      &           workd, workl, lworkl, rwork, iwork, info)
 c
@@ -294,11 +294,11 @@ c
             rd(j,2) = aimag(d(j))
             rd(j,3) = scnrm2(n, ax, 1)
             rd(j,3) = rd(j,3) / slapy2(rd(j,1),rd(j,2))
- 90      continue 
+ 90      continue
 
          call smout(6, nconv, 3, rd, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -309,8 +309,8 @@ c
           print *, ' '
           print *, ' Error with _nband, info= ', info
           print *, ' Check the documentation of _nband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/cnbdr2.f

@@ -49,13 +49,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -64,12 +64,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Complex  
+      Complex
      &                 a(lda,maxn), m(lda,maxn), fac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn),
      &                 workev(2*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv), ax(maxn)
-      Real  
+      Real
      &                 rwork(maxn), rd(maxncv,3)
 c
 c     %---------------%
@@ -81,18 +81,18 @@ c
      &                 n, nxi, lo, isub, isup, idiag, maxitr, mode,
      &                 nconv
       logical          rvec
-      Real  
+      Real
      &                 tol
-      Complex 
+      Complex
      &                 rho, h, h2, sigma
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Complex  
+      Complex
      &                 one, zero, two
-      parameter        (one  = (1.0E+0, 0.0E+0) , 
+      parameter        (one  = (1.0E+0, 0.0E+0) ,
      &                  zero = (0.0E+0, 0.0E+0) ,
      &                  two  = (2.0E+0, 0.0E+0) )
 c
@@ -100,7 +100,7 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  scnrm2, slapy2
       external          scnrm2, cgbmv, caxpy, slapy2, claset
 c
@@ -112,7 +112,7 @@ c     %-------------------------------------------------%
 c     | The number NX is the number of interior points  |
 c     | in the discretization of the 2-dimensional      |
 c     | convection-diffusion operator on the unit       |
-c     | square with zero Dirichlet boundary condition.  | 
+c     | square with zero Dirichlet boundary condition.  |
 c     | The number N(=NX*NX) is the dimension of the    |
 c     | matrix.  A standard eigenvalue problem is       |
 c     | solved (BMAT = 'I').  NEV is the number of      |
@@ -122,16 +122,16 @@ c     | is used, WHICH is set to 'LM'.  The user can    |
 c     | modify NX, NEV and NCV to solve problems of     |
 c     | different sizes, and to get different parts the |
 c     | spectrum.  However, the following conditions    |
-c     | must be satisfied:                              | 
+c     | must be satisfied:                              |
 c     |                   N <= MAXN                     |
 c     |                 NEV <= MAXNEV                   |
-c     |           NEV + 2 <= NCV <= MAXNCV              | 
-c     %-------------------------------------------------% 
+c     |           NEV + 2 <= NCV <= MAXNCV              |
+c     %-------------------------------------------------%
 c
-      nxi  = 10 
+      nxi  = 10
       n    = nxi*nxi
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR2: N is greater than MAXN '
          go to 9000
@@ -157,7 +157,7 @@ c     | Arnoldi iteration.                                  |
 c     %-----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+5*ncv
-      tol  = 0.0 
+      tol  = 0.0
       info = 0
 c
 c     %---------------------------------------------------%
@@ -193,10 +193,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = nxi 
-      ku   = nxi 
+      kl   = nxi
+      ku   = nxi
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -206,13 +206,13 @@ c
       idiag = kl+ku+1
       do 30 j = 1, n
          a(idiag,j) = (4.0E+0, 0.0E+0)  / h2
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
-      rho = (1.0E+2, 0.0E+0)  
+c
+      rho = (1.0E+2, 0.0E+0)
       isup = kl+ku
       isub = kl+ku+2
       do 50 i = 1, nxi
@@ -220,8 +220,8 @@ c
         do 40 j = lo+1, lo+nxi-1
            a(isup,j+1) = -one/h2 + rho/two/h
            a(isub,j) = -one/h2 - rho/two/h
-  40    continue      
-  50  continue 
+  40    continue
+  50  continue
 c
 c     %------------------------------------%
 c     | KL-th subdiagonal and KU-th super- |
@@ -235,8 +235,8 @@ c
          do 70 j = lo+1, lo+nxi
             a(isup,nxi+j)  = -one / h2
             a(isub,j) = -one / h2
- 70      continue 
- 80   continue 
+ 70      continue
+ 80   continue
 c
 c     %-----------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues |
@@ -244,11 +244,11 @@ c     | and eigenvectors. Eigenvalues are returned in |
 c     | the one dimensional array D.  Eigenvectors    |
 c     | are returned in the first NCONV (=IPARAM(5))  |
 c     | columns of V.                                 |
-c     %-----------------------------------------------% 
+c     %-----------------------------------------------%
 c
-      rvec = .true. 
+      rvec = .true.
       call cnband(rvec, 'A', select, d, v, ldv, sigma,
-     &           workev, n, a, m, lda, fac, kl, ku, which, 
+     &           workev, n, a, m, lda, fac, kl, ku, which,
      &           bmat, nev, tol, resid, ncv, v, ldv, iparam,
      &           workd, workl, lworkl, rwork, iwork, info)
 c
@@ -297,11 +297,11 @@ c
             rd(j,2) = aimag(d(j))
             rd(j,3) = scnrm2(n, ax, 1)
             rd(j,3) = rd(j,3) / slapy2(rd(j,1),rd(j,2))
- 90      continue 
+ 90      continue
 
          call smout(6, nconv, 3, rd, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -312,8 +312,8 @@ c
           print *, ' '
           print *, ' Error with _nband, info= ', info
           print *, ' Check the documentation of _nband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/cnbdr3.f

@@ -1,9 +1,9 @@
       program cnbdr3
 c
 c     ... Construct matrices A and M in LAPACK-style band form.
-c         Matrices A and M are derived from the finite 
-c         element discretization of the 1-dimensional 
-c         convection-diffusion operator 
+c         Matrices A and M are derived from the finite
+c         element discretization of the 1-dimensional
+c         convection-diffusion operator
 c                         (d^2u/dx^2) + rho*(du/dx)
 c         on the interval [0,1] with zero boundary condition using
 c         piecewise linear elements.
@@ -51,13 +51,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn)
 c
 c     %--------------%
@@ -66,12 +66,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Complex  
+      Complex
      &                 a(lda,maxn), m(lda,maxn), fac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn),
      &                 workev(2*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv), ax(maxn), mx(maxn)
-      Real  
+      Real
      &                 rwork(maxn), rd(maxncv,3)
 c
 c     %---------------%
@@ -83,16 +83,16 @@ c
      &                 n, idiag, isup, isub, maxitr,
      &                 mode, nconv
       logical          rvec
-      Real  
+      Real
      &                 tol
-      Complex 
+      Complex
      &                 rho, h, sigma
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Complex  
+      Complex
      &                 one, zero, two
       parameter        (one  = (1.0E+0, 0.0E+0) ,
      &                  zero = (0.0E+0, 0.0E+0) ,
@@ -102,9 +102,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  scnrm2, slapy2
-      external          scnrm2, cgbmv, caxpy, slapy2, claset 
+      external          scnrm2, cgbmv, caxpy, slapy2, claset
 c
 c     %-----------------------%
 c     | Executable Statements |
@@ -129,8 +129,8 @@ c     |           NEV + 2 <= NCV <= MAXNCV              |
 c     %-------------------------------------------------%
 c
       n    = 100
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR3: N is greater than MAXN '
          go to 9000
@@ -146,13 +146,13 @@ c
       sigma = zero
 c
 c     %----------------------------------------------------%
-c     | The work array WORKL is used in CNAUPD as          | 
+c     | The work array WORKL is used in CNAUPD as          |
 c     | workspace.  Its dimension LWORKL has to be set as  |
 c     | illustrated below.  The parameter TOL determines   |
 c     | the stopping criterion. If TOL<=0, machine machine |
 c     | precision is used.  Setting INFO=0 indicates that  |
 c     | using a randomly generated vector to start the     |
-c     | the ARNOLDI process.                               | 
+c     | the ARNOLDI process.                               |
 c     %----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+5*ncv
@@ -195,7 +195,7 @@ c
       kl   = 1
       ku   = 1
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -203,23 +203,23 @@ c
 c
       idiag = kl+ku+1
       do 30 j = 1, n
-         a(idiag,j) = (2.0E+0, 0.0E+0)  / h 
-         m(idiag,j) = (4.0E+0, 0.0E+0)  * h 
-  30  continue 
-c 
+         a(idiag,j) = (2.0E+0, 0.0E+0)  / h
+         m(idiag,j) = (4.0E+0, 0.0E+0)  * h
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+ku+2
-      rho = (1.0E+1, 0.0E+0) 
+      rho = (1.0E+1, 0.0E+0)
       do 40 j = 1, n-1
            a(isup,j+1) = -one/h + rho/two
            a(isub,j) = -one/h - rho/two
            m(isup,j+1) = one*h
            m(isub,j) = one*h
-  40  continue      
+  40  continue
 c
 c     %-----------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues |
@@ -229,7 +229,7 @@ c     | are returned in the first NCONV (=IPARAM(5))  |
 c     | columns of V.                                 |
 c     %-----------------------------------------------%
 c
-      rvec = .true. 
+      rvec = .true.
       call cnband(rvec, 'A', select, d, v, ldv, sigma,
      &           workev, n, a, m, lda, fac, kl, ku, which,
      &           bmat, nev, tol, resid, ncv, v, ldv, iparam,
@@ -277,24 +277,24 @@ c
             rd(j,1) = real (d(j))
             rd(j,2) = aimag(d(j))
             rd(j,3) = scnrm2(n, ax, 1)
-            rd(j,3) = rd(j,3) / slapy2(rd(j,1), rd(j,2))         
- 50      continue 
+            rd(j,3) = rd(j,3) / slapy2(rd(j,1), rd(j,2))
+ 50      continue
 
          call smout(6, nconv, 3, rd, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
 c        | is error.  Check the documentation  |
-c        | for cnband.                         | 
+c        | for cnband.                         |
 c        %-------------------------------------%
 c
           print *, ' '
           print *, ' Error with _band, info= ', info
           print *, ' Check the documentation of _band '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/cnbdr4.f

@@ -49,13 +49,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn)
 c
 c     %--------------%
@@ -64,12 +64,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Complex  
+      Complex
      &                 a(lda,maxn), m(lda,maxn), fac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn),
      &                 workev(2*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv), ax(maxn), mx(maxn)
-      Real  
+      Real
      &                 rwork(maxn), rd(maxncv,3)
 c
 c     %---------------%
@@ -81,16 +81,16 @@ c
      &                 n, idiag, isup, isub, maxitr, mode,
      &                 nconv
       logical          rvec
-      Real  
+      Real
      &                 tol
-      Complex 
+      Complex
      &                 rho, h, sigma
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Complex  
+      Complex
      &                 one, zero, two, four, six
       parameter        (one  = (1.0E+0, 0.0E+0)  ,
      &                  zero = (0.0E+0, 0.0E+0) ,
@@ -102,7 +102,7 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  scnrm2, slapy2
       external          scnrm2, cgbmv, caxpy, slapy2, claset
 c
@@ -121,7 +121,7 @@ c     | solved (BMAT = 'G').  NEV is the number of      |
 c     | eigenvalues (closest to the shift SIGMA) to be  |
 c     | approximated.  Since the shift and invert mode  |
 c     | is used, WHICH is set to 'LM'.  The user can    |
-c     | modify NX, NEV and NCV to solve problems of     | 
+c     | modify NX, NEV and NCV to solve problems of     |
 c     | different sizes, and to get different parts the |
 c     | spectrum.  However, the following conditions    |
 c     | must be satisfied:                              |
@@ -131,8 +131,8 @@ c     |           NEV + 2 <= NCV <= MAXNCV              |
 c     %-------------------------------------------------%
 c
       n    = 100
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR4: N is greater than MAXN '
          go to 9000
@@ -145,16 +145,16 @@ c
       end if
       bmat = 'G'
       which = 'LM'
-      sigma = (1.0E+1, 0.0E+0) 
+      sigma = (1.0E+1, 0.0E+0)
 c
 c     %----------------------------------------------------%
-c     | The work array WORKL is used in CNAUPD as          | 
+c     | The work array WORKL is used in CNAUPD as          |
 c     | workspace.  Its dimension LWORKL has to be set as  |
 c     | illustrated below.  The parameter TOL determines   |
 c     | the stopping criterion. If TOL<=0, machine machine |
 c     | precision is used.  Setting INFO=0 indicates that  |
 c     | we using a randomly generated vector to start the  |
-c     | the ARNOLDI process.                               | 
+c     | the ARNOLDI process.                               |
 c     %----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+5*ncv
@@ -197,30 +197,30 @@ c
       kl   = 1
       ku   = 1
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
       h = one / cmplx(n+1)
       idiag = kl+ku+1
       do 30 j = 1, n
-         a(idiag,j) = two / h 
+         a(idiag,j) = two / h
          m(idiag,j) = four * h / six
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+ku+2
-      rho = (1.0E+1, 0.0E+0) 
+      rho = (1.0E+1, 0.0E+0)
       do 40 j = 1, n-1
          a(isup,j+1) = -one/h + rho/two
          a(isub,j) = -one/h - rho/two
          m(isup,j+1) = one*h / six
          m(isub,j) = one*h / six
-  40  continue 
+  40  continue
 c
 c     %-----------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues |
@@ -230,7 +230,7 @@ c     | are returned in the first NCONV (=IPARAM(5))  |
 c     | columns of V.                                 |
 c     %-----------------------------------------------%
 c
-      rvec = .true. 
+      rvec = .true.
       call cnband(rvec, 'A', select, d, v, ldv, sigma,
      &           workev, n, a, m, lda, fac, kl, ku, which,
      &           bmat, nev, tol, resid, ncv, v, ldv, iparam,
@@ -279,11 +279,11 @@ c
             rd(j,2) = aimag(d(j))
             rd(j,3) = scnrm2(n, ax, 1)
             rd(j,3) = rd(j,3) / slapy2(rd(j,1), rd(j,2))
- 90      continue 
+ 90      continue
 
          call smout(6, nconv, 3, rd, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -294,8 +294,8 @@ c
           print *, ' '
           print *, ' Error with _band, info= ', info
           print *, ' Check the documentation of _band '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/dnband.f

@@ -35,18 +35,18 @@ c  Mode 2:  A*z = lambda*M*z, M symmetric positive definite
 c           ===> OP = inv[M]*A  and  B = M.
 c
 c  Mode 3:  A*z = lambda*M*z, M symmetric semi-definite
-c           ===> OP = Real_Part{ inv[A - sigma*M]*M }  and  B = M. 
+c           ===> OP = Real_Part{ inv[A - sigma*M]*M }  and  B = M.
 c           ===> shift-and-invert mode (in real arithmetic)
-c           If OP*z = amu*z, then 
+c           If OP*z = amu*z, then
 c           amu = 1/2 * [ 1/(lambda-sigma) + 1/(lambda-conjg(sigma)) ].
 c           Note: If sigma is real, i.e. imaginary part of sigma is zero;
-c                 Real_Part{ inv[A - sigma*M]*M } == inv[A - sigma*M]*M 
-c                 amu == 1/(lambda-sigma). 
-c  
+c                 Real_Part{ inv[A - sigma*M]*M } == inv[A - sigma*M]*M
+c                 amu == 1/(lambda-sigma).
+c
 c  Mode 4:  A*z = lambda*M*z, M symmetric semi-definite
-c           ===> OP = Imaginary_Part{ inv[A - sigma*M]*M }  and  B = M. 
+c           ===> OP = Imaginary_Part{ inv[A - sigma*M]*M }  and  B = M.
 c           ===> shift-and-invert mode (in real arithmetic)
-c           If OP*z = amu*z, then 
+c           If OP*z = amu*z, then
 c           amu = 1/2i * [ 1/(lambda-sigma) - 1/(lambda-conjg(sigma)) ].
 c
 c
@@ -54,28 +54,28 @@ c  The choice of mode must be specified in IPARAM(7) defined below.
 c
 c \Usage
 c   call dnband
-c      ( RVEC, HOWMNY, SELECT, DR, DI, Z, LDZ, SIGMAR, SIGMAI, 
-c        WORKEV, V, N, AB, MB, LDA, RFAC, CFAC, KL, KU, WHICH, 
-c        BMAT, NEV, TOL, RESID, NCV, V, LDV, IPARAM, WORKD, 
+c      ( RVEC, HOWMNY, SELECT, DR, DI, Z, LDZ, SIGMAR, SIGMAI,
+c        WORKEV, V, N, AB, MB, LDA, RFAC, CFAC, KL, KU, WHICH,
+c        BMAT, NEV, TOL, RESID, NCV, V, LDV, IPARAM, WORKD,
 c        WORKL, LWORKL, WORKC, IWORK, INFO )
 c
 c \Arguments
-c 
-c  RVEC    LOGICAL  (INPUT) 
-c          Specifies whether a basis for the invariant subspace corresponding 
-c          to the converged Ritz value approximations for the eigenproblem 
+c
+c  RVEC    LOGICAL  (INPUT)
+c          Specifies whether a basis for the invariant subspace corresponding
+c          to the converged Ritz value approximations for the eigenproblem
 c          A*z = lambda*B*z is computed.
 c
 c             RVEC = .FALSE.     Compute Ritz values only.
 c
 c             RVEC = .TRUE.      Compute the Ritz vectors or Schur vectors.
-c                                See Remarks below. 
+c                                See Remarks below.
 c
-c  HOWMNY  Character*1  (INPUT) 
-c          Specifies the form of the basis for the invariant subspace 
+c  HOWMNY  Character*1  (INPUT)
+c          Specifies the form of the basis for the invariant subspace
 c          corresponding to the converged Ritz values that is to be computed.
 c
-c          = 'A': Compute NEV Ritz vectors; 
+c          = 'A': Compute NEV Ritz vectors;
 c          = 'P': Compute NEV Schur vectors;
 c          = 'S': compute some of the Ritz vectors, specified
 c                 by the logical array SELECT.
@@ -83,23 +83,23 @@ c
 c  SELECT  Logical array of dimension NCV.  (INPUT)
 c          If HOWMNY = 'S', SELECT specifies the Ritz vectors to be
 c          computed. To select the Ritz vector corresponding to a
-c          Ritz value (DR(j), DI(j)), SELECT(j) must be set to .TRUE.. 
+c          Ritz value (DR(j), DI(j)), SELECT(j) must be set to .TRUE..
 c          If HOWMNY = 'A' or 'P', SELECT is used as internal workspace.
 c
 c  DR      Double precision array of dimension NEV+1.  (OUTPUT)
-c          On exit, DR contains the real part of the Ritz value approximations 
-c          to the eigenvalues of A*z = lambda*B*z. 
+c          On exit, DR contains the real part of the Ritz value approximations
+c          to the eigenvalues of A*z = lambda*B*z.
 c
 c  DI      Double precision array of dimension NEV+1.  (OUTPUT)
-c          On exit, DI contains the imaginary part of the Ritz value 
+c          On exit, DI contains the imaginary part of the Ritz value
 c          approximations to the eigenvalues of A*z = lambda*B*z associated
-c          with DR. 
+c          with DR.
 c
-c          NOTE: When Ritz values are complex, they will come in complex 
-c                conjugate pairs.  If eigenvectors are requested, the 
-c                corresponding Ritz vectors will also come in conjugate 
-c                pairs and the real and imaginary parts of these are 
-c                represented in two consecutive columns of the array Z 
+c          NOTE: When Ritz values are complex, they will come in complex
+c                conjugate pairs.  If eigenvectors are requested, the
+c                corresponding Ritz vectors will also come in conjugate
+c                pairs and the real and imaginary parts of these are
+c                represented in two consecutive columns of the array Z
 c                (see below).
 c
 c  Z       Real N by NEV+1 array if RVEC = .TRUE. and HOWMNY = 'A'. (OUTPUT)
@@ -124,24 +124,24 @@ c          the array Z may be set equal to first NEV+1 columns of the Arnoldi
 c          basis array V computed by DNAUPD.  In this case the Arnoldi basis
 c          will be destroyed and overwritten with the eigenvector basis.
 c
-c  LDZ     Integer.  (INPUT) 
-c          The leading dimension of the array Z.  If Ritz vectors are 
-c          desired, then  LDZ >= max( 1, N ).  In any case,  LDZ >= 1.  
-c 
-c  SIGMAR  Double precision  (INPUT) 
-c          If IPARAM(7) = 3 or 4, represents the real part of the shift. 
-c          Not referenced if IPARAM(7) = 1 or 2.  
-c 
-c  SIGMAI  Double precision  (INPUT) 
-c          If IPARAM(7) = 3 or 4, represents the imaginary part of the 
-c          shift. 
-c          Not referenced if IPARAM(7) = 1 or 2.  
-c 
-c  WORKEV  Double precision work array of dimension 3*NCV.  (WORKSPACE) 
-c 
-c  N       Integer.  (INPUT) 
-c          Dimension of the eigenproblem.  
-c 
+c  LDZ     Integer.  (INPUT)
+c          The leading dimension of the array Z.  If Ritz vectors are
+c          desired, then  LDZ >= max( 1, N ).  In any case,  LDZ >= 1.
+c
+c  SIGMAR  Double precision  (INPUT)
+c          If IPARAM(7) = 3 or 4, represents the real part of the shift.
+c          Not referenced if IPARAM(7) = 1 or 2.
+c
+c  SIGMAI  Double precision  (INPUT)
+c          If IPARAM(7) = 3 or 4, represents the imaginary part of the
+c          shift.
+c          Not referenced if IPARAM(7) = 1 or 2.
+c
+c  WORKEV  Double precision work array of dimension 3*NCV.  (WORKSPACE)
+c
+c  N       Integer.  (INPUT)
+c          Dimension of the eigenproblem.
+c
 c  AB      Double precision array of dimension LDA by N. (INPUT)
 c          The matrix A in band storage, in rows KL+1 to
 c          2*KL+KU+1; rows 1 to KL of the array need not be set.
@@ -151,25 +151,25 @@ c          AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
 c
 c  MB      Double precision array of dimension LDA by N. (INPUT)
 c          The matrix M in band storage, in rows KL+1 to
-c          2*KL+KU+1; rows 1 to KL of the array need not be set. 
+c          2*KL+KU+1; rows 1 to KL of the array need not be set.
 c          The j-th column of M is stored in the j-th column of the
 c          array AB as follows:
 c          MB(kl+ku+1+i-j,j) = M(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
 c          Not referenced if IPARAM(7) = 1
 c
 c  LDA     Integer. (INPUT)
-c          Leading dimension of AB, MB, RFAC and CFAC. 
+c          Leading dimension of AB, MB, RFAC and CFAC.
 c
 c  RFAC    Double precision array of LDA by N. (WORKSPACE/OUTPUT)
-c          RFAC is used to store the LU factors of MB when IPARAM(7) = 2 
+c          RFAC is used to store the LU factors of MB when IPARAM(7) = 2
 c          is invoked.  It is used to store the LU factors of
 c          (A-sigma*M) when IPARAM(7) = 3 is invoked with a real shift.
 c          It is not referenced when IPARAM(7) = 1 or 4.
 c
 c  CFAC    Complex*16 array of LDA by N. (WORKSPACE/OUTPUT)
 c          CFAC is used to store (A-SIGMA*M) and its LU factors
-c          when IPARAM(7) = 3 or 4 are used with a complex shift SIGMA.  
-c          On exit, it contains the LU factors of (A-SIGMA*M).  
+c          when IPARAM(7) = 3 or 4 are used with a complex shift SIGMA.
+c          On exit, it contains the LU factors of (A-SIGMA*M).
 c          It is not referenced when IPARAM(7) = 1 or 2.
 c
 c  KL      Integer. (INPUT)
@@ -181,7 +181,7 @@ c
 c  WHICH   Character*2.  (INPUT)
 c          When IPARAM(7)= 1 or 2,  WHICH can be set to any one of
 c          the following.
-c  
+c
 c            'LM' -> want the NEV eigenvalues of largest magnitude.
 c            'SM' -> want the NEV eigenvalues of smallest magnitude.
 c            'LR' -> want the NEV eigenvalues of largest real part.
@@ -189,8 +189,8 @@ c            'SR' -> want the NEV eigenvalues of smallest real part.
 c            'LI' -> want the NEV eigenvalues of largest imaginary part.
 c            'SI' -> want the NEV eigenvalues of smallest imaginary part.
 c
-c          When IPARAM(7) = 3 or 4, WHICH should be set to 'LM' only. 
-c          
+c          When IPARAM(7) = 3 or 4, WHICH should be set to 'LM' only.
+c
 c  BMAT    Character*1.  (INPUT)
 c          BMAT specifies the type of the matrix B that defines the
 c          semi-inner product for the operator OP.
@@ -199,9 +199,9 @@ c          BMAT = 'G' -> generalized eigenvalue problem A*z = lambda*M*z
 
 c  NEV     Integer. (INPUT)
 c          Number of eigenvalues to be computed.
-c   
+c
 c  TOL     Double precision scalar.  (INPUT)
-c          Stopping criteria: the relative accuracy of the Ritz value 
+c          Stopping criteria: the relative accuracy of the Ritz value
 c          is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)).
 c          If TOL .LE. 0. is passed a default is set:
 c          DEFAULT = DLAMCH('EPS')  (machine precision as computed
@@ -221,12 +221,12 @@ c          Represents the dimension of the Arnoldi basis constructed
 c          by dnaupd for OP.
 c
 c  V       Double precision array N by NCV+1.  (OUTPUT)
-c          Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns 
-c                       represent approximate Schur vectors that span the 
+c          Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns
+c                       represent approximate Schur vectors that span the
 c                       desired invariant subspace.
-c          NOTE: The array Z may be set equal to first NEV+1 columns of the 
+c          NOTE: The array Z may be set equal to first NEV+1 columns of the
 c          Arnoldi basis vector array V computed by DNAUPD. In this case
-c          if RVEC = .TRUE. and HOWMNY='A', then the first NCONV=IPARAM(5) 
+c          if RVEC = .TRUE. and HOWMNY='A', then the first NCONV=IPARAM(5)
 c          are the desired Ritz vectors.
 c
 c  LDV     Integer.  (INPUT)
@@ -234,7 +234,7 @@ c          Leading dimension of V exactly as declared in the calling
 c          program.
 c
 c  IPARAM  Integer array of length 11.  (INPUT/OUTPUT)
-c          IPARAM(1) = ISHIFT: 
+c          IPARAM(1) = ISHIFT:
 c          The shifts selected at each iteration are used to restart
 c          the Arnoldi iteration in an implicit fashion.
 c          It is set to 1 in this subroutine.  The user do not need
@@ -248,7 +248,7 @@ c                      combination of Ritz vectors associated with the
 c                      "wanted" eigenvalues.
 c          -------------------------------------------------------------
 c
-c          IPARAM(2) = No longer referenced. 
+c          IPARAM(2) = No longer referenced.
 c
 c          IPARAM(3) = MXITER
 c          On INPUT:  max number of Arnoldi update iterations allowed.
@@ -262,9 +262,9 @@ c
 c          IPARAM(6) = IUPD
 c          Not referenced. Implicit restarting is ALWAYS used.
 c
-c          IPARAM(7) = IPARAM(7): 
+c          IPARAM(7) = IPARAM(7):
 c          On INPUT determines what type of eigenproblem is being solved.
-c          Must be 1,2,3,4; See under \Description of dnband for the 
+c          Must be 1,2,3,4; See under \Description of dnband for the
 c          four modes available.
 c
 c          IPARAM(9) = NUMOP, IPARAM(10) = NUMOPB, IPARAM(11) = NUMREO,
@@ -280,22 +280,22 @@ c LWORKL   Integer.  (INPUT)
 c          LWORKL must be at least 3*NCV**2 + 6*NCV.
 c
 c WORKC    Complex*16 array of length N. (WORKSPACE)
-c          Workspace used when IPARAM(7) = 3 or 4 for storing a temporary 
+c          Workspace used when IPARAM(7) = 3 or 4 for storing a temporary
 c          complex vector.
 c
 c IWORK    Integer array of dimension at least N. (WORKSPACE)
-c          Used when IPARAM(7)=2,3,4 to store the pivot information in the 
+c          Used when IPARAM(7)=2,3,4 to store the pivot information in the
 c          factorization of M or (A-SIGMA*M).
-c            
+c
 c INFO     Integer.  (INPUT/OUTPUT)
 c          Error flag on output.
 c          =  0: Normal exit.
 c          =  1: The Schur form computed by LAPACK routine dlahqr
 c                could not be reordered by LAPACK routine dtrsen.
-c                Re-enter subroutine DNEUPD with IPARAM(5)=NCV and 
-c                increase the size of the arrays DR and DI to have 
-c                dimension at least NCV and allocate at least NCV 
-c                columns for Z. NOTE: Not necessary if Z and V share 
+c                Re-enter subroutine DNEUPD with IPARAM(5)=NCV and
+c                increase the size of the arrays DR and DI to have
+c                dimension at least NCV and allocate at least NCV
+c                columns for Z. NOTE: Not necessary if Z and V share
 c                the same space. Please notify the authors.
 c
 c          = -1: N must be positive.
@@ -314,9 +314,9 @@ c          = -12: HOWMNY = 'S' not yet implemented
 c          = -13: HOWMNY must be one of 'A' or 'P'
 c          = -14: DNAUPD did not find any eigenvalues to sufficient
 c                 accuracy.
-c          = -15: Overflow occurs when we try to transform the Ritz 
+c          = -15: Overflow occurs when we try to transform the Ritz
 c                 values returned from DNAUPD to those of the original
-c                 problem using Rayleigh Quotient. 
+c                 problem using Rayleigh Quotient.
 c          = -9999: Could not build an Arnoldi factorization.
 c                   IPARAM(5) returns the size of the current
 c                   Arnoldi factorization.
@@ -332,7 +332,7 @@ c  1. D.C. Sorensen, "Implicit Application of Polynomial Filters in
 c     a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992),
 c     pp 357-385.
 c
-c  2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly 
+c  2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly
 c     Restarted Arnoldi Iteration", Ph.D thesis, TR95-13, Rice Univ,
 c     May 1995.
 c
@@ -363,9 +363,9 @@ c     Ritz vectors. Thus, their numerical properties are often superior.
 c     If RVEC = .TRUE. then the relationship
 c             A * V(:,1:IPARAM(5)) = V(:,1:IPARAM(5)) * T, and
 c     V(:,1:IPARAM(5))' * V(:,1:IPARAM(5)) = I are approximately satisfied.
-c     Here T is the leading submatrix of order IPARAM(5) of the real 
+c     Here T is the leading submatrix of order IPARAM(5) of the real
 c     upper quasi-triangular matrix stored workl(ipntr(12)). That is,
-c     T is block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; 
+c     T is block upper triangular with 1-by-1 and 2-by-2 diagonal blocks;
 c     each 2-by-2 diagonal block has its diagonal elements equal and its
 c     off-diagonal elements of opposite sign.  Corresponding to each 2-by-2
 c     diagonal block is a complex conjugate pair of Ritz values. The real
@@ -387,20 +387,20 @@ c\EndLib
 c
 c---------------------------------------------------------------------
 c
-      subroutine dnband( rvec, howmny, select, dr, di, z, ldz,  sigmar, 
-     &           sigmai, workev, n, ab, mb, lda, rfac,  cfac, kl, ku, 
-     &           which, bmat, nev, tol, resid,  ncv, v, ldv, 
+      subroutine dnband( rvec, howmny, select, dr, di, z, ldz,  sigmar,
+     &           sigmai, workev, n, ab, mb, lda, rfac,  cfac, kl, ku,
+     &           which, bmat, nev, tol, resid,  ncv, v, ldv,
      &           iparam, workd, workl, lworkl, workc, iwork, info)
 c
 c     %------------------%
 c     | Scalar Arguments |
 c     %------------------%
-c 
+c
       character        which*2, bmat, howmny
       integer          n, lda, kl, ku, nev, ncv, ldv,
-     &                 ldz, lworkl, info  
+     &                 ldz, lworkl, info
       Double precision
-     &                 tol, sigmar, sigmai 
+     &                 tol, sigmar, sigmai
 c
 c     %-----------------%
 c     | Array Arguments |
@@ -410,7 +410,7 @@ c
       logical          select(*)
       Double precision
      &                 dr(*), di(*), resid(*), v(ldv,*), z(ldz,*),
-     &                 ab(lda,*), mb(lda,*), rfac(lda,*), 
+     &                 ab(lda,*), mb(lda,*), rfac(lda,*),
      &                 workd(*), workl(*), workev(*)
       Complex*16
      &                 cfac(lda,*), workc(*)
@@ -426,9 +426,9 @@ c     | Local Scalars |
 c     %---------------%
 c
       integer          ido, i, j, type, imid, itop, ibot, ierr
-      Double precision        
-     &                 numr, denr, deni, dmdul, safmin 
-      logical          rvec, first 
+      Double precision
+     &                 numr, denr, deni, dmdul, safmin
+      logical          rvec, first
 c
 c     %------------%
 c     | Parameters |
@@ -445,7 +445,7 @@ c     %-----------------------------%
 c
       Double precision
      &                 ddot, dnrm2, dlapy2, dlamch
-      external         ddot, dcopy, dgbmv, zgbtrf, zgbtrs, dgbtrf, 
+      external         ddot, dcopy, dgbmv, zgbtrf, zgbtrs, dgbtrf,
      &                 dgbtrs, dnrm2, dlapy2, dlacpy, dlamch
 c
 c     %---------------------%
@@ -464,17 +464,17 @@ c     | that 1/sfmin does not overflow |
 c     %--------------------------------%
 c
       safmin = dlamch('safmin')
-c     
+c
 c     %----------------------------------------------------------------%
 c     | Set type of the problem to be solved. Check consistency        |
 c     | between BMAT and IPARAM(7).                                    |
 c     | type = 1 --> Solving standard problem in regular mode.         |
-c     | type = 2 --> Solving standard problem in shift-invert mode.    | 
+c     | type = 2 --> Solving standard problem in shift-invert mode.    |
 c     | type = 3 --> Solving generalized problem in regular mode.      |
 c     | type = 4 --> Solving generalized problem in shift-invert mode. |
 c     | type = 5 --> Solving standard problem in shift-invert mode     |
 c     |              using iparam(7) = 4 in DNAUPD.                    |
-c     | type = 6 --> Solving generalized problem in shift-invert mode. | 
+c     | type = 6 --> Solving generalized problem in shift-invert mode. |
 c     |              using iparam(7) = 4 in DNAUPD.                    |
 c     %----------------------------------------------------------------%
 c
@@ -485,19 +485,19 @@ c
       else if ( iparam(7) .eq. 2 ) then
          type = 3
       else if ( iparam(7) .eq. 3 .and. bmat .eq. 'G') then
-         type = 4 
+         type = 4
       else if ( iparam(7) .eq. 4 .and. bmat .eq. 'I') then
          type = 5
-      else if ( iparam(7) .eq. 4 .and. bmat .eq. 'G') then 
+      else if ( iparam(7) .eq. 4 .and. bmat .eq. 'G') then
          type = 6
       else
          print*, ' '
          print*, 'BMAT is inconsistent with IPARAM(7).'
-         print*, ' ' 
+         print*, ' '
          go to 9000
       end if
 c
-c     %----------------------------------%       
+c     %----------------------------------%
 c     | When type = 5,6 are used, sigmai |
 c     | must be nonzero.                 |
 c     %----------------------------------%
@@ -505,16 +505,16 @@ c
       if ( type .eq. 5 .or. type .eq. 6 ) then
           if ( sigmai .eq. zero ) then
              print*, ' '
-             print*, '_NBAND: sigmai must be nonzero when type 5 or 6 
+             print*, '_NBAND: sigmai must be nonzero when type 5 or 6
      &                is used. '
              print*, ' '
              go to 9000
-          end if    
+          end if
       end if
 c
 c     %------------------------%
 c     | Initialize the reverse |
-c     | communication flag.    |         
+c     | communication flag.    |
 c     %------------------------%
 c
       ido   = 0
@@ -546,7 +546,7 @@ c         | Factor (A-sigma*I).           |
 c         %-------------------------------%
 c
           if (sigmai .eq. zero) then
-c            
+c
 c            %-----------------------------------%
 c            | Construct (A-sigmar*I) and factor |
 c            | in real arithmetic.               |
@@ -558,7 +558,7 @@ c
   10         continue
              call dgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr )
              if (ierr .ne. 0) then
-                print*, ' ' 
+                print*, ' '
                 print*, ' _NBAND: Error with _gbtrf. '
                 print*, ' '
                 go to  9000
@@ -574,24 +574,24 @@ c
              do 30 j = 1, n
                 do 20 i = itop, ibot
                    cfac(i,j) = dcmplx(ab(i,j))
-  20            continue 
+  20            continue
   30         continue
 c
              do 40 j = 1, n
-                cfac(imid,j) = cfac(imid,j) 
+                cfac(imid,j) = cfac(imid,j)
      $                         - dcmplx(sigmar, sigmai)
-  40         continue 
-c 
-             call zgbtrf(n, n, kl, ku, cfac, lda, iwork, ierr ) 
+  40         continue
+c
+             call zgbtrf(n, n, kl, ku, cfac, lda, iwork, ierr )
              if ( ierr .ne. 0) then
                 print*, ' '
                 print*, ' _NBAND: Error with _gbtrf. '
                 print*, ' '
                 go to  9000
              end if
-c        
+c
           end if
-      
+
       else if ( type .eq. 3 ) then
 c
 c        %-----------------------------------------------%
@@ -603,7 +603,7 @@ c
          call dlacpy ('A', ibot, n, mb, lda, rfac, lda )
          call dgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr)
          if (ierr .ne. 0) then
-             print*, ' ' 
+             print*, ' '
              print*,'_NBAND:  Error with _gbtrf.'
              print*, ' '
              go to 9000
@@ -615,7 +615,7 @@ c        %-------------------------------------------%
 c        | Solving generalized eigenvalue problem in |
 c        | shift-invert mode.                        |
 c        %-------------------------------------------%
-c 
+c
          if ( sigmai .eq. zero ) then
 c
 c            %--------------------------------------------%
@@ -624,7 +624,7 @@ c            | arithmetic.                                |
 c            %--------------------------------------------%
 c
              do 60 j = 1,n
-                do 50 i = itop, ibot 
+                do 50 i = itop, ibot
                    rfac(i,j) = ab(i,j) - sigmar*mb(i,j)
   50            continue
   60         continue
@@ -642,13 +642,13 @@ c
 c            %-----------------------------------------------%
 c            | Construct (A - sigma*M) and factor in complex |
 c            | arithmetic.                                   |
-c            %-----------------------------------------------% 
+c            %-----------------------------------------------%
 c
              do 80 j = 1,n
-                do 70 i = itop, ibot 
-                   cfac(i,j) = dcmplx( ab(i,j)-sigmar*mb(i,j), 
+                do 70 i = itop, ibot
+                   cfac(i,j) = dcmplx( ab(i,j)-sigmar*mb(i,j),
      &                         -sigmai*mb(i,j) )
-  70            continue 
+  70            continue
   80         continue
 c
              call zgbtrf(n, n, kl, ku, cfac, lda, iwork, ierr)
@@ -658,7 +658,7 @@ c
                 print*, ' '
                 go to 9000
              end if
-c 
+c
          end if
 c
       end if
@@ -667,7 +667,7 @@ c     %--------------------------------------------%
 c     |  M A I N   L O O P (reverse communication) |
 c     %--------------------------------------------%
 c
-  90  continue 
+  90  continue
 c
       call dnaupd ( ido, bmat, n, which, nev, tol, resid, ncv,
      &              v, ldv, iparam, ipntr, workd, workl, lworkl,
@@ -681,8 +681,8 @@ c           %----------------------------%
 c           | Perform  y <--- OP*x = A*x |
 c           %----------------------------%
 c
-            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
          else if ( type .eq. 2 ) then
@@ -690,7 +690,7 @@ c
             if (sigmai .eq. zero) then
 c
 c              %----------------------------------%
-c              | Shift is real.  Perform          | 
+c              | Shift is real.  Perform          |
 c              | y <--- OP*x = inv[A-sigmar*I]*x  |
 c              | to force the starting vector     |
 c              | into the range of OP.            |
@@ -700,7 +700,7 @@ c
                call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                       iwork, workd(ipntr(2)), n, ierr)
                if ( ierr .ne. 0 ) then
-                  print*, ' ' 
+                  print*, ' '
                   print*, ' _NBAND: Error with _bgtrs. '
                   print*, ' '
                   go to 9000
@@ -711,8 +711,8 @@ c
 c              %--------------------------------------------%
 c              | Shift is COMPLEX. Perform                  |
 c              | y <--- OP*x = Real_Part{inv[A-sigma*I]*x}  |
-c              | to force the starting vector into the      | 
-c              | range of OP.                               | 
+c              | to force the starting vector into the      |
+c              | range of OP.                               |
 c              %--------------------------------------------%
 c
                do 100 j = 1, n
@@ -732,21 +732,21 @@ c
                   workd(ipntr(2)+j-1) = dble(workc(j))
   110          continue
 c
-            end if 
-c 
+            end if
+c
          else if ( type .eq. 3 ) then
 c
 c           %-----------------------------------%
 c           | Perform  y <--- OP*x = inv[M]*A*x |
-c           | to force the starting vector into | 
+c           | to force the starting vector into |
 c           | the range of OP.                  |
 c           %-----------------------------------%
 c
-            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                  lda, workd(ipntr(1)), 1, zero, 
+            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                  lda, workd(ipntr(1)), 1, zero,
      &                  workd(ipntr(2)), 1)
 c
-            call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                    iwork, workd(ipntr(2)), n, ierr)
             if (ierr .ne. 0) then
                print*, ' '
@@ -759,13 +759,13 @@ c
 c
 c           %-----------------------------------------%
 c           | Perform y <-- OP*x                      |
-c           |         = Real_part{inv[A-SIGMA*M]*M}*x | 
+c           |         = Real_part{inv[A-SIGMA*M]*M}*x |
 c           | to force the starting vector into the   |
 c           | range of OP.                            |
 c           %-----------------------------------------%
 c
-            call dgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call dgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
             if ( sigmai .eq. zero ) then
@@ -773,14 +773,14 @@ c
 c              %---------------------%
 c              | Shift is real, stay |
 c              | in real arithmetic. |
-c              %---------------------%            
+c              %---------------------%
 c
-               call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+               call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                      iwork, workd(ipntr(2)), n, ierr)
                if (ierr .ne. 0) then
-                  print*, ' ' 
+                  print*, ' '
                   print*, '_NBAND: Error with _gbtrs.'
-                  print*, ' ' 
+                  print*, ' '
                   go to 9000
                end if
 c
@@ -792,26 +792,26 @@ c              %--------------------------%
 c
                do 120 i = 1,n
                   workc(i) = dcmplx(workd(ipntr(2)+i-1))
-  120           continue 
+  120           continue
 c
-               call zgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, 
+               call zgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda,
      &                      iwork, workc, n, ierr)
-               if (ierr .ne. 0) then 
+               if (ierr .ne. 0) then
                   print*, ' '
-                  print*, '_NBAND: Error with _gbtrs.' 
+                  print*, '_NBAND: Error with _gbtrs.'
                   print*, ' '
                   go to 9000
                end if
 c
                do  130 i = 1, n
                   workd(ipntr(2)+i-1) = dble(workc(i))
-  130          continue 
+  130          continue
 c
             end if
 c
          else if ( type .eq. 5) then
 c
-c           %---------------------------------------% 
+c           %---------------------------------------%
 c           | Perform y <-- OP*x                    |
 c           |    = Imaginary_part{inv[A-SIGMA*I]}*x |
 c           | to force the starting vector into the |
@@ -839,32 +839,32 @@ c
 c
 c           %----------------------------------------%
 c           | Perform y <-- OP*x                     |
-c           |       Imaginary_part{inv[A-SIGMA*M]*M} | 
+c           |       Imaginary_part{inv[A-SIGMA*M]*M} |
 c           | to force the starting vector into the  |
 c           | range of OP.                           |
 c           %----------------------------------------%
 c
-            call dgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call dgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
             do 160 i = 1,n
                workc(i) = dcmplx(workd(ipntr(2)+i-1))
-  160       continue 
+  160       continue
 c
-            call zgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, 
+            call zgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda,
      &                   iwork, workc, n, ierr)
-            if (ierr .ne. 0) then 
+            if (ierr .ne. 0) then
                print*, ' '
-               print*, '_NBAND: Error with _gbtrs.' 
+               print*, '_NBAND: Error with _gbtrs.'
                print*, ' '
                go to 9000
             end if
 c
             do  170 i = 1, n
                workd(ipntr(2)+i-1) = dimag(workc(i))
-  170       continue 
-c 
+  170       continue
+c
          end if
 c
       else if (ido .eq. 1) then
@@ -875,8 +875,8 @@ c           %----------------------------%
 c           | Perform  y <--- OP*x = A*x |
 c           %----------------------------%
 c
-            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
          else if ( type .eq. 2) then
@@ -907,7 +907,7 @@ c
      &                       iwork, workc, n, ierr)
                if ( ierr .ne. 0 ) then
                   print*, ' '
-                  print*, '_NBAND: Error with _gbtrs.' 
+                  print*, '_NBAND: Error with _gbtrs.'
                   print*, ' '
                   go to 9000
                end if
@@ -924,16 +924,16 @@ c           %-----------------------------------%
 c           | Perform  y <--- OP*x = inv[M]*A*x |
 c           %-----------------------------------%
 c
-            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                  lda, workd(ipntr(1)), 1, zero, 
+            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                  lda, workd(ipntr(1)), 1, zero,
      &                  workd(ipntr(2)), 1)
 c
-            call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                    iwork, workd(ipntr(2)), n, ierr)
             if (ierr .ne. 0) then
                print*, ' '
                print*, '_NBAND: Error with _bgtrs.'
-               print*, ' ' 
+               print*, ' '
                go to 9000
             end if
 c
@@ -942,7 +942,7 @@ c
 c           %--------------------------------------%
 c           | Perform  y <-- inv(A-sigma*M)*(M*x). |
 c           | (M*x) has been computed and stored   |
-c           | in workd(ipntr(3)).                  |           
+c           | in workd(ipntr(3)).                  |
 c           %--------------------------------------%
 c
             if ( sigmai .eq. zero ) then
@@ -953,16 +953,16 @@ c              | real arithmetic.       |
 c              %------------------------%
 c
                call dcopy(n, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-               call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+               call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                       iwork, workd(ipntr(2)), n, ierr)
-               if (ierr .ne. 0) then 
+               if (ierr .ne. 0) then
                   print*, ' '
-                  print*, '_NBAND: Error with _gbtrs.' 
+                  print*, '_NBAND: Error with _gbtrs.'
                   print*, ' '
                   go to 9000
                end if
-c 
-            else 
+c
+            else
 c
 c              %---------------------------%
 c              | Go to COMPLEX arithmetic. |
@@ -970,26 +970,26 @@ c              %---------------------------%
 c
                do 200 i = 1,n
                   workc(i) = dcmplx(workd(ipntr(3)+i-1))
-  200          continue 
+  200          continue
 c
-               call zgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, 
+               call zgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda,
      &                       iwork, workc, n, ierr)
-               if (ierr .ne. 0) then 
+               if (ierr .ne. 0) then
+                  print*, ' '
+                  print*, '_NBAND: Error in _gbtrs.'
                   print*, ' '
-                  print*, '_NBAND: Error in _gbtrs.' 
-                  print*, ' ' 
                   go to 9000
                end if
 c
                do 210 i = 1,n
                   workd(ipntr(2)+i-1) = dble(workc(i))
-  210          continue 
+  210          continue
 c
             end if
 c
          else if ( type .eq. 5 ) then
 c
-c           %---------------------------------------% 
+c           %---------------------------------------%
 c           | Perform y <-- OP*x                    |
 c           |    = Imaginary_part{inv[A-SIGMA*I]*x} |
 c           %---------------------------------------%
@@ -1015,25 +1015,25 @@ c
 c
 c           %-----------------------------------------%
 c           | Perform y <-- OP*x                      |
-c           |   = Imaginary_part{inv[A-SIGMA*M]*M}*x. | 
+c           |   = Imaginary_part{inv[A-SIGMA*M]*M}*x. |
 c           %-----------------------------------------%
 c
             do 240 i = 1,n
                workc(i) = dcmplx(workd(ipntr(3)+i-1))
-  240       continue 
+  240       continue
 c
-            call zgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, 
+            call zgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda,
      &                   iwork, workc, n, ierr)
-            if (ierr .ne. 0) then 
+            if (ierr .ne. 0) then
                print*, ' '
-               print*, '_NBAND: Error with _gbtrs.' 
+               print*, '_NBAND: Error with _gbtrs.'
                print*, ' '
                go to 9000
             end if
 c
             do  250 i = 1, n
                workd(ipntr(2)+i-1) = dimag(workc(i))
-  250       continue 
+  250       continue
 c
          end if
 c
@@ -1045,14 +1045,14 @@ c        | Not used when      |
 c        | type = 1,2.        |
 c        %--------------------%
 c
-          call dgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), 
-     &                lda, workd(ipntr(1)), 1, zero, 
+          call dgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1),
+     &                lda, workd(ipntr(1)), 1, zero,
      &                workd(ipntr(2)), 1)
 c
-      else 
+      else
 c
 c        %-----------------------------------------%
-c        | Either we have convergence, or there is | 
+c        | Either we have convergence, or there is |
 c        | error.                                  |
 c        %-----------------------------------------%
 c
@@ -1069,7 +1069,7 @@ c
             print *, ' '
             go to 9000
 c
-         else 
+         else
 c
             if ( info .eq. 1) then
                print *, ' '
@@ -1084,29 +1084,29 @@ c
 c
             if (iparam(5) .gt. 0) then
 c
-               call dneupd ( rvec, 'A', select, dr, di, z, ldz, 
-     &                 sigmar, sigmai, workev, bmat, n, which, 
+               call dneupd ( rvec, 'A', select, dr, di, z, ldz,
+     &                 sigmar, sigmai, workev, bmat, n, which,
      &                 nev, tol, resid, ncv, v, ldv, iparam,
-     &                 ipntr, workd, workl, lworkl, info )            
+     &                 ipntr, workd, workl, lworkl, info )
 c
                if ( info .ne. 0) then
-c 
+c
 c                 %------------------------------------%
 c                 | Check the documentation of DNEUPD. |
 c                 %------------------------------------%
 c
-                  print *, ' ' 
+                  print *, ' '
                   print *, ' Error with _neupd = ', info
                   print *, ' Check the documentation of _neupd '
-                  print *, ' ' 
+                  print *, ' '
                   go to 9000
 c
-               else if ( sigmai .ne. zero ) then 
-c 
+               else if ( sigmai .ne. zero ) then
+c
                   if ( type .eq. 4 .or. type .eq. 6 ) then
-c 
+c
                      first = .true.
-                     do 270 j = 1, iparam(5) 
+                     do 270 j = 1, iparam(5)
 c
 c                    %----------------------------------%
 c                    | Use Rayleigh Quotient to recover |
@@ -1118,16 +1118,16 @@ c
 c
 c                       %--------------------------------------%
 c                       | Eigenvalue is real. Compute          |
-c                       | d = (x'*inv[A-sigma*M]*M*x) / (x'*x) | 
+c                       | d = (x'*inv[A-sigma*M]*M*x) / (x'*x) |
 c                       %--------------------------------------%
 c
-                        call dgbmv('Nontranspose', n, n, kl, ku, one, 
+                        call dgbmv('Nontranspose', n, n, kl, ku, one,
      $                     mb(itop,1), lda, z(1,j), 1, zero,
      $                     workd, 1)
                         do i = 1, n
                            workc(i) = dcmplx(workd(i))
                         end do
-                        call zgbtrs ('Notranspose', n, kl, ku, 1, 
+                        call zgbtrs ('Notranspose', n, kl, ku, 1,
      $                        cfac, lda, iwork, workc, n, info)
                         do i = 1, n
                            workd(i) = dble(workc(i))
@@ -1151,7 +1151,7 @@ c
                            go to 9000
                         end if
 c
-                     else if (first) then 
+                     else if (first) then
 c
 c                       %------------------------%
 c                       | Eigenvalue is complex. |
@@ -1166,7 +1166,7 @@ c
                         call dgbmv('Nontranspose', n, n, kl, ku,
      $                      one, mb(itop,1), lda, z(1,j), 1, zero,
      $                      workd, 1)
-                        call dgbmv('Nontranspose', n, n, kl, ku, 
+                        call dgbmv('Nontranspose', n, n, kl, ku,
      $                       one, mb(itop,1), lda, z(1,j+1), 1,
      $                       zero, workd(n+1), 1)
                         do i = 1, n
@@ -1177,7 +1177,7 @@ c                       %----------------------------%
 c                       | Compute inv(A-sigma*M)*M*x |
 c                       %----------------------------%
 c
-                        call zgbtrs('Notranspose',n,kl,ku,1,cfac, 
+                        call zgbtrs('Notranspose',n,kl,ku,1,cfac,
      $                     lda, iwork, workc, n, info)
 c
 c                       %-------------------------------%
@@ -1197,7 +1197,7 @@ c                       %----------------%
 c                       | Compute (x'*x) |
 c                       %----------------%
 c
-                        numr = dlapy2( dnrm2(n, z(1,j), 1), 
+                        numr = dlapy2( dnrm2(n, z(1,j), 1),
      &                         dnrm2(n, z(1, j+1), 1) )**2
 c
 c                       %----------------------------------------%
@@ -1237,7 +1237,7 @@ c
 c
                      end if
 c
-  270                continue 
+  270                continue
 c
                   else if ( type .eq. 2 .or. type .eq. 5) then
 c
@@ -1260,7 +1260,7 @@ c
                         do i = 1, n
                            workc(i) = dcmplx(z(i,j))
                         end do
-                        call zgbtrs ('Notranspose', n, kl, ku, 1, 
+                        call zgbtrs ('Notranspose', n, kl, ku, 1,
      $                        cfac, lda, iwork, workc, n, info)
                         do i = 1, n
                            workd(i) = dble(workc(i))
@@ -1329,7 +1329,7 @@ c                       | Compute (x'x) / (x'*inv(A-sigma*I)*x). |
 c                       %----------------------------------------%
 c
                         dmdul = dlapy2(denr,deni)**2
-                        if (dmdul .ge. safmin) then  
+                        if (dmdul .ge. safmin) then
                            dr(j) = sigmar+numr*denr / dmdul
                            di(j) = sigmai-numr*deni / dmdul
                            first = .false.
@@ -1378,7 +1378,7 @@ c     %----------------------------------------%
 c     | L O O P  B A C K to call DNAUPD again. |
 c     %----------------------------------------%
 c
-      go to 90 
+      go to 90
 c
  9000 continue
 c

EXAMPLES/BAND/dnbdr1.f

@@ -1,4 +1,4 @@
-      program dnbdr1 
+      program dnbdr1
 c
 c     ... Construct the matrix A in LAPACK-style band form.
 c         The matrix A is derived from the discretization of
@@ -49,13 +49,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -64,12 +64,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Double precision 
+      Double precision
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn),
      &                 workev(3*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv, 3), ax(maxn)
-      Complex*16  
+      Complex*16
      &                 cfac(lda, maxn), workc(maxn)
 c
 c     %---------------%
@@ -81,25 +81,25 @@ c
      &                 n, nx, lo, isub, isup, idiag, mode, maxitr,
      &                 nconv
       logical          rvec, first
-      Double precision  
+      Double precision
      &                 tol, rho, h, h2, sigmar, sigmai
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Double precision  
+      Double precision
      &                 one, zero, two
-      parameter        (one = 1.0D+0 , zero = 0.0D+0 , 
+      parameter        (one = 1.0D+0 , zero = 0.0D+0 ,
      &                  two = 2.0D+0 )
 c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dlapy2 , dnrm2 
-      external          dlapy2 , dnrm2 , dgbmv , daxpy  
+      Double precision
+     &                  dlapy2 , dnrm2
+      external          dlapy2 , dnrm2 , dgbmv , daxpy
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -115,7 +115,7 @@ c     %-------------------------------------------------%
 c     | The number NX is the number of interior points  |
 c     | in the discretization of the 2-dimensional      |
 c     | convection-diffusion operator on the unit       |
-c     | square with zero Dirichlet boundary condition.  | 
+c     | square with zero Dirichlet boundary condition.  |
 c     | The number N(=NX*NX) is the dimension of the    |
 c     | matrix.  A standard eigenvalue problem is       |
 c     | solved (BMAT = 'I').  NEV is the number of      |
@@ -126,13 +126,13 @@ c     | spectrum.  However, The following conditions    |
 c     | must be satisfied:                              |
 c     |                   N <= MAXN                     |
 c     |                 NEV <= MAXNEV                   |
-c     |           NEV + 2 <= NCV <= MAXNCV              | 
-c     %-------------------------------------------------% 
+c     |           NEV + 2 <= NCV <= MAXNCV              |
+c     %-------------------------------------------------%
 c
-      nx  = 10 
+      nx  = 10
       n    = nx*nx
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR1: N is greater than MAXN '
          go to 9000
@@ -158,7 +158,7 @@ c     | generated in DNAUPD  to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+6*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -173,7 +173,7 @@ c
       maxitr = 300
       mode   = 1
 c
-      iparam(3) = maxitr 
+      iparam(3) = maxitr
       iparam(7) = mode
 c
 c     %----------------------------------------%
@@ -195,10 +195,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = nx 
-      ku   = nx 
+      kl   = nx
+      ku   = nx
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -208,13 +208,13 @@ c
       idiag = kl+ku+1
       do 30 j = 1, n
          a(idiag,j) = 4.0D+0  / h2
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
-      rho = 1.0D+2  
+c
+      rho = 1.0D+2
       isup = kl+ku
       isub = kl+ku+2
       do 50 i = 1, nx
@@ -222,8 +222,8 @@ c
         do 40 j = lo+1, lo+nx-1
            a(isup,j+1) = -one/h2 + rho/two/h
            a(isub,j) = -one/h2 - rho/two/h
-  40    continue      
-  50  continue 
+  40    continue
+  50  continue
 c
 c     %------------------------------------%
 c     | KL-th subdiagonal and KU-th super- |
@@ -237,8 +237,8 @@ c
          do 70 j = lo+1, lo+nx
             a(isup,nx+j)  = -one / h2
             a(isub,j) = -one / h2
- 70      continue 
- 80   continue 
+ 70      continue
+ 80   continue
 c
 c     %------------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues  |
@@ -247,12 +247,12 @@ c     | eigenvalues are returned in the first column   |
 c     | of D, the imaginary parts are returned in the  |
 c     | second column of D.  Eigenvectors are returned |
 c     | in the first NCONV (=IPARAM(5)) columns of V.  |
-c     %------------------------------------------------% 
+c     %------------------------------------------------%
 c
-      rvec = .true. 
-      call dnband (rvec, 'A', select, d, d(1,2), v, ldv, sigmar, sigmai, 
-     &           workev, n, a, m, lda, rfac, cfac, kl, ku, which, 
-     &           bmat, nev, tol, resid, ncv, v, ldv, iparam, workd, 
+      rvec = .true.
+      call dnband (rvec, 'A', select, d, d(1,2), v, ldv, sigmar, sigmai,
+     &           workev, n, a, m, lda, rfac, cfac, kl, ku, which,
+     &           bmat, nev, tol, resid, ncv, v, ldv, iparam, workd,
      &           workl, lworkl, workc, iwork, info)
 c
       if ( info .eq. 0) then
@@ -285,8 +285,8 @@ c        | Compute the residual norm. |
 c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
-         first = .true. 
-         do 90 j = 1, nconv 
+         first = .true.
+         do 90 j = 1, nconv
 c
             if ( d(j,2) .eq. zero ) then
 c
@@ -294,11 +294,11 @@ c              %--------------------%
 c              | Ritz value is real |
 c              %--------------------%
 c
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
                call daxpy (n, -d(j,1), v(1,j), 1, ax, 1)
-               d(j,3) = dnrm2 (n, ax, 1) 
+               d(j,3) = dnrm2 (n, ax, 1)
                d(j,3) = d(j,3) / abs(d(j,1))
 c
             else if ( first ) then
@@ -307,17 +307,17 @@ c              %------------------------%
 c              | Ritz value is complex  |
 c              | Residual of one Ritz   |
 c              | value of the conjugate |
-c              | pair is computed.      | 
+c              | pair is computed.      |
 c              %------------------------%
 c
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
                call daxpy (n, -d(j,1), v(1,j), 1, ax, 1)
                call daxpy (n, d(j,2), v(1,j+1), 1, ax, 1)
                d(j,3) = dnrm2 (n, ax, 1)
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    ax, 1)
                call daxpy (n, -d(j,2), v(1,j), 1, ax, 1)
                call daxpy (n, -d(j,1), v(1,j+1), 1, ax, 1)
@@ -329,11 +329,11 @@ c
                first = .true.
             end if
 c
- 90      continue 
+ 90      continue
 
          call dmout (6, nconv, 3, d, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -344,8 +344,8 @@ c
           print *, ' '
           print *, ' Error with _nband, info= ', info
           print *, ' Check the documentation of _nband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/dnbdr2.f

@@ -1,4 +1,4 @@
-      program dnbdr2 
+      program dnbdr2
 c
 c     ... Construct matrices A in LAPACK-style band form.
 c         The matrix A is derived from the discretization of
@@ -53,13 +53,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -68,12 +68,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Double precision 
+      Double precision
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn),
      &                 workev(3*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv, 3), ax(maxn)
-      Complex*16  
+      Complex*16
      &                 cfac(lda, maxn), workc(maxn)
 c
 c     %---------------%
@@ -85,25 +85,25 @@ c
      &                 n, nx, lo, idiag, isub, isup, mode, maxitr,
      &                 nconv
       logical          rvec, first
-      Double precision  
+      Double precision
      &                 tol, rho, h2, h, sigmar, sigmai
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Double precision  
+      Double precision
      &                 one, zero, two
-      parameter        (one = 1.0D+0 , zero = 0.0D+0 , 
+      parameter        (one = 1.0D+0 , zero = 0.0D+0 ,
      &                  two = 2.0D+0 )
 c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dlapy2 , dnrm2 
-      external          dlapy2 , dnrm2 , daxpy , dgbmv  
+      Double precision
+     &                  dlapy2 , dnrm2
+      external          dlapy2 , dnrm2 , daxpy , dgbmv
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -135,10 +135,10 @@ c     |                 NEV <= MAXNEV                   |
 c     |           NEV + 2 <= NCV <= MAXNCV              |
 c     %-------------------------------------------------%
 c
-      nx  = 10 
+      nx  = 10
       n    = nx*nx
-      nev  = 4 
-      ncv  = 20 
+      nev  = 4
+      ncv  = 20
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR2: N is greater than MAXN '
          go to 9000
@@ -151,8 +151,8 @@ c
       end if
       bmat = 'I'
       which = 'LM'
-      sigmar = 1.0D+4 
-      sigmai = 0.0D+0 
+      sigmar = 1.0D+4
+      sigmai = 0.0D+0
 c
 c     %-----------------------------------------------------%
 c     | The work array WORKL is used in DNAUPD  as           |
@@ -166,7 +166,7 @@ c     | generated in DNAUPD  to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+6*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -181,7 +181,7 @@ c
       maxitr = 300
       mode   = 3
 c
-      iparam(3) = maxitr 
+      iparam(3) = maxitr
       iparam(7) = mode
 c
 c     %----------------------------------------%
@@ -203,10 +203,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A.                   |
 c     %-------------------------------------%
 c
-      kl   = nx 
-      ku   = nx 
+      kl   = nx
+      ku   = nx
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -216,22 +216,22 @@ c
       idiag = kl+ku+1
       do 30 j = 1, n
          a(idiag,j) = 4.0D+0  / h2
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+ku+2
-      rho = 1.0D+1 
+      rho = 1.0D+1
       do 50 i = 1, nx
         lo = (i-1)*nx
         do 40 j = lo+1, lo+nx-1
            a(isub,j+1) = -one/h2 + rho/two/h
            a(isup,j) = -one/h2 - rho/two/h
-  40    continue      
-  50  continue 
+  40    continue
+  50  continue
 c
 c     %------------------------------------%
 c     | KL-th subdiagonal and KU-th super- |
@@ -245,8 +245,8 @@ c
          do 70 j = lo+1, lo+nx
             a(isup,nx+j)  = -one / h2
             a(isub,j) = -one / h2
- 70      continue 
- 80   continue 
+ 70      continue
+ 80   continue
 c
 c     %------------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues  |
@@ -258,9 +258,9 @@ c     | in the first NCONV (=IPARAM(5)) columns of V.  |
 c     %------------------------------------------------%
 c
       rvec = .true.
-      call dnband (rvec, 'A', select, d, d(1,2), v, ldv, sigmar, 
-     &     sigmai, workev, n, a, m, lda, rfac, cfac, kl, ku, 
-     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam, 
+      call dnband (rvec, 'A', select, d, d(1,2), v, ldv, sigmar,
+     &     sigmai, workev, n, a, m, lda, rfac, cfac, kl, ku,
+     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam,
      &     workd, workl, lworkl, workc, iwork, info)
 c
       if ( info .eq. 0) then
@@ -293,8 +293,8 @@ c        | Compute the residual norm. |
 c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
-         first = .true. 
-         do 90 j = 1, nconv 
+         first = .true.
+         do 90 j = 1, nconv
 c
             if ( d(j,2) .eq. zero ) then
 c
@@ -302,8 +302,8 @@ c              %--------------------%
 c              | Ritz value is real |
 c              %--------------------%
 c
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
                call daxpy (n, -d(j,1), v(1,j), 1, ax, 1)
                d(j,3) = dnrm2 (n, ax, 1)
@@ -315,17 +315,17 @@ c              %------------------------%
 c              | Ritz value is complex  |
 c              | Residual of one Ritz   |
 c              | value of the conjugate |
-c              | pair is computed.      | 
+c              | pair is computed.      |
 c              %------------------------%
 c
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
                call daxpy (n, -d(j,1), v(1,j), 1, ax, 1)
                call daxpy (n, d(j,2), v(1,j+1), 1, ax, 1)
                d(j,3) = dnrm2 (n, ax, 1)
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    ax, 1)
                call daxpy (n, -d(j,1), v(1,j+1), 1, ax, 1)
                call daxpy (n, -d(j,2), v(1,j), 1, ax, 1)
@@ -337,11 +337,11 @@ c
                first = .true.
             end if
 c
- 90      continue 
+ 90      continue
 
          call dmout (6, nconv, 3, d, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -352,8 +352,8 @@ c
           print *, ' '
           print *, ' Error with _nband, info= ', info
           print *, ' Check the documentation of _nband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/dnbdr3.f

@@ -1,8 +1,8 @@
-      program dnbdr3 
+      program dnbdr3
 c
 c     ... Construct matrices A and M in LAPACK-style band form.
 c         The matrix A and M are derived from the finite element
-c         discretization of the 1-dimensional convection-diffusion operator 
+c         discretization of the 1-dimensional convection-diffusion operator
 c                         (d^2u/dx^2) + rho*(du/dx)
 c         on the interval [0,1] with zero boundary condition,
 
@@ -49,13 +49,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn)
 c
 c     %--------------%
@@ -64,12 +64,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Double precision 
+      Double precision
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn),
      &                 workev(3*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv, 3), ax(maxn), mx(maxn)
-      Complex*16  
+      Complex*16
      &                 cfac(lda, maxn), workc(maxn)
 c
 c     %---------------%
@@ -81,25 +81,25 @@ c
      &                 n, idiag, isup, isub, mode, maxitr,
      &                 nconv
       logical          rvec, first
-      Double precision  
+      Double precision
      &                 tol, rho, h, sigmar, sigmai
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Double precision  
+      Double precision
      &                 one, zero, two
-      parameter        (one = 1.0D+0 , zero = 0.0D+0 , 
+      parameter        (one = 1.0D+0 , zero = 0.0D+0 ,
      &                  two = 2.0D+0 )
 c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dlapy2 , dnrm2 
-      external          dlapy2 , dnrm2 , dgbmv , daxpy  
+      Double precision
+     &                  dlapy2 , dnrm2
+      external          dlapy2 , dnrm2 , dgbmv , daxpy
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -126,8 +126,8 @@ c     |           NEV + 2 <= NCV <= MAXNCV              |
 c     %-------------------------------------------------%
 c
       n    = 100
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR3: N is greater than MAXN '
          go to 9000
@@ -142,7 +142,7 @@ c
       which = 'LM'
 c
 c     %----------------------------------------------------%
-c     | The work array WORKL is used in DNAUPD  as          | 
+c     | The work array WORKL is used in DNAUPD  as          |
 c     | workspace.  Its dimension LWORKL has to be set as  |
 c     | illustrated below.  The parameter TOL determines   |
 c     | the stopping criterion. If TOL<=0, machine machine |
@@ -150,12 +150,12 @@ c     | precision is used.  The number IDO is used for     |
 c     | reverse communication and has to be set to 0 at    |
 c     | the beginning.  Setting INFO=0 indicates that we   |
 c     | using a randomly generated vector to start the     |
-c     | the ARNOLDI process.                               | 
+c     | the ARNOLDI process.                               |
 c     %----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+6*ncv
       info = 0
-      tol  = zero 
+      tol  = zero
       ido  = 0
 c
 c     %---------------------------------------------------%
@@ -169,8 +169,8 @@ c
       mode = 2
       maxitr = 300
 c
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %--------------------------------------------%
 c     | Construct matrices A and M in LAPACK-style |
@@ -191,10 +191,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = 1 
-      ku   = 1 
+      kl   = 1
+      ku   = 1
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -204,21 +204,21 @@ c
       do 30 j = 1, n
          a(idiag,j) = 2.0D+0  / h
          m(idiag,j) = 4.0D+0  * h
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+ku+2
-      rho = 1.0D+1 
+      rho = 1.0D+1
       do 50 j = 1, n
          a(isup,j+1) = -one/h + rho/two
          a(isub,j) = -one/h - rho/two
          m(isup,j+1) = one*h
          m(isub,j) = one*h
-  50  continue 
+  50  continue
 c
 c     %------------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues  |
@@ -229,10 +229,10 @@ c     | second column of D.  Eigenvectors are returned |
 c     | in the first NCONV (=IPARAM(5)) columns of V.  |
 c     %------------------------------------------------%
 c
-      rvec = .true. 
-      call dnband ( rvec, 'A', select, d, d(1,2), v, ldv, sigmar, 
-     &     sigmai, workev, n, A, M, lda, rfac, cfac, kl, ku, 
-     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam, 
+      rvec = .true.
+      call dnband ( rvec, 'A', select, d, d(1,2), v, ldv, sigmar,
+     &     sigmai, workev, n, A, M, lda, rfac, cfac, kl, ku,
+     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam,
      &     workd, workl, lworkl, workc, iwork, info)
 c
       if ( info .eq. 0) then
@@ -265,7 +265,7 @@ c        | Compute the residual norm. |
 c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
-         first = .true. 
+         first = .true.
          do 90 j = 1, nconv
 c
             if ( d(j,2) .eq. zero ) then
@@ -274,11 +274,11 @@ c              %--------------------%
 c              | Ritz value is real |
 c              %--------------------%
 c
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call daxpy (n, -d(j,1), mx, 1, ax, 1)
                d(j,3) = dnrm2 (n, ax, 1)
@@ -290,30 +290,30 @@ c              %------------------------%
 c              | Ritz value is complex  |
 c              | Residual of one Ritz   |
 c              | value of the conjugate |
-c              | pair is computed.      | 
+c              | pair is computed.      |
 c              %------------------------%
 c
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call daxpy (n, -d(j,1), mx, 1, ax, 1)
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    mx, 1)
                call daxpy (n, d(j,2), mx, 1, ax, 1)
                d(j,3) = dnrm2 (n, ax, 1)
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    ax, 1)
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    mx, 1)
                call daxpy (n, -d(j,1), mx, 1, ax, 1)
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call daxpy (n, -d(j,2), mx, 1, ax, 1)
                d(j,3) = dlapy2 ( d(j,3), dnrm2 (n, ax, 1) )
@@ -324,11 +324,11 @@ c
                first = .true.
             end if
 c
- 90      continue 
+ 90      continue
 
          call dmout (6, nconv, 3, d, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -339,8 +339,8 @@ c
           print *, ' '
           print *, ' Error with _nband, info= ', info
           print *, ' Check the documentation of _nband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/dnbdr4.f

@@ -50,14 +50,14 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
-     &                   maxbdw=50, lda = maxbdw, ldv = maxn) 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
+     &                   maxbdw=50, lda = maxbdw, ldv = maxn)
 c
 c     %--------------%
 c     | Local Arrays |
@@ -67,10 +67,10 @@ c
       logical          select(maxncv)
       Double precision
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn),
      &                 workev(3*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv, 3), ax(maxn), mx(maxn)
-      Complex*16 
+      Complex*16
      &                 cfac(lda, maxn), workc(maxn)
 c
 c     %---------------%
@@ -82,16 +82,16 @@ c
      &                 n, idiag, isup, isub, mode, maxitr,
      &                 nconv
       logical          rvec, first
-      Double precision 
+      Double precision
      &                 tol, rho, h, sigmar, sigmai
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Double precision 
+      Double precision
      &                 one, zero, two, six
-      parameter        (one = 1.0D+0, zero = 0.0D+0, 
+      parameter        (one = 1.0D+0, zero = 0.0D+0,
      &                  two = 2.0D+0, six = 6.0D+0)
 c
 c     %-----------------------------%
@@ -100,7 +100,7 @@ c     %-----------------------------%
 c
       Double precision
      &                  dlapy2, dnrm2
-      external          dlapy2, dnrm2, dgbmv, daxpy 
+      external          dlapy2, dnrm2, dgbmv, daxpy
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -127,8 +127,8 @@ c     |           NEV + 2 <= NCV <= MAXNCV              |
 c     %-------------------------------------------------%
 c
       n    = 100
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR4: N is greater than MAXN '
          go to 9000
@@ -142,7 +142,7 @@ c
       bmat = 'G'
       which = 'LM'
       sigmar = 1.0D+1
-      sigmai = 0.0D+0 
+      sigmai = 0.0D+0
 c
 c     %-----------------------------------------------------%
 c     | The work array WORKL is used in DNAUPD as           |
@@ -157,7 +157,7 @@ c     %-----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+6*ncv
       info = 0
-      tol  = zero 
+      tol  = zero
       ido  = 0
 c
 c     %---------------------------------------------------%
@@ -171,7 +171,7 @@ c
       maxitr = 300
       mode   = 3
 c
-      iparam(3) = n 
+      iparam(3) = n
       iparam(7) = 3
 c
 c     %--------------------------------------------%
@@ -194,9 +194,9 @@ c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
       kl   = 1
-      ku   = 1 
+      ku   = 1
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -205,12 +205,12 @@ c
       do 30 j = 1, n
          a(idiag,j) = 2.0D+0 / h
          m(idiag,j) = 4.0D+0 * h / six
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+ku+2
       rho = 1.0D+1
@@ -218,8 +218,8 @@ c
          a(isup,j+1) = -one/h + rho/two
          a(isub,j) = -one/h - rho/two
          m(isup,j+1) = one*h/six
-         m(isub,j) = one*h/six 
-  40    continue      
+         m(isub,j) = one*h/six
+  40    continue
 c
 c     %------------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues  |
@@ -231,9 +231,9 @@ c     | in the first NCONV (=IPARAM(5)) columns of V.  |
 c     %------------------------------------------------%
 c
       rvec = .true.
-      call dnband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar, 
+      call dnband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar,
      &     sigmai, workev, n, A, M, lda, rfac, cfac, kl, ku,
-     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam, 
+     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam,
      &     workd, workl, lworkl, workc, iwork, info)
 c
       if ( info .eq. 0) then
@@ -266,7 +266,7 @@ c        | Compute the residual norm. |
 c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
-         first = .true. 
+         first = .true.
          do 50 j = 1, nconv
 c
             if ( d(j,2) .eq. zero ) then
@@ -275,11 +275,11 @@ c              %--------------------%
 c              | Ritz value is real |
 c              %--------------------%
 c
-               call dgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
-               call dgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call daxpy(n, -d(j,1), mx, 1, ax, 1)
                d(j,3) = dnrm2(n, ax, 1)
@@ -291,30 +291,30 @@ c              %------------------------%
 c              | Ritz value is complex  |
 c              | Residual of one Ritz   |
 c              | value of the conjugate |
-c              | pair is computed.      | 
+c              | pair is computed.      |
 c              %------------------------%
 c
-               call dgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
-               call dgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call daxpy(n, -d(j,1), mx, 1, ax, 1)
-               call dgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call dgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    mx, 1)
                call daxpy(n, d(j,2), mx, 1, ax, 1)
                d(j,3) = dnrm2(n, ax, 1)
-               call dgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call dgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    ax, 1)
-               call dgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call dgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    mx, 1)
                call daxpy(n, -d(j,1), mx, 1, ax, 1)
-               call dgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call daxpy(n, -d(j,2), mx, 1, ax, 1)
                d(j,3) = dlapy2( d(j,3), dnrm2(n, ax, 1) )
@@ -325,11 +325,11 @@ c
                first = .true.
             end if
 c
- 50      continue 
+ 50      continue
 
          call dmout(6, nconv, 3, d, maxncv, -6,
      &             'Ritz values (Real,Imag) and relatve residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -340,8 +340,8 @@ c
           print *, ' '
           print *, ' Error with _nband, info= ', info
           print *, ' Check the documentation of _nband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/dnbdr5.f

@@ -1,7 +1,7 @@
-      program dnbdr5 
+      program dnbdr5
 c
 c     ... Construct matrices A and M in LAPACK-style band form.
-c         The matrix A is a block tridiagonal matrix.  Each 
+c         The matrix A is a block tridiagonal matrix.  Each
 c         diagonal block is a tridiagonal matrix with
 c         4 on the diagonal, 1-rho*h/2 on the subdiagonal and
 c         1+rho*h/2 on the superdiagonal.  Each off-diagonal block
@@ -51,13 +51,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -66,12 +66,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Double precision 
+      Double precision
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn),
      &                 workev(3*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv, 3), ax(maxn)
-      Complex*16  
+      Complex*16
      &                 cfac(lda, maxn), workc(maxn)
 c
 c     %---------------%
@@ -83,25 +83,25 @@ c
      &                 n, nx, lo, idiag, isup, isub, mode, maxitr,
      &                 nconv
       logical          rvec, first
-      Double precision  
+      Double precision
      &                 tol, rho, h, sigmar, sigmai
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Double precision  
+      Double precision
      &                 one, zero, two
-      parameter        (one = 1.0D+0 , zero = 0.0D+0 , 
+      parameter        (one = 1.0D+0 , zero = 0.0D+0 ,
      &                  two = 2.0D+0 )
 c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dlapy2 , dnrm2 
-      external          dlapy2 , dnrm2 , dgbmv , daxpy  
+      Double precision
+     &                  dlapy2 , dnrm2
+      external          dlapy2 , dnrm2 , dgbmv , daxpy
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -132,8 +132,8 @@ c     %--------------------------------------------------%
 c
       nx   = 10
       n    = nx*nx
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR5: N is greater than MAXN '
          go to 9000
@@ -146,8 +146,8 @@ c
       end if
       bmat = 'I'
       which = 'LM'
-      sigmar = 4.0D-1 
-      sigmai = 6.0D-1 
+      sigmar = 4.0D-1
+      sigmai = 6.0D-1
 c
 c     %-----------------------------------------------------%
 c     | The work array WORKL is used in DNAUPD  as           |
@@ -161,7 +161,7 @@ c     | generated in DNAUPD  to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+6*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -198,34 +198,34 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = nx 
-      ku   = nx 
+      kl   = nx
+      ku   = nx
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
       idiag = kl+ku+1
       do 30 j = 1, n
-         a(idiag,j) = 4.0D+0 
-         m(idiag,j) = 4.0D+0 
-  30  continue 
-c 
+         a(idiag,j) = 4.0D+0
+         m(idiag,j) = 4.0D+0
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+kl+2
       h = one / dble (nx+1)
-      rho = 1.0D+2  
+      rho = 1.0D+2
       do 50 i = 1, nx
         lo = (i-1)*nx
         do 40 j = lo+1, lo+nx-1
            a(isup,j+1) = -one+h*rho/two
            a(isub,j) = -one-h*rho/two
-  40    continue      
-  50  continue 
+  40    continue
+  50  continue
 c
       do 60 j = 1, n-1
          m(isup,j+1) = one
@@ -244,8 +244,8 @@ c
          do 70 j = lo+1, lo+nx
             a(isup,nx+j)  = -one
             a(isub,j) = -one
- 70      continue 
- 80   continue 
+ 70      continue
+ 80   continue
 c
 c     %------------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues  |
@@ -253,13 +253,13 @@ c     | and eigenvectors. The real parts of the        |
 c     | eigenvalues are returned in the first column   |
 c     | of D, the imaginary parts are returned in the  |
 c     | second column of D.  Eigenvectors are returned |
-c     | in the first NCONV (=IPARAM(5)) columns of V.  | 
+c     | in the first NCONV (=IPARAM(5)) columns of V.  |
 c     %------------------------------------------------%
 c
       rvec = .true.
-      call dnband (rvec, 'A', select, d, d(1,2), v, ldv, sigmar, 
-     &     sigmai, workev, n, a, m, lda, rfac, cfac, ku, kl, 
-     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam, 
+      call dnband (rvec, 'A', select, d, d(1,2), v, ldv, sigmar,
+     &     sigmai, workev, n, a, m, lda, rfac, cfac, ku, kl,
+     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam,
      &     workd, workl, lworkl, workc, iwork, info)
 c
       if ( info .eq. 0) then
@@ -292,7 +292,7 @@ c        | Compute the residual norm. |
 c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
-         first = .true. 
+         first = .true.
          do 90 j = 1, nconv
 c
             if ( d(j,2) .eq. zero ) then
@@ -301,8 +301,8 @@ c              %--------------------%
 c              | Ritz value is real |
 c              %--------------------%
 c
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
                call daxpy (n, -d(j,1), v(1,j), 1, ax, 1)
                d(j,3) = dnrm2 (n, ax, 1)
@@ -314,17 +314,17 @@ c              %------------------------%
 c              | Ritz value is complex  |
 c              | Residual of one Ritz   |
 c              | value of the conjugate |
-c              | pair is computed.      | 
+c              | pair is computed.      |
 c              %------------------------%
 c
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
                call daxpy (n, -d(j,1), v(1,j), 1, ax, 1)
                call daxpy (n, d(j,2), v(1,j+1), 1, ax, 1)
                d(j,3) = dnrm2 (n, ax, 1)
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    ax, 1)
                call daxpy (n, -d(j,1), v(1,j+1), 1, ax, 1)
                call daxpy (n, -d(j,2), v(1,j), 1, ax, 1)
@@ -336,11 +336,11 @@ c
                first = .true.
             end if
 c
- 90      continue 
+ 90      continue
 
          call dmout (6, nconv, 3, d, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -351,8 +351,8 @@ c
           print *, ' '
           print *, ' Error with _nband, info= ', info
           print *, ' Check the documentation of _nband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/dnbdr6.f

@@ -1,7 +1,7 @@
-      program dnbdr6 
+      program dnbdr6
 c
 c     ... Construct matrices A and M in LAPACK-style band form.
-c         The matrix A is a block tridiagonal matrix.  Each 
+c         The matrix A is a block tridiagonal matrix.  Each
 c         diagonal block is a tridiagonal matrix with
 c         4 on the diagonal, 1-rho*h/2 on the subdiagonal and
 c         1+rho*h/2 on the superdiagonal.  Each subdiagonal block
@@ -53,13 +53,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -68,12 +68,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Double precision 
+      Double precision
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn),
      &                 workev(3*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv, 3), ax(maxn), mx(maxn)
-      Complex*16  
+      Complex*16
      &                 cfac(lda, maxn), workc(maxn)
 c
 c     %---------------%
@@ -85,16 +85,16 @@ c
      &                 n, nx, lo, idiag, isup, isub, mode, maxitr,
      &                 nconv
       logical          rvec, first
-      Double precision  
+      Double precision
      &                 tol, rho, h, sigmar, sigmai
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Double precision  
+      Double precision
      &                 one, zero, two
-      parameter        (one = 1.0D+0 , zero = 0.0D+0 , 
+      parameter        (one = 1.0D+0 , zero = 0.0D+0 ,
      &                  two = 2.0D+0 )
 c
 c     %--------------------%
@@ -107,9 +107,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dlapy2 , dnrm2 
-      external          dlapy2 , dnrm2 , dgbmv , daxpy  
+      Double precision
+     &                  dlapy2 , dnrm2
+      external          dlapy2 , dnrm2 , dgbmv , daxpy
 c
 c     %-----------------------%
 c     | Executable Statements |
@@ -129,13 +129,13 @@ c     | to get different parts the spectrum. However, the   |
 c     | following rules must be satisfied:                  |
 c     |                   N <= MAXN                         |
 c     |                 NEV <= MAXNEV                       |
-c     |           NEV + 2 <= NCV <= MAXNCV                  | 
-c     %-----------------------------------------------------% 
+c     |           NEV + 2 <= NCV <= MAXNCV                  |
+c     %-----------------------------------------------------%
 c
-      nx  = 10 
+      nx  = 10
       n    = nx*nx
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR6: N is greater than MAXN '
          go to 9000
@@ -148,8 +148,8 @@ c
       end if
       bmat = 'G'
       which = 'LM'
-      sigmar = 4.0D-1 
-      sigmai = 6.0D-1 
+      sigmar = 4.0D-1
+      sigmai = 6.0D-1
 c
 c     %-----------------------------------------------------%
 c     | The work array WORKL is used in DNAUPD  as           |
@@ -163,7 +163,7 @@ c     | generated in DNAUPD  to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+6*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -178,7 +178,7 @@ c
       maxitr = 300
       mode = 4
 c
-      iparam(3) = maxitr 
+      iparam(3) = maxitr
       iparam(7) = mode
 c
 c     %--------------------------------------------%
@@ -200,34 +200,34 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = nx 
-      ku   = nx 
+      kl   = nx
+      ku   = nx
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
       idiag = kl+ku+1
       do 30 j = 1, n
-         a(idiag,j) = 4.0D+0 
-         m(idiag,j) = 4.0D+0 
-  30  continue 
-c 
+         a(idiag,j) = 4.0D+0
+         m(idiag,j) = 4.0D+0
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+ku+2
       h = one / dble (nx+1)
-      rho = 1.0D+2 
+      rho = 1.0D+2
       do 50 i = 1, nx
         lo = (i-1)*nx
         do 40 j = lo+1, lo+nx-1
            a(isub,j+1) = -one+h*rho/two
            a(isup,j) = -one-h*rho/two
-  40    continue      
-  50  continue 
+  40    continue
+  50  continue
 c
       do 60 j = 1, n-1
          m(isub,j+1) = one
@@ -246,8 +246,8 @@ c
          do 70 j = lo+1, lo+nx
             a(isup,nx+j)  = -one
             a(isub,j) = -one
- 70      continue 
- 80   continue 
+ 70      continue
+ 80   continue
 c
 c     %------------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues  |
@@ -259,9 +259,9 @@ c     | in the first NCONV (=IPARAM(5)) columns of V.  |
 c     %------------------------------------------------%
 c
       rvec = .true.
-      call dnband (rvec, 'A', select, d, d(1,2), v, ldv, sigmar, 
-     &     sigmai, workev, n, a, m, lda, rfac, cfac, ku, kl, 
-     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam, 
+      call dnband (rvec, 'A', select, d, d(1,2), v, ldv, sigmar,
+     &     sigmai, workev, n, a, m, lda, rfac, cfac, ku, kl,
+     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam,
      &     workd, workl, lworkl, workc, iwork, info)
 c
       if ( info .eq. 0) then
@@ -294,7 +294,7 @@ c        | Compute the residual norm. |
 c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
-         first = .true. 
+         first = .true.
          do 90 j = 1, nconv
 c
             if ( d(j,2) .eq. zero ) then
@@ -303,11 +303,11 @@ c              %--------------------%
 c              | Ritz value is real |
 c              %--------------------%
 c
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call daxpy (n, -d(j,1), mx, 1, ax, 1)
                d(j,3) = dnrm2 (n, ax, 1)
@@ -319,30 +319,30 @@ c              %------------------------%
 c              | Ritz value is complex  |
 c              | Residual of one Ritz   |
 c              | value of the conjugate |
-c              | pair is computed.      | 
+c              | pair is computed.      |
 c              %------------------------%
 c
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call daxpy (n, -d(j,1), mx, 1, ax, 1)
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    mx, 1)
                call daxpy (n, d(j,2), mx, 1, ax, 1)
                d(j,3) = dnrm2 (n, ax, 1)
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    ax, 1)
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    mx, 1)
                call daxpy (n, -d(j,1), mx, 1, ax, 1)
-               call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call daxpy (n, -d(j,2), mx, 1, ax, 1)
                d(j,3) = dlapy2 ( d(j,3), dnrm2 (n, ax, 1) )
@@ -353,11 +353,11 @@ c
                first = .true.
             end if
 c
- 90      continue 
+ 90      continue
 
          call dmout (6, nconv, 3, d, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -368,8 +368,8 @@ c
           print *, ' '
           print *, ' Error with _nband, info= ', info
           print *, ' Check the documentation of _nband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/dsband.f

@@ -17,19 +17,19 @@ c
 c  Matrices A and B are stored in LAPACK-style band form.
 c
 c  There is negligible additional cost to obtain eigenvectors.  An orthonormal
-c  (Lanczos) basis is always computed.  There is an additional storage cost 
-c  of n*nev if both are requested (in this case a separate array Z must be 
+c  (Lanczos) basis is always computed.  There is an additional storage cost
+c  of n*nev if both are requested (in this case a separate array Z must be
 c  supplied).
 c
 c  The approximate eigenvalues and eigenvectors of  A*z = lambda*B*z
-c  are called Ritz values and Ritz vectors respectively.  They are referred 
-c  to as such in the comments that follow.  The computed orthonormal basis 
-c  for the invariant subspace corresponding to these Ritz values is referred 
+c  are called Ritz values and Ritz vectors respectively.  They are referred
+c  to as such in the comments that follow.  The computed orthonormal basis
+c  for the invariant subspace corresponding to these Ritz values is referred
 c  to as a Lanczos basis.
 c
 c  dsband can be called with one of the following modes:
 c
-c  Mode 1:  A*x = lambda*x, A symmetric 
+c  Mode 1:  A*x = lambda*x, A symmetric
 c           ===> OP = A  and  B = I.
 c
 c  Mode 2:  A*x = lambda*M*x, A symmetric, M symmetric positive definite
@@ -37,10 +37,10 @@ c           ===> OP = inv[M]*A  and  B = M.
 c           ===> (If M can be factored see remark 3 in DSAUPD)
 c
 c  Mode 3:  K*x = lambda*M*x, K symmetric, M symmetric positive semi-definite
-c           ===> OP = (inv[K - sigma*M])*M  and  B = M. 
+c           ===> OP = (inv[K - sigma*M])*M  and  B = M.
 c           ===> Shift-and-Invert mode
 c
-c  Mode 4:  K*x = lambda*KG*x, K symmetric positive semi-definite, 
+c  Mode 4:  K*x = lambda*KG*x, K symmetric positive semi-definite,
 c           KG symmetric indefinite
 c           ===> OP = (inv[K - sigma*KG])*K  and  B = K.
 c           ===> Buckling mode
@@ -53,21 +53,21 @@ c  The choice of mode must be specified in IPARAM(7) defined below.
 c
 c \Usage
 c   call dsband
-c      ( RVEC, HOWMNY, SELECT, D, Z, LDZ, SIGMA, N, AB, MB, LDA, 
-c        RFAC, KL, KU, WHICH, BMAT, NEV, TOL, RESID, NCV, V, 
+c      ( RVEC, HOWMNY, SELECT, D, Z, LDZ, SIGMA, N, AB, MB, LDA,
+c        RFAC, KL, KU, WHICH, BMAT, NEV, TOL, RESID, NCV, V,
 c        LDV, IPARAM, WORKD, WORKL, LWORKL, IWORK, INFO )
 c
 c \Arguments
 c
 c  RVEC    Logical (INPUT)
-c          Specifies whether Ritz vectors corresponding to the Ritz value 
+c          Specifies whether Ritz vectors corresponding to the Ritz value
 c          approximations to the eigenproblem A*z = lambda*B*z are computed.
 c
 c             RVEC = .FALSE.     Compute Ritz values only.
 c
-c             RVEC = .TRUE.      Compute the associated Ritz vectors. 
+c             RVEC = .TRUE.      Compute the associated Ritz vectors.
 c
-c  HOWMNY  Character*1  (INPUT) 
+c  HOWMNY  Character*1  (INPUT)
 c          Specifies how many Ritz vectors are wanted and the form of Z
 c          the matrix of Ritz vectors. See remark 1 below.
 c          = 'A': compute all Ritz vectors;
@@ -77,7 +77,7 @@ c
 c  SELECT  Logical array of dimension NCV.  (INPUT)
 c          If HOWMNY = 'S', SELECT specifies the Ritz vectors to be
 c          computed. To select the Ritz vector corresponding to a
-c          Ritz value D(j), SELECT(j) must be set to .TRUE.. 
+c          Ritz value D(j), SELECT(j) must be set to .TRUE..
 c          If HOWMNY = 'A' , SELECT is not referenced.
 c
 c  D       Double precision array of dimension NEV.  (OUTPUT)
@@ -85,8 +85,8 @@ c          On exit, D contains the Ritz value approximations to the
 c          eigenvalues of A*z = lambda*B*z. The values are returned
 c          in ascending order. If IPARAM(7) = 3,4,5 then D represents
 c          the Ritz values of OP computed by dsaupd transformed to
-c          those of the original eigensystem A*z = lambda*B*z. If 
-c          IPARAM(7) = 1,2 then the Ritz values of OP are the same 
+c          those of the original eigensystem A*z = lambda*B*z. If
+c          IPARAM(7) = 1,2 then the Ritz values of OP are the same
 c          as the those of A*z = lambda*B*z.
 c
 c  Z       Double precision N by NEV array if HOWMNY = 'A'.  (OUTPUT)
@@ -95,20 +95,20 @@ c          eigensystem A*z = lambda*B*z corresponding to the Ritz
 c          value approximations.
 c
 c          If  RVEC = .FALSE. then Z is not referenced.
-c          NOTE: The array Z may be set equal to first NEV columns of the 
+c          NOTE: The array Z may be set equal to first NEV columns of the
 c          Lanczos basis array V computed by DSAUPD.
 c
-c  LDZ     Integer.  (INPUT) 
+c  LDZ     Integer.  (INPUT)
 c          The leading dimension of the array Z.  If Ritz vectors are
 c          desired, then  LDZ .ge.  max( 1, N ).  In any case,  LDZ .ge. 1.
 c
 c  SIGMA   Double precision  (INPUT)
 c          If IPARAM(7) = 3,4,5 represents the shift. Not referenced if
 c          IPARAM(7) = 1 or 2.
-c 
-c  N       Integer.  (INPUT) 
-c          Dimension of the eigenproblem.  
-c 
+c
+c  N       Integer.  (INPUT)
+c          Dimension of the eigenproblem.
+c
 c  AB      Double precision array of dimension LDA by N. (INPUT)
 c          The matrix A in band storage, in rows KL+1 to
 c          2*KL+KU+1; rows 1 to KL of the array need not be set.
@@ -118,7 +118,7 @@ c          AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
 c
 c  MB      Double precision array of dimension LDA by N. (INPUT)
 c          The matrix M in band storage, in rows KL+1 to
-c          2*KL+KU+1; rows 1 to KL of the array need not be set. 
+c          2*KL+KU+1; rows 1 to KL of the array need not be set.
 c          The j-th column of M is stored in the j-th column of the
 c          array AB as follows:
 c          MB(kl+ku+1+i-j,j) = M(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
@@ -128,7 +128,7 @@ c  LDA     Integer. (INPUT)
 c          Leading dimension of AB, MB, RFAC.
 c
 c  RFAC    Double precision array of LDA by N. (WORKSPACE/OUTPUT)
-c          RFAC is used to store the LU factors of MB when IPARAM(7) = 2 
+c          RFAC is used to store the LU factors of MB when IPARAM(7) = 2
 c          is invoked.  It is used to store the LU factors of
 c          (A-sigma*M) when IPARAM(7) = 3,4,5 is invoked.
 c          It is not referenced when IPARAM(7) = 1.
@@ -142,17 +142,17 @@ c
 c  WHICH   Character*2.  (INPUT)
 c          When IPARAM(7)= 1 or 2,  WHICH can be set to any one of
 c          the following.
-c  
+c
 c            'LM' -> want the NEV eigenvalues of largest magnitude.
 c            'SM' -> want the NEV eigenvalues of smallest magnitude.
 c            'LA' -> want the NEV eigenvalues of largest REAL part.
 c            'SA' -> want the NEV eigenvalues of smallest REAL part.
-c            'BE' -> Compute NEV eigenvalues, half from each end of the 
-c                    spectrum.  When NEV is odd, compute one more from 
-c                    the high end than from the low end. 
+c            'BE' -> Compute NEV eigenvalues, half from each end of the
+c                    spectrum.  When NEV is odd, compute one more from
+c                    the high end than from the low end.
+c
+c          When IPARAM(7) = 3, 4, or 5,  WHICH should be set to 'LM' only.
 c
-c          When IPARAM(7) = 3, 4, or 5,  WHICH should be set to 'LM' only. 
-c          
 c  BMAT    Character*1.  (INPUT)
 c          BMAT specifies the type of the matrix B that defines the
 c          semi-inner product for the operator OP.
@@ -161,9 +161,9 @@ c          BMAT = 'G' -> generalized eigenvalue problem A*x = lambda*M*x
 
 c  NEV     Integer. (INPUT)
 c          Number of eigenvalues of OP to be computed.
-c   
+c
 c  TOL     Double precision scalar.  (INPUT)
-c          Stopping criterion: the relative accuracy of the Ritz value 
+c          Stopping criterion: the relative accuracy of the Ritz value
 c          is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)).
 c          If TOL .LE. 0. is passed a default is set:
 c          DEFAULT = DLAMCH('EPS')  (machine precision as computed
@@ -183,35 +183,35 @@ c          Represents the dimension of the Lanczos basis constructed
 c          by dsaupd for OP.
 c
 c  V       Double precision array N by NCV.  (OUTPUT)
-c          Upon INPUT: the NCV columns of V contain the Lanczos basis 
+c          Upon INPUT: the NCV columns of V contain the Lanczos basis
 c                      vectors as constructed by dsaupd for OP.
-c          Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns 
-c                       represent the Ritz vectors that span the desired 
+c          Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns
+c                       represent the Ritz vectors that span the desired
 c                       invariant subspace.
-c          NOTE: The array Z may be set equal to first NEV columns of the 
+c          NOTE: The array Z may be set equal to first NEV columns of the
 c          Lanczos basis vector array V computed by dsaupd. In this case
 c          if RVEC=.TRUE., the first NCONV=IPARAM(5) columns of V contain
-c          the desired Ritz vectors. 
+c          the desired Ritz vectors.
 c
 c  LDV     Integer.  (INPUT)
 c          Leading dimension of V exactly as declared in the calling
 c          program.
 c
 c  IPARAM  Integer array of length 11.  (INPUT/OUTPUT)
-c          IPARAM(1) = ISHIFT: 
+c          IPARAM(1) = ISHIFT:
 c          The shifts selected at each iteration are used to restart
 c          the Arnoldi iteration in an implicit fashion.
 c          It is set to 1 in this subroutine.  The user do not need
 c          to set this parameter.
 c          ------------------------------------------------------------
-c          ISHIFT = 1: exact shifts with respect to the reduced 
-c                      tridiagonal matrix T.  This is equivalent to 
-c                      restarting the iteration with a starting vector 
-c                      that is a linear combination of Ritz vectors 
+c          ISHIFT = 1: exact shifts with respect to the reduced
+c                      tridiagonal matrix T.  This is equivalent to
+c                      restarting the iteration with a starting vector
+c                      that is a linear combination of Ritz vectors
 c                      associated with the "wanted" Ritz values.
 c          -------------------------------------------------------------
 c
-c          IPARAM(2) = No longer referenced. 
+c          IPARAM(2) = No longer referenced.
 c
 c          IPARAM(3) = MXITER
 c          On INPUT:  max number of Arnoldi update iterations allowed.
@@ -225,11 +225,11 @@ c          This represents the number of Ritz values that satisfy
 c          the convergence criterion.
 c
 c          IPARAM(6) = IUPD
-c          No longer referenced. Implicit restarting is ALWAYS used. 
+c          No longer referenced. Implicit restarting is ALWAYS used.
 c
 c          IPARAM(7) = MODE
 c          On INPUT determines what type of eigenproblem is being solved.
-c          Must be 1,2,3,4,5; See under \Description of dsband for the 
+c          Must be 1,2,3,4,5; See under \Description of dsband for the
 c          five modes available.
 c
 c          IPARAM(8) = NP
@@ -248,18 +248,18 @@ c LWORKL   Integer.  (INPUT)
 c          LWORKL must be at least NCV**2 + 8*NCV.
 c
 c IWORK    Integer array of dimension at least N. (WORKSPACE)
-c          Used when IPARAM(7)=2,3,4,5 to store the pivot information in the 
+c          Used when IPARAM(7)=2,3,4,5 to store the pivot information in the
 c          factorization of M or (A-SIGMA*M).
-c            
+c
 c INFO     Integer.  (INPUT/OUTPUT)
 c          Error flag on output.
 c          =  0: Normal exit.
 c          =  1: Maximum number of iterations taken.
-c                All possible eigenvalues of OP has been found. IPARAM(5)  
+c                All possible eigenvalues of OP has been found. IPARAM(5)
 c                returns the number of wanted converged Ritz values.
-c          =  3: No shifts could be applied during a cycle of the 
-c                Implicitly restarted Arnoldi iteration. One possibility 
-c                is to increase the size of NCV relative to NEV. 
+c          =  3: No shifts could be applied during a cycle of the
+c                Implicitly restarted Arnoldi iteration. One possibility
+c                is to increase the size of NCV relative to NEV.
 c                See remark 4 in DSAUPD.
 c
 c          = -1: N must be positive.
@@ -292,7 +292,7 @@ c  1. D.C. Sorensen, "Implicit Application of Polynomial Filters in
 c     a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992),
 c     pp 357-385.
 c
-c  2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly 
+c  2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly
 c     Restarted Arnoldi Iteration", Ph.D thesis, TR95-13, Rice Univ,
 c     May 1995.
 c
@@ -301,7 +301,7 @@ c     dsaupd  ARPACK reverse communication interface routine.
 c     dseupd  ARPACK routine that returns Ritz values and (optionally)
 c             Ritz vectors.
 c     dgbtrf  LAPACK band matrix factorization routine.
-c     dgbtrs  LAPACK band linear system solve routine. 
+c     dgbtrs  LAPACK band linear system solve routine.
 c     dlacpy  LAPACK matrix copy routine.
 c     dlapy2  LAPACK routine to compute sqrt(x**2+y**2) carefully.
 c     dcopy   Level 1 BLAS that copies one vector to another.
@@ -310,13 +310,13 @@ c     dnrm2   Level 1 BLAS that computes the norm of a vector.
 c     dgbmv   Level 2 BLAS that computes the band matrix vector product.
 c
 c\Remarks
-c  1. The converged Ritz values are always returned in increasing 
+c  1. The converged Ritz values are always returned in increasing
 c     (algebraic) order.
 c
 c  2. Currently only HOWMNY = 'A' is implemented. It is included at this
 c     stage for the user who wants to incorporate it.
 c
-c\Author    
+c\Author
 c     Danny Sorensen
 c     Richard Lehoucq
 c     Chao Yang
@@ -332,18 +332,18 @@ c\EndLib
 c
 c---------------------------------------------------------------------
 c
-      subroutine dsband( rvec, howmny, select, d, z, ldz, sigma, 
-     &           n, ab, mb, lda, rfac, kl, ku, which, bmat, nev, 
-     &           tol, resid, ncv, v, ldv, iparam, workd, workl, 
+      subroutine dsband( rvec, howmny, select, d, z, ldz, sigma,
+     &           n, ab, mb, lda, rfac, kl, ku, which, bmat, nev,
+     &           tol, resid, ncv, v, ldv, iparam, workd, workl,
      &           lworkl, iwork, info)
 c
 c     %------------------%
 c     | Scalar Arguments |
 c     %------------------%
-c 
+c
       character        which*2, bmat, howmny
       integer          n, lda, kl, ku, nev, ncv, ldv,
-     &                 ldz, lworkl, info  
+     &                 ldz, lworkl, info
       Double precision
      &                 tol, sigma
       logical          rvec
@@ -356,7 +356,7 @@ c
       logical          select(*)
       Double precision
      &                 d(*), resid(*), v(ldv,*), z(ldz,*),
-     &                 ab(lda,*), mb(lda,*), rfac(lda,*), 
+     &                 ab(lda,*), mb(lda,*), rfac(lda,*),
      &                 workd(*), workl(*)
 c
 c     %--------------%
@@ -386,22 +386,22 @@ c     %-----------------------------%
 c
       Double precision
      &                 ddot, dnrm2, dlapy2
-      external         ddot, dcopy, dgbmv, dgbtrf, 
+      external         ddot, dcopy, dgbmv, dgbtrf,
      &                 dgbtrs, dnrm2, dlapy2, dlacpy
 c
 c     %-----------------------%
 c     | Executable Statements |
 c     %-----------------------%
-c     
+c
 c     %----------------------------------------------------------------%
 c     | Set type of the problem to be solved. Check consistency        |
 c     | between BMAT and IPARAM(7).                                    |
 c     | type = 1 --> Solving standard problem in regular mode.         |
-c     | type = 2 --> Solving standard problem in shift-invert mode.    | 
+c     | type = 2 --> Solving standard problem in shift-invert mode.    |
 c     | type = 3 --> Solving generalized problem in regular mode.      |
 c     | type = 4 --> Solving generalized problem in shift-invert mode. |
 c     | type = 5 --> Solving generalized problem in Buckling mode.     |
-c     | type = 6 --> Solving generalized problem in Cayley mode.       | 
+c     | type = 6 --> Solving generalized problem in Cayley mode.       |
 c     %----------------------------------------------------------------%
 c
       if ( iparam(7) .eq. 1 ) then
@@ -411,15 +411,15 @@ c
       else if ( iparam(7) .eq. 2 ) then
          type = 3
       else if ( iparam(7) .eq. 3 .and. bmat .eq. 'G') then
-         type = 4 
+         type = 4
       else if ( iparam(7) .eq. 4 ) then
          type = 5
-      else if ( iparam(7) .eq. 5 ) then 
+      else if ( iparam(7) .eq. 5 ) then
          type = 6
       else
          print*, ' '
          print*, 'BMAT is inconsistent with IPARAM(7).'
-         print*, ' ' 
+         print*, ' '
          go to 9000
       end if
 c
@@ -432,9 +432,9 @@ c
 c
 c     %----------------%
 c     | Exact shift is |
-c     | used.          | 
+c     | used.          |
 c     %----------------%
-c 
+c
       iparam(1) = 1
 c
 c     %-----------------------------------%
@@ -462,7 +462,7 @@ c
   10      continue
           call dgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr )
           if (ierr .ne. 0) then
-             print*, ' ' 
+             print*, ' '
              print*, ' _SBAND: Error with _gbtrf. '
              print*, ' '
              go to  9000
@@ -477,28 +477,28 @@ c        | routine dgbtrf to factor M.                  |
 c        %----------------------------------------------%
 c
          call dlacpy ('A', ibot, n, mb, lda, rfac, lda )
-         call dgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr) 
-         if (ierr .ne. 0) then 
+         call dgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr)
+         if (ierr .ne. 0) then
              print*, ' '
-             print*,'_SBAND:  Error with _gbtrf.' 
-             print*, ' ' 
-             go to 9000 
+             print*,'_SBAND:  Error with _gbtrf.'
+             print*, ' '
+             go to 9000
          end if
 c
-      else if ( type .eq. 4 .or. type .eq. 5 .or. type .eq. 6 
+      else if ( type .eq. 4 .or. type .eq. 5 .or. type .eq. 6
      &         .and. bmat .eq. 'G' ) then
 c
 c        %-------------------------------------------%
 c        | Solving generalized eigenvalue problem in |
 c        | shift-invert, Buckling, or Cayley mode.   |
 c        %-------------------------------------------%
-c 
+c
 c        %-------------------------------------%
 c        | Construct and factor (A - sigma*M). |
 c        %-------------------------------------%
 c
          do 60 j = 1,n
-            do 50 i = itop, ibot 
+            do 50 i = itop, ibot
                rfac(i,j) = ab(i,j) - sigma*mb(i,j)
   50        continue
   60     continue
@@ -510,14 +510,14 @@ c
              print*, ' '
              go to 9000
          end if
-c 
-      end if 
+c
+      end if
 c
 c     %--------------------------------------------%
 c     |  M A I N   L O O P (reverse communication) |
 c     %--------------------------------------------%
 c
-  90  continue 
+  90  continue
 c
       call dsaupd ( ido, bmat, n, which, nev, tol, resid, ncv,
      &              v, ldv, iparam, ipntr, workd, workl, lworkl,
@@ -531,8 +531,8 @@ c           %----------------------------%
 c           | Perform  y <--- OP*x = A*x |
 c           %----------------------------%
 c
-            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
          else if ( type .eq. 2 ) then
@@ -548,7 +548,7 @@ c
             call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                    iwork, workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
-               print*, ' ' 
+               print*, ' '
                print*, ' _SBAND: Error with _bgtrs. '
                print*, ' '
                go to 9000
@@ -558,15 +558,15 @@ c
 c
 c           %-----------------------------------%
 c           | Perform  y <--- OP*x = inv[M]*A*x |
-c           | to force the starting vector into | 
+c           | to force the starting vector into |
 c           | the range of OP.                  |
 c           %-----------------------------------%
 c
-            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                  lda, workd(ipntr(1)), 1, zero, 
+            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                  lda, workd(ipntr(1)), 1, zero,
      &                  workd(ipntr(2)), 1)
             call dcopy(n, workd(ipntr(2)), 1, workd(ipntr(1)), 1)
-            call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                    iwork, workd(ipntr(2)), n, ierr)
             if (ierr .ne. 0) then
                print*, ' '
@@ -579,36 +579,36 @@ c
 c
 c           %-----------------------------------------%
 c           | Perform y <-- OP*x                      |
-c           |           = inv[A-SIGMA*M]*M            | 
+c           |           = inv[A-SIGMA*M]*M            |
 c           | to force the starting vector into the   |
 c           | range of OP.                            |
 c           %-----------------------------------------%
 c
-            call dgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call dgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
-            call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                   iwork, workd(ipntr(2)), n, ierr)
             if (ierr .ne. 0) then
-               print*, ' ' 
+               print*, ' '
                print*, '_SBAND: Error with _gbtrs.'
-               print*, ' ' 
+               print*, ' '
                go to 9000
             end if
 c
          else if ( type .eq. 5) then
 c
-c           %---------------------------------------% 
+c           %---------------------------------------%
 c           | Perform y <-- OP*x                    |
 c           |    = inv[A-SIGMA*M]*A                 |
 c           | to force the starting vector into the |
 c           | range of OP.                          |
 c           %---------------------------------------%
 c
-            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
-            call dgbtrs('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call dgbtrs('Notranspose', n, kl, ku, 1, rfac, lda,
      &                   iwork, workd(ipntr(2)), n, ierr)
 c
             if ( ierr .ne. 0 ) then
@@ -622,31 +622,31 @@ c
 c
 c           %---------------------------------------%
 c           | Perform y <-- OP*x                    |
-c           | = (inv[A-SIGMA*M])*(A+SIGMA*M)*x      | 
+c           | = (inv[A-SIGMA*M])*(A+SIGMA*M)*x      |
 c           | to force the starting vector into the |
-c           | range of OP.                          | 
+c           | range of OP.                          |
 c           %---------------------------------------%
 c
             if ( bmat .eq. 'G' ) then
-               call dgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    ab(itop,1), lda, workd(ipntr(1)), 1, 
+               call dgbmv('Notranspose', n, n, kl, ku, one,
+     &                    ab(itop,1), lda, workd(ipntr(1)), 1,
      &                    zero, workd(ipntr(2)), 1)
-               call dgbmv('Notranspose', n, n, kl, ku, sigma, 
-     &                    mb(itop,1), lda, workd(ipntr(1)), 1, 
+               call dgbmv('Notranspose', n, n, kl, ku, sigma,
+     &                    mb(itop,1), lda, workd(ipntr(1)), 1,
      &                    one, workd(ipntr(2)), 1)
-            else 
+            else
                call dcopy(n, workd(ipntr(1)), 1, workd(ipntr(2)), 1)
-               call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                    lda, workd(ipntr(1)), 1, sigma, 
+               call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                    lda, workd(ipntr(1)), 1, sigma,
      &                    workd(ipntr(2)), 1)
-            end if   
+            end if
 c
-            call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                   iwork, workd(ipntr(2)), n, ierr)
 c
-            if (ierr .ne. 0) then 
+            if (ierr .ne. 0) then
                print*, ' '
-               print*, '_SBAND: Error with _gbtrs.' 
+               print*, '_SBAND: Error with _gbtrs.'
                print*, ' '
                go to 9000
             end if
@@ -661,8 +661,8 @@ c           %----------------------------%
 c           | Perform  y <--- OP*x = A*x |
 c           %----------------------------%
 c
-            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
          else if ( type .eq. 2) then
@@ -677,7 +677,7 @@ c
      &                       iwork, workd(ipntr(2)), n, ierr)
                if ( ierr .ne. 0 ) then
                   print*, ' '
-                  print*, '_SBAND: Error with _gbtrs.' 
+                  print*, '_SBAND: Error with _gbtrs.'
                   print*, ' '
                   go to 9000
                end if
@@ -688,16 +688,16 @@ c           %-----------------------------------%
 c           | Perform  y <--- OP*x = inv[M]*A*x |
 c           %-----------------------------------%
 c
-            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                  lda, workd(ipntr(1)), 1, zero, 
+            call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                  lda, workd(ipntr(1)), 1, zero,
      &                  workd(ipntr(2)), 1)
-            call dcopy(n, workd(ipntr(2)), 1, workd(ipntr(1)), 1) 
-            call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call dcopy(n, workd(ipntr(2)), 1, workd(ipntr(1)), 1)
+            call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                    iwork, workd(ipntr(2)), n, ierr)
             if (ierr .ne. 0) then
                print*, ' '
                print*, '_SBAND: error with _bgtrs.'
-               print*, ' ' 
+               print*, ' '
                go to 9000
             end if
 c
@@ -706,22 +706,22 @@ c
 c           %-------------------------------------%
 c           | Perform y <-- inv(A-sigma*M)*(M*x). |
 c           | (M*x) has been computed and stored  |
-c           | in workd(ipntr(3)).                 |           
+c           | in workd(ipntr(3)).                 |
 c           %-------------------------------------%
 c
             call dcopy(n, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-            call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                    iwork, workd(ipntr(2)), n, ierr)
-            if (ierr .ne. 0) then 
+            if (ierr .ne. 0) then
                print*, ' '
-               print*, '_SBAND: Error with _gbtrs.' 
+               print*, '_SBAND: Error with _gbtrs.'
                print*, ' '
                go to 9000
             end if
-c 
+c
          else if ( type .eq. 5 ) then
 c
-c           %-------------------------------% 
+c           %-------------------------------%
 c           | Perform y <-- OP*x            |
 c           |    = inv[A-SIGMA*M]*A*x       |
 c           | B*x = A*x has been computed   |
@@ -729,7 +729,7 @@ c           | and saved in workd(ipntr(3)). |
 c           %-------------------------------%
 c
             call dcopy (n, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-            call dgbtrs('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call dgbtrs('Notranspose', n, kl, ku, 1, rfac, lda,
      &                   iwork, workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
@@ -742,24 +742,24 @@ c
 c
 c           %---------------------------------%
 c           | Perform y <-- OP*x              |
-c           | = inv[A-SIGMA*M]*(A+SIGMA*M)*x. | 
+c           | = inv[A-SIGMA*M]*(A+SIGMA*M)*x. |
 c           | (M*x) has been saved in         |
 c           | workd(ipntr(3)).                |
 c           %---------------------------------%
 c
             if ( bmat .eq. 'G' ) then
-               call dgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    ab(itop,1), lda, workd(ipntr(1)), 1, 
+               call dgbmv('Notranspose', n, n, kl, ku, one,
+     &                    ab(itop,1), lda, workd(ipntr(1)), 1,
      &                    zero, workd(ipntr(2)), 1)
-               call daxpy( n, sigma, workd(ipntr(3)), 1, 
+               call daxpy( n, sigma, workd(ipntr(3)), 1,
      &                    workd(ipntr(2)), 1 )
-            else 
+            else
                call dcopy (n, workd(ipntr(1)), 1, workd(ipntr(2)), 1)
-               call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                    lda, workd(ipntr(1)), 1, sigma, 
+               call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                    lda, workd(ipntr(1)), 1, sigma,
      &                    workd(ipntr(2)), 1)
             end if
-            call dgbtrs('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call dgbtrs('Notranspose', n, kl, ku, 1, rfac, lda,
      &                   iwork, workd(ipntr(2)), n, ierr)
 c
          end if
@@ -767,9 +767,9 @@ c
       else if (ido .eq. 2) then
 c
 c        %----------------------------------%
-c        |        Perform y <-- B*x         | 
+c        |        Perform y <-- B*x         |
 c        | Note when Buckling mode is used, |
-c        | B = A, otherwise B=M.            | 
+c        | B = A, otherwise B=M.            |
 c        %----------------------------------%
 c
          if (type .eq. 5) then
@@ -778,20 +778,20 @@ c           %---------------------%
 c           | Buckling Mode, B=A. |
 c           %---------------------%
 c
-            call dgbmv('Notranspose', n, n, kl, ku, one, 
-     &                ab(itop,1), lda, workd(ipntr(1)), 1, 
+            call dgbmv('Notranspose', n, n, kl, ku, one,
+     &                ab(itop,1), lda, workd(ipntr(1)), 1,
      &                zero, workd(ipntr(2)), 1)
          else
 
-            call dgbmv('Notranspose', n, n, kl, ku, one, 
-     &                mb(itop,1), lda, workd(ipntr(1)), 1, 
+            call dgbmv('Notranspose', n, n, kl, ku, one,
+     &                mb(itop,1), lda, workd(ipntr(1)), 1,
      &                zero, workd(ipntr(2)), 1)
          end if
 c
-      else 
+      else
 c
 c        %-----------------------------------------%
-c        | Either we have convergence, or there is | 
+c        | Either we have convergence, or there is |
 c        | error.                                  |
 c        %-----------------------------------------%
 c
@@ -808,7 +808,7 @@ c
             print *, ' '
             go to 9000
 c
-         else 
+         else
 c
             if ( info .eq. 1) then
                print *, ' '
@@ -823,22 +823,22 @@ c
 c
             if (iparam(5) .gt. 0) then
 c
-               call dseupd ( rvec, 'A', select, d, z, ldz, sigma, 
-     &                  bmat, n, which, nev, tol, resid, ncv, v, ldv, 
-     &                  iparam, ipntr, workd, workl, lworkl, info )            
+               call dseupd ( rvec, 'A', select, d, z, ldz, sigma,
+     &                  bmat, n, which, nev, tol, resid, ncv, v, ldv,
+     &                  iparam, ipntr, workd, workl, lworkl, info )
 c
                if ( info .ne. 0) then
-c 
+c
 c                 %------------------------------------%
 c                 | Check the documentation of dneupd. |
 c                 %------------------------------------%
 c
-                  print *, ' ' 
+                  print *, ' '
                   print *, ' Error with _neupd = ', info
                   print *, ' Check the documentation of _neupd '
-                  print *, ' ' 
+                  print *, ' '
                   go to 9000
-c 
+c
                end if
 c
             end if
@@ -853,7 +853,7 @@ c     %----------------------------------------%
 c     | L O O P  B A C K to call DSAUPD again. |
 c     %----------------------------------------%
 c
-      go to 90 
+      go to 90
 c
  9000 continue
 c

EXAMPLES/BAND/dsbdr1.f

@@ -1,14 +1,14 @@
-      program dsbdr1 
+      program dsbdr1
 c
 c     ... Construct the matrix A in LAPACK-style band form.
 c         The matrix A is derived from the discretization of
-c         the 2-dimensional Laplacian on the unit square with 
-c         zero Dirichlet boundary condition using standard 
+c         the 2-dimensional Laplacian on the unit square with
+c         zero Dirichlet boundary condition using standard
 c         central difference.
 c
 c     ... Call DSBAND  to find eigenvalues LAMBDA such that
 c                          A*x = x*LAMBDA.
-c       
+c
 c     ... Use mode 1 of DSAUPD .
 c
 c\BeginLib
@@ -47,13 +47,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -62,9 +62,9 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Double precision 
+      Double precision
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn), 
+     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn),
      &                 v(ldv, maxncv), resid(maxn), d(maxncv, 2),
      &                 ax(maxn)
 c
@@ -76,15 +76,15 @@ c
       integer          nev, ncv, ku, kl, info, i, j, ido,
      &                 n, nx, lo, isub, isup, idiag, maxitr, mode,
      &                 nconv
-      Double precision  
+      Double precision
      &                 tol, sigma, h2
       logical          rvec
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Double precision  
+      Double precision
      &                 one, zero, two
       parameter        (one = 1.0D+0 , zero = 0.0D+0 , two = 2.0D+0 )
 c
@@ -92,9 +92,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dlapy2 , dnrm2 
-      external          dlapy2 , dnrm2 , dgbmv , daxpy  
+      Double precision
+     &                  dlapy2 , dnrm2
+      external          dlapy2 , dnrm2 , dgbmv , daxpy
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -121,13 +121,13 @@ c     | However, the following conditions must be       |
 c     | satisfied:                                      |
 c     |                   N <= MAXN                     |
 c     |                 NEV <= MAXNEV                   |
-c     |           NEV + 1 <= NCV <= MAXNCV              | 
-c     %-------------------------------------------------% 
+c     |           NEV + 1 <= NCV <= MAXNCV              |
+c     %-------------------------------------------------%
 c
-      nx  = 10 
+      nx  = 10
       n    = nx*nx
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _SBDR1: N is greater than MAXN '
          go to 9000
@@ -153,7 +153,7 @@ c     | generated in DSAUPD  to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = ncv**2+8*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -169,7 +169,7 @@ c
       mode = 1
 c
       iparam(3) = maxitr
-      iparam(7) = mode 
+      iparam(7) = mode
 c
 c     %----------------------------------------%
 c     | Construct the matrix A in LAPACK-style |
@@ -190,10 +190,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = nx 
-      ku   = nx 
+      kl   = nx
+      ku   = nx
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -201,12 +201,12 @@ c
       idiag = kl+ku+1
       do 30 j = 1, n
          a(idiag,j) = 4.0D+0  / h2
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+ku+2
       do 50 i = 1, nx
@@ -214,8 +214,8 @@ c
         do 40 j = lo+1, lo+nx-1
            a(isup,j+1) = -one / h2
            a(isub,j) = -one / h2
-  40    continue      
-  50  continue 
+  40    continue
+  50  continue
 c
 c     %------------------------------------%
 c     | KL-th subdiagonal and KU-th super- |
@@ -229,8 +229,8 @@ c
          do 70 j = lo+1, lo+nx
             a(isup,nx+j)  = -one / h2
             a(isub,j) = -one / h2
- 70      continue 
- 80   continue 
+ 70      continue
+ 80   continue
 c
 c     %-------------------------------------%
 c     | Call DSBAND  to find eigenvalues and |
@@ -239,18 +239,18 @@ c     | returned in the first column of D.  |
 c     | Eigenvectors are returned in the    |
 c     | first NCONV (=IPARAM(5)) columns of |
 c     | V.                                  |
-c     %-------------------------------------% 
+c     %-------------------------------------%
 c
       rvec = .true.
-      call dsband ( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda, 
-     &             rfac, kl, ku, which, bmat, nev, tol, 
-     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl, 
+      call dsband ( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda,
+     &             rfac, kl, ku, which, bmat, nev, tol,
+     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl,
      &             iwork, info)
 c
       if ( info .eq. 0) then
 c
          nconv = iparam(5)
-c 
+c
 c        %-----------------------------------%
 c        | Print out convergence information |
 c        %-----------------------------------%
@@ -278,18 +278,18 @@ c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
          do 90 j = 1, nconv
-            call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                 a(kl+1,1), lda, v(1,j), 1, zero, 
+            call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                 a(kl+1,1), lda, v(1,j), 1, zero,
      &                 ax, 1)
             call daxpy (n, -d(j,1), v(1,j), 1, ax, 1)
             d(j,2) = dnrm2 (n, ax, 1)
             d(j,2) = d(j,2) / abs(d(j,1))
 c
- 90      continue 
+ 90      continue
 
          call dmout (6, nconv, 2, d, maxncv, -6,
      &             'Ritz values and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -300,8 +300,8 @@ c
           print *, ' '
           print *, ' Error with _sband, info= ', info
           print *, ' Check the documentation of _sband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/dsbdr2.f

@@ -1,12 +1,12 @@
-      program dsbdr2 
+      program dsbdr2
 c
 c     ... Construct the matrix A in LAPACK-style band form.
 c         The matrix A is derived from the discretization of
-c         the 2-dimensional Laplacian on the unit square 
+c         the 2-dimensional Laplacian on the unit square
 c         with zero Dirichlet boundary condition using standard
 c         central difference.
 c
-c     ... Call DSBAND  to find eigenvalues LAMBDA closest to 
+c     ... Call DSBAND  to find eigenvalues LAMBDA closest to
 c         SIGMA such that
 c                          A*x = x*LAMBDA.
 c
@@ -48,13 +48,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -63,10 +63,10 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Double precision 
+      Double precision
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), 
-     &                 v(ldv, maxncv), resid(maxn), d(maxncv, 2), 
+     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn),
+     &                 v(ldv, maxncv), resid(maxn), d(maxncv, 2),
      &                 ax(maxn)
 c
 c     %---------------%
@@ -77,15 +77,15 @@ c
       integer          nev, ncv, ku, kl, info, i, j, ido,
      &                 n, nx, lo, isub, isup, idiag, maxitr, mode,
      &                 nconv
-      Double precision  
+      Double precision
      &                 tol, sigma, h2
       logical          rvec
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Double precision  
+      Double precision
      &                 one, zero, two
       parameter        (one = 1.0D+0 , zero = 0.0D+0 , two = 2.0D+0 )
 c
@@ -93,9 +93,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dlapy2 , dnrm2 
-      external          dlapy2 , dnrm2 , daxpy , dgbmv  
+      Double precision
+     &                  dlapy2 , dnrm2
+      external          dlapy2 , dnrm2 , daxpy , dgbmv
 c
 c     %-----------------------%
 c     | Executable Statements |
@@ -118,13 +118,13 @@ c     | However, the following conditions must be        |
 c     | satisfied:                                       |
 c     |                   N <= MAXN                      |
 c     |                 NEV <= MAXNEV                    |
-c     |           NEV + 1 <= NCV <= MAXNCV               | 
-c     %--------------------------------------------------% 
+c     |           NEV + 1 <= NCV <= MAXNCV               |
+c     %--------------------------------------------------%
 c
-      nx  = 10 
+      nx  = 10
       n    = nx*nx
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _SBDR2: N is greater than MAXN '
          go to 9000
@@ -151,7 +151,7 @@ c     | generated in DSAUPD  to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+6*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -167,7 +167,7 @@ c
       mode = 3
 c
       iparam(3) = maxitr
-      iparam(7) = mode 
+      iparam(7) = mode
 c
 c     %----------------------------------------%
 c     | Construct the matrix A in LAPACK-style |
@@ -188,10 +188,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = nx 
-      ku   = nx 
+      kl   = nx
+      ku   = nx
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -199,12 +199,12 @@ c
       idiag = kl+ku+1
       do 30 j = 1, n
          a(idiag,j) = 4.0D+0  / h2
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+ku+2
       do 50 i = 1, nx
@@ -212,8 +212,8 @@ c
         do 40 j = lo+1, lo+nx-1
            a(isup,j+1) = -one / h2
            a(isub,j) = -one / h2
-  40    continue      
-  50  continue 
+  40    continue
+  50  continue
 c
 c     %------------------------------------%
 c     | KL-th subdiagonal and KU-th super- |
@@ -227,8 +227,8 @@ c
          do 70 j = lo+1, lo+nx
             a(isup,nx+j)  = -one / h2
             a(isub,j) = -one / h2
- 70      continue 
- 80   continue 
+ 70      continue
+ 80   continue
 c
 c     %-------------------------------------%
 c     | Call DSBAND  to find eigenvalues and |
@@ -239,10 +239,10 @@ c     | first NCONV (=IPARAM(5)) columns of |
 c     | V.                                  |
 c     %-------------------------------------%
 c
-      rvec = .true. 
-      call dsband ( rvec,'A', select, d, v, ldv, sigma, n, a, m, 
-     &             lda, rfac, kl, ku, which, bmat, nev, tol, 
-     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl, 
+      rvec = .true.
+      call dsband ( rvec,'A', select, d, v, ldv, sigma, n, a, m,
+     &             lda, rfac, kl, ku, which, bmat, nev, tol,
+     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl,
      &             iwork, info)
 c
       if ( info .eq. 0) then
@@ -276,18 +276,18 @@ c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
          do 90 j = 1, nconv
-            call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                 a(kl+1,1), lda, v(1,j), 1, zero, 
+            call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                 a(kl+1,1), lda, v(1,j), 1, zero,
      &                 ax, 1)
             call daxpy (n, -d(j,1), v(1,j), 1, ax, 1)
             d(j,2) = dnrm2 (n, ax, 1)
             d(j,2) = d(j,2) / abs(d(j,1))
 c
- 90      continue 
+ 90      continue
 
          call dmout (6, nconv, 2, d, maxncv, -6,
      &             'Ritz values and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -298,8 +298,8 @@ c
           print *, ' '
           print *, ' Error with _sband, info= ', info
           print *, ' Check the documentation of _sband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/dsbdr3.f

@@ -1,11 +1,11 @@
-      program dsbdr3 
+      program dsbdr3
 c
 c     ... Construct the matrix A in LAPACK-style band form.
 c         The matrix A is the 1-dimensional discrete Laplacian on [0,1]
 c         with zero Dirichlet boundary condition, M is the mass
 c         formed by using piecewise linear elements on [0,1].
 c
-c     ... Call DSBAND  with regular mode to find eigenvalues LAMBDA 
+c     ... Call DSBAND  with regular mode to find eigenvalues LAMBDA
 c         such that
 c                          A*x = LAMBDA*M*x.
 c
@@ -46,13 +46,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -61,9 +61,9 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Double precision 
+      Double precision
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn), 
+     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn),
      &                 v(ldv, maxncv), resid(maxn), d(maxncv, 2),
      &                 ax(maxn), mx(maxn)
 c
@@ -74,15 +74,15 @@ c
       character        which*2, bmat
       integer          nev, ncv, ku, kl, info, j, ido,
      &                 n, isub, isup, idiag, maxitr, mode, nconv
-      Double precision  
+      Double precision
      &                 tol, h, sigma, r1, r2
       logical          rvec
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Double precision  
+      Double precision
      &                 one, zero, two, four, six
       parameter        (one = 1.0D+0 , zero = 0.0D+0 , two = 2.0D+0 ,
      &                  four = 4.0D+0 , six = 6.0D+0 )
@@ -91,9 +91,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dlapy2 , dnrm2 
-      external          dlapy2 , dnrm2 , daxpy , dgbmv  
+      Double precision
+     &                  dlapy2 , dnrm2
+      external          dlapy2 , dnrm2 , daxpy , dgbmv
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -116,12 +116,12 @@ c     | However, the following conditions must be       |
 c     | satisfied:                                      |
 c     |                   N <= MAXN                     |
 c     |                 NEV <= MAXNEV                   |
-c     |           NEV + 1 <= NCV <= MAXNCV              | 
-c     %-------------------------------------------------% 
+c     |           NEV + 1 <= NCV <= MAXNCV              |
+c     %-------------------------------------------------%
 c
-      n    = 100 
-      nev  = 4 
-      ncv  = 10 
+      n    = 100
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _SBDR3: N is greater than MAXN '
          go to 9000
@@ -147,7 +147,7 @@ c     | generated in DSAUPD  to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = ncv**2+8*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -184,10 +184,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = 1 
-      ku   = 1 
+      kl   = 1
+      ku   = 1
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -197,12 +197,12 @@ c
       do 30 j = 1, n
          a(idiag,j) = two / h
          m(idiag,j) = r1 * h
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       r2 = one / six
       isup = kl+ku
       isub = kl+ku+2
@@ -223,9 +223,9 @@ c     | V.                                  |
 c     %-------------------------------------%
 c
       rvec = .true.
-      call dsband ( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda, 
-     &             rfac, kl, ku, which, bmat, nev, tol, 
-     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl, 
+      call dsband ( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda,
+     &             rfac, kl, ku, which, bmat, nev, tol,
+     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl,
      &             iwork, info)
 c
       if ( info .eq. 0) then
@@ -259,21 +259,21 @@ c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
          do 90 j = 1, nconv
-            call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                 a(kl+1,1), lda, v(1,j), 1, zero, 
+            call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                 a(kl+1,1), lda, v(1,j), 1, zero,
      &                 ax, 1)
-            call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                 m(kl+1,1), lda, v(1,j), 1, zero, 
+            call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                 m(kl+1,1), lda, v(1,j), 1, zero,
      &                 mx, 1)
             call daxpy (n, -d(j,1), mx, 1, ax, 1)
             d(j,2) = dnrm2 (n, ax, 1)
             d(j,2) = d(j,2) / abs(d(j,1))
 c
- 90      continue 
+ 90      continue
 
          call dmout (6, nconv, 2, d, maxncv, -6,
      &             'Ritz values and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -284,8 +284,8 @@ c
           print *, ' '
           print *, ' Error with _sband, info= ', info
           print *, ' Check the documentation of _sband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/dsbdr4.f

@@ -1,11 +1,11 @@
-      program dsbdr4 
+      program dsbdr4
 c
 c     ... Construct the matrix A in LAPACK-style band form.
 c         The matrix A is the 1-dimensional discrete Laplacian on [0,1]
 c         with zero Dirichlet boundary condition, M is the mass
 c         formed by using piecewise linear elements on [0,1].
 c
-c     ... Call DSBAND  with shift-invert mode to find eigenvalues LAMBDA 
+c     ... Call DSBAND  with shift-invert mode to find eigenvalues LAMBDA
 c         closest to SIGMA such that
 c                          A*x = LAMBDA*M*x.
 c
@@ -47,13 +47,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -62,9 +62,9 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Double precision 
+      Double precision
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn), 
+     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn),
      &                 v(ldv, maxncv), resid(maxn), d(maxncv, 2),
      &                 ax(maxn), mx(maxn)
 c
@@ -75,15 +75,15 @@ c
       character        which*2, bmat
       integer          nev, ncv, ku, kl, info, j, ido,
      &                 n, isub, isup, idiag, maxitr, mode, nconv
-      Double precision  
+      Double precision
      &                 tol, h, sigma, r1, r2
       logical          rvec
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Double precision  
+      Double precision
      &                 one, zero, two, four, six
       parameter        (one = 1.0D+0 , zero = 0.0D+0 , two = 2.0D+0 ,
      &                  four = 4.0D+0 , six = 6.0D+0 )
@@ -92,9 +92,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dlapy2 , dnrm2 
-      external          dlapy2 , dnrm2 , daxpy , dgbmv  
+      Double precision
+     &                  dlapy2 , dnrm2
+      external          dlapy2 , dnrm2 , daxpy , dgbmv
 c
 c     %-----------------------%
 c     | Executable Statements |
@@ -113,12 +113,12 @@ c     | However, the following conditions must be        |
 c     | satisfied:                                       |
 c     |                   N <= MAXN                      |
 c     |                 NEV <= MAXNEV                    |
-c     |           NEV + 1 <= NCV <= MAXNCV               | 
-c     %--------------------------------------------------% 
+c     |           NEV + 1 <= NCV <= MAXNCV               |
+c     %--------------------------------------------------%
 c
       n    = 100
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _SBDR4: N is greater than MAXN '
          go to 9000
@@ -145,7 +145,7 @@ c     | generated in DSAUPD  to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = ncv**2+8*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -182,10 +182,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = 1 
-      ku   = 1 
+      kl   = 1
+      ku   = 1
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -195,19 +195,19 @@ c
       do 30 j = 1, n
          a(idiag,j) = two / h
          m(idiag,j) = r1 * h
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       r2 = one / six
       isup = kl+ku
       isub = kl+ku+2
       do 60 j = 1, n-1
          a(isup,j+1) = -one / h
          a(isub,j) = -one / h
-         m(isup,j+1) = r2 * h 
+         m(isup,j+1) = r2 * h
          m(isub,j) = r2 * h
   60  continue
 c
@@ -221,9 +221,9 @@ c     | V.                                  |
 c     %-------------------------------------%
 c
       rvec = .true.
-      call dsband ( rvec, 'A', select, d, v, ldv, sigma, n, a, m, 
-     &             lda, rfac, kl, ku, which, bmat, nev, tol, 
-     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl, 
+      call dsband ( rvec, 'A', select, d, v, ldv, sigma, n, a, m,
+     &             lda, rfac, kl, ku, which, bmat, nev, tol,
+     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl,
      &             iwork, info)
 c
       if ( info .eq. 0) then
@@ -243,7 +243,7 @@ c
          print *, ' The number of Lanczos vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' The number of converged Ritz values is ',
-     &              nconv 
+     &              nconv
          print *, ' What portion of the spectrum ', which
          print *, ' The number of Implicit Arnoldi',
      &              ' update taken is ', iparam(3)
@@ -257,21 +257,21 @@ c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
          do 90 j = 1, nconv
-            call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                 a(kl+1,1), lda, v(1,j), 1, zero, 
+            call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                 a(kl+1,1), lda, v(1,j), 1, zero,
      &                 ax, 1)
-            call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                 m(kl+1,1), lda, v(1,j), 1, zero, 
+            call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                 m(kl+1,1), lda, v(1,j), 1, zero,
      &                 mx, 1)
             call daxpy (n, -d(j,1), mx, 1, ax, 1)
             d(j,2) = dnrm2 (n, ax, 1)
             d(j,2) = d(j,2) / abs(d(j,1))
 c
- 90      continue 
+ 90      continue
 
          call dmout (6, nconv, 2, d, maxncv, -6,
      &             'Ritz values and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -282,8 +282,8 @@ c
           print *, ' '
           print *, ' Error with _sband, info= ', info
           print *, ' Check the documentation of _sband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/dsbdr5.f

@@ -1,11 +1,11 @@
-      program dsbdr5 
+      program dsbdr5
 c
 c     ... Construct the matrix A in LAPACK-style band form.
 c         The matrix A is the 1-dimensional discrete Laplacian on [0,1]
 c         with zero Dirichlet boundary condition, KG is the mass
-c         formed by using piecewise linear elements on [0,1]. 
+c         formed by using piecewise linear elements on [0,1].
 c
-c     ... Call DSBAND  with Buckling mode to find eigenvalues LAMBDA 
+c     ... Call DSBAND  with Buckling mode to find eigenvalues LAMBDA
 c         such that
 c                          A*x = M*x*LAMBDA.
 c
@@ -47,13 +47,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -62,9 +62,9 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Double precision 
+      Double precision
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn), 
+     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn),
      &                 v(ldv, maxncv), resid(maxn), d(maxncv, 2),
      &                 ax(maxn), mx(maxn)
 c
@@ -75,15 +75,15 @@ c
       character        which*2, bmat
       integer          nev, ncv, kl, ku, info, j, ido,
      &                 n, isub, isup, idiag, maxitr, mode, nconv
-      Double precision  
+      Double precision
      &                 tol, h, sigma, r1, r2
       logical          rvec
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Double precision  
+      Double precision
      &                 one, zero, two, four, six
       parameter        (one = 1.0D+0 , zero = 0.0D+0 , two = 2.0D+0 ,
      &                  four = 4.0D+0 , six = 6.0D+0 )
@@ -92,9 +92,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dlapy2 , dnrm2 
-      external          dlapy2 , dnrm2 , dgbmv , daxpy  
+      Double precision
+     &                  dlapy2 , dnrm2
+      external          dlapy2 , dnrm2 , dgbmv , daxpy
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -118,12 +118,12 @@ c     | the spectrum.  However, the following conditions |
 c     | must be satisfied:                               |
 c     |                   N <= MAXN                      |
 c     |                 NEV <= MAXNEV                    |
-c     |           NEV + 1 <= NCV <= MAXNCV               | 
-c     %--------------------------------------------------% 
+c     |           NEV + 1 <= NCV <= MAXNCV               |
+c     %--------------------------------------------------%
 c
       n    = 100
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _SBDR5: N is greater than MAXN '
          go to 9000
@@ -150,7 +150,7 @@ c     | generated in DSAUPD  to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = ncv**2+8*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -187,10 +187,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = 1 
-      ku   = 1 
+      kl   = 1
+      ku   = 1
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -200,12 +200,12 @@ c
       do 30 j = 1, n
          a(idiag,j) = two / h
          m(idiag,j) = r1 * h
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       r2 = one / six
       isup = kl+ku
       isub = kl+ku+2
@@ -226,9 +226,9 @@ c     | V.                                  |
 c     %-------------------------------------%
 c
       rvec = .true.
-      call dsband ( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda, 
-     &             rfac, kl, ku, which, bmat, nev, tol, 
-     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl, 
+      call dsband ( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda,
+     &             rfac, kl, ku, which, bmat, nev, tol,
+     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl,
      &             iwork, info)
 c
       if ( info .eq. 0) then
@@ -262,21 +262,21 @@ c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
          do 90 j = 1, nconv
-            call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                 a(kl+1,1), lda, v(1,j), 1, zero, 
+            call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                 a(kl+1,1), lda, v(1,j), 1, zero,
      &                 ax, 1)
-            call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                 m(kl+1,1), lda, v(1,j), 1, zero, 
+            call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                 m(kl+1,1), lda, v(1,j), 1, zero,
      &                 mx, 1)
             call daxpy (n, -d(j,1), mx, 1, ax, 1)
             d(j,2) = dnrm2 (n, ax, 1)
             d(j,2) = d(j,2) / abs(d(j,1))
 c
- 90      continue 
+ 90      continue
 
          call dmout (6, nconv, 2, d, maxncv, -6,
      &             'Ritz values and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -287,8 +287,8 @@ c
           print *, ' '
           print *, ' Error with _sband, info= ', info
           print *, ' Check the documentation of _sband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/dsbdr6.f

@@ -1,10 +1,10 @@
-      program dsbdr6 
+      program dsbdr6
 c
 c     ... Construct the matrix A in LAPACK-style band form.
 c         The matrix A is the 1-dimensional discrete Laplacian on [0,1]
 c         with zero Dirichlet boundary condition, M is the mass
 c         formed by using piecewise linear elements on [0,1].
-c 
+c
 c     ... Call DSBAND  with Cayley mode to find eigenvalues LAMBDA such that
 c                          A*x = LAMBDA*M*x.
 c
@@ -46,13 +46,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -61,9 +61,9 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Double precision 
+      Double precision
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn), 
+     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn),
      &                 v(ldv, maxncv), resid(maxn), d(maxncv, 2),
      &                 ax(maxn), mx(maxn)
 c
@@ -74,15 +74,15 @@ c
       character        which*2, bmat
       integer          nev, ncv, ku, kl, info, j, ido,
      &                 n, isub, isup, idiag, maxitr, mode, nconv
-      Double precision  
+      Double precision
      &                 tol, h, sigma, r1, r2
       logical          rvec
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Double precision  
+      Double precision
      &                 one, zero, two, four, six
       parameter        (one = 1.0D+0 , zero = 0.0D+0 , two = 2.0D+0 ,
      &                  four = 4.0D+0 , six = 6.0D+0 )
@@ -91,9 +91,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dlapy2 , dnrm2 
-      external          dlapy2 , dnrm2 , daxpy , dgbmv  
+      Double precision
+     &                  dlapy2 , dnrm2
+      external          dlapy2 , dnrm2 , daxpy , dgbmv
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -117,12 +117,12 @@ c     | the spectrum.  However, the following conditions |
 c     | must be satisfied:                               |
 c     |                   N <= MAXN                      |
 c     |                 NEV <= MAXNEV                    |
-c     |           NEV + 1 <= NCV <= MAXNCV               | 
-c     %--------------------------------------------------% 
+c     |           NEV + 1 <= NCV <= MAXNCV               |
+c     %--------------------------------------------------%
 c
       n    = 100
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _SBDR6: N is greater than MAXN '
          go to 9000
@@ -149,7 +149,7 @@ c     | generated in DSAUPD  to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = ncv**2+8*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -186,10 +186,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = 1 
-      ku   = 1 
+      kl   = 1
+      ku   = 1
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -199,12 +199,12 @@ c
       do 30 j = 1, n
          a(idiag,j) = two / h
          m(idiag,j) = r1 * h
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       r2 = one / six
       isup = kl+ku
       isub = kl+ku+2
@@ -225,9 +225,9 @@ c     | V.                                  |
 c     %-------------------------------------%
 c
       rvec = .true.
-      call dsband ( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda, 
-     &             rfac, kl, ku, which, bmat, nev, tol, 
-     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl, 
+      call dsband ( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda,
+     &             rfac, kl, ku, which, bmat, nev, tol,
+     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl,
      &             iwork, info)
 c
       if ( info .eq. 0) then
@@ -261,21 +261,21 @@ c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
          do 90 j = 1, nconv
-            call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                 a(kl+1,1), lda, v(1,j), 1, zero, 
+            call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                 a(kl+1,1), lda, v(1,j), 1, zero,
      &                 ax, 1)
-            call dgbmv ('Notranspose', n, n, kl, ku, one, 
-     &                 m(kl+1,1), lda, v(1,j), 1, zero, 
+            call dgbmv ('Notranspose', n, n, kl, ku, one,
+     &                 m(kl+1,1), lda, v(1,j), 1, zero,
      &                 mx, 1)
             call daxpy (n, -d(j,1), mx, 1, ax, 1)
             d(j,2) = dnrm2 (n, ax, 1)
             d(j,2) = d(j,2) / abs(d(j,1))
 c
- 90      continue 
+ 90      continue
 
          call dmout (6, nconv, 2, d, maxncv, -6,
      &             'Ritz values and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -286,8 +286,8 @@ c
           print *, ' '
           print *, ' Error with _band, info= ', info
           print *, ' Check the documentation of _band '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/makefile

@@ -1,158 +0,0 @@
-#
-# makefile to run simple examples of the reverse communication
-# protocol.
-#
-# Modify if ARPACK library was built somewhere else.
-#
-# If ALIBS (defined in ../../ARmake.inc) contains the BLAS and LAPACK
-# libraries installed on your system, you DO NOT need to change this
-# makefile. OTHERWISE, you may need to modify the Makefile in the top level
-# ARPACK directory tree to include sdrv, ddrv, cdrv, or zdrv in the
-# definition of the PRECISION variable, and issue 'make lib' there.
-# For example:
-#
-#         PRECISION = single double sdrv ddrv
-#
-#\SCCS Information: @(#) 
-# FILE: makefile   SID: 2.2   DATE OF SID: 9/24/96   RELEASE: 2 
-#
-include ../../ARmake.inc
-
-# Issue "make band" to make all 32 band drivers.
-# Issue "make ssbdr" to make 6 single precision symmetric band drivers.
-# Issue "make dsbdr" to make 6 double precision symmetric band drivers.
-# Issue "make snbdr" to make 6 single precision nonsymmetric band drivers.
-# Issue "make dnbdr" to make 6 double precision nonsymmetric band drivers.
-# Issue "make cnbdr" to make 4 single precision complex band drivers.
-# Issue "make znbdr" to make 4 double precision complex band drivers. 
-#
-
-band: ssbdr dsbdr snbdr dnbdr cnbdr znbdr
-
-#
-#---------------------------------------------------------------------
-# Simple symetric problem using BAND solver (single precision)
-#
-ssbdr: ssbdr1 ssbdr2 ssbdr3 ssbdr4 ssbdr5 ssbdr6
-
-ssbdr1: ssbdr1.o ssband.o
-	$(FC) $(FFLAGS) ssbdr1.o ssband.o $(ALIBS) -o ssbdr1
-#
-ssbdr2: ssbdr2.o ssband.o
-	$(FC) $(FFLAGS) ssbdr2.o ssband.o $(ALIBS) -o ssbdr2
-#
-ssbdr3: ssbdr3.o ssband.o
-	$(FC) $(FFLAGS) ssbdr3.o ssband.o $(ALIBS) -o ssbdr3
-#
-ssbdr4: ssbdr4.o ssband.o
-	$(FC) $(FFLAGS) ssbdr4.o ssband.o $(ALIBS) -o ssbdr4
-#
-ssbdr5: ssbdr5.o ssband.o
-	$(FC) $(FFLAGS) ssbdr5.o ssband.o $(ALIBS) -o ssbdr5
-#
-ssbdr6: ssbdr6.o ssband.o
-	$(FC) $(FFLAGS) ssbdr6.o ssband.o $(ALIBS) -o ssbdr6
-#
-#-------------------------------------------------------------
-#
-# Simple symmetric problem using BAND solver (double precision)
-#
-dsbdr: dsbdr1 dsbdr2 dsbdr3 dsbdr4 dsbdr5 dsbdr6
-
-dsbdr1: dsbdr1.o dsband.o
-	$(FC) $(FFLAGS) dsbdr1.o dsband.o $(ALIBS) -o dsbdr1
-#
-dsbdr2: dsbdr2.o dsband.o 
-	$(FC) $(FFLAGS) dsbdr2.o dsband.o $(ALIBS) -o dsbdr2
-#
-dsbdr3: dsbdr3.o dsband.o
-	$(FC) $(FFLAGS) dsbdr3.o dsband.o $(ALIBS) -o dsbdr3
-#
-dsbdr4: dsbdr4.o dsband.o
-	$(FC) $(FFLAGS) dsbdr4.o dsband.o $(ALIBS) -o dsbdr4
-#
-dsbdr5: dsbdr5.o dsband.o
-	$(FC) $(FFLAGS) dsbdr5.o dsband.o $(ALIBS) -o dsbdr5
-#
-dsbdr6: dsbdr6.o dsband.o
-	$(FC) $(FFLAGS) dsbdr6.o dsband.o $(ALIBS) -o dsbdr6
-#
-#----------------------------------------------------------------------
-# Simple nonsymmetric problem using BAND solver (single precision)
-#
-snbdr: snbdr1 snbdr2 snbdr3 snbdr4 snbdr5 snbdr6
-
-snbdr1: snbdr1.o snband.o 
-	$(FC) $(FFLAGS) snbdr1.o snband.o $(ALIBS) -o snbdr1
-#
-snbdr2: snbdr2.o snband.o 
-	$(FC) $(FFLAGS) snbdr2.o snband.o $(ALIBS) -o snbdr2
-#
-snbdr3: snbdr3.o snband.o 
-	$(FC) $(FFLAGS) snbdr3.o snband.o $(ALIBS) -o snbdr3
-#
-snbdr4: snbdr4.o snband.o 
-	$(FC) $(FFLAGS) snbdr4.o snband.o $(ALIBS) -o snbdr4
-#
-snbdr5: snbdr5.o snband.o 
-	$(FC) $(FFLAGS) snbdr5.o snband.o $(ALIBS) -o snbdr5
-#
-snbdr6: snbdr6.o snband.o 
-	$(FC) $(FFLAGS) snbdr6.o snband.o $(ALIBS) -o snbdr6
-#
-#-------------------------------------------------------------------------
-# Simple nonsymmetric problem using BAND solver (double precision)
-#
-dnbdr: dnbdr1 dnbdr2 dnbdr3 dnbdr4 dnbdr5 dnbdr6
-
-dnbdr1: dnbdr1.o dnband.o 
-	$(FC) $(FFLAGS) dnbdr1.o dnband.o $(ALIBS) -o dnbdr1
-#
-dnbdr2: dnbdr2.o dnband.o 
-	$(FC) $(FFLAGS) dnbdr2.o dnband.o $(ALIBS) -o dnbdr2
-#
-dnbdr3: dnbdr3.o dnband.o 
-	$(FC) $(FFLAGS) dnbdr3.o dnband.o $(ALIBS) -o dnbdr3
-#
-dnbdr4: dnbdr4.o dnband.o 
-	$(FC) $(FFLAGS) dnbdr4.o dnband.o $(ALIBS) -o dnbdr4
-#
-dnbdr5: dnbdr5.o dnband.o 
-	$(FC) $(FFLAGS) dnbdr5.o dnband.o $(ALIBS) -o dnbdr5
-#
-dnbdr6: dnbdr6.o dnband.o 
-	$(FC) $(FFLAGS) dnbdr6.o dnband.o $(ALIBS) -o dnbdr6
-#
-#-------------------------------------------------------------------------
-# Complex problem using BAND solver (single precision complex)
-#
-cnbdr:  cnbdr1 cnbdr2 cnbdr3 cnbdr4
-
-cnbdr1: cnbdr1.o cnband.o
-	$(FC) $(FFLAGS) cnbdr1.o cnband.o $(ALIBS) -o cnbdr1
-#
-cnbdr2: cnbdr2.o cnband.o
-	$(FC) $(FFLAGS) cnbdr2.o cnband.o $(ALIBS) -o cnbdr2
-#
-cnbdr3: cnbdr3.o cnband.o
-	$(FC) $(FFLAGS) cnbdr3.o cnband.o $(ALIBS) -o cnbdr3
-#
-cnbdr4: cnbdr4.o cnband.o
-	$(FC) $(FFLAGS) cnbdr4.o cnband.o $(ALIBS) -o cnbdr4
-#
-#-------------------------------------------------------------------------
-# Complex problem using BAND solver (double precision complex)
-#
-znbdr: znbdr1 znbdr2 znbdr3 znbdr4
-
-znbdr1: znbdr1.o znband.o
-	$(FC) $(FFLAGS) znbdr1.o znband.o $(ALIBS) -o znbdr1
-#
-znbdr2: znbdr2.o znband.o
-	$(FC) $(FFLAGS) znbdr2.o znband.o $(ALIBS) -o znbdr2
-#
-znbdr3: znbdr3.o znband.o
-	$(FC) $(FFLAGS) znbdr3.o znband.o $(ALIBS) -o znbdr3
-#
-znbdr4: znbdr4.o znband.o
-	$(FC) $(FFLAGS) znbdr4.o znband.o $(ALIBS) -o znbdr4

EXAMPLES/BAND/snband.f

@@ -35,18 +35,18 @@ c  Mode 2:  A*z = lambda*M*z, M symmetric positive definite
 c           ===> OP = inv[M]*A  and  B = M.
 c
 c  Mode 3:  A*z = lambda*M*z, M symmetric semi-definite
-c           ===> OP = Real_Part{ inv[A - sigma*M]*M }  and  B = M. 
+c           ===> OP = Real_Part{ inv[A - sigma*M]*M }  and  B = M.
 c           ===> shift-and-invert mode (in real arithmetic)
-c           If OP*z = amu*z, then 
+c           If OP*z = amu*z, then
 c           amu = 1/2 * [ 1/(lambda-sigma) + 1/(lambda-conjg(sigma)) ].
 c           Note: If sigma is real, i.e. imaginary part of sigma is zero;
-c                 Real_Part{ inv[A - sigma*M]*M } == inv[A - sigma*M]*M 
-c                 amu == 1/(lambda-sigma). 
-c  
+c                 Real_Part{ inv[A - sigma*M]*M } == inv[A - sigma*M]*M
+c                 amu == 1/(lambda-sigma).
+c
 c  Mode 4:  A*z = lambda*M*z, M symmetric semi-definite
-c           ===> OP = Imaginary_Part{ inv[A - sigma*M]*M }  and  B = M. 
+c           ===> OP = Imaginary_Part{ inv[A - sigma*M]*M }  and  B = M.
 c           ===> shift-and-invert mode (in real arithmetic)
-c           If OP*z = amu*z, then 
+c           If OP*z = amu*z, then
 c           amu = 1/2i * [ 1/(lambda-sigma) - 1/(lambda-conjg(sigma)) ].
 c
 c
@@ -54,28 +54,28 @@ c  The choice of mode must be specified in IPARAM(7) defined below.
 c
 c \Usage
 c   call snband
-c      ( RVEC, HOWMNY, SELECT, DR, DI, Z, LDZ, SIGMAR, SIGMAI, 
-c        WORKEV, V, N, AB, MB, LDA, RFAC, CFAC, KL, KU, WHICH, 
-c        BMAT, NEV, TOL, RESID, NCV, V, LDV, IPARAM, WORKD, 
+c      ( RVEC, HOWMNY, SELECT, DR, DI, Z, LDZ, SIGMAR, SIGMAI,
+c        WORKEV, V, N, AB, MB, LDA, RFAC, CFAC, KL, KU, WHICH,
+c        BMAT, NEV, TOL, RESID, NCV, V, LDV, IPARAM, WORKD,
 c        WORKL, LWORKL, WORKC, IWORK, INFO )
 c
 c \Arguments
-c 
-c  RVEC    LOGICAL  (INPUT) 
-c          Specifies whether a basis for the invariant subspace corresponding 
-c          to the converged Ritz value approximations for the eigenproblem 
+c
+c  RVEC    LOGICAL  (INPUT)
+c          Specifies whether a basis for the invariant subspace corresponding
+c          to the converged Ritz value approximations for the eigenproblem
 c          A*z = lambda*B*z is computed.
 c
 c             RVEC = .FALSE.     Compute Ritz values only.
 c
 c             RVEC = .TRUE.      Compute the Ritz vectors or Schur vectors.
-c                                See Remarks below. 
+c                                See Remarks below.
 c
-c  HOWMNY  Character*1  (INPUT) 
-c          Specifies the form of the basis for the invariant subspace 
+c  HOWMNY  Character*1  (INPUT)
+c          Specifies the form of the basis for the invariant subspace
 c          corresponding to the converged Ritz values that is to be computed.
 c
-c          = 'A': Compute NEV Ritz vectors; 
+c          = 'A': Compute NEV Ritz vectors;
 c          = 'P': Compute NEV Schur vectors;
 c          = 'S': compute some of the Ritz vectors, specified
 c                 by the logical array SELECT.
@@ -83,23 +83,23 @@ c
 c  SELECT  Logical array of dimension NCV.  (INPUT)
 c          If HOWMNY = 'S', SELECT specifies the Ritz vectors to be
 c          computed. To select the Ritz vector corresponding to a
-c          Ritz value (DR(j), DI(j)), SELECT(j) must be set to .TRUE.. 
+c          Ritz value (DR(j), DI(j)), SELECT(j) must be set to .TRUE..
 c          If HOWMNY = 'A' or 'P', SELECT is used as internal workspace.
 c
 c  DR      Real array of dimension NEV+1.  (OUTPUT)
-c          On exit, DR contains the real part of the Ritz value approximations 
-c          to the eigenvalues of A*z = lambda*B*z. 
+c          On exit, DR contains the real part of the Ritz value approximations
+c          to the eigenvalues of A*z = lambda*B*z.
 c
 c  DI      Real array of dimension NEV+1.  (OUTPUT)
-c          On exit, DI contains the imaginary part of the Ritz value 
+c          On exit, DI contains the imaginary part of the Ritz value
 c          approximations to the eigenvalues of A*z = lambda*B*z associated
-c          with DR. 
+c          with DR.
 c
-c          NOTE: When Ritz values are complex, they will come in complex 
-c                conjugate pairs.  If eigenvectors are requested, the 
-c                corresponding Ritz vectors will also come in conjugate 
-c                pairs and the real and imaginary parts of these are 
-c                represented in two consecutive columns of the array Z 
+c          NOTE: When Ritz values are complex, they will come in complex
+c                conjugate pairs.  If eigenvectors are requested, the
+c                corresponding Ritz vectors will also come in conjugate
+c                pairs and the real and imaginary parts of these are
+c                represented in two consecutive columns of the array Z
 c                (see below).
 c
 c  Z       Real N by NEV+1 array if RVEC = .TRUE. and HOWMNY = 'A'. (OUTPUT)
@@ -124,24 +124,24 @@ c          the array Z may be set equal to first NEV+1 columns of the Arnoldi
 c          basis array V computed by SNAUPD.  In this case the Arnoldi basis
 c          will be destroyed and overwritten with the eigenvector basis.
 c
-c  LDZ     Integer.  (INPUT) 
-c          The leading dimension of the array Z.  If Ritz vectors are 
-c          desired, then  LDZ >= max( 1, N ).  In any case,  LDZ >= 1.  
-c 
-c  SIGMAR  Real  (INPUT) 
-c          If IPARAM(7) = 3 or 4, represents the real part of the shift. 
-c          Not referenced if IPARAM(7) = 1 or 2.  
-c 
-c  SIGMAI  Real  (INPUT) 
-c          If IPARAM(7) = 3 or 4, represents the imaginary part of the 
-c          shift. 
-c          Not referenced if IPARAM(7) = 1 or 2.  
-c 
-c  WORKEV  Real work array of dimension 3*NCV.  (WORKSPACE) 
-c 
-c  N       Integer.  (INPUT) 
-c          Dimension of the eigenproblem.  
-c 
+c  LDZ     Integer.  (INPUT)
+c          The leading dimension of the array Z.  If Ritz vectors are
+c          desired, then  LDZ >= max( 1, N ).  In any case,  LDZ >= 1.
+c
+c  SIGMAR  Real  (INPUT)
+c          If IPARAM(7) = 3 or 4, represents the real part of the shift.
+c          Not referenced if IPARAM(7) = 1 or 2.
+c
+c  SIGMAI  Real  (INPUT)
+c          If IPARAM(7) = 3 or 4, represents the imaginary part of the
+c          shift.
+c          Not referenced if IPARAM(7) = 1 or 2.
+c
+c  WORKEV  Real work array of dimension 3*NCV.  (WORKSPACE)
+c
+c  N       Integer.  (INPUT)
+c          Dimension of the eigenproblem.
+c
 c  AB      Real array of dimension LDA by N. (INPUT)
 c          The matrix A in band storage, in rows KL+1 to
 c          2*KL+KU+1; rows 1 to KL of the array need not be set.
@@ -151,25 +151,25 @@ c          AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
 c
 c  MB      Real array of dimension LDA by N. (INPUT)
 c          The matrix M in band storage, in rows KL+1 to
-c          2*KL+KU+1; rows 1 to KL of the array need not be set. 
+c          2*KL+KU+1; rows 1 to KL of the array need not be set.
 c          The j-th column of M is stored in the j-th column of the
 c          array AB as follows:
 c          MB(kl+ku+1+i-j,j) = M(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
 c          Not referenced if IPARAM(7) = 1
 c
 c  LDA     Integer. (INPUT)
-c          Leading dimension of AB, MB, RFAC and CFAC. 
+c          Leading dimension of AB, MB, RFAC and CFAC.
 c
 c  RFAC    Real array of LDA by N. (WORKSPACE/OUTPUT)
-c          RFAC is used to store the LU factors of MB when IPARAM(7) = 2 
+c          RFAC is used to store the LU factors of MB when IPARAM(7) = 2
 c          is invoked.  It is used to store the LU factors of
 c          (A-sigma*M) when IPARAM(7) = 3 is invoked with a real shift.
 c          It is not referenced when IPARAM(7) = 1 or 4.
 c
 c  CFAC    Complex array of LDA by N. (WORKSPACE/OUTPUT)
 c          CFAC is used to store (A-SIGMA*M) and its LU factors
-c          when IPARAM(7) = 3 or 4 are used with a complex shift SIGMA.  
-c          On exit, it contains the LU factors of (A-SIGMA*M).  
+c          when IPARAM(7) = 3 or 4 are used with a complex shift SIGMA.
+c          On exit, it contains the LU factors of (A-SIGMA*M).
 c          It is not referenced when IPARAM(7) = 1 or 2.
 c
 c  KL      Integer. (INPUT)
@@ -181,7 +181,7 @@ c
 c  WHICH   Character*2.  (INPUT)
 c          When IPARAM(7)= 1 or 2,  WHICH can be set to any one of
 c          the following.
-c  
+c
 c            'LM' -> want the NEV eigenvalues of largest magnitude.
 c            'SM' -> want the NEV eigenvalues of smallest magnitude.
 c            'LR' -> want the NEV eigenvalues of largest real part.
@@ -189,8 +189,8 @@ c            'SR' -> want the NEV eigenvalues of smallest real part.
 c            'LI' -> want the NEV eigenvalues of largest imaginary part.
 c            'SI' -> want the NEV eigenvalues of smallest imaginary part.
 c
-c          When IPARAM(7) = 3 or 4, WHICH should be set to 'LM' only. 
-c          
+c          When IPARAM(7) = 3 or 4, WHICH should be set to 'LM' only.
+c
 c  BMAT    Character*1.  (INPUT)
 c          BMAT specifies the type of the matrix B that defines the
 c          semi-inner product for the operator OP.
@@ -199,9 +199,9 @@ c          BMAT = 'G' -> generalized eigenvalue problem A*z = lambda*M*z
 
 c  NEV     Integer. (INPUT)
 c          Number of eigenvalues to be computed.
-c   
+c
 c  TOL     Real scalar.  (INPUT)
-c          Stopping criteria: the relative accuracy of the Ritz value 
+c          Stopping criteria: the relative accuracy of the Ritz value
 c          is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)).
 c          If TOL .LE. 0. is passed a default is set:
 c          DEFAULT = SLAMCH('EPS')  (machine precision as computed
@@ -221,12 +221,12 @@ c          Represents the dimension of the Arnoldi basis constructed
 c          by snaupd for OP.
 c
 c  V       Real array N by NCV+1.  (OUTPUT)
-c          Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns 
-c                       represent approximate Schur vectors that span the 
+c          Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns
+c                       represent approximate Schur vectors that span the
 c                       desired invariant subspace.
-c          NOTE: The array Z may be set equal to first NEV+1 columns of the 
+c          NOTE: The array Z may be set equal to first NEV+1 columns of the
 c          Arnoldi basis vector array V computed by SNAUPD. In this case
-c          if RVEC = .TRUE. and HOWMNY='A', then the first NCONV=IPARAM(5) 
+c          if RVEC = .TRUE. and HOWMNY='A', then the first NCONV=IPARAM(5)
 c          are the desired Ritz vectors.
 c
 c  LDV     Integer.  (INPUT)
@@ -234,7 +234,7 @@ c          Leading dimension of V exactly as declared in the calling
 c          program.
 c
 c  IPARAM  Integer array of length 11.  (INPUT/OUTPUT)
-c          IPARAM(1) = ISHIFT: 
+c          IPARAM(1) = ISHIFT:
 c          The shifts selected at each iteration are used to restart
 c          the Arnoldi iteration in an implicit fashion.
 c          It is set to 1 in this subroutine.  The user do not need
@@ -248,7 +248,7 @@ c                      combination of Ritz vectors associated with the
 c                      "wanted" eigenvalues.
 c          -------------------------------------------------------------
 c
-c          IPARAM(2) = No longer referenced. 
+c          IPARAM(2) = No longer referenced.
 c
 c          IPARAM(3) = MXITER
 c          On INPUT:  max number of Arnoldi update iterations allowed.
@@ -262,9 +262,9 @@ c
 c          IPARAM(6) = IUPD
 c          Not referenced. Implicit restarting is ALWAYS used.
 c
-c          IPARAM(7) = IPARAM(7): 
+c          IPARAM(7) = IPARAM(7):
 c          On INPUT determines what type of eigenproblem is being solved.
-c          Must be 1,2,3,4; See under \Description of snband for the 
+c          Must be 1,2,3,4; See under \Description of snband for the
 c          four modes available.
 c
 c          IPARAM(9) = NUMOP, IPARAM(10) = NUMOPB, IPARAM(11) = NUMREO,
@@ -280,22 +280,22 @@ c LWORKL   Integer.  (INPUT)
 c          LWORKL must be at least 3*NCV**2 + 6*NCV.
 c
 c WORKC    Complex array of length N. (WORKSPACE)
-c          Workspace used when IPARAM(7) = 3 or 4 for storing a temporary 
+c          Workspace used when IPARAM(7) = 3 or 4 for storing a temporary
 c          complex vector.
 c
 c IWORK    Integer array of dimension at least N. (WORKSPACE)
-c          Used when IPARAM(7)=2,3,4 to store the pivot information in the 
+c          Used when IPARAM(7)=2,3,4 to store the pivot information in the
 c          factorization of M or (A-SIGMA*M).
-c            
+c
 c INFO     Integer.  (INPUT/OUTPUT)
 c          Error flag on output.
 c          =  0: Normal exit.
 c          =  1: The Schur form computed by LAPACK routine slahqr
 c                could not be reordered by LAPACK routine strsen.
-c                Re-enter subroutine SNEUPD with IPARAM(5)=NCV and 
-c                increase the size of the arrays DR and DI to have 
-c                dimension at least NCV and allocate at least NCV 
-c                columns for Z. NOTE: Not necessary if Z and V share 
+c                Re-enter subroutine SNEUPD with IPARAM(5)=NCV and
+c                increase the size of the arrays DR and DI to have
+c                dimension at least NCV and allocate at least NCV
+c                columns for Z. NOTE: Not necessary if Z and V share
 c                the same space. Please notify the authors.
 c
 c          = -1: N must be positive.
@@ -314,9 +314,9 @@ c          = -12: HOWMNY = 'S' not yet implemented
 c          = -13: HOWMNY must be one of 'A' or 'P'
 c          = -14: SNAUPD did not find any eigenvalues to sufficient
 c                 accuracy.
-c          = -15: Overflow occurs when we try to transform the Ritz 
+c          = -15: Overflow occurs when we try to transform the Ritz
 c                 values returned from SNAUPD to those of the original
-c                 problem using Rayleigh Quotient. 
+c                 problem using Rayleigh Quotient.
 c          = -9999: Could not build an Arnoldi factorization.
 c                   IPARAM(5) returns the size of the current
 c                   Arnoldi factorization.
@@ -332,7 +332,7 @@ c  1. D.C. Sorensen, "Implicit Application of Polynomial Filters in
 c     a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992),
 c     pp 357-385.
 c
-c  2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly 
+c  2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly
 c     Restarted Arnoldi Iteration", Ph.D thesis, TR95-13, Rice Univ,
 c     May 1995.
 c
@@ -363,9 +363,9 @@ c     Ritz vectors. Thus, their numerical properties are often superior.
 c     If RVEC = .TRUE. then the relationship
 c             A * V(:,1:IPARAM(5)) = V(:,1:IPARAM(5)) * T, and
 c     V(:,1:IPARAM(5))' * V(:,1:IPARAM(5)) = I are approximately satisfied.
-c     Here T is the leading submatrix of order IPARAM(5) of the real 
+c     Here T is the leading submatrix of order IPARAM(5) of the real
 c     upper quasi-triangular matrix stored workl(ipntr(12)). That is,
-c     T is block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; 
+c     T is block upper triangular with 1-by-1 and 2-by-2 diagonal blocks;
 c     each 2-by-2 diagonal block has its diagonal elements equal and its
 c     off-diagonal elements of opposite sign.  Corresponding to each 2-by-2
 c     diagonal block is a complex conjugate pair of Ritz values. The real
@@ -387,20 +387,20 @@ c\EndLib
 c
 c---------------------------------------------------------------------
 c
-      subroutine snband( rvec, howmny, select, dr, di, z, ldz,  sigmar, 
-     &           sigmai, workev, n, ab, mb, lda, rfac,  cfac, kl, ku, 
-     &           which, bmat, nev, tol, resid,  ncv, v, ldv, 
+      subroutine snband( rvec, howmny, select, dr, di, z, ldz,  sigmar,
+     &           sigmai, workev, n, ab, mb, lda, rfac,  cfac, kl, ku,
+     &           which, bmat, nev, tol, resid,  ncv, v, ldv,
      &           iparam, workd, workl, lworkl, workc, iwork, info)
 c
 c     %------------------%
 c     | Scalar Arguments |
 c     %------------------%
-c 
+c
       character        which*2, bmat, howmny
       integer          n, lda, kl, ku, nev, ncv, ldv,
-     &                 ldz, lworkl, info  
+     &                 ldz, lworkl, info
       Real
-     &                 tol, sigmar, sigmai 
+     &                 tol, sigmar, sigmai
 c
 c     %-----------------%
 c     | Array Arguments |
@@ -410,7 +410,7 @@ c
       logical          select(*)
       Real
      &                 dr(*), di(*), resid(*), v(ldv,*), z(ldz,*),
-     &                 ab(lda,*), mb(lda,*), rfac(lda,*), 
+     &                 ab(lda,*), mb(lda,*), rfac(lda,*),
      &                 workd(*), workl(*), workev(*)
       Complex
      &                 cfac(lda,*), workc(*)
@@ -426,9 +426,9 @@ c     | Local Scalars |
 c     %---------------%
 c
       integer          ido, i, j, type, imid, itop, ibot, ierr
-      Real        
-     &                 numr, denr, deni, dmdul, safmin 
-      logical          rvec, first 
+      Real
+     &                 numr, denr, deni, dmdul, safmin
+      logical          rvec, first
 c
 c     %------------%
 c     | Parameters |
@@ -445,7 +445,7 @@ c     %-----------------------------%
 c
       Real
      &                 sdot, snrm2, slapy2, slamch
-      external         sdot, scopy, sgbmv, cgbtrf, cgbtrs, sgbtrf, 
+      external         sdot, scopy, sgbmv, cgbtrf, cgbtrs, sgbtrf,
      &                 sgbtrs, snrm2, slapy2, slacpy, slamch
 c
 c     %---------------------%
@@ -464,17 +464,17 @@ c     | that 1/sfmin does not overflow |
 c     %--------------------------------%
 c
       safmin = slamch('safmin')
-c     
+c
 c     %----------------------------------------------------------------%
 c     | Set type of the problem to be solved. Check consistency        |
 c     | between BMAT and IPARAM(7).                                    |
 c     | type = 1 --> Solving standard problem in regular mode.         |
-c     | type = 2 --> Solving standard problem in shift-invert mode.    | 
+c     | type = 2 --> Solving standard problem in shift-invert mode.    |
 c     | type = 3 --> Solving generalized problem in regular mode.      |
 c     | type = 4 --> Solving generalized problem in shift-invert mode. |
 c     | type = 5 --> Solving standard problem in shift-invert mode     |
 c     |              using iparam(7) = 4 in SNAUPD.                    |
-c     | type = 6 --> Solving generalized problem in shift-invert mode. | 
+c     | type = 6 --> Solving generalized problem in shift-invert mode. |
 c     |              using iparam(7) = 4 in SNAUPD.                    |
 c     %----------------------------------------------------------------%
 c
@@ -485,19 +485,19 @@ c
       else if ( iparam(7) .eq. 2 ) then
          type = 3
       else if ( iparam(7) .eq. 3 .and. bmat .eq. 'G') then
-         type = 4 
+         type = 4
       else if ( iparam(7) .eq. 4 .and. bmat .eq. 'I') then
          type = 5
-      else if ( iparam(7) .eq. 4 .and. bmat .eq. 'G') then 
+      else if ( iparam(7) .eq. 4 .and. bmat .eq. 'G') then
          type = 6
       else
          print*, ' '
          print*, 'BMAT is inconsistent with IPARAM(7).'
-         print*, ' ' 
+         print*, ' '
          go to 9000
       end if
 c
-c     %----------------------------------%       
+c     %----------------------------------%
 c     | When type = 5,6 are used, sigmai |
 c     | must be nonzero.                 |
 c     %----------------------------------%
@@ -505,16 +505,16 @@ c
       if ( type .eq. 5 .or. type .eq. 6 ) then
           if ( sigmai .eq. zero ) then
              print*, ' '
-             print*, '_NBAND: sigmai must be nonzero when type 5 or 6 
+             print*, '_NBAND: sigmai must be nonzero when type 5 or 6
      &                is used. '
              print*, ' '
              go to 9000
-          end if    
+          end if
       end if
 c
 c     %------------------------%
 c     | Initialize the reverse |
-c     | communication flag.    |         
+c     | communication flag.    |
 c     %------------------------%
 c
       ido   = 0
@@ -546,7 +546,7 @@ c         | Factor (A-sigma*I).           |
 c         %-------------------------------%
 c
           if (sigmai .eq. zero) then
-c            
+c
 c            %-----------------------------------%
 c            | Construct (A-sigmar*I) and factor |
 c            | in real arithmetic.               |
@@ -558,7 +558,7 @@ c
   10         continue
              call sgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr )
              if (ierr .ne. 0) then
-                print*, ' ' 
+                print*, ' '
                 print*, ' _NBAND: Error with _gbtrf. '
                 print*, ' '
                 go to  9000
@@ -574,24 +574,24 @@ c
              do 30 j = 1, n
                 do 20 i = itop, ibot
                    cfac(i,j) = cmplx(ab(i,j))
-  20            continue 
+  20            continue
   30         continue
 c
              do 40 j = 1, n
-                cfac(imid,j) = cfac(imid,j) 
+                cfac(imid,j) = cfac(imid,j)
      $                         - cmplx(sigmar, sigmai)
-  40         continue 
-c 
-             call cgbtrf(n, n, kl, ku, cfac, lda, iwork, ierr ) 
+  40         continue
+c
+             call cgbtrf(n, n, kl, ku, cfac, lda, iwork, ierr )
              if ( ierr .ne. 0) then
                 print*, ' '
                 print*, ' _NBAND: Error with _gbtrf. '
                 print*, ' '
                 go to  9000
              end if
-c        
+c
           end if
-      
+
       else if ( type .eq. 3 ) then
 c
 c        %-----------------------------------------------%
@@ -603,7 +603,7 @@ c
          call slacpy ('A', ibot, n, mb, lda, rfac, lda )
          call sgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr)
          if (ierr .ne. 0) then
-             print*, ' ' 
+             print*, ' '
              print*,'_NBAND:  Error with _gbtrf.'
              print*, ' '
              go to 9000
@@ -615,7 +615,7 @@ c        %-------------------------------------------%
 c        | Solving generalized eigenvalue problem in |
 c        | shift-invert mode.                        |
 c        %-------------------------------------------%
-c 
+c
          if ( sigmai .eq. zero ) then
 c
 c            %--------------------------------------------%
@@ -624,7 +624,7 @@ c            | arithmetic.                                |
 c            %--------------------------------------------%
 c
              do 60 j = 1,n
-                do 50 i = itop, ibot 
+                do 50 i = itop, ibot
                    rfac(i,j) = ab(i,j) - sigmar*mb(i,j)
   50            continue
   60         continue
@@ -642,13 +642,13 @@ c
 c            %-----------------------------------------------%
 c            | Construct (A - sigma*M) and factor in complex |
 c            | arithmetic.                                   |
-c            %-----------------------------------------------% 
+c            %-----------------------------------------------%
 c
              do 80 j = 1,n
-                do 70 i = itop, ibot 
-                   cfac(i,j) = cmplx( ab(i,j)-sigmar*mb(i,j), 
+                do 70 i = itop, ibot
+                   cfac(i,j) = cmplx( ab(i,j)-sigmar*mb(i,j),
      &                         -sigmai*mb(i,j) )
-  70            continue 
+  70            continue
   80         continue
 c
              call cgbtrf(n, n, kl, ku, cfac, lda, iwork, ierr)
@@ -658,7 +658,7 @@ c
                 print*, ' '
                 go to 9000
              end if
-c 
+c
          end if
 c
       end if
@@ -667,7 +667,7 @@ c     %--------------------------------------------%
 c     |  M A I N   L O O P (reverse communication) |
 c     %--------------------------------------------%
 c
-  90  continue 
+  90  continue
 c
       call snaupd ( ido, bmat, n, which, nev, tol, resid, ncv,
      &              v, ldv, iparam, ipntr, workd, workl, lworkl,
@@ -681,8 +681,8 @@ c           %----------------------------%
 c           | Perform  y <--- OP*x = A*x |
 c           %----------------------------%
 c
-            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
          else if ( type .eq. 2 ) then
@@ -690,7 +690,7 @@ c
             if (sigmai .eq. zero) then
 c
 c              %----------------------------------%
-c              | Shift is real.  Perform          | 
+c              | Shift is real.  Perform          |
 c              | y <--- OP*x = inv[A-sigmar*I]*x  |
 c              | to force the starting vector     |
 c              | into the range of OP.            |
@@ -700,7 +700,7 @@ c
                call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                       iwork, workd(ipntr(2)), n, ierr)
                if ( ierr .ne. 0 ) then
-                  print*, ' ' 
+                  print*, ' '
                   print*, ' _NBAND: Error with _bgtrs. '
                   print*, ' '
                   go to 9000
@@ -711,8 +711,8 @@ c
 c              %--------------------------------------------%
 c              | Shift is COMPLEX. Perform                  |
 c              | y <--- OP*x = Real_Part{inv[A-sigma*I]*x}  |
-c              | to force the starting vector into the      | 
-c              | range of OP.                               | 
+c              | to force the starting vector into the      |
+c              | range of OP.                               |
 c              %--------------------------------------------%
 c
                do 100 j = 1, n
@@ -732,21 +732,21 @@ c
                   workd(ipntr(2)+j-1) = real(workc(j))
   110          continue
 c
-            end if 
-c 
+            end if
+c
          else if ( type .eq. 3 ) then
 c
 c           %-----------------------------------%
 c           | Perform  y <--- OP*x = inv[M]*A*x |
-c           | to force the starting vector into | 
+c           | to force the starting vector into |
 c           | the range of OP.                  |
 c           %-----------------------------------%
 c
-            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                  lda, workd(ipntr(1)), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                  lda, workd(ipntr(1)), 1, zero,
      &                  workd(ipntr(2)), 1)
 c
-            call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                    iwork, workd(ipntr(2)), n, ierr)
             if (ierr .ne. 0) then
                print*, ' '
@@ -759,13 +759,13 @@ c
 c
 c           %-----------------------------------------%
 c           | Perform y <-- OP*x                      |
-c           |         = Real_part{inv[A-SIGMA*M]*M}*x | 
+c           |         = Real_part{inv[A-SIGMA*M]*M}*x |
 c           | to force the starting vector into the   |
 c           | range of OP.                            |
 c           %-----------------------------------------%
 c
-            call sgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
             if ( sigmai .eq. zero ) then
@@ -773,14 +773,14 @@ c
 c              %---------------------%
 c              | Shift is real, stay |
 c              | in real arithmetic. |
-c              %---------------------%            
+c              %---------------------%
 c
-               call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+               call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                      iwork, workd(ipntr(2)), n, ierr)
                if (ierr .ne. 0) then
-                  print*, ' ' 
+                  print*, ' '
                   print*, '_NBAND: Error with _gbtrs.'
-                  print*, ' ' 
+                  print*, ' '
                   go to 9000
                end if
 c
@@ -792,26 +792,26 @@ c              %--------------------------%
 c
                do 120 i = 1,n
                   workc(i) = cmplx(workd(ipntr(2)+i-1))
-  120           continue 
+  120           continue
 c
-               call cgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, 
+               call cgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda,
      &                      iwork, workc, n, ierr)
-               if (ierr .ne. 0) then 
+               if (ierr .ne. 0) then
                   print*, ' '
-                  print*, '_NBAND: Error with _gbtrs.' 
+                  print*, '_NBAND: Error with _gbtrs.'
                   print*, ' '
                   go to 9000
                end if
 c
                do  130 i = 1, n
                   workd(ipntr(2)+i-1) = real(workc(i))
-  130          continue 
+  130          continue
 c
             end if
 c
          else if ( type .eq. 5) then
 c
-c           %---------------------------------------% 
+c           %---------------------------------------%
 c           | Perform y <-- OP*x                    |
 c           |    = Imaginary_part{inv[A-SIGMA*I]}*x |
 c           | to force the starting vector into the |
@@ -839,32 +839,32 @@ c
 c
 c           %----------------------------------------%
 c           | Perform y <-- OP*x                     |
-c           |       Imaginary_part{inv[A-SIGMA*M]*M} | 
+c           |       Imaginary_part{inv[A-SIGMA*M]*M} |
 c           | to force the starting vector into the  |
 c           | range of OP.                           |
 c           %----------------------------------------%
 c
-            call sgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
             do 160 i = 1,n
                workc(i) = cmplx(workd(ipntr(2)+i-1))
-  160       continue 
+  160       continue
 c
-            call cgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, 
+            call cgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda,
      &                   iwork, workc, n, ierr)
-            if (ierr .ne. 0) then 
+            if (ierr .ne. 0) then
                print*, ' '
-               print*, '_NBAND: Error with _gbtrs.' 
+               print*, '_NBAND: Error with _gbtrs.'
                print*, ' '
                go to 9000
             end if
 c
             do  170 i = 1, n
                workd(ipntr(2)+i-1) = aimag(workc(i))
-  170       continue 
-c 
+  170       continue
+c
          end if
 c
       else if (ido .eq. 1) then
@@ -875,8 +875,8 @@ c           %----------------------------%
 c           | Perform  y <--- OP*x = A*x |
 c           %----------------------------%
 c
-            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
          else if ( type .eq. 2) then
@@ -907,7 +907,7 @@ c
      &                       iwork, workc, n, ierr)
                if ( ierr .ne. 0 ) then
                   print*, ' '
-                  print*, '_NBAND: Error with _gbtrs.' 
+                  print*, '_NBAND: Error with _gbtrs.'
                   print*, ' '
                   go to 9000
                end if
@@ -924,16 +924,16 @@ c           %-----------------------------------%
 c           | Perform  y <--- OP*x = inv[M]*A*x |
 c           %-----------------------------------%
 c
-            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                  lda, workd(ipntr(1)), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                  lda, workd(ipntr(1)), 1, zero,
      &                  workd(ipntr(2)), 1)
 c
-            call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                    iwork, workd(ipntr(2)), n, ierr)
             if (ierr .ne. 0) then
                print*, ' '
                print*, '_NBAND: Error with _bgtrs.'
-               print*, ' ' 
+               print*, ' '
                go to 9000
             end if
 c
@@ -942,7 +942,7 @@ c
 c           %--------------------------------------%
 c           | Perform  y <-- inv(A-sigma*M)*(M*x). |
 c           | (M*x) has been computed and stored   |
-c           | in workd(ipntr(3)).                  |           
+c           | in workd(ipntr(3)).                  |
 c           %--------------------------------------%
 c
             if ( sigmai .eq. zero ) then
@@ -953,16 +953,16 @@ c              | real arithmetic.       |
 c              %------------------------%
 c
                call scopy(n, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-               call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+               call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                       iwork, workd(ipntr(2)), n, ierr)
-               if (ierr .ne. 0) then 
+               if (ierr .ne. 0) then
                   print*, ' '
-                  print*, '_NBAND: Error with _gbtrs.' 
+                  print*, '_NBAND: Error with _gbtrs.'
                   print*, ' '
                   go to 9000
                end if
-c 
-            else 
+c
+            else
 c
 c              %---------------------------%
 c              | Go to COMPLEX arithmetic. |
@@ -970,26 +970,26 @@ c              %---------------------------%
 c
                do 200 i = 1,n
                   workc(i) = cmplx(workd(ipntr(3)+i-1))
-  200          continue 
+  200          continue
 c
-               call cgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, 
+               call cgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda,
      &                       iwork, workc, n, ierr)
-               if (ierr .ne. 0) then 
+               if (ierr .ne. 0) then
+                  print*, ' '
+                  print*, '_NBAND: Error in _gbtrs.'
                   print*, ' '
-                  print*, '_NBAND: Error in _gbtrs.' 
-                  print*, ' ' 
                   go to 9000
                end if
 c
                do 210 i = 1,n
                   workd(ipntr(2)+i-1) = real(workc(i))
-  210          continue 
+  210          continue
 c
             end if
 c
          else if ( type .eq. 5 ) then
 c
-c           %---------------------------------------% 
+c           %---------------------------------------%
 c           | Perform y <-- OP*x                    |
 c           |    = Imaginary_part{inv[A-SIGMA*I]*x} |
 c           %---------------------------------------%
@@ -1015,25 +1015,25 @@ c
 c
 c           %-----------------------------------------%
 c           | Perform y <-- OP*x                      |
-c           |   = Imaginary_part{inv[A-SIGMA*M]*M}*x. | 
+c           |   = Imaginary_part{inv[A-SIGMA*M]*M}*x. |
 c           %-----------------------------------------%
 c
             do 240 i = 1,n
                workc(i) = cmplx(workd(ipntr(3)+i-1))
-  240       continue 
+  240       continue
 c
-            call cgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, 
+            call cgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda,
      &                   iwork, workc, n, ierr)
-            if (ierr .ne. 0) then 
+            if (ierr .ne. 0) then
                print*, ' '
-               print*, '_NBAND: Error with _gbtrs.' 
+               print*, '_NBAND: Error with _gbtrs.'
                print*, ' '
                go to 9000
             end if
 c
             do  250 i = 1, n
                workd(ipntr(2)+i-1) = aimag(workc(i))
-  250       continue 
+  250       continue
 c
          end if
 c
@@ -1045,14 +1045,14 @@ c        | Not used when      |
 c        | type = 1,2.        |
 c        %--------------------%
 c
-          call sgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), 
-     &                lda, workd(ipntr(1)), 1, zero, 
+          call sgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1),
+     &                lda, workd(ipntr(1)), 1, zero,
      &                workd(ipntr(2)), 1)
 c
-      else 
+      else
 c
 c        %-----------------------------------------%
-c        | Either we have convergence, or there is | 
+c        | Either we have convergence, or there is |
 c        | error.                                  |
 c        %-----------------------------------------%
 c
@@ -1069,7 +1069,7 @@ c
             print *, ' '
             go to 9000
 c
-         else 
+         else
 c
             if ( info .eq. 1) then
                print *, ' '
@@ -1084,29 +1084,29 @@ c
 c
             if (iparam(5) .gt. 0) then
 c
-               call sneupd ( rvec, 'A', select, dr, di, z, ldz, 
-     &                 sigmar, sigmai, workev, bmat, n, which, 
+               call sneupd ( rvec, 'A', select, dr, di, z, ldz,
+     &                 sigmar, sigmai, workev, bmat, n, which,
      &                 nev, tol, resid, ncv, v, ldv, iparam,
-     &                 ipntr, workd, workl, lworkl, info )            
+     &                 ipntr, workd, workl, lworkl, info )
 c
                if ( info .ne. 0) then
-c 
+c
 c                 %------------------------------------%
 c                 | Check the documentation of SNEUPD. |
 c                 %------------------------------------%
 c
-                  print *, ' ' 
+                  print *, ' '
                   print *, ' Error with _neupd = ', info
                   print *, ' Check the documentation of _neupd '
-                  print *, ' ' 
+                  print *, ' '
                   go to 9000
 c
-               else if ( sigmai .ne. zero ) then 
-c 
+               else if ( sigmai .ne. zero ) then
+c
                   if ( type .eq. 4 .or. type .eq. 6 ) then
-c 
+c
                      first = .true.
-                     do 270 j = 1, iparam(5) 
+                     do 270 j = 1, iparam(5)
 c
 c                    %----------------------------------%
 c                    | Use Rayleigh Quotient to recover |
@@ -1118,16 +1118,16 @@ c
 c
 c                       %--------------------------------------%
 c                       | Eigenvalue is real. Compute          |
-c                       | d = (x'*inv[A-sigma*M]*M*x) / (x'*x) | 
+c                       | d = (x'*inv[A-sigma*M]*M*x) / (x'*x) |
 c                       %--------------------------------------%
 c
-                        call sgbmv('Nontranspose', n, n, kl, ku, one, 
+                        call sgbmv('Nontranspose', n, n, kl, ku, one,
      $                     mb(itop,1), lda, z(1,j), 1, zero,
      $                     workd, 1)
                         do i = 1, n
                            workc(i) = cmplx(workd(i))
                         end do
-                        call cgbtrs ('Notranspose', n, kl, ku, 1, 
+                        call cgbtrs ('Notranspose', n, kl, ku, 1,
      $                        cfac, lda, iwork, workc, n, info)
                         do i = 1, n
                            workd(i) = real(workc(i))
@@ -1151,7 +1151,7 @@ c
                            go to 9000
                         end if
 c
-                     else if (first) then 
+                     else if (first) then
 c
 c                       %------------------------%
 c                       | Eigenvalue is complex. |
@@ -1166,7 +1166,7 @@ c
                         call sgbmv('Nontranspose', n, n, kl, ku,
      $                      one, mb(itop,1), lda, z(1,j), 1, zero,
      $                      workd, 1)
-                        call sgbmv('Nontranspose', n, n, kl, ku, 
+                        call sgbmv('Nontranspose', n, n, kl, ku,
      $                       one, mb(itop,1), lda, z(1,j+1), 1,
      $                       zero, workd(n+1), 1)
                         do i = 1, n
@@ -1177,7 +1177,7 @@ c                       %----------------------------%
 c                       | Compute inv(A-sigma*M)*M*x |
 c                       %----------------------------%
 c
-                        call cgbtrs('Notranspose',n,kl,ku,1,cfac, 
+                        call cgbtrs('Notranspose',n,kl,ku,1,cfac,
      $                     lda, iwork, workc, n, info)
 c
 c                       %-------------------------------%
@@ -1197,7 +1197,7 @@ c                       %----------------%
 c                       | Compute (x'*x) |
 c                       %----------------%
 c
-                        numr = slapy2( snrm2(n, z(1,j), 1), 
+                        numr = slapy2( snrm2(n, z(1,j), 1),
      &                         snrm2(n, z(1, j+1), 1) )**2
 c
 c                       %----------------------------------------%
@@ -1237,7 +1237,7 @@ c
 c
                      end if
 c
-  270                continue 
+  270                continue
 c
                   else if ( type .eq. 2 .or. type .eq. 5) then
 c
@@ -1260,7 +1260,7 @@ c
                         do i = 1, n
                            workc(i) = cmplx(z(i,j))
                         end do
-                        call cgbtrs ('Notranspose', n, kl, ku, 1, 
+                        call cgbtrs ('Notranspose', n, kl, ku, 1,
      $                        cfac, lda, iwork, workc, n, info)
                         do i = 1, n
                            workd(i) = real(workc(i))
@@ -1329,7 +1329,7 @@ c                       | Compute (x'x) / (x'*inv(A-sigma*I)*x). |
 c                       %----------------------------------------%
 c
                         dmdul = slapy2(denr,deni)**2
-                        if (dmdul .ge. safmin) then  
+                        if (dmdul .ge. safmin) then
                            dr(j) = sigmar+numr*denr / dmdul
                            di(j) = sigmai-numr*deni / dmdul
                            first = .false.
@@ -1378,7 +1378,7 @@ c     %----------------------------------------%
 c     | L O O P  B A C K to call SNAUPD again. |
 c     %----------------------------------------%
 c
-      go to 90 
+      go to 90
 c
  9000 continue
 c

EXAMPLES/BAND/snbdr1.f

@@ -49,13 +49,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -64,12 +64,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Real 
+      Real
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn),
      &                 workev(3*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv, 3), ax(maxn)
-      Complex  
+      Complex
      &                 cfac(lda, maxn), workc(maxn)
 c
 c     %---------------%
@@ -81,25 +81,25 @@ c
      &                 n, nx, lo, isub, isup, idiag, mode, maxitr,
      &                 nconv
       logical          rvec, first
-      Real  
+      Real
      &                 tol, rho, h, h2, sigmar, sigmai
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Real  
+      Real
      &                 one, zero, two
-      parameter        (one = 1.0E+0 , zero = 0.0E+0 , 
+      parameter        (one = 1.0E+0 , zero = 0.0E+0 ,
      &                  two = 2.0E+0 )
 c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  slapy2, snrm2
-      external          slapy2, snrm2, sgbmv, saxpy 
+      external          slapy2, snrm2, sgbmv, saxpy
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -115,7 +115,7 @@ c     %-------------------------------------------------%
 c     | The number NX is the number of interior points  |
 c     | in the discretization of the 2-dimensional      |
 c     | convection-diffusion operator on the unit       |
-c     | square with zero Dirichlet boundary condition.  | 
+c     | square with zero Dirichlet boundary condition.  |
 c     | The number N(=NX*NX) is the dimension of the    |
 c     | matrix.  A standard eigenvalue problem is       |
 c     | solved (BMAT = 'I').  NEV is the number of      |
@@ -126,13 +126,13 @@ c     | spectrum.  However, The following conditions    |
 c     | must be satisfied:                              |
 c     |                   N <= MAXN                     |
 c     |                 NEV <= MAXNEV                   |
-c     |           NEV + 2 <= NCV <= MAXNCV              | 
-c     %-------------------------------------------------% 
+c     |           NEV + 2 <= NCV <= MAXNCV              |
+c     %-------------------------------------------------%
 c
-      nx  = 10 
+      nx  = 10
       n    = nx*nx
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR1: N is greater than MAXN '
          go to 9000
@@ -158,7 +158,7 @@ c     | generated in SNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+6*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -173,7 +173,7 @@ c
       maxitr = 300
       mode   = 1
 c
-      iparam(3) = maxitr 
+      iparam(3) = maxitr
       iparam(7) = mode
 c
 c     %----------------------------------------%
@@ -195,10 +195,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = nx 
-      ku   = nx 
+      kl   = nx
+      ku   = nx
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -208,13 +208,13 @@ c
       idiag = kl+ku+1
       do 30 j = 1, n
          a(idiag,j) = 4.0E+0  / h2
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
-      rho = 1.0E+2  
+c
+      rho = 1.0E+2
       isup = kl+ku
       isub = kl+ku+2
       do 50 i = 1, nx
@@ -222,8 +222,8 @@ c
         do 40 j = lo+1, lo+nx-1
            a(isup,j+1) = -one/h2 + rho/two/h
            a(isub,j) = -one/h2 - rho/two/h
-  40    continue      
-  50  continue 
+  40    continue
+  50  continue
 c
 c     %------------------------------------%
 c     | KL-th subdiagonal and KU-th super- |
@@ -237,8 +237,8 @@ c
          do 70 j = lo+1, lo+nx
             a(isup,nx+j)  = -one / h2
             a(isub,j) = -one / h2
- 70      continue 
- 80   continue 
+ 70      continue
+ 80   continue
 c
 c     %------------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues  |
@@ -247,12 +247,12 @@ c     | eigenvalues are returned in the first column   |
 c     | of D, the imaginary parts are returned in the  |
 c     | second column of D.  Eigenvectors are returned |
 c     | in the first NCONV (=IPARAM(5)) columns of V.  |
-c     %------------------------------------------------% 
+c     %------------------------------------------------%
 c
-      rvec = .true. 
-      call snband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar, sigmai, 
-     &           workev, n, a, m, lda, rfac, cfac, kl, ku, which, 
-     &           bmat, nev, tol, resid, ncv, v, ldv, iparam, workd, 
+      rvec = .true.
+      call snband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar, sigmai,
+     &           workev, n, a, m, lda, rfac, cfac, kl, ku, which,
+     &           bmat, nev, tol, resid, ncv, v, ldv, iparam, workd,
      &           workl, lworkl, workc, iwork, info)
 c
       if ( info .eq. 0) then
@@ -285,8 +285,8 @@ c        | Compute the residual norm. |
 c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
-         first = .true. 
-         do 90 j = 1, nconv 
+         first = .true.
+         do 90 j = 1, nconv
 c
             if ( d(j,2) .eq. zero ) then
 c
@@ -294,11 +294,11 @@ c              %--------------------%
 c              | Ritz value is real |
 c              %--------------------%
 c
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
                call saxpy(n, -d(j,1), v(1,j), 1, ax, 1)
-               d(j,3) = snrm2(n, ax, 1) 
+               d(j,3) = snrm2(n, ax, 1)
                d(j,3) = d(j,3) / abs(d(j,1))
 c
             else if ( first ) then
@@ -307,17 +307,17 @@ c              %------------------------%
 c              | Ritz value is complex  |
 c              | Residual of one Ritz   |
 c              | value of the conjugate |
-c              | pair is computed.      | 
+c              | pair is computed.      |
 c              %------------------------%
 c
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
                call saxpy(n, -d(j,1), v(1,j), 1, ax, 1)
                call saxpy(n, d(j,2), v(1,j+1), 1, ax, 1)
                d(j,3) = snrm2(n, ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    ax, 1)
                call saxpy(n, -d(j,2), v(1,j), 1, ax, 1)
                call saxpy(n, -d(j,1), v(1,j+1), 1, ax, 1)
@@ -329,11 +329,11 @@ c
                first = .true.
             end if
 c
- 90      continue 
+ 90      continue
 
          call smout(6, nconv, 3, d, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -344,8 +344,8 @@ c
           print *, ' '
           print *, ' Error with _nband, info= ', info
           print *, ' Check the documentation of _nband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/snbdr2.f

@@ -53,13 +53,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -68,12 +68,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Real 
+      Real
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn),
      &                 workev(3*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv, 3), ax(maxn)
-      Complex  
+      Complex
      &                 cfac(lda, maxn), workc(maxn)
 c
 c     %---------------%
@@ -85,25 +85,25 @@ c
      &                 n, nx, lo, idiag, isub, isup, mode, maxitr,
      &                 nconv
       logical          rvec, first
-      Real  
+      Real
      &                 tol, rho, h2, h, sigmar, sigmai
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Real  
+      Real
      &                 one, zero, two
-      parameter        (one = 1.0E+0 , zero = 0.0E+0 , 
+      parameter        (one = 1.0E+0 , zero = 0.0E+0 ,
      &                  two = 2.0E+0 )
 c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  slapy2, snrm2
-      external          slapy2, snrm2, saxpy, sgbmv 
+      external          slapy2, snrm2, saxpy, sgbmv
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -135,10 +135,10 @@ c     |                 NEV <= MAXNEV                   |
 c     |           NEV + 2 <= NCV <= MAXNCV              |
 c     %-------------------------------------------------%
 c
-      nx  = 10 
+      nx  = 10
       n    = nx*nx
-      nev  = 4 
-      ncv  = 20 
+      nev  = 4
+      ncv  = 20
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR2: N is greater than MAXN '
          go to 9000
@@ -151,8 +151,8 @@ c
       end if
       bmat = 'I'
       which = 'LM'
-      sigmar = 1.0E+4 
-      sigmai = 0.0E+0 
+      sigmar = 1.0E+4
+      sigmai = 0.0E+0
 c
 c     %-----------------------------------------------------%
 c     | The work array WORKL is used in SNAUPD as           |
@@ -166,7 +166,7 @@ c     | generated in SNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+6*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -181,7 +181,7 @@ c
       maxitr = 300
       mode   = 3
 c
-      iparam(3) = maxitr 
+      iparam(3) = maxitr
       iparam(7) = mode
 c
 c     %----------------------------------------%
@@ -203,10 +203,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A.                   |
 c     %-------------------------------------%
 c
-      kl   = nx 
-      ku   = nx 
+      kl   = nx
+      ku   = nx
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -216,22 +216,22 @@ c
       idiag = kl+ku+1
       do 30 j = 1, n
          a(idiag,j) = 4.0E+0  / h2
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+ku+2
-      rho = 1.0E+1 
+      rho = 1.0E+1
       do 50 i = 1, nx
         lo = (i-1)*nx
         do 40 j = lo+1, lo+nx-1
            a(isub,j+1) = -one/h2 + rho/two/h
            a(isup,j) = -one/h2 - rho/two/h
-  40    continue      
-  50  continue 
+  40    continue
+  50  continue
 c
 c     %------------------------------------%
 c     | KL-th subdiagonal and KU-th super- |
@@ -245,8 +245,8 @@ c
          do 70 j = lo+1, lo+nx
             a(isup,nx+j)  = -one / h2
             a(isub,j) = -one / h2
- 70      continue 
- 80   continue 
+ 70      continue
+ 80   continue
 c
 c     %------------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues  |
@@ -258,9 +258,9 @@ c     | in the first NCONV (=IPARAM(5)) columns of V.  |
 c     %------------------------------------------------%
 c
       rvec = .true.
-      call snband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar, 
-     &     sigmai, workev, n, a, m, lda, rfac, cfac, kl, ku, 
-     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam, 
+      call snband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar,
+     &     sigmai, workev, n, a, m, lda, rfac, cfac, kl, ku,
+     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam,
      &     workd, workl, lworkl, workc, iwork, info)
 c
       if ( info .eq. 0) then
@@ -293,8 +293,8 @@ c        | Compute the residual norm. |
 c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
-         first = .true. 
-         do 90 j = 1, nconv 
+         first = .true.
+         do 90 j = 1, nconv
 c
             if ( d(j,2) .eq. zero ) then
 c
@@ -302,8 +302,8 @@ c              %--------------------%
 c              | Ritz value is real |
 c              %--------------------%
 c
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
                call saxpy(n, -d(j,1), v(1,j), 1, ax, 1)
                d(j,3) = snrm2(n, ax, 1)
@@ -315,17 +315,17 @@ c              %------------------------%
 c              | Ritz value is complex  |
 c              | Residual of one Ritz   |
 c              | value of the conjugate |
-c              | pair is computed.      | 
+c              | pair is computed.      |
 c              %------------------------%
 c
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
                call saxpy(n, -d(j,1), v(1,j), 1, ax, 1)
                call saxpy(n, d(j,2), v(1,j+1), 1, ax, 1)
                d(j,3) = snrm2(n, ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    ax, 1)
                call saxpy(n, -d(j,1), v(1,j+1), 1, ax, 1)
                call saxpy(n, -d(j,2), v(1,j), 1, ax, 1)
@@ -337,11 +337,11 @@ c
                first = .true.
             end if
 c
- 90      continue 
+ 90      continue
 
          call smout(6, nconv, 3, d, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -352,8 +352,8 @@ c
           print *, ' '
           print *, ' Error with _nband, info= ', info
           print *, ' Check the documentation of _nband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/snbdr3.f

@@ -2,7 +2,7 @@
 c
 c     ... Construct matrices A and M in LAPACK-style band form.
 c         The matrix A and M are derived from the finite element
-c         discretization of the 1-dimensional convection-diffusion operator 
+c         discretization of the 1-dimensional convection-diffusion operator
 c                         (d^2u/dx^2) + rho*(du/dx)
 c         on the interval [0,1] with zero boundary condition,
 
@@ -49,13 +49,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn)
 c
 c     %--------------%
@@ -64,12 +64,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Real 
+      Real
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn),
      &                 workev(3*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv, 3), ax(maxn), mx(maxn)
-      Complex  
+      Complex
      &                 cfac(lda, maxn), workc(maxn)
 c
 c     %---------------%
@@ -81,25 +81,25 @@ c
      &                 n, idiag, isup, isub, mode, maxitr,
      &                 nconv
       logical          rvec, first
-      Real  
+      Real
      &                 tol, rho, h, sigmar, sigmai
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Real  
+      Real
      &                 one, zero, two
-      parameter        (one = 1.0E+0 , zero = 0.0E+0 , 
+      parameter        (one = 1.0E+0 , zero = 0.0E+0 ,
      &                  two = 2.0E+0 )
 c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  slapy2, snrm2
-      external          slapy2, snrm2, sgbmv, saxpy 
+      external          slapy2, snrm2, sgbmv, saxpy
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -126,8 +126,8 @@ c     |           NEV + 2 <= NCV <= MAXNCV              |
 c     %-------------------------------------------------%
 c
       n    = 100
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR3: N is greater than MAXN '
          go to 9000
@@ -142,7 +142,7 @@ c
       which = 'LM'
 c
 c     %----------------------------------------------------%
-c     | The work array WORKL is used in SNAUPD as          | 
+c     | The work array WORKL is used in SNAUPD as          |
 c     | workspace.  Its dimension LWORKL has to be set as  |
 c     | illustrated below.  The parameter TOL determines   |
 c     | the stopping criterion. If TOL<=0, machine machine |
@@ -150,12 +150,12 @@ c     | precision is used.  The number IDO is used for     |
 c     | reverse communication and has to be set to 0 at    |
 c     | the beginning.  Setting INFO=0 indicates that we   |
 c     | using a randomly generated vector to start the     |
-c     | the ARNOLDI process.                               | 
+c     | the ARNOLDI process.                               |
 c     %----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+6*ncv
       info = 0
-      tol  = zero 
+      tol  = zero
       ido  = 0
 c
 c     %---------------------------------------------------%
@@ -169,8 +169,8 @@ c
       mode = 2
       maxitr = 300
 c
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %--------------------------------------------%
 c     | Construct matrices A and M in LAPACK-style |
@@ -191,10 +191,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = 1 
-      ku   = 1 
+      kl   = 1
+      ku   = 1
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -204,21 +204,21 @@ c
       do 30 j = 1, n
          a(idiag,j) = 2.0E+0  / h
          m(idiag,j) = 4.0E+0  * h
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+ku+2
-      rho = 1.0E+1 
+      rho = 1.0E+1
       do 50 j = 1, n
          a(isup,j+1) = -one/h + rho/two
          a(isub,j) = -one/h - rho/two
          m(isup,j+1) = one*h
          m(isub,j) = one*h
-  50  continue 
+  50  continue
 c
 c     %------------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues  |
@@ -229,10 +229,10 @@ c     | second column of D.  Eigenvectors are returned |
 c     | in the first NCONV (=IPARAM(5)) columns of V.  |
 c     %------------------------------------------------%
 c
-      rvec = .true. 
-      call snband( rvec, 'A', select, d, d(1,2), v, ldv, sigmar, 
-     &     sigmai, workev, n, A, M, lda, rfac, cfac, kl, ku, 
-     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam, 
+      rvec = .true.
+      call snband( rvec, 'A', select, d, d(1,2), v, ldv, sigmar,
+     &     sigmai, workev, n, A, M, lda, rfac, cfac, kl, ku,
+     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam,
      &     workd, workl, lworkl, workc, iwork, info)
 c
       if ( info .eq. 0) then
@@ -265,7 +265,7 @@ c        | Compute the residual norm. |
 c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
-         first = .true. 
+         first = .true.
          do 90 j = 1, nconv
 c
             if ( d(j,2) .eq. zero ) then
@@ -274,11 +274,11 @@ c              %--------------------%
 c              | Ritz value is real |
 c              %--------------------%
 c
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call saxpy(n, -d(j,1), mx, 1, ax, 1)
                d(j,3) = snrm2(n, ax, 1)
@@ -290,30 +290,30 @@ c              %------------------------%
 c              | Ritz value is complex  |
 c              | Residual of one Ritz   |
 c              | value of the conjugate |
-c              | pair is computed.      | 
+c              | pair is computed.      |
 c              %------------------------%
 c
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call saxpy(n, -d(j,1), mx, 1, ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    mx, 1)
                call saxpy(n, d(j,2), mx, 1, ax, 1)
                d(j,3) = snrm2(n, ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    mx, 1)
                call saxpy(n, -d(j,1), mx, 1, ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call saxpy(n, -d(j,2), mx, 1, ax, 1)
                d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) )
@@ -324,11 +324,11 @@ c
                first = .true.
             end if
 c
- 90      continue 
+ 90      continue
 
          call smout(6, nconv, 3, d, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -339,8 +339,8 @@ c
           print *, ' '
           print *, ' Error with _nband, info= ', info
           print *, ' Check the documentation of _nband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/snbdr4.f

@@ -50,14 +50,14 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
-     &                   maxbdw=50, lda = maxbdw, ldv = maxn) 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
+     &                   maxbdw=50, lda = maxbdw, ldv = maxn)
 c
 c     %--------------%
 c     | Local Arrays |
@@ -67,10 +67,10 @@ c
       logical          select(maxncv)
       Real
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn),
      &                 workev(3*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv, 3), ax(maxn), mx(maxn)
-      Complex 
+      Complex
      &                 cfac(lda, maxn), workc(maxn)
 c
 c     %---------------%
@@ -82,16 +82,16 @@ c
      &                 n, idiag, isup, isub, mode, maxitr,
      &                 nconv
       logical          rvec, first
-      Real 
+      Real
      &                 tol, rho, h, sigmar, sigmai
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Real 
+      Real
      &                 one, zero, two, six
-      parameter        (one = 1.0E+0, zero = 0.0E+0, 
+      parameter        (one = 1.0E+0, zero = 0.0E+0,
      &                  two = 2.0E+0, six = 6.0E+0)
 c
 c     %-----------------------------%
@@ -100,7 +100,7 @@ c     %-----------------------------%
 c
       Real
      &                  slapy2, snrm2
-      external          slapy2, snrm2, sgbmv, saxpy 
+      external          slapy2, snrm2, sgbmv, saxpy
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -127,8 +127,8 @@ c     |           NEV + 2 <= NCV <= MAXNCV              |
 c     %-------------------------------------------------%
 c
       n    = 100
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR4: N is greater than MAXN '
          go to 9000
@@ -142,7 +142,7 @@ c
       bmat = 'G'
       which = 'LM'
       sigmar = 1.0E+1
-      sigmai = 0.0E+0 
+      sigmai = 0.0E+0
 c
 c     %-----------------------------------------------------%
 c     | The work array WORKL is used in SNAUPD as           |
@@ -157,7 +157,7 @@ c     %-----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+6*ncv
       info = 0
-      tol  = zero 
+      tol  = zero
       ido  = 0
 c
 c     %---------------------------------------------------%
@@ -171,7 +171,7 @@ c
       maxitr = 300
       mode   = 3
 c
-      iparam(3) = n 
+      iparam(3) = n
       iparam(7) = 3
 c
 c     %--------------------------------------------%
@@ -194,9 +194,9 @@ c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
       kl   = 1
-      ku   = 1 
+      ku   = 1
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -205,12 +205,12 @@ c
       do 30 j = 1, n
          a(idiag,j) = 2.0E+0 / h
          m(idiag,j) = 4.0E+0 * h / six
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+ku+2
       rho = 1.0E+1
@@ -218,8 +218,8 @@ c
          a(isup,j+1) = -one/h + rho/two
          a(isub,j) = -one/h - rho/two
          m(isup,j+1) = one*h/six
-         m(isub,j) = one*h/six 
-  40    continue      
+         m(isub,j) = one*h/six
+  40    continue
 c
 c     %------------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues  |
@@ -231,9 +231,9 @@ c     | in the first NCONV (=IPARAM(5)) columns of V.  |
 c     %------------------------------------------------%
 c
       rvec = .true.
-      call snband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar, 
+      call snband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar,
      &     sigmai, workev, n, A, M, lda, rfac, cfac, kl, ku,
-     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam, 
+     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam,
      &     workd, workl, lworkl, workc, iwork, info)
 c
       if ( info .eq. 0) then
@@ -266,7 +266,7 @@ c        | Compute the residual norm. |
 c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
-         first = .true. 
+         first = .true.
          do 50 j = 1, nconv
 c
             if ( d(j,2) .eq. zero ) then
@@ -275,11 +275,11 @@ c              %--------------------%
 c              | Ritz value is real |
 c              %--------------------%
 c
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call saxpy(n, -d(j,1), mx, 1, ax, 1)
                d(j,3) = snrm2(n, ax, 1)
@@ -291,30 +291,30 @@ c              %------------------------%
 c              | Ritz value is complex  |
 c              | Residual of one Ritz   |
 c              | value of the conjugate |
-c              | pair is computed.      | 
+c              | pair is computed.      |
 c              %------------------------%
 c
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call saxpy(n, -d(j,1), mx, 1, ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    mx, 1)
                call saxpy(n, d(j,2), mx, 1, ax, 1)
                d(j,3) = snrm2(n, ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    mx, 1)
                call saxpy(n, -d(j,1), mx, 1, ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call saxpy(n, -d(j,2), mx, 1, ax, 1)
                d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) )
@@ -325,11 +325,11 @@ c
                first = .true.
             end if
 c
- 50      continue 
+ 50      continue
 
          call smout(6, nconv, 3, d, maxncv, -6,
      &             'Ritz values (Real,Imag) and relatve residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -340,8 +340,8 @@ c
           print *, ' '
           print *, ' Error with _nband, info= ', info
           print *, ' Check the documentation of _nband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/snbdr5.f

@@ -1,7 +1,7 @@
       program snbdr5
 c
 c     ... Construct matrices A and M in LAPACK-style band form.
-c         The matrix A is a block tridiagonal matrix.  Each 
+c         The matrix A is a block tridiagonal matrix.  Each
 c         diagonal block is a tridiagonal matrix with
 c         4 on the diagonal, 1-rho*h/2 on the subdiagonal and
 c         1+rho*h/2 on the superdiagonal.  Each off-diagonal block
@@ -51,13 +51,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -66,12 +66,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Real 
+      Real
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn),
      &                 workev(3*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv, 3), ax(maxn)
-      Complex  
+      Complex
      &                 cfac(lda, maxn), workc(maxn)
 c
 c     %---------------%
@@ -83,25 +83,25 @@ c
      &                 n, nx, lo, idiag, isup, isub, mode, maxitr,
      &                 nconv
       logical          rvec, first
-      Real  
+      Real
      &                 tol, rho, h, sigmar, sigmai
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Real  
+      Real
      &                 one, zero, two
-      parameter        (one = 1.0E+0 , zero = 0.0E+0 , 
+      parameter        (one = 1.0E+0 , zero = 0.0E+0 ,
      &                  two = 2.0E+0 )
 c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  slapy2, snrm2
-      external          slapy2, snrm2, sgbmv, saxpy 
+      external          slapy2, snrm2, sgbmv, saxpy
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -132,8 +132,8 @@ c     %--------------------------------------------------%
 c
       nx   = 10
       n    = nx*nx
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR5: N is greater than MAXN '
          go to 9000
@@ -146,8 +146,8 @@ c
       end if
       bmat = 'I'
       which = 'LM'
-      sigmar = 4.0E-1 
-      sigmai = 6.0E-1 
+      sigmar = 4.0E-1
+      sigmai = 6.0E-1
 c
 c     %-----------------------------------------------------%
 c     | The work array WORKL is used in SNAUPD as           |
@@ -161,7 +161,7 @@ c     | generated in SNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+6*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -198,34 +198,34 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = nx 
-      ku   = nx 
+      kl   = nx
+      ku   = nx
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
       idiag = kl+ku+1
       do 30 j = 1, n
-         a(idiag,j) = 4.0E+0 
-         m(idiag,j) = 4.0E+0 
-  30  continue 
-c 
+         a(idiag,j) = 4.0E+0
+         m(idiag,j) = 4.0E+0
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+kl+2
       h = one / real (nx+1)
-      rho = 1.0E+2  
+      rho = 1.0E+2
       do 50 i = 1, nx
         lo = (i-1)*nx
         do 40 j = lo+1, lo+nx-1
            a(isup,j+1) = -one+h*rho/two
            a(isub,j) = -one-h*rho/two
-  40    continue      
-  50  continue 
+  40    continue
+  50  continue
 c
       do 60 j = 1, n-1
          m(isup,j+1) = one
@@ -244,8 +244,8 @@ c
          do 70 j = lo+1, lo+nx
             a(isup,nx+j)  = -one
             a(isub,j) = -one
- 70      continue 
- 80   continue 
+ 70      continue
+ 80   continue
 c
 c     %------------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues  |
@@ -253,13 +253,13 @@ c     | and eigenvectors. The real parts of the        |
 c     | eigenvalues are returned in the first column   |
 c     | of D, the imaginary parts are returned in the  |
 c     | second column of D.  Eigenvectors are returned |
-c     | in the first NCONV (=IPARAM(5)) columns of V.  | 
+c     | in the first NCONV (=IPARAM(5)) columns of V.  |
 c     %------------------------------------------------%
 c
       rvec = .true.
-      call snband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar, 
-     &     sigmai, workev, n, a, m, lda, rfac, cfac, ku, kl, 
-     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam, 
+      call snband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar,
+     &     sigmai, workev, n, a, m, lda, rfac, cfac, ku, kl,
+     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam,
      &     workd, workl, lworkl, workc, iwork, info)
 c
       if ( info .eq. 0) then
@@ -292,7 +292,7 @@ c        | Compute the residual norm. |
 c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
-         first = .true. 
+         first = .true.
          do 90 j = 1, nconv
 c
             if ( d(j,2) .eq. zero ) then
@@ -301,8 +301,8 @@ c              %--------------------%
 c              | Ritz value is real |
 c              %--------------------%
 c
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
                call saxpy(n, -d(j,1), v(1,j), 1, ax, 1)
                d(j,3) = snrm2(n, ax, 1)
@@ -314,17 +314,17 @@ c              %------------------------%
 c              | Ritz value is complex  |
 c              | Residual of one Ritz   |
 c              | value of the conjugate |
-c              | pair is computed.      | 
+c              | pair is computed.      |
 c              %------------------------%
 c
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
                call saxpy(n, -d(j,1), v(1,j), 1, ax, 1)
                call saxpy(n, d(j,2), v(1,j+1), 1, ax, 1)
                d(j,3) = snrm2(n, ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    ax, 1)
                call saxpy(n, -d(j,1), v(1,j+1), 1, ax, 1)
                call saxpy(n, -d(j,2), v(1,j), 1, ax, 1)
@@ -336,11 +336,11 @@ c
                first = .true.
             end if
 c
- 90      continue 
+ 90      continue
 
          call smout(6, nconv, 3, d, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -351,8 +351,8 @@ c
           print *, ' '
           print *, ' Error with _nband, info= ', info
           print *, ' Check the documentation of _nband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/snbdr6.f

@@ -1,7 +1,7 @@
       program snbdr6
 c
 c     ... Construct matrices A and M in LAPACK-style band form.
-c         The matrix A is a block tridiagonal matrix.  Each 
+c         The matrix A is a block tridiagonal matrix.  Each
 c         diagonal block is a tridiagonal matrix with
 c         4 on the diagonal, 1-rho*h/2 on the subdiagonal and
 c         1+rho*h/2 on the superdiagonal.  Each subdiagonal block
@@ -53,13 +53,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -68,12 +68,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Real 
+      Real
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn),
      &                 workev(3*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv, 3), ax(maxn), mx(maxn)
-      Complex  
+      Complex
      &                 cfac(lda, maxn), workc(maxn)
 c
 c     %---------------%
@@ -85,16 +85,16 @@ c
      &                 n, nx, lo, idiag, isup, isub, mode, maxitr,
      &                 nconv
       logical          rvec, first
-      Real  
+      Real
      &                 tol, rho, h, sigmar, sigmai
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Real  
+      Real
      &                 one, zero, two
-      parameter        (one = 1.0E+0 , zero = 0.0E+0 , 
+      parameter        (one = 1.0E+0 , zero = 0.0E+0 ,
      &                  two = 2.0E+0 )
 c
 c     %--------------------%
@@ -107,9 +107,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  slapy2, snrm2
-      external          slapy2, snrm2, sgbmv, saxpy 
+      external          slapy2, snrm2, sgbmv, saxpy
 c
 c     %-----------------------%
 c     | Executable Statements |
@@ -129,13 +129,13 @@ c     | to get different parts the spectrum. However, the   |
 c     | following rules must be satisfied:                  |
 c     |                   N <= MAXN                         |
 c     |                 NEV <= MAXNEV                       |
-c     |           NEV + 2 <= NCV <= MAXNCV                  | 
-c     %-----------------------------------------------------% 
+c     |           NEV + 2 <= NCV <= MAXNCV                  |
+c     %-----------------------------------------------------%
 c
-      nx  = 10 
+      nx  = 10
       n    = nx*nx
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR6: N is greater than MAXN '
          go to 9000
@@ -148,8 +148,8 @@ c
       end if
       bmat = 'G'
       which = 'LM'
-      sigmar = 4.0E-1 
-      sigmai = 6.0E-1 
+      sigmar = 4.0E-1
+      sigmai = 6.0E-1
 c
 c     %-----------------------------------------------------%
 c     | The work array WORKL is used in SNAUPD as           |
@@ -163,7 +163,7 @@ c     | generated in SNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+6*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -178,7 +178,7 @@ c
       maxitr = 300
       mode = 4
 c
-      iparam(3) = maxitr 
+      iparam(3) = maxitr
       iparam(7) = mode
 c
 c     %--------------------------------------------%
@@ -200,34 +200,34 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = nx 
-      ku   = nx 
+      kl   = nx
+      ku   = nx
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
       idiag = kl+ku+1
       do 30 j = 1, n
-         a(idiag,j) = 4.0E+0 
-         m(idiag,j) = 4.0E+0 
-  30  continue 
-c 
+         a(idiag,j) = 4.0E+0
+         m(idiag,j) = 4.0E+0
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+ku+2
       h = one / real (nx+1)
-      rho = 1.0E+2 
+      rho = 1.0E+2
       do 50 i = 1, nx
         lo = (i-1)*nx
         do 40 j = lo+1, lo+nx-1
            a(isub,j+1) = -one+h*rho/two
            a(isup,j) = -one-h*rho/two
-  40    continue      
-  50  continue 
+  40    continue
+  50  continue
 c
       do 60 j = 1, n-1
          m(isub,j+1) = one
@@ -246,8 +246,8 @@ c
          do 70 j = lo+1, lo+nx
             a(isup,nx+j)  = -one
             a(isub,j) = -one
- 70      continue 
- 80   continue 
+ 70      continue
+ 80   continue
 c
 c     %------------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues  |
@@ -259,9 +259,9 @@ c     | in the first NCONV (=IPARAM(5)) columns of V.  |
 c     %------------------------------------------------%
 c
       rvec = .true.
-      call snband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar, 
-     &     sigmai, workev, n, a, m, lda, rfac, cfac, ku, kl, 
-     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam, 
+      call snband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar,
+     &     sigmai, workev, n, a, m, lda, rfac, cfac, ku, kl,
+     &     which, bmat, nev, tol, resid, ncv, v, ldv, iparam,
      &     workd, workl, lworkl, workc, iwork, info)
 c
       if ( info .eq. 0) then
@@ -294,7 +294,7 @@ c        | Compute the residual norm. |
 c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
-         first = .true. 
+         first = .true.
          do 90 j = 1, nconv
 c
             if ( d(j,2) .eq. zero ) then
@@ -303,11 +303,11 @@ c              %--------------------%
 c              | Ritz value is real |
 c              %--------------------%
 c
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call saxpy(n, -d(j,1), mx, 1, ax, 1)
                d(j,3) = snrm2(n, ax, 1)
@@ -319,30 +319,30 @@ c              %------------------------%
 c              | Ritz value is complex  |
 c              | Residual of one Ritz   |
 c              | value of the conjugate |
-c              | pair is computed.      | 
+c              | pair is computed.      |
 c              %------------------------%
 c
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j), 1, zero,
      &                    ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call saxpy(n, -d(j,1), mx, 1, ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    mx, 1)
                call saxpy(n, d(j,2), mx, 1, ax, 1)
                d(j,3) = snrm2(n, ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    a(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    a(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j+1), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j+1), 1, zero,
      &                    mx, 1)
                call saxpy(n, -d(j,1), mx, 1, ax, 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    m(kl+1,1), lda, v(1,j), 1, zero, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    m(kl+1,1), lda, v(1,j), 1, zero,
      &                    mx, 1)
                call saxpy(n, -d(j,2), mx, 1, ax, 1)
                d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) )
@@ -353,11 +353,11 @@ c
                first = .true.
             end if
 c
- 90      continue 
+ 90      continue
 
          call smout(6, nconv, 3, d, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -368,8 +368,8 @@ c
           print *, ' '
           print *, ' Error with _nband, info= ', info
           print *, ' Check the documentation of _nband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/ssband.f

@@ -17,19 +17,19 @@ c
 c  Matrices A and B are stored in LAPACK-style band form.
 c
 c  There is negligible additional cost to obtain eigenvectors.  An orthonormal
-c  (Lanczos) basis is always computed.  There is an additional storage cost 
-c  of n*nev if both are requested (in this case a separate array Z must be 
+c  (Lanczos) basis is always computed.  There is an additional storage cost
+c  of n*nev if both are requested (in this case a separate array Z must be
 c  supplied).
 c
 c  The approximate eigenvalues and eigenvectors of  A*z = lambda*B*z
-c  are called Ritz values and Ritz vectors respectively.  They are referred 
-c  to as such in the comments that follow.  The computed orthonormal basis 
-c  for the invariant subspace corresponding to these Ritz values is referred 
+c  are called Ritz values and Ritz vectors respectively.  They are referred
+c  to as such in the comments that follow.  The computed orthonormal basis
+c  for the invariant subspace corresponding to these Ritz values is referred
 c  to as a Lanczos basis.
 c
 c  ssband can be called with one of the following modes:
 c
-c  Mode 1:  A*x = lambda*x, A symmetric 
+c  Mode 1:  A*x = lambda*x, A symmetric
 c           ===> OP = A  and  B = I.
 c
 c  Mode 2:  A*x = lambda*M*x, A symmetric, M symmetric positive definite
@@ -37,10 +37,10 @@ c           ===> OP = inv[M]*A  and  B = M.
 c           ===> (If M can be factored see remark 3 in SSAUPD)
 c
 c  Mode 3:  K*x = lambda*M*x, K symmetric, M symmetric positive semi-definite
-c           ===> OP = (inv[K - sigma*M])*M  and  B = M. 
+c           ===> OP = (inv[K - sigma*M])*M  and  B = M.
 c           ===> Shift-and-Invert mode
 c
-c  Mode 4:  K*x = lambda*KG*x, K symmetric positive semi-definite, 
+c  Mode 4:  K*x = lambda*KG*x, K symmetric positive semi-definite,
 c           KG symmetric indefinite
 c           ===> OP = (inv[K - sigma*KG])*K  and  B = K.
 c           ===> Buckling mode
@@ -53,21 +53,21 @@ c  The choice of mode must be specified in IPARAM(7) defined below.
 c
 c \Usage
 c   call ssband
-c      ( RVEC, HOWMNY, SELECT, D, Z, LDZ, SIGMA, N, AB, MB, LDA, 
-c        RFAC, KL, KU, WHICH, BMAT, NEV, TOL, RESID, NCV, V, 
+c      ( RVEC, HOWMNY, SELECT, D, Z, LDZ, SIGMA, N, AB, MB, LDA,
+c        RFAC, KL, KU, WHICH, BMAT, NEV, TOL, RESID, NCV, V,
 c        LDV, IPARAM, WORKD, WORKL, LWORKL, IWORK, INFO )
 c
 c \Arguments
 c
 c  RVEC    Logical (INPUT)
-c          Specifies whether Ritz vectors corresponding to the Ritz value 
+c          Specifies whether Ritz vectors corresponding to the Ritz value
 c          approximations to the eigenproblem A*z = lambda*B*z are computed.
 c
 c             RVEC = .FALSE.     Compute Ritz values only.
 c
-c             RVEC = .TRUE.      Compute the associated Ritz vectors. 
+c             RVEC = .TRUE.      Compute the associated Ritz vectors.
 c
-c  HOWMNY  Character*1  (INPUT) 
+c  HOWMNY  Character*1  (INPUT)
 c          Specifies how many Ritz vectors are wanted and the form of Z
 c          the matrix of Ritz vectors. See remark 1 below.
 c          = 'A': compute all Ritz vectors;
@@ -77,7 +77,7 @@ c
 c  SELECT  Logical array of dimension NCV.  (INPUT)
 c          If HOWMNY = 'S', SELECT specifies the Ritz vectors to be
 c          computed. To select the Ritz vector corresponding to a
-c          Ritz value D(j), SELECT(j) must be set to .TRUE.. 
+c          Ritz value D(j), SELECT(j) must be set to .TRUE..
 c          If HOWMNY = 'A' , SELECT is not referenced.
 c
 c  D       Real array of dimension NEV.  (OUTPUT)
@@ -85,8 +85,8 @@ c          On exit, D contains the Ritz value approximations to the
 c          eigenvalues of A*z = lambda*B*z. The values are returned
 c          in ascending order. If IPARAM(7) = 3,4,5 then D represents
 c          the Ritz values of OP computed by ssaupd transformed to
-c          those of the original eigensystem A*z = lambda*B*z. If 
-c          IPARAM(7) = 1,2 then the Ritz values of OP are the same 
+c          those of the original eigensystem A*z = lambda*B*z. If
+c          IPARAM(7) = 1,2 then the Ritz values of OP are the same
 c          as the those of A*z = lambda*B*z.
 c
 c  Z       Real N by NEV array if HOWMNY = 'A'.  (OUTPUT)
@@ -95,20 +95,20 @@ c          eigensystem A*z = lambda*B*z corresponding to the Ritz
 c          value approximations.
 c
 c          If  RVEC = .FALSE. then Z is not referenced.
-c          NOTE: The array Z may be set equal to first NEV columns of the 
+c          NOTE: The array Z may be set equal to first NEV columns of the
 c          Lanczos basis array V computed by SSAUPD.
 c
-c  LDZ     Integer.  (INPUT) 
+c  LDZ     Integer.  (INPUT)
 c          The leading dimension of the array Z.  If Ritz vectors are
 c          desired, then  LDZ .ge.  max( 1, N ).  In any case,  LDZ .ge. 1.
 c
 c  SIGMA   Real  (INPUT)
 c          If IPARAM(7) = 3,4,5 represents the shift. Not referenced if
 c          IPARAM(7) = 1 or 2.
-c 
-c  N       Integer.  (INPUT) 
-c          Dimension of the eigenproblem.  
-c 
+c
+c  N       Integer.  (INPUT)
+c          Dimension of the eigenproblem.
+c
 c  AB      Real array of dimension LDA by N. (INPUT)
 c          The matrix A in band storage, in rows KL+1 to
 c          2*KL+KU+1; rows 1 to KL of the array need not be set.
@@ -118,7 +118,7 @@ c          AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
 c
 c  MB      Real array of dimension LDA by N. (INPUT)
 c          The matrix M in band storage, in rows KL+1 to
-c          2*KL+KU+1; rows 1 to KL of the array need not be set. 
+c          2*KL+KU+1; rows 1 to KL of the array need not be set.
 c          The j-th column of M is stored in the j-th column of the
 c          array AB as follows:
 c          MB(kl+ku+1+i-j,j) = M(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
@@ -128,7 +128,7 @@ c  LDA     Integer. (INPUT)
 c          Leading dimension of AB, MB, RFAC.
 c
 c  RFAC    Real array of LDA by N. (WORKSPACE/OUTPUT)
-c          RFAC is used to store the LU factors of MB when IPARAM(7) = 2 
+c          RFAC is used to store the LU factors of MB when IPARAM(7) = 2
 c          is invoked.  It is used to store the LU factors of
 c          (A-sigma*M) when IPARAM(7) = 3,4,5 is invoked.
 c          It is not referenced when IPARAM(7) = 1.
@@ -142,17 +142,17 @@ c
 c  WHICH   Character*2.  (INPUT)
 c          When IPARAM(7)= 1 or 2,  WHICH can be set to any one of
 c          the following.
-c  
+c
 c            'LM' -> want the NEV eigenvalues of largest magnitude.
 c            'SM' -> want the NEV eigenvalues of smallest magnitude.
 c            'LA' -> want the NEV eigenvalues of largest REAL part.
 c            'SA' -> want the NEV eigenvalues of smallest REAL part.
-c            'BE' -> Compute NEV eigenvalues, half from each end of the 
-c                    spectrum.  When NEV is odd, compute one more from 
-c                    the high end than from the low end. 
+c            'BE' -> Compute NEV eigenvalues, half from each end of the
+c                    spectrum.  When NEV is odd, compute one more from
+c                    the high end than from the low end.
+c
+c          When IPARAM(7) = 3, 4, or 5,  WHICH should be set to 'LM' only.
 c
-c          When IPARAM(7) = 3, 4, or 5,  WHICH should be set to 'LM' only. 
-c          
 c  BMAT    Character*1.  (INPUT)
 c          BMAT specifies the type of the matrix B that defines the
 c          semi-inner product for the operator OP.
@@ -161,9 +161,9 @@ c          BMAT = 'G' -> generalized eigenvalue problem A*x = lambda*M*x
 
 c  NEV     Integer. (INPUT)
 c          Number of eigenvalues of OP to be computed.
-c   
+c
 c  TOL     Real scalar.  (INPUT)
-c          Stopping criterion: the relative accuracy of the Ritz value 
+c          Stopping criterion: the relative accuracy of the Ritz value
 c          is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)).
 c          If TOL .LE. 0. is passed a default is set:
 c          DEFAULT = SLAMCH('EPS')  (machine precision as computed
@@ -183,35 +183,35 @@ c          Represents the dimension of the Lanczos basis constructed
 c          by ssaupd for OP.
 c
 c  V       Real array N by NCV.  (OUTPUT)
-c          Upon INPUT: the NCV columns of V contain the Lanczos basis 
+c          Upon INPUT: the NCV columns of V contain the Lanczos basis
 c                      vectors as constructed by ssaupd for OP.
-c          Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns 
-c                       represent the Ritz vectors that span the desired 
+c          Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns
+c                       represent the Ritz vectors that span the desired
 c                       invariant subspace.
-c          NOTE: The array Z may be set equal to first NEV columns of the 
+c          NOTE: The array Z may be set equal to first NEV columns of the
 c          Lanczos basis vector array V computed by ssaupd. In this case
 c          if RVEC=.TRUE., the first NCONV=IPARAM(5) columns of V contain
-c          the desired Ritz vectors. 
+c          the desired Ritz vectors.
 c
 c  LDV     Integer.  (INPUT)
 c          Leading dimension of V exactly as declared in the calling
 c          program.
 c
 c  IPARAM  Integer array of length 11.  (INPUT/OUTPUT)
-c          IPARAM(1) = ISHIFT: 
+c          IPARAM(1) = ISHIFT:
 c          The shifts selected at each iteration are used to restart
 c          the Arnoldi iteration in an implicit fashion.
 c          It is set to 1 in this subroutine.  The user do not need
 c          to set this parameter.
 c          ------------------------------------------------------------
-c          ISHIFT = 1: exact shifts with respect to the reduced 
-c                      tridiagonal matrix T.  This is equivalent to 
-c                      restarting the iteration with a starting vector 
-c                      that is a linear combination of Ritz vectors 
+c          ISHIFT = 1: exact shifts with respect to the reduced
+c                      tridiagonal matrix T.  This is equivalent to
+c                      restarting the iteration with a starting vector
+c                      that is a linear combination of Ritz vectors
 c                      associated with the "wanted" Ritz values.
 c          -------------------------------------------------------------
 c
-c          IPARAM(2) = No longer referenced. 
+c          IPARAM(2) = No longer referenced.
 c
 c          IPARAM(3) = MXITER
 c          On INPUT:  max number of Arnoldi update iterations allowed.
@@ -225,11 +225,11 @@ c          This represents the number of Ritz values that satisfy
 c          the convergence criterion.
 c
 c          IPARAM(6) = IUPD
-c          No longer referenced. Implicit restarting is ALWAYS used. 
+c          No longer referenced. Implicit restarting is ALWAYS used.
 c
 c          IPARAM(7) = MODE
 c          On INPUT determines what type of eigenproblem is being solved.
-c          Must be 1,2,3,4,5; See under \Description of ssband for the 
+c          Must be 1,2,3,4,5; See under \Description of ssband for the
 c          five modes available.
 c
 c          IPARAM(8) = NP
@@ -248,18 +248,18 @@ c LWORKL   Integer.  (INPUT)
 c          LWORKL must be at least NCV**2 + 8*NCV.
 c
 c IWORK    Integer array of dimension at least N. (WORKSPACE)
-c          Used when IPARAM(7)=2,3,4,5 to store the pivot information in the 
+c          Used when IPARAM(7)=2,3,4,5 to store the pivot information in the
 c          factorization of M or (A-SIGMA*M).
-c            
+c
 c INFO     Integer.  (INPUT/OUTPUT)
 c          Error flag on output.
 c          =  0: Normal exit.
 c          =  1: Maximum number of iterations taken.
-c                All possible eigenvalues of OP has been found. IPARAM(5)  
+c                All possible eigenvalues of OP has been found. IPARAM(5)
 c                returns the number of wanted converged Ritz values.
-c          =  3: No shifts could be applied during a cycle of the 
-c                Implicitly restarted Arnoldi iteration. One possibility 
-c                is to increase the size of NCV relative to NEV. 
+c          =  3: No shifts could be applied during a cycle of the
+c                Implicitly restarted Arnoldi iteration. One possibility
+c                is to increase the size of NCV relative to NEV.
 c                See remark 4 in SSAUPD.
 c
 c          = -1: N must be positive.
@@ -292,7 +292,7 @@ c  1. D.C. Sorensen, "Implicit Application of Polynomial Filters in
 c     a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992),
 c     pp 357-385.
 c
-c  2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly 
+c  2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly
 c     Restarted Arnoldi Iteration", Ph.D thesis, TR95-13, Rice Univ,
 c     May 1995.
 c
@@ -301,7 +301,7 @@ c     ssaupd  ARPACK reverse communication interface routine.
 c     sseupd  ARPACK routine that returns Ritz values and (optionally)
 c             Ritz vectors.
 c     sgbtrf  LAPACK band matrix factorization routine.
-c     sgbtrs  LAPACK band linear system solve routine. 
+c     sgbtrs  LAPACK band linear system solve routine.
 c     slacpy  LAPACK matrix copy routine.
 c     slapy2  LAPACK routine to compute sqrt(x**2+y**2) carefully.
 c     scopy   Level 1 BLAS that copies one vector to another.
@@ -310,13 +310,13 @@ c     snrm2   Level 1 BLAS that computes the norm of a vector.
 c     sgbmv   Level 2 BLAS that computes the band matrix vector product.
 c
 c\Remarks
-c  1. The converged Ritz values are always returned in increasing 
+c  1. The converged Ritz values are always returned in increasing
 c     (algebraic) order.
 c
 c  2. Currently only HOWMNY = 'A' is implemented. It is included at this
 c     stage for the user who wants to incorporate it.
 c
-c\Author    
+c\Author
 c     Danny Sorensen
 c     Richard Lehoucq
 c     Chao Yang
@@ -332,18 +332,18 @@ c\EndLib
 c
 c---------------------------------------------------------------------
 c
-      subroutine ssband( rvec, howmny, select, d, z, ldz, sigma, 
-     &           n, ab, mb, lda, rfac, kl, ku, which, bmat, nev, 
-     &           tol, resid, ncv, v, ldv, iparam, workd, workl, 
+      subroutine ssband( rvec, howmny, select, d, z, ldz, sigma,
+     &           n, ab, mb, lda, rfac, kl, ku, which, bmat, nev,
+     &           tol, resid, ncv, v, ldv, iparam, workd, workl,
      &           lworkl, iwork, info)
 c
 c     %------------------%
 c     | Scalar Arguments |
 c     %------------------%
-c 
+c
       character        which*2, bmat, howmny
       integer          n, lda, kl, ku, nev, ncv, ldv,
-     &                 ldz, lworkl, info  
+     &                 ldz, lworkl, info
       Real
      &                 tol, sigma
       logical          rvec
@@ -356,7 +356,7 @@ c
       logical          select(*)
       Real
      &                 d(*), resid(*), v(ldv,*), z(ldz,*),
-     &                 ab(lda,*), mb(lda,*), rfac(lda,*), 
+     &                 ab(lda,*), mb(lda,*), rfac(lda,*),
      &                 workd(*), workl(*)
 c
 c     %--------------%
@@ -386,22 +386,22 @@ c     %-----------------------------%
 c
       Real
      &                 sdot, snrm2, slapy2
-      external         sdot, scopy, sgbmv, sgbtrf, 
+      external         sdot, scopy, sgbmv, sgbtrf,
      &                 sgbtrs, snrm2, slapy2, slacpy
 c
 c     %-----------------------%
 c     | Executable Statements |
 c     %-----------------------%
-c     
+c
 c     %----------------------------------------------------------------%
 c     | Set type of the problem to be solved. Check consistency        |
 c     | between BMAT and IPARAM(7).                                    |
 c     | type = 1 --> Solving standard problem in regular mode.         |
-c     | type = 2 --> Solving standard problem in shift-invert mode.    | 
+c     | type = 2 --> Solving standard problem in shift-invert mode.    |
 c     | type = 3 --> Solving generalized problem in regular mode.      |
 c     | type = 4 --> Solving generalized problem in shift-invert mode. |
 c     | type = 5 --> Solving generalized problem in Buckling mode.     |
-c     | type = 6 --> Solving generalized problem in Cayley mode.       | 
+c     | type = 6 --> Solving generalized problem in Cayley mode.       |
 c     %----------------------------------------------------------------%
 c
       if ( iparam(7) .eq. 1 ) then
@@ -411,15 +411,15 @@ c
       else if ( iparam(7) .eq. 2 ) then
          type = 3
       else if ( iparam(7) .eq. 3 .and. bmat .eq. 'G') then
-         type = 4 
+         type = 4
       else if ( iparam(7) .eq. 4 ) then
          type = 5
-      else if ( iparam(7) .eq. 5 ) then 
+      else if ( iparam(7) .eq. 5 ) then
          type = 6
       else
          print*, ' '
          print*, 'BMAT is inconsistent with IPARAM(7).'
-         print*, ' ' 
+         print*, ' '
          go to 9000
       end if
 c
@@ -432,9 +432,9 @@ c
 c
 c     %----------------%
 c     | Exact shift is |
-c     | used.          | 
+c     | used.          |
 c     %----------------%
-c 
+c
       iparam(1) = 1
 c
 c     %-----------------------------------%
@@ -462,7 +462,7 @@ c
   10      continue
           call sgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr )
           if (ierr .ne. 0) then
-             print*, ' ' 
+             print*, ' '
              print*, ' _SBAND: Error with _gbtrf. '
              print*, ' '
              go to  9000
@@ -477,28 +477,28 @@ c        | routine sgbtrf to factor M.                  |
 c        %----------------------------------------------%
 c
          call slacpy ('A', ibot, n, mb, lda, rfac, lda )
-         call sgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr) 
-         if (ierr .ne. 0) then 
+         call sgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr)
+         if (ierr .ne. 0) then
              print*, ' '
-             print*,'_SBAND:  Error with _gbtrf.' 
-             print*, ' ' 
-             go to 9000 
+             print*,'_SBAND:  Error with _gbtrf.'
+             print*, ' '
+             go to 9000
          end if
 c
-      else if ( type .eq. 4 .or. type .eq. 5 .or. type .eq. 6 
+      else if ( type .eq. 4 .or. type .eq. 5 .or. type .eq. 6
      &         .and. bmat .eq. 'G' ) then
 c
 c        %-------------------------------------------%
 c        | Solving generalized eigenvalue problem in |
 c        | shift-invert, Buckling, or Cayley mode.   |
 c        %-------------------------------------------%
-c 
+c
 c        %-------------------------------------%
 c        | Construct and factor (A - sigma*M). |
 c        %-------------------------------------%
 c
          do 60 j = 1,n
-            do 50 i = itop, ibot 
+            do 50 i = itop, ibot
                rfac(i,j) = ab(i,j) - sigma*mb(i,j)
   50        continue
   60     continue
@@ -510,14 +510,14 @@ c
              print*, ' '
              go to 9000
          end if
-c 
-      end if 
+c
+      end if
 c
 c     %--------------------------------------------%
 c     |  M A I N   L O O P (reverse communication) |
 c     %--------------------------------------------%
 c
-  90  continue 
+  90  continue
 c
       call ssaupd ( ido, bmat, n, which, nev, tol, resid, ncv,
      &              v, ldv, iparam, ipntr, workd, workl, lworkl,
@@ -531,8 +531,8 @@ c           %----------------------------%
 c           | Perform  y <--- OP*x = A*x |
 c           %----------------------------%
 c
-            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
          else if ( type .eq. 2 ) then
@@ -548,7 +548,7 @@ c
             call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                    iwork, workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
-               print*, ' ' 
+               print*, ' '
                print*, ' _SBAND: Error with _bgtrs. '
                print*, ' '
                go to 9000
@@ -558,15 +558,15 @@ c
 c
 c           %-----------------------------------%
 c           | Perform  y <--- OP*x = inv[M]*A*x |
-c           | to force the starting vector into | 
+c           | to force the starting vector into |
 c           | the range of OP.                  |
 c           %-----------------------------------%
 c
-            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                  lda, workd(ipntr(1)), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                  lda, workd(ipntr(1)), 1, zero,
      &                  workd(ipntr(2)), 1)
             call scopy(n, workd(ipntr(2)), 1, workd(ipntr(1)), 1)
-            call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                    iwork, workd(ipntr(2)), n, ierr)
             if (ierr .ne. 0) then
                print*, ' '
@@ -579,36 +579,36 @@ c
 c
 c           %-----------------------------------------%
 c           | Perform y <-- OP*x                      |
-c           |           = inv[A-SIGMA*M]*M            | 
+c           |           = inv[A-SIGMA*M]*M            |
 c           | to force the starting vector into the   |
 c           | range of OP.                            |
 c           %-----------------------------------------%
 c
-            call sgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
-            call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                   iwork, workd(ipntr(2)), n, ierr)
             if (ierr .ne. 0) then
-               print*, ' ' 
+               print*, ' '
                print*, '_SBAND: Error with _gbtrs.'
-               print*, ' ' 
+               print*, ' '
                go to 9000
             end if
 c
          else if ( type .eq. 5) then
 c
-c           %---------------------------------------% 
+c           %---------------------------------------%
 c           | Perform y <-- OP*x                    |
 c           |    = inv[A-SIGMA*M]*A                 |
 c           | to force the starting vector into the |
 c           | range of OP.                          |
 c           %---------------------------------------%
 c
-            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
-            call sgbtrs('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call sgbtrs('Notranspose', n, kl, ku, 1, rfac, lda,
      &                   iwork, workd(ipntr(2)), n, ierr)
 c
             if ( ierr .ne. 0 ) then
@@ -622,31 +622,31 @@ c
 c
 c           %---------------------------------------%
 c           | Perform y <-- OP*x                    |
-c           | = (inv[A-SIGMA*M])*(A+SIGMA*M)*x      | 
+c           | = (inv[A-SIGMA*M])*(A+SIGMA*M)*x      |
 c           | to force the starting vector into the |
-c           | range of OP.                          | 
+c           | range of OP.                          |
 c           %---------------------------------------%
 c
             if ( bmat .eq. 'G' ) then
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    ab(itop,1), lda, workd(ipntr(1)), 1, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    ab(itop,1), lda, workd(ipntr(1)), 1,
      &                    zero, workd(ipntr(2)), 1)
-               call sgbmv('Notranspose', n, n, kl, ku, sigma, 
-     &                    mb(itop,1), lda, workd(ipntr(1)), 1, 
+               call sgbmv('Notranspose', n, n, kl, ku, sigma,
+     &                    mb(itop,1), lda, workd(ipntr(1)), 1,
      &                    one, workd(ipntr(2)), 1)
-            else 
+            else
                call scopy(n, workd(ipntr(1)), 1, workd(ipntr(2)), 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                    lda, workd(ipntr(1)), 1, sigma, 
+               call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                    lda, workd(ipntr(1)), 1, sigma,
      &                    workd(ipntr(2)), 1)
-            end if   
+            end if
 c
-            call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                   iwork, workd(ipntr(2)), n, ierr)
 c
-            if (ierr .ne. 0) then 
+            if (ierr .ne. 0) then
                print*, ' '
-               print*, '_SBAND: Error with _gbtrs.' 
+               print*, '_SBAND: Error with _gbtrs.'
                print*, ' '
                go to 9000
             end if
@@ -661,8 +661,8 @@ c           %----------------------------%
 c           | Perform  y <--- OP*x = A*x |
 c           %----------------------------%
 c
-            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
          else if ( type .eq. 2) then
@@ -677,7 +677,7 @@ c
      &                       iwork, workd(ipntr(2)), n, ierr)
                if ( ierr .ne. 0 ) then
                   print*, ' '
-                  print*, '_SBAND: Error with _gbtrs.' 
+                  print*, '_SBAND: Error with _gbtrs.'
                   print*, ' '
                   go to 9000
                end if
@@ -688,16 +688,16 @@ c           %-----------------------------------%
 c           | Perform  y <--- OP*x = inv[M]*A*x |
 c           %-----------------------------------%
 c
-            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                  lda, workd(ipntr(1)), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                  lda, workd(ipntr(1)), 1, zero,
      &                  workd(ipntr(2)), 1)
-            call scopy(n, workd(ipntr(2)), 1, workd(ipntr(1)), 1) 
-            call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call scopy(n, workd(ipntr(2)), 1, workd(ipntr(1)), 1)
+            call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                    iwork, workd(ipntr(2)), n, ierr)
             if (ierr .ne. 0) then
                print*, ' '
                print*, '_SBAND: error with _bgtrs.'
-               print*, ' ' 
+               print*, ' '
                go to 9000
             end if
 c
@@ -706,22 +706,22 @@ c
 c           %-------------------------------------%
 c           | Perform y <-- inv(A-sigma*M)*(M*x). |
 c           | (M*x) has been computed and stored  |
-c           | in workd(ipntr(3)).                 |           
+c           | in workd(ipntr(3)).                 |
 c           %-------------------------------------%
 c
             call scopy(n, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-            call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda,
      &                    iwork, workd(ipntr(2)), n, ierr)
-            if (ierr .ne. 0) then 
+            if (ierr .ne. 0) then
                print*, ' '
-               print*, '_SBAND: Error with _gbtrs.' 
+               print*, '_SBAND: Error with _gbtrs.'
                print*, ' '
                go to 9000
             end if
-c 
+c
          else if ( type .eq. 5 ) then
 c
-c           %-------------------------------% 
+c           %-------------------------------%
 c           | Perform y <-- OP*x            |
 c           |    = inv[A-SIGMA*M]*A*x       |
 c           | B*x = A*x has been computed   |
@@ -729,7 +729,7 @@ c           | and saved in workd(ipntr(3)). |
 c           %-------------------------------%
 c
             call scopy (n, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-            call sgbtrs('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call sgbtrs('Notranspose', n, kl, ku, 1, rfac, lda,
      &                   iwork, workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
@@ -742,24 +742,24 @@ c
 c
 c           %---------------------------------%
 c           | Perform y <-- OP*x              |
-c           | = inv[A-SIGMA*M]*(A+SIGMA*M)*x. | 
+c           | = inv[A-SIGMA*M]*(A+SIGMA*M)*x. |
 c           | (M*x) has been saved in         |
 c           | workd(ipntr(3)).                |
 c           %---------------------------------%
 c
             if ( bmat .eq. 'G' ) then
-               call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                    ab(itop,1), lda, workd(ipntr(1)), 1, 
+               call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                    ab(itop,1), lda, workd(ipntr(1)), 1,
      &                    zero, workd(ipntr(2)), 1)
-               call saxpy( n, sigma, workd(ipntr(3)), 1, 
+               call saxpy( n, sigma, workd(ipntr(3)), 1,
      &                    workd(ipntr(2)), 1 )
-            else 
+            else
                call scopy (n, workd(ipntr(1)), 1, workd(ipntr(2)), 1)
-               call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                    lda, workd(ipntr(1)), 1, sigma, 
+               call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                    lda, workd(ipntr(1)), 1, sigma,
      &                    workd(ipntr(2)), 1)
             end if
-            call sgbtrs('Notranspose', n, kl, ku, 1, rfac, lda, 
+            call sgbtrs('Notranspose', n, kl, ku, 1, rfac, lda,
      &                   iwork, workd(ipntr(2)), n, ierr)
 c
          end if
@@ -767,9 +767,9 @@ c
       else if (ido .eq. 2) then
 c
 c        %----------------------------------%
-c        |        Perform y <-- B*x         | 
+c        |        Perform y <-- B*x         |
 c        | Note when Buckling mode is used, |
-c        | B = A, otherwise B=M.            | 
+c        | B = A, otherwise B=M.            |
 c        %----------------------------------%
 c
          if (type .eq. 5) then
@@ -778,20 +778,20 @@ c           %---------------------%
 c           | Buckling Mode, B=A. |
 c           %---------------------%
 c
-            call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                ab(itop,1), lda, workd(ipntr(1)), 1, 
+            call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                ab(itop,1), lda, workd(ipntr(1)), 1,
      &                zero, workd(ipntr(2)), 1)
          else
 
-            call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                mb(itop,1), lda, workd(ipntr(1)), 1, 
+            call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                mb(itop,1), lda, workd(ipntr(1)), 1,
      &                zero, workd(ipntr(2)), 1)
          end if
 c
-      else 
+      else
 c
 c        %-----------------------------------------%
-c        | Either we have convergence, or there is | 
+c        | Either we have convergence, or there is |
 c        | error.                                  |
 c        %-----------------------------------------%
 c
@@ -808,7 +808,7 @@ c
             print *, ' '
             go to 9000
 c
-         else 
+         else
 c
             if ( info .eq. 1) then
                print *, ' '
@@ -823,22 +823,22 @@ c
 c
             if (iparam(5) .gt. 0) then
 c
-               call sseupd ( rvec, 'A', select, d, z, ldz, sigma, 
-     &                  bmat, n, which, nev, tol, resid, ncv, v, ldv, 
-     &                  iparam, ipntr, workd, workl, lworkl, info )            
+               call sseupd ( rvec, 'A', select, d, z, ldz, sigma,
+     &                  bmat, n, which, nev, tol, resid, ncv, v, ldv,
+     &                  iparam, ipntr, workd, workl, lworkl, info )
 c
                if ( info .ne. 0) then
-c 
+c
 c                 %------------------------------------%
 c                 | Check the documentation of sneupd. |
 c                 %------------------------------------%
 c
-                  print *, ' ' 
+                  print *, ' '
                   print *, ' Error with _neupd = ', info
                   print *, ' Check the documentation of _neupd '
-                  print *, ' ' 
+                  print *, ' '
                   go to 9000
-c 
+c
                end if
 c
             end if
@@ -853,7 +853,7 @@ c     %----------------------------------------%
 c     | L O O P  B A C K to call SSAUPD again. |
 c     %----------------------------------------%
 c
-      go to 90 
+      go to 90
 c
  9000 continue
 c

EXAMPLES/BAND/ssbdr1.f

@@ -2,13 +2,13 @@
 c
 c     ... Construct the matrix A in LAPACK-style band form.
 c         The matrix A is derived from the discretization of
-c         the 2-dimensional Laplacian on the unit square with 
-c         zero Dirichlet boundary condition using standard 
+c         the 2-dimensional Laplacian on the unit square with
+c         zero Dirichlet boundary condition using standard
 c         central difference.
 c
 c     ... Call SSBAND to find eigenvalues LAMBDA such that
 c                          A*x = x*LAMBDA.
-c       
+c
 c     ... Use mode 1 of SSAUPD.
 c
 c\BeginLib
@@ -47,13 +47,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -62,9 +62,9 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Real 
+      Real
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn), 
+     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn),
      &                 v(ldv, maxncv), resid(maxn), d(maxncv, 2),
      &                 ax(maxn)
 c
@@ -76,15 +76,15 @@ c
       integer          nev, ncv, ku, kl, info, i, j, ido,
      &                 n, nx, lo, isub, isup, idiag, maxitr, mode,
      &                 nconv
-      Real  
+      Real
      &                 tol, sigma, h2
       logical          rvec
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Real  
+      Real
      &                 one, zero, two
       parameter        (one = 1.0E+0 , zero = 0.0E+0 , two = 2.0E+0 )
 c
@@ -92,9 +92,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  slapy2, snrm2
-      external          slapy2, snrm2, sgbmv, saxpy 
+      external          slapy2, snrm2, sgbmv, saxpy
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -121,13 +121,13 @@ c     | However, the following conditions must be       |
 c     | satisfied:                                      |
 c     |                   N <= MAXN                     |
 c     |                 NEV <= MAXNEV                   |
-c     |           NEV + 1 <= NCV <= MAXNCV              | 
-c     %-------------------------------------------------% 
+c     |           NEV + 1 <= NCV <= MAXNCV              |
+c     %-------------------------------------------------%
 c
-      nx  = 10 
+      nx  = 10
       n    = nx*nx
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _SBDR1: N is greater than MAXN '
          go to 9000
@@ -153,7 +153,7 @@ c     | generated in SSAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = ncv**2+8*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -169,7 +169,7 @@ c
       mode = 1
 c
       iparam(3) = maxitr
-      iparam(7) = mode 
+      iparam(7) = mode
 c
 c     %----------------------------------------%
 c     | Construct the matrix A in LAPACK-style |
@@ -190,10 +190,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = nx 
-      ku   = nx 
+      kl   = nx
+      ku   = nx
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -201,12 +201,12 @@ c
       idiag = kl+ku+1
       do 30 j = 1, n
          a(idiag,j) = 4.0E+0  / h2
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+ku+2
       do 50 i = 1, nx
@@ -214,8 +214,8 @@ c
         do 40 j = lo+1, lo+nx-1
            a(isup,j+1) = -one / h2
            a(isub,j) = -one / h2
-  40    continue      
-  50  continue 
+  40    continue
+  50  continue
 c
 c     %------------------------------------%
 c     | KL-th subdiagonal and KU-th super- |
@@ -229,8 +229,8 @@ c
          do 70 j = lo+1, lo+nx
             a(isup,nx+j)  = -one / h2
             a(isub,j) = -one / h2
- 70      continue 
- 80   continue 
+ 70      continue
+ 80   continue
 c
 c     %-------------------------------------%
 c     | Call SSBAND to find eigenvalues and |
@@ -239,18 +239,18 @@ c     | returned in the first column of D.  |
 c     | Eigenvectors are returned in the    |
 c     | first NCONV (=IPARAM(5)) columns of |
 c     | V.                                  |
-c     %-------------------------------------% 
+c     %-------------------------------------%
 c
       rvec = .true.
-      call ssband( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda, 
-     &             rfac, kl, ku, which, bmat, nev, tol, 
-     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl, 
+      call ssband( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda,
+     &             rfac, kl, ku, which, bmat, nev, tol,
+     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl,
      &             iwork, info)
 c
       if ( info .eq. 0) then
 c
          nconv = iparam(5)
-c 
+c
 c        %-----------------------------------%
 c        | Print out convergence information |
 c        %-----------------------------------%
@@ -278,18 +278,18 @@ c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
          do 90 j = 1, nconv
-            call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                 a(kl+1,1), lda, v(1,j), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                 a(kl+1,1), lda, v(1,j), 1, zero,
      &                 ax, 1)
             call saxpy(n, -d(j,1), v(1,j), 1, ax, 1)
             d(j,2) = snrm2(n, ax, 1)
             d(j,2) = d(j,2) / abs(d(j,1))
 c
- 90      continue 
+ 90      continue
 
          call smout(6, nconv, 2, d, maxncv, -6,
      &             'Ritz values and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -300,8 +300,8 @@ c
           print *, ' '
           print *, ' Error with _sband, info= ', info
           print *, ' Check the documentation of _sband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/ssbdr2.f

@@ -2,11 +2,11 @@
 c
 c     ... Construct the matrix A in LAPACK-style band form.
 c         The matrix A is derived from the discretization of
-c         the 2-dimensional Laplacian on the unit square 
+c         the 2-dimensional Laplacian on the unit square
 c         with zero Dirichlet boundary condition using standard
 c         central difference.
 c
-c     ... Call SSBAND to find eigenvalues LAMBDA closest to 
+c     ... Call SSBAND to find eigenvalues LAMBDA closest to
 c         SIGMA such that
 c                          A*x = x*LAMBDA.
 c
@@ -48,13 +48,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -63,10 +63,10 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Real 
+      Real
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), 
-     &                 v(ldv, maxncv), resid(maxn), d(maxncv, 2), 
+     &                 workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn),
+     &                 v(ldv, maxncv), resid(maxn), d(maxncv, 2),
      &                 ax(maxn)
 c
 c     %---------------%
@@ -77,15 +77,15 @@ c
       integer          nev, ncv, ku, kl, info, i, j, ido,
      &                 n, nx, lo, isub, isup, idiag, maxitr, mode,
      &                 nconv
-      Real  
+      Real
      &                 tol, sigma, h2
       logical          rvec
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Real  
+      Real
      &                 one, zero, two
       parameter        (one = 1.0E+0 , zero = 0.0E+0 , two = 2.0E+0 )
 c
@@ -93,9 +93,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  slapy2, snrm2
-      external          slapy2, snrm2, saxpy, sgbmv 
+      external          slapy2, snrm2, saxpy, sgbmv
 c
 c     %-----------------------%
 c     | Executable Statements |
@@ -118,13 +118,13 @@ c     | However, the following conditions must be        |
 c     | satisfied:                                       |
 c     |                   N <= MAXN                      |
 c     |                 NEV <= MAXNEV                    |
-c     |           NEV + 1 <= NCV <= MAXNCV               | 
-c     %--------------------------------------------------% 
+c     |           NEV + 1 <= NCV <= MAXNCV               |
+c     %--------------------------------------------------%
 c
-      nx  = 10 
+      nx  = 10
       n    = nx*nx
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _SBDR2: N is greater than MAXN '
          go to 9000
@@ -151,7 +151,7 @@ c     | generated in SSAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+6*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -167,7 +167,7 @@ c
       mode = 3
 c
       iparam(3) = maxitr
-      iparam(7) = mode 
+      iparam(7) = mode
 c
 c     %----------------------------------------%
 c     | Construct the matrix A in LAPACK-style |
@@ -188,10 +188,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = nx 
-      ku   = nx 
+      kl   = nx
+      ku   = nx
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -199,12 +199,12 @@ c
       idiag = kl+ku+1
       do 30 j = 1, n
          a(idiag,j) = 4.0E+0  / h2
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+ku+2
       do 50 i = 1, nx
@@ -212,8 +212,8 @@ c
         do 40 j = lo+1, lo+nx-1
            a(isup,j+1) = -one / h2
            a(isub,j) = -one / h2
-  40    continue      
-  50  continue 
+  40    continue
+  50  continue
 c
 c     %------------------------------------%
 c     | KL-th subdiagonal and KU-th super- |
@@ -227,8 +227,8 @@ c
          do 70 j = lo+1, lo+nx
             a(isup,nx+j)  = -one / h2
             a(isub,j) = -one / h2
- 70      continue 
- 80   continue 
+ 70      continue
+ 80   continue
 c
 c     %-------------------------------------%
 c     | Call SSBAND to find eigenvalues and |
@@ -239,10 +239,10 @@ c     | first NCONV (=IPARAM(5)) columns of |
 c     | V.                                  |
 c     %-------------------------------------%
 c
-      rvec = .true. 
-      call ssband( rvec,'A', select, d, v, ldv, sigma, n, a, m, 
-     &             lda, rfac, kl, ku, which, bmat, nev, tol, 
-     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl, 
+      rvec = .true.
+      call ssband( rvec,'A', select, d, v, ldv, sigma, n, a, m,
+     &             lda, rfac, kl, ku, which, bmat, nev, tol,
+     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl,
      &             iwork, info)
 c
       if ( info .eq. 0) then
@@ -276,18 +276,18 @@ c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
          do 90 j = 1, nconv
-            call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                 a(kl+1,1), lda, v(1,j), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                 a(kl+1,1), lda, v(1,j), 1, zero,
      &                 ax, 1)
             call saxpy(n, -d(j,1), v(1,j), 1, ax, 1)
             d(j,2) = snrm2(n, ax, 1)
             d(j,2) = d(j,2) / abs(d(j,1))
 c
- 90      continue 
+ 90      continue
 
          call smout(6, nconv, 2, d, maxncv, -6,
      &             'Ritz values and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -298,8 +298,8 @@ c
           print *, ' '
           print *, ' Error with _sband, info= ', info
           print *, ' Check the documentation of _sband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/ssbdr3.f

@@ -5,7 +5,7 @@ c         The matrix A is the 1-dimensional discrete Laplacian on [0,1]
 c         with zero Dirichlet boundary condition, M is the mass
 c         formed by using piecewise linear elements on [0,1].
 c
-c     ... Call SSBAND with regular mode to find eigenvalues LAMBDA 
+c     ... Call SSBAND with regular mode to find eigenvalues LAMBDA
 c         such that
 c                          A*x = LAMBDA*M*x.
 c
@@ -46,13 +46,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -61,9 +61,9 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Real 
+      Real
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn), 
+     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn),
      &                 v(ldv, maxncv), resid(maxn), d(maxncv, 2),
      &                 ax(maxn), mx(maxn)
 c
@@ -74,15 +74,15 @@ c
       character        which*2, bmat
       integer          nev, ncv, ku, kl, info, j, ido,
      &                 n, isub, isup, idiag, maxitr, mode, nconv
-      Real  
+      Real
      &                 tol, h, sigma, r1, r2
       logical          rvec
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Real  
+      Real
      &                 one, zero, two, four, six
       parameter        (one = 1.0E+0 , zero = 0.0E+0 , two = 2.0E+0 ,
      &                  four = 4.0E+0 , six = 6.0E+0 )
@@ -91,9 +91,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  slapy2, snrm2
-      external          slapy2, snrm2, saxpy, sgbmv 
+      external          slapy2, snrm2, saxpy, sgbmv
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -116,12 +116,12 @@ c     | However, the following conditions must be       |
 c     | satisfied:                                      |
 c     |                   N <= MAXN                     |
 c     |                 NEV <= MAXNEV                   |
-c     |           NEV + 1 <= NCV <= MAXNCV              | 
-c     %-------------------------------------------------% 
+c     |           NEV + 1 <= NCV <= MAXNCV              |
+c     %-------------------------------------------------%
 c
-      n    = 100 
-      nev  = 4 
-      ncv  = 10 
+      n    = 100
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _SBDR3: N is greater than MAXN '
          go to 9000
@@ -147,7 +147,7 @@ c     | generated in SSAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = ncv**2+8*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -184,10 +184,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = 1 
-      ku   = 1 
+      kl   = 1
+      ku   = 1
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -197,12 +197,12 @@ c
       do 30 j = 1, n
          a(idiag,j) = two / h
          m(idiag,j) = r1 * h
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       r2 = one / six
       isup = kl+ku
       isub = kl+ku+2
@@ -223,9 +223,9 @@ c     | V.                                  |
 c     %-------------------------------------%
 c
       rvec = .true.
-      call ssband( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda, 
-     &             rfac, kl, ku, which, bmat, nev, tol, 
-     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl, 
+      call ssband( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda,
+     &             rfac, kl, ku, which, bmat, nev, tol,
+     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl,
      &             iwork, info)
 c
       if ( info .eq. 0) then
@@ -259,21 +259,21 @@ c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
          do 90 j = 1, nconv
-            call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                 a(kl+1,1), lda, v(1,j), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                 a(kl+1,1), lda, v(1,j), 1, zero,
      &                 ax, 1)
-            call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                 m(kl+1,1), lda, v(1,j), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                 m(kl+1,1), lda, v(1,j), 1, zero,
      &                 mx, 1)
             call saxpy(n, -d(j,1), mx, 1, ax, 1)
             d(j,2) = snrm2(n, ax, 1)
             d(j,2) = d(j,2) / abs(d(j,1))
 c
- 90      continue 
+ 90      continue
 
          call smout(6, nconv, 2, d, maxncv, -6,
      &             'Ritz values and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -284,8 +284,8 @@ c
           print *, ' '
           print *, ' Error with _sband, info= ', info
           print *, ' Check the documentation of _sband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/ssbdr4.f

@@ -5,7 +5,7 @@ c         The matrix A is the 1-dimensional discrete Laplacian on [0,1]
 c         with zero Dirichlet boundary condition, M is the mass
 c         formed by using piecewise linear elements on [0,1].
 c
-c     ... Call SSBAND with shift-invert mode to find eigenvalues LAMBDA 
+c     ... Call SSBAND with shift-invert mode to find eigenvalues LAMBDA
 c         closest to SIGMA such that
 c                          A*x = LAMBDA*M*x.
 c
@@ -47,13 +47,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -62,9 +62,9 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Real 
+      Real
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn), 
+     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn),
      &                 v(ldv, maxncv), resid(maxn), d(maxncv, 2),
      &                 ax(maxn), mx(maxn)
 c
@@ -75,15 +75,15 @@ c
       character        which*2, bmat
       integer          nev, ncv, ku, kl, info, j, ido,
      &                 n, isub, isup, idiag, maxitr, mode, nconv
-      Real  
+      Real
      &                 tol, h, sigma, r1, r2
       logical          rvec
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Real  
+      Real
      &                 one, zero, two, four, six
       parameter        (one = 1.0E+0 , zero = 0.0E+0 , two = 2.0E+0 ,
      &                  four = 4.0E+0 , six = 6.0E+0 )
@@ -92,9 +92,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  slapy2, snrm2
-      external          slapy2, snrm2, saxpy, sgbmv 
+      external          slapy2, snrm2, saxpy, sgbmv
 c
 c     %-----------------------%
 c     | Executable Statements |
@@ -113,12 +113,12 @@ c     | However, the following conditions must be        |
 c     | satisfied:                                       |
 c     |                   N <= MAXN                      |
 c     |                 NEV <= MAXNEV                    |
-c     |           NEV + 1 <= NCV <= MAXNCV               | 
-c     %--------------------------------------------------% 
+c     |           NEV + 1 <= NCV <= MAXNCV               |
+c     %--------------------------------------------------%
 c
       n    = 100
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _SBDR4: N is greater than MAXN '
          go to 9000
@@ -145,7 +145,7 @@ c     | generated in SSAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = ncv**2+8*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -182,10 +182,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = 1 
-      ku   = 1 
+      kl   = 1
+      ku   = 1
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -195,19 +195,19 @@ c
       do 30 j = 1, n
          a(idiag,j) = two / h
          m(idiag,j) = r1 * h
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       r2 = one / six
       isup = kl+ku
       isub = kl+ku+2
       do 60 j = 1, n-1
          a(isup,j+1) = -one / h
          a(isub,j) = -one / h
-         m(isup,j+1) = r2 * h 
+         m(isup,j+1) = r2 * h
          m(isub,j) = r2 * h
   60  continue
 c
@@ -221,9 +221,9 @@ c     | V.                                  |
 c     %-------------------------------------%
 c
       rvec = .true.
-      call ssband( rvec, 'A', select, d, v, ldv, sigma, n, a, m, 
-     &             lda, rfac, kl, ku, which, bmat, nev, tol, 
-     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl, 
+      call ssband( rvec, 'A', select, d, v, ldv, sigma, n, a, m,
+     &             lda, rfac, kl, ku, which, bmat, nev, tol,
+     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl,
      &             iwork, info)
 c
       if ( info .eq. 0) then
@@ -243,7 +243,7 @@ c
          print *, ' The number of Lanczos vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' The number of converged Ritz values is ',
-     &              nconv 
+     &              nconv
          print *, ' What portion of the spectrum ', which
          print *, ' The number of Implicit Arnoldi',
      &              ' update taken is ', iparam(3)
@@ -257,21 +257,21 @@ c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
          do 90 j = 1, nconv
-            call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                 a(kl+1,1), lda, v(1,j), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                 a(kl+1,1), lda, v(1,j), 1, zero,
      &                 ax, 1)
-            call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                 m(kl+1,1), lda, v(1,j), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                 m(kl+1,1), lda, v(1,j), 1, zero,
      &                 mx, 1)
             call saxpy(n, -d(j,1), mx, 1, ax, 1)
             d(j,2) = snrm2(n, ax, 1)
             d(j,2) = d(j,2) / abs(d(j,1))
 c
- 90      continue 
+ 90      continue
 
          call smout(6, nconv, 2, d, maxncv, -6,
      &             'Ritz values and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -282,8 +282,8 @@ c
           print *, ' '
           print *, ' Error with _sband, info= ', info
           print *, ' Check the documentation of _sband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/ssbdr5.f

@@ -3,9 +3,9 @@ c
 c     ... Construct the matrix A in LAPACK-style band form.
 c         The matrix A is the 1-dimensional discrete Laplacian on [0,1]
 c         with zero Dirichlet boundary condition, KG is the mass
-c         formed by using piecewise linear elements on [0,1]. 
+c         formed by using piecewise linear elements on [0,1].
 c
-c     ... Call SSBAND with Buckling mode to find eigenvalues LAMBDA 
+c     ... Call SSBAND with Buckling mode to find eigenvalues LAMBDA
 c         such that
 c                          A*x = M*x*LAMBDA.
 c
@@ -47,13 +47,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -62,9 +62,9 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Real 
+      Real
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn), 
+     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn),
      &                 v(ldv, maxncv), resid(maxn), d(maxncv, 2),
      &                 ax(maxn), mx(maxn)
 c
@@ -75,15 +75,15 @@ c
       character        which*2, bmat
       integer          nev, ncv, kl, ku, info, j, ido,
      &                 n, isub, isup, idiag, maxitr, mode, nconv
-      Real  
+      Real
      &                 tol, h, sigma, r1, r2
       logical          rvec
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Real  
+      Real
      &                 one, zero, two, four, six
       parameter        (one = 1.0E+0 , zero = 0.0E+0 , two = 2.0E+0 ,
      &                  four = 4.0E+0 , six = 6.0E+0 )
@@ -92,9 +92,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  slapy2, snrm2
-      external          slapy2, snrm2, sgbmv, saxpy 
+      external          slapy2, snrm2, sgbmv, saxpy
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -118,12 +118,12 @@ c     | the spectrum.  However, the following conditions |
 c     | must be satisfied:                               |
 c     |                   N <= MAXN                      |
 c     |                 NEV <= MAXNEV                    |
-c     |           NEV + 1 <= NCV <= MAXNCV               | 
-c     %--------------------------------------------------% 
+c     |           NEV + 1 <= NCV <= MAXNCV               |
+c     %--------------------------------------------------%
 c
       n    = 100
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _SBDR5: N is greater than MAXN '
          go to 9000
@@ -150,7 +150,7 @@ c     | generated in SSAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = ncv**2+8*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -187,10 +187,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = 1 
-      ku   = 1 
+      kl   = 1
+      ku   = 1
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -200,12 +200,12 @@ c
       do 30 j = 1, n
          a(idiag,j) = two / h
          m(idiag,j) = r1 * h
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       r2 = one / six
       isup = kl+ku
       isub = kl+ku+2
@@ -226,9 +226,9 @@ c     | V.                                  |
 c     %-------------------------------------%
 c
       rvec = .true.
-      call ssband( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda, 
-     &             rfac, kl, ku, which, bmat, nev, tol, 
-     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl, 
+      call ssband( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda,
+     &             rfac, kl, ku, which, bmat, nev, tol,
+     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl,
      &             iwork, info)
 c
       if ( info .eq. 0) then
@@ -262,21 +262,21 @@ c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
          do 90 j = 1, nconv
-            call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                 a(kl+1,1), lda, v(1,j), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                 a(kl+1,1), lda, v(1,j), 1, zero,
      &                 ax, 1)
-            call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                 m(kl+1,1), lda, v(1,j), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                 m(kl+1,1), lda, v(1,j), 1, zero,
      &                 mx, 1)
             call saxpy(n, -d(j,1), mx, 1, ax, 1)
             d(j,2) = snrm2(n, ax, 1)
             d(j,2) = d(j,2) / abs(d(j,1))
 c
- 90      continue 
+ 90      continue
 
          call smout(6, nconv, 2, d, maxncv, -6,
      &             'Ritz values and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -287,8 +287,8 @@ c
           print *, ' '
           print *, ' Error with _sband, info= ', info
           print *, ' Check the documentation of _sband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/ssbdr6.f

@@ -4,7 +4,7 @@ c     ... Construct the matrix A in LAPACK-style band form.
 c         The matrix A is the 1-dimensional discrete Laplacian on [0,1]
 c         with zero Dirichlet boundary condition, M is the mass
 c         formed by using piecewise linear elements on [0,1].
-c 
+c
 c     ... Call SSBAND with Cayley mode to find eigenvalues LAMBDA such that
 c                          A*x = LAMBDA*M*x.
 c
@@ -46,13 +46,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -61,9 +61,9 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Real 
+      Real
      &                 a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
-     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn), 
+     &                 workl(maxncv*maxncv+8*maxncv), workd(3*maxn),
      &                 v(ldv, maxncv), resid(maxn), d(maxncv, 2),
      &                 ax(maxn), mx(maxn)
 c
@@ -74,15 +74,15 @@ c
       character        which*2, bmat
       integer          nev, ncv, ku, kl, info, j, ido,
      &                 n, isub, isup, idiag, maxitr, mode, nconv
-      Real  
+      Real
      &                 tol, h, sigma, r1, r2
       logical          rvec
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Real  
+      Real
      &                 one, zero, two, four, six
       parameter        (one = 1.0E+0 , zero = 0.0E+0 , two = 2.0E+0 ,
      &                  four = 4.0E+0 , six = 6.0E+0 )
@@ -91,9 +91,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  slapy2, snrm2
-      external          slapy2, snrm2, saxpy, sgbmv 
+      external          slapy2, snrm2, saxpy, sgbmv
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -117,12 +117,12 @@ c     | the spectrum.  However, the following conditions |
 c     | must be satisfied:                               |
 c     |                   N <= MAXN                      |
 c     |                 NEV <= MAXNEV                    |
-c     |           NEV + 1 <= NCV <= MAXNCV               | 
-c     %--------------------------------------------------% 
+c     |           NEV + 1 <= NCV <= MAXNCV               |
+c     %--------------------------------------------------%
 c
       n    = 100
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _SBDR6: N is greater than MAXN '
          go to 9000
@@ -149,7 +149,7 @@ c     | generated in SSAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl  = ncv**2+8*ncv
-      tol  = zero 
+      tol  = zero
       ido  = 0
       info = 0
 c
@@ -186,10 +186,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = 1 
-      ku   = 1 
+      kl   = 1
+      ku   = 1
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -199,12 +199,12 @@ c
       do 30 j = 1, n
          a(idiag,j) = two / h
          m(idiag,j) = r1 * h
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       r2 = one / six
       isup = kl+ku
       isub = kl+ku+2
@@ -225,9 +225,9 @@ c     | V.                                  |
 c     %-------------------------------------%
 c
       rvec = .true.
-      call ssband( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda, 
-     &             rfac, kl, ku, which, bmat, nev, tol, 
-     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl, 
+      call ssband( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda,
+     &             rfac, kl, ku, which, bmat, nev, tol,
+     &             resid, ncv, v, ldv, iparam, workd, workl, lworkl,
      &             iwork, info)
 c
       if ( info .eq. 0) then
@@ -261,21 +261,21 @@ c        |    ||  A*x - lambda*x ||   |
 c        %----------------------------%
 c
          do 90 j = 1, nconv
-            call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                 a(kl+1,1), lda, v(1,j), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                 a(kl+1,1), lda, v(1,j), 1, zero,
      &                 ax, 1)
-            call sgbmv('Notranspose', n, n, kl, ku, one, 
-     &                 m(kl+1,1), lda, v(1,j), 1, zero, 
+            call sgbmv('Notranspose', n, n, kl, ku, one,
+     &                 m(kl+1,1), lda, v(1,j), 1, zero,
      &                 mx, 1)
             call saxpy(n, -d(j,1), mx, 1, ax, 1)
             d(j,2) = snrm2(n, ax, 1)
             d(j,2) = d(j,2) / abs(d(j,1))
 c
- 90      continue 
+ 90      continue
 
          call smout(6, nconv, 2, d, maxncv, -6,
      &             'Ritz values and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -286,8 +286,8 @@ c
           print *, ' '
           print *, ' Error with _band, info= ', info
           print *, ' Check the documentation of _band '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/znband.f

@@ -1,29 +1,29 @@
 c \BeginDoc
 c
-c \Name: znband 
+c \Name: znband
 c
 c \Description:
-c  This subroutine returns the converged approximations to eigenvalues 
-c  of A*z = lambda*B*z and (optionally): 
-c 
-c      (1) The corresponding approximate eigenvectors; 
-c 
-c      (2) An orthonormal basis for the associated approximate 
-c          invariant subspace; 
-c 
-c      (3) Both.  
+c  This subroutine returns the converged approximations to eigenvalues
+c  of A*z = lambda*B*z and (optionally):
+c
+c      (1) The corresponding approximate eigenvectors;
+c
+c      (2) An orthonormal basis for the associated approximate
+c          invariant subspace;
+c
+c      (3) Both.
 c
 c  Matrices A and B are stored in LAPACK-style banded form.
 c
-c  There is negligible additional cost to obtain eigenvectors.  An orthonormal 
+c  There is negligible additional cost to obtain eigenvectors.  An orthonormal
 c  basis is always computed.  There is an additional storage cost of n*nev
-c  if both are requested (in this case a separate array Z must be supplied). 
+c  if both are requested (in this case a separate array Z must be supplied).
 c
 c  The approximate eigenvalues and eigenvectors of  A*z = lambda*B*z
-c  are commonly called Ritz values and Ritz vectors respectively.  They are 
-c  referred to as such in the comments that follow.  The computed orthonormal 
-c  basis for the invariant subspace corresponding to these Ritz values is 
-c  referred to as a Schur basis. 
+c  are commonly called Ritz values and Ritz vectors respectively.  They are
+c  referred to as such in the comments that follow.  The computed orthonormal
+c  basis for the invariant subspace corresponding to these Ritz values is
+c  referred to as a Schur basis.
 c
 c  znband  can be called with one of the following modes:
 c
@@ -40,15 +40,15 @@ c
 c  Choice of different modes can be specified in IPARAM(7) defined below.
 c
 c \Usage
-c   call znband 
-c      ( RVEC, HOWMNY, SELECT, D , Z, LDZ, SIGMA, WORKEV, N, AB, 
-c        MB, LDA, FAC, KL, KU, WHICH, BMAT, NEV, TOL, RESID, NCV, 
+c   call znband
+c      ( RVEC, HOWMNY, SELECT, D , Z, LDZ, SIGMA, WORKEV, N, AB,
+c        MB, LDA, FAC, KL, KU, WHICH, BMAT, NEV, TOL, RESID, NCV,
 c        V, LDV, IPARAM, WORKD, WORKL, LWORKL, RWORK, IWORK, INFO )
 c
 c \Arguments
-c  RVEC    LOGICAL  (INPUT) 
+c  RVEC    LOGICAL  (INPUT)
 c          Specifies whether a basis for the invariant subspace corresponding
-c          to the converged Ritz value approximations for the eigenproblem 
+c          to the converged Ritz value approximations for the eigenproblem
 c          A*z = lambda*B*z is computed.
 c
 c             RVEC = .FALSE.     Compute Ritz values only.
@@ -56,8 +56,8 @@ c
 c             RVEC = .TRUE.      Compute Ritz vectors or Schur vectors.
 c                                See Remarks below.
 c
-c  HOWMNY  Character*1  (INPUT) 
-c          Specifies the form of the invariant subspace to be computed 
+c  HOWMNY  Character*1  (INPUT)
+c          Specifies the form of the invariant subspace to be computed
 c          corresponding to the converged Ritz values.
 c          = 'A': Compute NEV Ritz vectors;
 c          = 'P': Compute NEV Schur vectors;
@@ -67,7 +67,7 @@ c
 c  SELECT  Logical array of dimension NCV.  (INPUT)
 c          If HOWMNY = 'S', SELECT specifies the Ritz vectors to be
 c          computed. To select the real Ritz vector corresponding to a
-c          Ritz value D(j), SELECT(j) must be set to .TRUE.. 
+c          Ritz value D(j), SELECT(j) must be set to .TRUE..
 c          If HOWMNY = 'A' or 'P', SELECT need not be initialized
 c          but it is used as internal workspace.
 c
@@ -76,16 +76,16 @@ c          On exit, D contains the  Ritz  approximations
 c          to the eigenvalues lambda for A*z = lambda*B*z.
 c
 c  Z       Complex*16  N by NEV array     (OUTPUT)
-c          On exit, if RVEC = .TRUE. and HOWMNY = 'A', then the columns of 
-c          Z represents approximate eigenvectors (Ritz vectors) corresponding 
+c          On exit, if RVEC = .TRUE. and HOWMNY = 'A', then the columns of
+c          Z represents approximate eigenvectors (Ritz vectors) corresponding
 c          to the NCONV=IPARAM(5) Ritz values for eigensystem
 c          A*z = lambda*B*z.
 c
 c          If RVEC = .FALSE. or HOWMNY = 'P', then Z is NOT REFERENCED.
 c
-c          NOTE: If if RVEC = .TRUE. and a Schur basis is not required, 
-c          the array Z may be set equal to first NEV columns of the 
-c          array V.  
+c          NOTE: If if RVEC = .TRUE. and a Schur basis is not required,
+c          the array Z may be set equal to first NEV columns of the
+c          array V.
 c
 c  LDZ     Integer.  (INPUT)
 c          The leading dimension of the array Z.  If Ritz vectors are
@@ -97,7 +97,7 @@ c          If IPARAM(7) = 3 then SIGMA represents the shift.
 c          Not referenced if IPARAM(7) = 1 or 2.
 c
 c  WORKEV  Complex*16  work array of dimension NCV.  (WORKSPACE)
-c 
+c
 c  N       Integer.  (INPUT)
 c          Dimension of the eigenproblem.
 c
@@ -110,7 +110,7 @@ c          AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
 c
 c  MB      Complex*16  array of dimension LDA by N. (INPUT)
 c          The matrix M in band storage, in rows KL+1 to
-c          2*KL+KU+1; rows 1 to KL of the array need not be set. 
+c          2*KL+KU+1; rows 1 to KL of the array need not be set.
 c          The j-th column of M is stored in the j-th column of the
 c          array MB as follows:
 c          MB(kl+ku+1+i-j,j) = M(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
@@ -134,7 +134,7 @@ c
 c  WHICH   Character*2.  (INPUT)
 c          When mode 1,2 are used, WHICH can be set to any one of
 c          the following.
-c  
+c
 c            'LM' -> want the NEV eigenvalues of largest magnitude.
 c            'SM' -> want the NEV eigenvalues of smallest magnitude.
 c            'LR' -> want the NEV eigenvalues of largest real part.
@@ -142,8 +142,8 @@ c            'SR' -> want the NEV eigenvalues of smallest real part.
 c            'LI' -> want the NEV eigenvalues of largest imaginary part.
 c            'SI' -> want the NEV eigenvalues of smallest imaginary part.
 c
-c          When mode 3 is used, WHICH should be set to 'LM' only. 
-c          
+c          When mode 3 is used, WHICH should be set to 'LM' only.
+c
 c  BMAT    Character*1.  (INPUT)
 c          BMAT specifies the type of the matrix B that defines the
 c          semi-inner product for the operator OP.
@@ -152,13 +152,13 @@ c          BMAT = 'G' -> generalized eigenvalue problem A*x = lambda*M*x
 
 c  NEV     Integer. (INPUT)
 c          Number of eigenvalues of to be computed.
-c   
+c
 c  TOL     Double precision  scalar.  (INPUT)
 c          Stopping criteria: the relative accuracy of the Ritz value
 c          is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I))
 c          where ABS(RITZ(I)) is the magnitude when RITZ(I) is complex.
 c          DEFAULT = dlamch ('EPS')  (machine precision as computed
-c                    by the LAPACK auxilliary subroutine dlamch ).
+c                    by the LAPACK auxiliary subroutine dlamch ).
 c
 c  RESID   Complex*16  array of length N.  (INPUT/OUTPUT)
 c          On INPUT:
@@ -171,12 +171,12 @@ c
 c  NCV     Integer.  (INPUT)
 c          Number of columns of the matrix V. NCV must satisfy the two
 c          inequalities 2 <= NCV-NEV and NCV <= N.
-c          This will indicate how many Arnoldi vectors are generated 
-c          at each iteration.  After the startup phase in which NEV 
-c          Arnoldi vectors are generated, the algorithm generates 
-c          approximately NCV-NEV Arnoldi vectors at each subsequent update 
-c          iteration. Most of the cost in generating each Arnoldi vector is 
-c          in the matrix-vector operation OP*x. 
+c          This will indicate how many Arnoldi vectors are generated
+c          at each iteration.  After the startup phase in which NEV
+c          Arnoldi vectors are generated, the algorithm generates
+c          approximately NCV-NEV Arnoldi vectors at each subsequent update
+c          iteration. Most of the cost in generating each Arnoldi vector is
+c          in the matrix-vector operation OP*x.
 c
 c  V       Complex*16  array N by NCV.  (OUTPUT)
 c          Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns
@@ -184,8 +184,8 @@ c                       contain approximate Schur vectors that span the
 c                       desired invariant subspace.
 c
 c          NOTE: If the array Z has been set equal to first NEV+1 columns
-c          of the array V and RVEC=.TRUE. and HOWMNY= 'A', then 
-c          the first NCONV=IPARAM(5) columns of V will contain Ritz vectors 
+c          of the array V and RVEC=.TRUE. and HOWMNY= 'A', then
+c          the first NCONV=IPARAM(5) columns of V will contain Ritz vectors
 c          of the eigensystem A*z = lambda*B*z.
 c
 c  LDV     Integer.  (INPUT)
@@ -193,7 +193,7 @@ c          Leading dimension of V exactly as declared in the calling
 c          program.  LDV must be great than or equal to N.
 c
 c  IPARAM  Integer array of length 11.  (INPUT/OUTPUT)
-c          IPARAM(1) = ISHIFT: 
+c          IPARAM(1) = ISHIFT:
 c          The shifts selected at each iteration are used to restart
 c          the Arnoldi iteration in an implicit fashion.
 c          It is set to 1 in this subroutine.  The user do not need
@@ -223,12 +223,12 @@ c          Not referenced. Implicit restarting is ALWAYS used.
 c
 c          IPARAM(7) = MODE
 c          On INPUT determines what type of eigenproblem is being solved.
-c          Must be 1,2 or 3; See under \Description of znband  for the 
+c          Must be 1,2 or 3; See under \Description of znband  for the
 c          three modes available.
 c
 c WORKD    Complex*16  work array of length at least 3*n. (WORKSPACE)
 c
-c WORKL    Complex*16  work array of length LWORKL. (WORKSPACE) 
+c WORKL    Complex*16  work array of length LWORKL. (WORKSPACE)
 c
 c LWORKL   Integer.  (INPUT)
 c          LWORKL must be at least 3*NCV**2 + 5*NCV.
@@ -237,9 +237,9 @@ c RWORK    Double precision  array of length N (WORKSPACE)
 c          Workspace used in znaupd .
 c
 c IWORK    Integer array of dimension at least N. (WORKSPACE)
-c          Used to mode 2,3. Store the pivot information in the 
+c          Used to mode 2,3. Store the pivot information in the
 c          factorization of M or (A-SIGMA*M).
-c            
+c
 c INFO     Integer.  (INPUT/OUTPUT)
 c          Error flag on output.
 c          =  0: Normal exit.
@@ -300,21 +300,21 @@ c
 c-----------------------------------------------------------------------
 c
       subroutine znband (rvec, howmny, select, d , z, ldz, sigma,
-     &                 workev, n, ab, mb, lda, fac, kl, ku, which, 
-     &                 bmat, nev, tol, resid, ncv, v, ldv, iparam, 
+     &                 workev, n, ab, mb, lda, fac, kl, ku, which,
+     &                 bmat, nev, tol, resid, ncv, v, ldv, iparam,
      &                 workd, workl, lworkl, rwork, iwork, info )
 c
 c     %------------------%
 c     | Scalar Arguments |
 c     %------------------%
-c 
+c
       Character        which*2, bmat, howmny
       Logical          rvec
       Integer          n, lda, kl, ku, nev, ncv, ldv,
-     &                 ldz, lworkl, info  
-      Complex*16          
-     &                 sigma 
-      Double precision 
+     &                 ldz, lworkl, info
+      Complex*16
+     &                 sigma
+      Double precision
      &                 tol
 c
 c     %-----------------%
@@ -323,11 +323,11 @@ c     %-----------------%
 c
       Integer          iparam(*), iwork(*)
       Logical          select(*)
-      Complex*16          
+      Complex*16
      &                 d(*), resid(*), v(ldv,*), z(ldz,*),
-     &                 ab(lda,*), mb(lda,*), fac(lda,*), 
+     &                 ab(lda,*), mb(lda,*), fac(lda,*),
      &                 workd(*), workl(*), workev(*)
-      Double precision 
+      Double precision
      &                 rwork(*)
 c
 c     %--------------%
@@ -346,7 +346,7 @@ c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Complex*16          
+      Complex*16
      &                  one, zero
       parameter        (one  = (1.0D+0, 0.0D+0) ,
      &                  zero = (0.0D+0, 0.0D+0) )
@@ -355,14 +355,14 @@ c     %-----------------------------%
 c     | LAPACK & BLAS routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                 dznrm2 
-      external         zcopy , zgbmv , zgbtrf , zgbtrs , dznrm2 , zlacpy 
+      Double precision
+     &                 dznrm2
+      external         zcopy , zgbmv , zgbtrf , zgbtrs , dznrm2 , zlacpy
 c
 c     %-----------------------%
 c     | Executable Statements |
 c     %-----------------------%
-c     
+c
       mode = iparam(7)
 c
 c     %------------------------%
@@ -398,9 +398,9 @@ c         | to factor M.                                  |
 c         %-----------------------------------------------%
 c
           call zlacpy  ('A', ibot, n, mb, lda, fac, lda )
-          call zgbtrf (n, n, kl, ku, fac, lda, iwork, ierr) 
+          call zgbtrf (n, n, kl, ku, fac, lda, iwork, ierr)
           if (ierr .ne. 0) then
-              print*, ' ' 
+              print*, ' '
               print*,'_band:  error in _gbtrf'
               print*, ' '
               go to 9000
@@ -426,7 +426,7 @@ c            | Construct (A - sigma*M)   |
 c            %---------------------------%
 c
              do 30 j = 1,n
-                do 20 i = itop, ibot 
+                do 20 i = itop, ibot
                    fac(i,j) = ab(i,j) - sigma*mb(i,j)
   20            continue
   30         continue
@@ -451,7 +451,7 @@ c     %--------------------------------------------%
 c     |  M A I N   L O O P (reverse communication) |
 c     %--------------------------------------------%
 c
-  40  continue 
+  40  continue
 c
       call znaupd  ( ido, bmat, n, which, nev, tol, resid, ncv,
      &              v, ldv, iparam, ipntr, workd, workl, lworkl,
@@ -466,8 +466,8 @@ c           %----------------------------%
 c           | Perform  y <--- OP*x = A*x |
 c           %----------------------------%
 c
-            call zgbmv ('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call zgbmv ('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
          else if ( mode .eq. 2 ) then
@@ -476,11 +476,11 @@ c           %-----------------------------------%
 c           | Perform  y <--- OP*x = inv[M]*A*x |
 c           %-----------------------------------%
 c
-            call zgbmv ('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                  lda, workd(ipntr(1)), 1, zero, 
+            call zgbmv ('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                  lda, workd(ipntr(1)), 1, zero,
      &                  workd(ipntr(2)), 1)
 c
-            call zgbtrs  ('Notranspose', n, kl, ku, 1, fac, lda, 
+            call zgbtrs  ('Notranspose', n, kl, ku, 1, fac, lda,
      &                    iwork, workd(ipntr(2)), n, ierr)
             if (ierr .ne. 0) then
                print*, ' '
@@ -493,21 +493,21 @@ c
 c
 c           %-----------------------------------------%
 c           | Perform y <-- OP*x                      |
-c           |           = inv[A-SIGMA*M]*M* x 
+c           |           = inv[A-SIGMA*M]*M* x
 c           | to force the starting vector into the   |
 c           | range of OP.                            |
 c           %-----------------------------------------%
 c
-            call zgbmv ('Notranspose', n, n, kl, ku, one, mb(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call zgbmv ('Notranspose', n, n, kl, ku, one, mb(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
-            call zgbtrs  ('Notranspose', n, kl, ku, 1, fac, lda, 
+            call zgbtrs  ('Notranspose', n, kl, ku, 1, fac, lda,
      &                   iwork, workd(ipntr(2)), n, ierr)
             if (ierr .ne. 0) then
-               print*, ' ' 
+               print*, ' '
                print*, '_band: error in _gbtrs.'
-               print*, ' ' 
+               print*, ' '
                go to 9000
             end if
 c
@@ -521,8 +521,8 @@ c           %----------------------------%
 c           | Perform  y <--- OP*x = A*x |
 c           %----------------------------%
 c
-            call zgbmv ('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                 lda, workd(ipntr(1)), 1, zero, 
+            call zgbmv ('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                 lda, workd(ipntr(1)), 1, zero,
      &                 workd(ipntr(2)), 1)
 c
          else if ( mode .eq. 2 ) then
@@ -531,16 +531,16 @@ c           %-----------------------------------%
 c           | Perform  y <--- OP*x = inv[M]*A*x |
 c           %-----------------------------------%
 c
-            call zgbmv ('Notranspose', n, n, kl, ku, one, ab(itop,1), 
-     &                  lda, workd(ipntr(1)), 1, zero, 
+            call zgbmv ('Notranspose', n, n, kl, ku, one, ab(itop,1),
+     &                  lda, workd(ipntr(1)), 1, zero,
      &                  workd(ipntr(2)), 1)
 c
-            call zgbtrs  ('Notranspose', n, kl, ku, 1, fac, lda, 
+            call zgbtrs  ('Notranspose', n, kl, ku, 1, fac, lda,
      &                    iwork, workd(ipntr(2)), ldv, ierr)
             if (ierr .ne. 0) then
                print*, ' '
                print*, '_band: error in sbgtrs.'
-               print*, ' ' 
+               print*, ' '
                go to 9000
             end if
 c
@@ -563,19 +563,19 @@ c
                end if
 c
             else
-c  
+c
 c              %--------------------------------------%
 c              | Perform  y <-- inv(A-sigma*M)*(M*x). |
 c              | (M*x) has been computed and stored   |
-c              | in workd(ipntr(3)).                  |           
+c              | in workd(ipntr(3)).                  |
 c              %--------------------------------------%
 c
                call zcopy (n, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-               call zgbtrs  ('Notranspose', n, kl, ku, 1, fac, lda, 
+               call zgbtrs  ('Notranspose', n, kl, ku, 1, fac, lda,
      &                      iwork, workd(ipntr(2)), n, ierr)
-               if (ierr .ne. 0) then 
+               if (ierr .ne. 0) then
                   print*, ' '
-                  print*, '_band: error in _gbtrs.' 
+                  print*, '_band: error in _gbtrs.'
                   print*, ' '
                   go to 9000
                end if
@@ -590,14 +590,14 @@ c        %--------------------%
 c        | Perform y <-- M*x  |
 c        %--------------------%
 c
-          call zgbmv ('Notranspose', n, n, kl, ku, one, mb(itop,1), 
-     &                lda, workd(ipntr(1)), 1, zero, 
+          call zgbmv ('Notranspose', n, n, kl, ku, one, mb(itop,1),
+     &                lda, workd(ipntr(1)), 1, zero,
      &                workd(ipntr(2)), 1)
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
-c        |   Either we have convergence, or there is | 
+c        |   Either we have convergence, or there is |
 c        |   error.                                  |
 c        %-------------------------------------------%
 c
@@ -613,7 +613,7 @@ c
             print *, ' Check the documentation of _naupd '
             print *, ' '
 c
-         else 
+         else
 c
             call zneupd  (rvec, howmny , select, d, z, ldz, sigma,
      &                   workev, bmat, n, which, nev, tol,
@@ -621,17 +621,17 @@ c
      &                   workl, lworkl, rwork, info)
 c
             if ( info .ne. 0) then
-c 
+c
 c              %------------------------------------%
 c              | Check the documentation of zneupd . |
 c              %------------------------------------%
 c
-               print *, ' ' 
+               print *, ' '
                print *, ' Error with _neupd = ', info
                print *, ' Check the documentation of _neupd '
-               print *, ' ' 
-c 
-            endif 
+               print *, ' '
+c
+            endif
 c
          end if
 c
@@ -643,7 +643,7 @@ c     %----------------------------------------%
 c     | L O O P  B A C K to call znaupd  again. |
 c     %----------------------------------------%
 c
-      go to 40 
+      go to 40
 c
  9000 continue
 c

EXAMPLES/BAND/znbdr1.f

@@ -1,4 +1,4 @@
-      program znbdr1 
+      program znbdr1
 c
 c     ... Construct the matrix A in LAPACK-style band form.
 c         The matrix A is derived from the discretization of
@@ -49,13 +49,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -64,12 +64,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Complex*16  
+      Complex*16
      &                 a(lda,maxn), m(lda,maxn), fac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn),
      &                 workev(2*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv), ax(maxn)
-      Double precision  
+      Double precision
      &                 rwork(maxn), rd(maxncv,3)
 c
 c     %---------------%
@@ -81,28 +81,28 @@ c
      &                 n, nx, lo, isub, isup, idiag, maxitr, mode,
      &                 nconv
       logical          rvec
-      Double precision  
+      Double precision
      &                 tol
-      Complex*16 
+      Complex*16
      &                 rho, h, h2, sigma
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Complex*16  
+      Complex*16
      &                 one, zero, two
-      parameter        ( one = (1.0D+0, 0.0D+0) , 
-     &                   zero = (0.0D+0, 0.0D+0) , 
+      parameter        ( one = (1.0D+0, 0.0D+0) ,
+     &                   zero = (0.0D+0, 0.0D+0) ,
      &                   two = (2.0D+0, 0.0D+0)  )
 c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dznrm2 , dlapy2 
-      external          dznrm2 , zgbmv , zaxpy , dlapy2 , zlaset  
+      Double precision
+     &                  dznrm2 , dlapy2
+      external          dznrm2 , zgbmv , zaxpy , dlapy2 , zlaset
 c
 c     %-----------------------%
 c     | Executable Statements |
@@ -112,7 +112,7 @@ c     %-------------------------------------------------%
 c     | The number NX is the number of interior points  |
 c     | in the discretization of the 2-dimensional      |
 c     | convection-diffusion operator on the unit       |
-c     | square with zero Dirichlet boundary condition.  | 
+c     | square with zero Dirichlet boundary condition.  |
 c     | The number N(=NX*NX) is the dimension of the    |
 c     | matrix.  A standard eigenvalue problem is       |
 c     | solved (BMAT = 'I').  NEV is the number of      |
@@ -123,13 +123,13 @@ c     | the spectrum.  However, the following           |
 c     | conditions must be satisfied:                   |
 c     |                   N <= MAXN                     |
 c     |                 NEV <= MAXNEV                   |
-c     |           NEV + 2 <= NCV <= MAXNCV              | 
-c     %-------------------------------------------------% 
+c     |           NEV + 2 <= NCV <= MAXNCV              |
+c     %-------------------------------------------------%
 c
-      nx  = 10 
+      nx  = 10
       n    = nx*nx
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR1: N is greater than MAXN '
          go to 9000
@@ -154,7 +154,7 @@ c     | Arnoldi iteration.                                  |
 c     %-----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+5*ncv
-      tol  = 0.0 
+      tol  = 0.0
       info = 0
 c
 c     %---------------------------------------------------%
@@ -168,7 +168,7 @@ c
       maxitr = 300
       mode   = 1
 c
-      iparam(3) = maxitr 
+      iparam(3) = maxitr
       iparam(7) = mode
 c
 c     %----------------------------------------%
@@ -190,10 +190,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = nx 
-      ku   = nx 
+      kl   = nx
+      ku   = nx
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -203,13 +203,13 @@ c
       idiag = kl+ku+1
       do 30 j = 1, n
          a(idiag,j) = (4.0D+0, 0.0D+0)  / h2
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
-      rho = (1.0D+2, 0.0D+0) 
+c
+      rho = (1.0D+2, 0.0D+0)
       isup = kl+ku
       isub = kl+ku+2
       do 50 i = 1, nx
@@ -217,8 +217,8 @@ c
         do 40 j = lo+1, lo+nx-1
            a(isup,j+1) = -one/h2 + rho/two/h
            a(isub,j) = -one/h2 - rho/two/h
-  40    continue      
-  50  continue 
+  40    continue
+  50  continue
 c
 c     %------------------------------------%
 c     | KL-th subdiagonal and KU-th super- |
@@ -232,8 +232,8 @@ c
          do 70 j = lo+1, lo+nx
             a(isup,nx+j)  = -one / h2
             a(isub,j) = -one / h2
- 70      continue 
- 80   continue 
+ 70      continue
+ 80   continue
 c
 c     %-----------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues |
@@ -241,11 +241,11 @@ c     | and eigenvectors. Eigenvalues are returned in |
 c     | the one dimensional array D.  Eigenvectors    |
 c     | are returned in the first NCONV (=IPARAM(5))  |
 c     | columns of V.                                 |
-c     %-----------------------------------------------% 
+c     %-----------------------------------------------%
 c
-      rvec = .true. 
+      rvec = .true.
       call znband (rvec, 'A', select, d, v, ldv, sigma,
-     &           workev, n, a, m, lda, fac, kl, ku, which, 
+     &           workev, n, a, m, lda, fac, kl, ku, which,
      &           bmat, nev, tol, resid, ncv, v, ldv, iparam,
      &           workd, workl, lworkl, rwork, iwork, info)
 c
@@ -294,11 +294,11 @@ c
             rd(j,2) = dimag (d(j))
             rd(j,3) = dznrm2 (n, ax, 1)
             rd(j,3) = rd(j,3) / dlapy2 (rd(j,1),rd(j,2))
- 90      continue 
+ 90      continue
 
          call dmout (6, nconv, 3, rd, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -309,8 +309,8 @@ c
           print *, ' '
           print *, ' Error with _nband, info= ', info
           print *, ' Check the documentation of _nband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/znbdr2.f

@@ -1,4 +1,4 @@
-      program znbdr2 
+      program znbdr2
 c
 c     ... Construct the matrix A in LAPACK-style band form.
 c         The matrix A is derived from the discretization of
@@ -49,13 +49,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn )
 c
 c     %--------------%
@@ -64,12 +64,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Complex*16  
+      Complex*16
      &                 a(lda,maxn), m(lda,maxn), fac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn),
      &                 workev(2*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv), ax(maxn)
-      Double precision  
+      Double precision
      &                 rwork(maxn), rd(maxncv,3)
 c
 c     %---------------%
@@ -81,18 +81,18 @@ c
      &                 n, nxi, lo, isub, isup, idiag, maxitr, mode,
      &                 nconv
       logical          rvec
-      Double precision  
+      Double precision
      &                 tol
-      Complex*16 
+      Complex*16
      &                 rho, h, h2, sigma
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Complex*16  
+      Complex*16
      &                 one, zero, two
-      parameter        (one  = (1.0D+0, 0.0D+0) , 
+      parameter        (one  = (1.0D+0, 0.0D+0) ,
      &                  zero = (0.0D+0, 0.0D+0) ,
      &                  two  = (2.0D+0, 0.0D+0) )
 c
@@ -100,9 +100,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dznrm2 , dlapy2 
-      external          dznrm2 , zgbmv , zaxpy , dlapy2 , zlaset 
+      Double precision
+     &                  dznrm2 , dlapy2
+      external          dznrm2 , zgbmv , zaxpy , dlapy2 , zlaset
 c
 c     %-----------------------%
 c     | Executable Statements |
@@ -112,7 +112,7 @@ c     %-------------------------------------------------%
 c     | The number NX is the number of interior points  |
 c     | in the discretization of the 2-dimensional      |
 c     | convection-diffusion operator on the unit       |
-c     | square with zero Dirichlet boundary condition.  | 
+c     | square with zero Dirichlet boundary condition.  |
 c     | The number N(=NX*NX) is the dimension of the    |
 c     | matrix.  A standard eigenvalue problem is       |
 c     | solved (BMAT = 'I').  NEV is the number of      |
@@ -122,16 +122,16 @@ c     | is used, WHICH is set to 'LM'.  The user can    |
 c     | modify NX, NEV and NCV to solve problems of     |
 c     | different sizes, and to get different parts the |
 c     | spectrum.  However, the following conditions    |
-c     | must be satisfied:                              | 
+c     | must be satisfied:                              |
 c     |                   N <= MAXN                     |
 c     |                 NEV <= MAXNEV                   |
-c     |           NEV + 2 <= NCV <= MAXNCV              | 
-c     %-------------------------------------------------% 
+c     |           NEV + 2 <= NCV <= MAXNCV              |
+c     %-------------------------------------------------%
 c
-      nxi  = 10 
+      nxi  = 10
       n    = nxi*nxi
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR2: N is greater than MAXN '
          go to 9000
@@ -157,7 +157,7 @@ c     | Arnoldi iteration.                                  |
 c     %-----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+5*ncv
-      tol  = 0.0 
+      tol  = 0.0
       info = 0
 c
 c     %---------------------------------------------------%
@@ -193,10 +193,10 @@ c     | and subdiagonals within the band of |
 c     | matrices A and M.                   |
 c     %-------------------------------------%
 c
-      kl   = nxi 
-      ku   = nxi 
+      kl   = nxi
+      ku   = nxi
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -206,13 +206,13 @@ c
       idiag = kl+ku+1
       do 30 j = 1, n
          a(idiag,j) = (4.0D+0, 0.0D+0)  / h2
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
-      rho = (1.0D+2, 0.0D+0)  
+c
+      rho = (1.0D+2, 0.0D+0)
       isup = kl+ku
       isub = kl+ku+2
       do 50 i = 1, nxi
@@ -220,8 +220,8 @@ c
         do 40 j = lo+1, lo+nxi-1
            a(isup,j+1) = -one/h2 + rho/two/h
            a(isub,j) = -one/h2 - rho/two/h
-  40    continue      
-  50  continue 
+  40    continue
+  50  continue
 c
 c     %------------------------------------%
 c     | KL-th subdiagonal and KU-th super- |
@@ -235,8 +235,8 @@ c
          do 70 j = lo+1, lo+nxi
             a(isup,nxi+j)  = -one / h2
             a(isub,j) = -one / h2
- 70      continue 
- 80   continue 
+ 70      continue
+ 80   continue
 c
 c     %-----------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues |
@@ -244,11 +244,11 @@ c     | and eigenvectors. Eigenvalues are returned in |
 c     | the one dimensional array D.  Eigenvectors    |
 c     | are returned in the first NCONV (=IPARAM(5))  |
 c     | columns of V.                                 |
-c     %-----------------------------------------------% 
+c     %-----------------------------------------------%
 c
-      rvec = .true. 
+      rvec = .true.
       call znband (rvec, 'A', select, d, v, ldv, sigma,
-     &           workev, n, a, m, lda, fac, kl, ku, which, 
+     &           workev, n, a, m, lda, fac, kl, ku, which,
      &           bmat, nev, tol, resid, ncv, v, ldv, iparam,
      &           workd, workl, lworkl, rwork, iwork, info)
 c
@@ -297,11 +297,11 @@ c
             rd(j,2) = dimag (d(j))
             rd(j,3) = dznrm2 (n, ax, 1)
             rd(j,3) = rd(j,3) / dlapy2 (rd(j,1),rd(j,2))
- 90      continue 
+ 90      continue
 
          call dmout (6, nconv, 3, rd, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -312,8 +312,8 @@ c
           print *, ' '
           print *, ' Error with _nband, info= ', info
           print *, ' Check the documentation of _nband '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/znbdr3.f

@@ -1,9 +1,9 @@
-      program znbdr3 
+      program znbdr3
 c
 c     ... Construct matrices A and M in LAPACK-style band form.
-c         Matrices A and M are derived from the finite 
-c         element discretization of the 1-dimensional 
-c         convection-diffusion operator 
+c         Matrices A and M are derived from the finite
+c         element discretization of the 1-dimensional
+c         convection-diffusion operator
 c                         (d^2u/dx^2) + rho*(du/dx)
 c         on the interval [0,1] with zero boundary condition using
 c         piecewise linear elements.
@@ -51,13 +51,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn)
 c
 c     %--------------%
@@ -66,12 +66,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Complex*16  
+      Complex*16
      &                 a(lda,maxn), m(lda,maxn), fac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn),
      &                 workev(2*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv), ax(maxn), mx(maxn)
-      Double precision  
+      Double precision
      &                 rwork(maxn), rd(maxncv,3)
 c
 c     %---------------%
@@ -83,16 +83,16 @@ c
      &                 n, idiag, isup, isub, maxitr,
      &                 mode, nconv
       logical          rvec
-      Double precision  
+      Double precision
      &                 tol
-      Complex*16 
+      Complex*16
      &                 rho, h, sigma
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Complex*16  
+      Complex*16
      &                 one, zero, two
       parameter        (one  = (1.0D+0, 0.0D+0) ,
      &                  zero = (0.0D+0, 0.0D+0) ,
@@ -102,9 +102,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dznrm2 , dlapy2 
-      external          dznrm2 , zgbmv , zaxpy , dlapy2 , zlaset  
+      Double precision
+     &                  dznrm2 , dlapy2
+      external          dznrm2 , zgbmv , zaxpy , dlapy2 , zlaset
 c
 c     %-----------------------%
 c     | Executable Statements |
@@ -129,8 +129,8 @@ c     |           NEV + 2 <= NCV <= MAXNCV              |
 c     %-------------------------------------------------%
 c
       n    = 100
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR3: N is greater than MAXN '
          go to 9000
@@ -146,13 +146,13 @@ c
       sigma = zero
 c
 c     %----------------------------------------------------%
-c     | The work array WORKL is used in ZNAUPD  as          | 
+c     | The work array WORKL is used in ZNAUPD  as          |
 c     | workspace.  Its dimension LWORKL has to be set as  |
 c     | illustrated below.  The parameter TOL determines   |
 c     | the stopping criterion. If TOL<=0, machine machine |
 c     | precision is used.  Setting INFO=0 indicates that  |
 c     | using a randomly generated vector to start the     |
-c     | the ARNOLDI process.                               | 
+c     | the ARNOLDI process.                               |
 c     %----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+5*ncv
@@ -195,7 +195,7 @@ c
       kl   = 1
       ku   = 1
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
@@ -203,23 +203,23 @@ c
 c
       idiag = kl+ku+1
       do 30 j = 1, n
-         a(idiag,j) = (2.0D+0, 0.0D+0)  / h 
-         m(idiag,j) = (4.0D+0, 0.0D+0)  * h 
-  30  continue 
-c 
+         a(idiag,j) = (2.0D+0, 0.0D+0)  / h
+         m(idiag,j) = (4.0D+0, 0.0D+0)  * h
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+ku+2
-      rho = (1.0D+1, 0.0D+0) 
+      rho = (1.0D+1, 0.0D+0)
       do 40 j = 1, n-1
            a(isup,j+1) = -one/h + rho/two
            a(isub,j) = -one/h - rho/two
            m(isup,j+1) = one*h
            m(isub,j) = one*h
-  40  continue      
+  40  continue
 c
 c     %-----------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues |
@@ -229,7 +229,7 @@ c     | are returned in the first NCONV (=IPARAM(5))  |
 c     | columns of V.                                 |
 c     %-----------------------------------------------%
 c
-      rvec = .true. 
+      rvec = .true.
       call znband (rvec, 'A', select, d, v, ldv, sigma,
      &           workev, n, a, m, lda, fac, kl, ku, which,
      &           bmat, nev, tol, resid, ncv, v, ldv, iparam,
@@ -277,24 +277,24 @@ c
             rd(j,1) = dble (d(j))
             rd(j,2) = dimag (d(j))
             rd(j,3) = dznrm2 (n, ax, 1)
-            rd(j,3) = rd(j,3) / dlapy2 (rd(j,1), rd(j,2))         
- 50      continue 
+            rd(j,3) = rd(j,3) / dlapy2 (rd(j,1), rd(j,2))
+ 50      continue
 
          call dmout (6, nconv, 3, rd, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
 c        | is error.  Check the documentation  |
-c        | for znband .                         | 
+c        | for znband .                         |
 c        %-------------------------------------%
 c
           print *, ' '
           print *, ' Error with _band, info= ', info
           print *, ' Check the documentation of _band '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/BAND/znbdr4.f

@@ -1,4 +1,4 @@
-      program zndrv4 
+      program zndrv4
 c
 c     ... Construct matrices A and M in LAPACK-style band form.
 c         Matries A and M are derived from the finite
@@ -49,13 +49,13 @@ c     | MAXN   - Maximum size of the matrix |
 c     | MAXNEV - Maximum number of          |
 c     |          eigenvalues to be computed |
 c     | MAXNCV - Maximum number of Arnoldi  |
-c     |          vectors stored             | 
+c     |          vectors stored             |
 c     | MAXBDW - Maximum bandwidth          |
 c     %-------------------------------------%
 c
       integer          maxn, maxnev, maxncv, maxbdw, lda,
      &                 lworkl, ldv
-      parameter        ( maxn = 1000, maxnev = 25, maxncv=50, 
+      parameter        ( maxn = 1000, maxnev = 25, maxncv=50,
      &                   maxbdw=50, lda = maxbdw, ldv = maxn)
 c
 c     %--------------%
@@ -64,12 +64,12 @@ c     %--------------%
 c
       integer          iparam(11), iwork(maxn)
       logical          select(maxncv)
-      Complex*16  
+      Complex*16
      &                 a(lda,maxn), m(lda,maxn), fac(lda,maxn),
-     &                 workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn), 
+     &                 workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn),
      &                 workev(2*maxncv), v(ldv, maxncv),
      &                 resid(maxn), d(maxncv), ax(maxn), mx(maxn)
-      Double precision  
+      Double precision
      &                 rwork(maxn), rd(maxncv,3)
 c
 c     %---------------%
@@ -81,16 +81,16 @@ c
      &                 n, idiag, isup, isub, maxitr, mode,
      &                 nconv
       logical          rvec
-      Double precision  
+      Double precision
      &                 tol
-      Complex*16 
+      Complex*16
      &                 rho, h, sigma
-c 
+c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Complex*16  
+      Complex*16
      &                 one, zero, two, four, six
       parameter        (one  = (1.0D+0, 0.0D+0)  ,
      &                  zero = (0.0D+0, 0.0D+0) ,
@@ -102,9 +102,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dznrm2 , dlapy2 
-      external          dznrm2 , zgbmv , zaxpy , dlapy2 , zlaset 
+      Double precision
+     &                  dznrm2 , dlapy2
+      external          dznrm2 , zgbmv , zaxpy , dlapy2 , zlaset
 c
 c     %-----------------------%
 c     | Executable Statements |
@@ -121,7 +121,7 @@ c     | solved (BMAT = 'G').  NEV is the number of      |
 c     | eigenvalues (closest to the shift SIGMA) to be  |
 c     | approximated.  Since the shift and invert mode  |
 c     | is used, WHICH is set to 'LM'.  The user can    |
-c     | modify NX, NEV and NCV to solve problems of     | 
+c     | modify NX, NEV and NCV to solve problems of     |
 c     | different sizes, and to get different parts the |
 c     | spectrum.  However, the following conditions    |
 c     | must be satisfied:                              |
@@ -131,8 +131,8 @@ c     |           NEV + 2 <= NCV <= MAXNCV              |
 c     %-------------------------------------------------%
 c
       n    = 100
-      nev  = 4 
-      ncv  = 10 
+      nev  = 4
+      ncv  = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NBDR4: N is greater than MAXN '
          go to 9000
@@ -145,16 +145,16 @@ c
       end if
       bmat = 'G'
       which = 'LM'
-      sigma = (1.0D+1, 0.0D+0) 
+      sigma = (1.0D+1, 0.0D+0)
 c
 c     %----------------------------------------------------%
-c     | The work array WORKL is used in ZNAUPD  as          | 
+c     | The work array WORKL is used in ZNAUPD  as          |
 c     | workspace.  Its dimension LWORKL has to be set as  |
 c     | illustrated below.  The parameter TOL determines   |
 c     | the stopping criterion. If TOL<=0, machine machine |
 c     | precision is used.  Setting INFO=0 indicates that  |
 c     | we using a randomly generated vector to start the  |
-c     | the ARNOLDI process.                               | 
+c     | the ARNOLDI process.                               |
 c     %----------------------------------------------------%
 c
       lworkl  = 3*ncv**2+5*ncv
@@ -197,30 +197,30 @@ c
       kl   = 1
       ku   = 1
 c
-c     %---------------% 
+c     %---------------%
 c     | Main diagonal |
 c     %---------------%
 c
       h = one / dcmplx (n+1)
       idiag = kl+ku+1
       do 30 j = 1, n
-         a(idiag,j) = two / h 
+         a(idiag,j) = two / h
          m(idiag,j) = four * h / six
-  30  continue 
-c 
+  30  continue
+c
 c     %-------------------------------------%
 c     | First subdiagonal and superdiagonal |
 c     %-------------------------------------%
-c 
+c
       isup = kl+ku
       isub = kl+ku+2
-      rho = (1.0D+1, 0.0D+0) 
+      rho = (1.0D+1, 0.0D+0)
       do 40 j = 1, n-1
          a(isup,j+1) = -one/h + rho/two
          a(isub,j) = -one/h - rho/two
          m(isup,j+1) = one*h / six
          m(isub,j) = one*h / six
-  40  continue 
+  40  continue
 c
 c     %-----------------------------------------------%
 c     | Call ARPACK banded solver to find eigenvalues |
@@ -230,7 +230,7 @@ c     | are returned in the first NCONV (=IPARAM(5))  |
 c     | columns of V.                                 |
 c     %-----------------------------------------------%
 c
-      rvec = .true. 
+      rvec = .true.
       call znband (rvec, 'A', select, d, v, ldv, sigma,
      &           workev, n, a, m, lda, fac, kl, ku, which,
      &           bmat, nev, tol, resid, ncv, v, ldv, iparam,
@@ -279,11 +279,11 @@ c
             rd(j,2) = dimag (d(j))
             rd(j,3) = dznrm2 (n, ax, 1)
             rd(j,3) = rd(j,3) / dlapy2 (rd(j,1), rd(j,2))
- 90      continue 
+ 90      continue
 
          call dmout (6, nconv, 3, rd, maxncv, -6,
      &             'Ritz values (Real,Imag) and relative residuals')
-      else 
+      else
 c
 c        %-------------------------------------%
 c        | Either convergence failed, or there |
@@ -294,8 +294,8 @@ c
           print *, ' '
           print *, ' Error with _band, info= ', info
           print *, ' Check the documentation of _band '
-          print *, ' ' 
+          print *, ' '
 c
       end if
 c
- 9000 end      
+ 9000 end

EXAMPLES/COMPLEX/Makefile.am

@@ -0,0 +1,22 @@
+LDADD = $(top_builddir)/SRC/libarpack$(LIBSUFFIX).la $(LAPACK_LIBS) $(BLAS_LIBS)
+
+CNDRV = cndrv1 cndrv2 cndrv3 cndrv4
+ZNDRV = zndrv1 zndrv2 zndrv3 zndrv4
+COMPLEX = $(CNDRV) $(ZNDRV)
+
+check_PROGRAMS = $(COMPLEX)
+TESTS = $(check_PROGRAMS)
+
+EXTRA_DIST = README
+
+# Complex problem using single complex
+cndrv1_SOURCES = cndrv1.f
+cndrv2_SOURCES = cndrv2.f
+cndrv3_SOURCES = cndrv3.f
+cndrv4_SOURCES = cndrv4.f
+
+# Complex problem using double complex
+zndrv1_SOURCES = zndrv1.f
+zndrv2_SOURCES = zndrv2.f
+zndrv3_SOURCES = zndrv3.f
+zndrv4_SOURCES = zndrv4.f

EXAMPLES/COMPLEX/cndrv1.f

@@ -1,14 +1,14 @@
-      program cndrv1 
+      program cndrv1
 c
 c     Example program to illustrate the idea of reverse communication
-c     for a standard complex nonsymmetric eigenvalue problem. 
+c     for a standard complex nonsymmetric eigenvalue problem.
 c
 c     We implement example one of ex-complex.doc in DOCUMENTS directory
 c
 c\Example-1
 c     ... Suppose we want to solve A*x = lambda*x in regular mode,
 c         where A is obtained from the standard central difference
-c         discretization of the convection-diffusion operator 
+c         discretization of the convection-diffusion operator
 c                 (Laplacian u) + rho*(du / dx)
 c         on the unit squre [0,1]x[0,1] with zero Dirichlet boundary
 c         condition.
@@ -69,12 +69,12 @@ c     %--------------%
 c
       integer           iparam(11), ipntr(14)
       logical           select(maxncv)
-      Complex 
-     &                  ax(maxn), d(maxncv), 
-     &                  v(ldv,maxncv), workd(3*maxn), 
-     &                  workev(3*maxncv), resid(maxn), 
+      Complex
+     &                  ax(maxn), d(maxncv),
+     &                  v(ldv,maxncv), workd(3*maxn),
+     &                  workev(3*maxncv), resid(maxn),
      &                  workl(3*maxncv*maxncv+5*maxncv)
-      Real  
+      Real
      &                  rwork(maxncv), rd(maxncv,3)
 c
 c     %---------------%
@@ -84,9 +84,9 @@ c
       character         bmat*1, which*2
       integer           ido, n, nx, nev, ncv, lworkl, info, j,
      &                  ierr, nconv, maxitr, ishfts, mode
-      Complex 
+      Complex
      &                  sigma
-      Real 
+      Real
      &                  tol
       logical           rvec
 c
@@ -94,19 +94,19 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  scnrm2, slapy2
-      external          scnrm2, caxpy, slapy2 
+      external          scnrm2, caxpy, slapy2
 c
 c     %-----------------------%
 c     | Executable Statements |
 c     %-----------------------%
-c 
+c
 c     %--------------------------------------------------%
 c     | The number NX is the number of interior points   |
 c     | in the discretization of the 2-dimensional       |
 c     | convection-diffusion operator on the unit        |
-c     | square with zero Dirichlet boundary condition.   | 
+c     | square with zero Dirichlet boundary condition.   |
 c     | The number N(=NX*NX) is the dimension of the     |
 c     | matrix.  A standard eigenvalue problem is        |
 c     | solved (BMAT = 'I').  NEV is the number of       |
@@ -117,13 +117,13 @@ c     | the spectrum.  However, The following            |
 c     | conditions must be satisfied:                    |
 c     |                   N <= MAXN                      |
 c     |                 NEV <= MAXNEV                    |
-c     |           NEV + 2 <= NCV <= MAXNCV               | 
-c     %--------------------------------------------------% 
+c     |           NEV + 2 <= NCV <= MAXNCV               |
+c     %--------------------------------------------------%
 c
-      nx    = 10 
-      n     = nx*nx 
+      nx    = 10
+      n     = nx*nx
       nev   = 4
-      ncv   = 20 
+      ncv   = 20
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NDRV1: N is greater than MAXN '
          go to 9000
@@ -138,18 +138,18 @@ c
       which = 'LM'
 c
 c     %---------------------------------------------------%
-c     | The work array WORKL is used in CNAUPD as         | 
+c     | The work array WORKL is used in CNAUPD as         |
 c     | workspace.  Its dimension LWORKL is set as        |
 c     | illustrated below.  The parameter TOL determines  |
 c     | the stopping criterion. If TOL<=0, machine        |
 c     | precision is used.  The variable IDO is used for  |
 c     | reverse communication, and is initially set to 0. |
 c     | Setting INFO=0 indicates that a random vector is  |
-c     | generated to start the ARNOLDI iteration.         | 
+c     | generated to start the ARNOLDI iteration.         |
 c     %---------------------------------------------------%
 c
-      lworkl  = 3*ncv**2+5*ncv 
-      tol    = 0.0 
+      lworkl  = 3*ncv**2+5*ncv
+      tol    = 0.0
       ido    = 0
       info   = 0
 c
@@ -168,11 +168,11 @@ c
       mode   = 1
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %-------------------------------------------%
-c     | M A I N   L O O P (Reverse communication) | 
+c     | M A I N   L O O P (Reverse communication) |
 c     %-------------------------------------------%
 c
  10   continue
@@ -197,7 +197,7 @@ c           | The user should supply his/her own        |
 c           | matrix vector multiplication routine here |
 c           | that takes workd(ipntr(1)) as the input   |
 c           | vector, and return the matrix vector      |
-c           | product to workd(ipntr(2)).               | 
+c           | product to workd(ipntr(2)).               |
 c           %-------------------------------------------%
 c
             call av (nx, workd(ipntr(1)), workd(ipntr(2)))
@@ -209,7 +209,7 @@ c
             go to 10
 
          end if
-c 
+c
 c     %----------------------------------------%
 c     | Either we have convergence or there is |
 c     | an error.                              |
@@ -227,7 +227,7 @@ c
          print *, ' Check the documentation of _naupd'
          print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
@@ -241,16 +241,16 @@ c        %-------------------------------------------%
 c
          rvec = .true.
 c
-         call cneupd (rvec, 'A', select, d, v, ldv, sigma, 
-     &        workev, bmat, n, which, nev, tol, resid, ncv, 
-     &        v, ldv, iparam, ipntr, workd, workl, lworkl, 
+         call cneupd (rvec, 'A', select, d, v, ldv, sigma,
+     &        workev, bmat, n, which, nev, tol, resid, ncv,
+     &        v, ldv, iparam, ipntr, workd, workl, lworkl,
      &        rwork, ierr)
 c
 c        %----------------------------------------------%
 c        | Eigenvalues are returned in the one          |
 c        | dimensional array D.  The corresponding      |
 c        | eigenvectors are returned in the first NCONV |
-c        | (=IPARAM(5)) columns of the two dimensional  | 
+c        | (=IPARAM(5)) columns of the two dimensional  |
 c        | array V if requested.  Otherwise, an         |
 c        | orthogonal basis for the invariant subspace  |
 c        | corresponding to the eigenvalues in D is     |
@@ -258,7 +258,7 @@ c        | returned in V.                               |
 c        %----------------------------------------------%
 c
          if ( ierr .ne. 0) then
-c 
+c
 c           %------------------------------------%
 c           | Error condition:                   |
 c           | Check the documentation of CNEUPD. |
@@ -312,11 +312,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, '_NDRV1'
@@ -327,8 +327,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -344,7 +344,7 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector subroutine
@@ -354,21 +354,21 @@ c     discretized using centered difference.
 c
       subroutine av (nx, v, w)
       integer           nx, j, lo
-      Complex          
+      Complex
      &                  v(nx*nx), w(nx*nx), one, h2
       parameter         (one = (1.0E+0, 0.0E+0) )
       external          caxpy, tv
 c
-c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block 
+c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block
 c     tridiagonal matrix
 c
-c                  | T -I          | 
+c                  | T -I          |
 c                  |-I  T -I       |
 c             OP = |   -I  T       |
 c                  |        ...  -I|
 c                  |           -I T|
 c
-c     derived from the standard central difference  discretization 
+c     derived from the standard central difference  discretization
 c     of the convection-diffusion operator (Laplacian u) + rho*(du/dx)
 c     with zero boundary condition.
 c
@@ -385,7 +385,7 @@ c
          call tv(nx, v(lo+1), w(lo+1))
          call caxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1)
          call caxpy(nx, -one/h2, v(lo+nx+1), 1, w(lo+1), 1)
-  10  continue 
+  10  continue
 c
       lo = (nx-1)*nx
       call tv(nx, v(lo+1), w(lo+1))
@@ -396,29 +396,29 @@ c
 c=========================================================================
       subroutine tv (nx, x, y)
 c
-      integer           nx, j 
-      Complex 
+      integer           nx, j
+      Complex
      &                  x(nx), y(nx), h, h2, dd, dl, du
 c
-      Complex 
+      Complex
      &                  one, rho
       parameter         (one = (1.0E+0, 0.0E+0) ,
      &                   rho = (1.0E+2, 0.0E+0) )
 c
 c     Compute the matrix vector multiplication y<---T*x
-c     where T is a nx by nx tridiagonal matrix with DD on the 
+c     where T is a nx by nx tridiagonal matrix with DD on the
 c     diagonal, DL on the subdiagonal, and DU on the superdiagonal
-c     
+c
       h   = one / cmplx(nx+1)
       h2  = h*h
       dd  = (4.0E+0, 0.0E+0)  / h2
       dl  = -one/h2 - (5.0E-1, 0.0E+0) *rho/h
       du  = -one/h2 + (5.0E-1, 0.0E+0) *rho/h
-c 
+c
       y(1) =  dd*x(1) + du*x(2)
       do 10 j = 2,nx-1
-         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 
- 10   continue 
-      y(nx) =  dl*x(nx-1) + dd*x(nx) 
+         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1)
+ 10   continue
+      y(nx) =  dl*x(nx-1) + dd*x(nx)
       return
       end

EXAMPLES/COMPLEX/cndrv2.f

@@ -1,7 +1,7 @@
       program cndrv2
 c
 c     Simple program to illustrate the idea of reverse communication
-c     in shift-invert mode for a standard complex nonsymmetric eigenvalue 
+c     in shift-invert mode for a standard complex nonsymmetric eigenvalue
 c     problem.
 c
 c     We implement example two of ex-complex.doc in DOCUMENTS directory
@@ -60,7 +60,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer           maxn, maxnev, maxncv, ldv
-      parameter         (maxn=256, maxnev=10, maxncv=25, 
+      parameter         (maxn=256, maxnev=10, maxncv=25,
      &                   ldv=maxn )
 c
 c     %--------------%
@@ -69,14 +69,14 @@ c     %--------------%
 c
       integer           iparam(11), ipntr(14), ipiv(maxn)
       logical           select(maxncv)
-      Complex 
+      Complex
      &                  ax(maxn), d(maxncv), resid(maxn),
      &                  v(ldv, maxncv), workd(3*maxn),
      &                  workev(2*maxncv),
      &                  workl(3*maxncv*maxncv+5*maxncv),
      &                  dd(maxn), dl(maxn), du(maxn),
      &                  du2(maxn)
-      Real 
+      Real
      &                  rwork(maxn), rd(maxncv,3)
 c
 c     %---------------%
@@ -86,11 +86,11 @@ c
       character         bmat*1, which*2
       integer           ido, n, nev, ncv, lworkl, info, j, ierr,
      &                  nconv, maxitr, ishfts, mode
-      Complex  
+      Complex
      &                  h, h2, s, sigma, s1, s2, s3, rho
       common            /convct/ rho
 c
-      Real 
+      Real
      &                  tol
       logical           rvec
 c
@@ -98,9 +98,9 @@ c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Complex  
-     &                   one, zero, two        
-      parameter         (one = (1.0E+0, 0.0E+0) , 
+      Complex
+     &                   one, zero, two
+      parameter         (one = (1.0E+0, 0.0E+0) ,
      &                   zero = (0.0E+0, 0.0E+0) ,
      &                   two = (2.0E+0, 0.0E+0) )
 c
@@ -108,7 +108,7 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  scnrm2, slapy2
       external          cgttrf, cgttrs, caxpy, ccopy, scnrm2,
      &                  slapy2
@@ -160,22 +160,22 @@ c     | the interval [0, 1] with zero Dirichlet boundary   |
 c     | condition.                                         |
 c     %----------------------------------------------------%
 c
-      rho = (1.0E+1, 0.0E+0) 
+      rho = (1.0E+1, 0.0E+0)
       h = one / cmplx(n+1)
       h2 = h*h
       s = rho / two
 c
-      s1 = -one/h2 - s/h 
+      s1 = -one/h2 - s/h
       s2 = two/h2 - sigma
-      s3 = -one/h2 + s/h  
+      s3 = -one/h2 + s/h
 c
       do 10 j = 1, n-1
-         dl(j) = s1 
+         dl(j) = s1
          dd(j) = s2
          du(j) = s3
-  10  continue 
-      dd(n) = s2 
-c 
+  10  continue
+      dd(n) = s2
+c
       call cgttrf(n, dl, dd, du, du2, ipiv, ierr)
       if ( ierr .ne. 0 ) then
          print*, ' '
@@ -195,8 +195,8 @@ c     | Setting INFO=0 indicates that a random vector is    |
 c     | generated in CNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl = 3*ncv**2+5*ncv 
-      tol    = 0.0 
+      lworkl = 3*ncv**2+5*ncv
+      tol    = 0.0
       ido    = 0
       info   = 0
 c
@@ -214,18 +214,18 @@ c
       maxitr = 300
       mode   = 3
 c
-      iparam(1) = ishfts 
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+      iparam(1) = ishfts
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %-------------------------------------------%
-c     | M A I N   L O O P (Reverse communication) | 
+c     | M A I N   L O O P (Reverse communication) |
 c     %-------------------------------------------%
 c
  20   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine CNAUPD and take | 
+c        | Repeatedly call the routine CNAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
@@ -247,8 +247,8 @@ c           %-------------------------------------------%
 c
             call ccopy( n, workd(ipntr(1)),1, workd(ipntr(2)), 1)
 c
-            call cgttrs('N', n, 1, dl, dd, du, du2, ipiv, 
-     &                  workd(ipntr(2)), n, ierr) 
+            call cgttrs('N', n, 1, dl, dd, du, du2, ipiv,
+     &                  workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
                print*, ' ERROR with _gttrs in _NDRV2.'
@@ -279,23 +279,23 @@ c
          print *, ' '
          print *, ' Error with _naupd, info = ',info
          print *, ' Check the documentation in _naupd.'
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using CNEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
-c 
+c
          rvec = .true.
 c
-         call cneupd (rvec, 'A', select, d, v, ldv, sigma, 
+         call cneupd (rvec, 'A', select, d, v, ldv, sigma,
      &                workev, bmat, n, which, nev, tol,
      &                resid, ncv, v, ldv, iparam, ipntr, workd,
      &                workl, lworkl, rwork, ierr)
@@ -312,19 +312,19 @@ c        | returned in V.                               |
 c        %----------------------------------------------%
 c
          if ( ierr .ne. 0) then
-c 
+c
 c           %------------------------------------%
-c           | Error condition:                   | 
+c           | Error condition:                   |
 c           | Check the documentation of CNEUPD. |
 c           %------------------------------------%
-c 
+c
             print *, ' '
             print *, ' Error with _neupd, info = ', ierr
             print *, ' Check the documentation of _neupd. '
             print *, ' '
          else
 c
-            nconv = iparam(5) 
+            nconv = iparam(5)
             do 60 j=1, nconv
 c
 c              %---------------------------%
@@ -366,11 +366,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, '_NDRV2 '
@@ -381,8 +381,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -405,7 +405,7 @@ c     matrix vector multiplication subroutine
 c
       subroutine av (n, v, w)
       integer           n, j
-      Complex  
+      Complex
      &                   v(n), w(n), rho, two, one, dd, dl, du, s, h,
      &                   h2
       parameter         (one = (1.0E+0, 0.0E+0) ,

EXAMPLES/COMPLEX/cndrv3.f

@@ -1,7 +1,7 @@
       program cndrv3
 c
 c     Simple program to illustrate the idea of reverse communication
-c     in inverse mode for a generalized complex nonsymmetric eigenvalue 
+c     in inverse mode for a generalized complex nonsymmetric eigenvalue
 c     problem.
 c
 c     We implement example three of ex-complex.doc in DOCUMENTS directory
@@ -11,8 +11,8 @@ c     ... Suppose we want to solve A*x = lambda*B*x in regular mode,
 c         where A and B are derived from the finite element discretization
 c         of the 1-dimensional convection-diffusion operator
 c                   (d^2u/dx^2) + rho*(du/dx)
-c         on the interval [0,1] with zero boundary condition using 
-c         piecewise linear elements. 
+c         on the interval [0,1] with zero boundary condition using
+c         piecewise linear elements.
 c
 c     ... OP = inv[M]*A  and  B = M.
 c
@@ -60,7 +60,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer           maxn, maxnev, maxncv, ldv
-      parameter         (maxn=256, maxnev=10, maxncv=25, 
+      parameter         (maxn=256, maxnev=10, maxncv=25,
      &                   ldv=maxn )
 c
 c     %--------------%
@@ -69,13 +69,13 @@ c     %--------------%
 c
       integer           iparam(11), ipntr(14), ipiv(maxn)
       logical           select(maxncv)
-      Complex 
+      Complex
      &                  ax(maxn), mx(maxn), d(maxncv), resid(maxn),
-     &                  v(ldv,maxncv), workd(3*maxn), 
+     &                  v(ldv,maxncv), workd(3*maxn),
      &                  workev(2*maxncv),
      &                  workl(3*maxncv*maxncv+5*maxncv),
      &                  dd(maxn), dl(maxn), du(maxn), du2(maxn)
-      Real             
+      Real
      &                  rwork(maxn), rd(maxncv,3)
 c
 c     %---------------%
@@ -85,9 +85,9 @@ c
       character         bmat*1, which*2
       integer           ido, n, nev, ncv, lworkl, info, ierr, j,
      &                  nconv, maxitr, ishfts, mode
-      Complex            
+      Complex
      &                  sigma, h
-      Real 
+      Real
      &                  tol
       logical           rvec
 c
@@ -95,7 +95,7 @@ c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Complex   
+      Complex
      &                  zero, one
       parameter         (zero = (0.0E+0, 0.0E+0) ,
      &                   one = (1.0E+0, 0.0E+0) )
@@ -104,7 +104,7 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real  
+      Real
      &                  scnrm2, slapy2
       external          caxpy, ccopy, scnrm2, cgttrf, cgttrs,
      &                  slapy2
@@ -126,9 +126,9 @@ c     |                  NEV <= MAXNEV,                    |
 c     |              NEV + 2 <= NCV <= MAXNCV              |
 c     %----------------------------------------------------%
 c
-      n     = 100 
-      nev   = 4 
-      ncv   = 20 
+      n     = 100
+      nev   = 4
+      ncv   = 20
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NDRV3: N is greater than MAXN '
          go to 9000
@@ -154,15 +154,15 @@ c
       do 20 j = 1, n-1
          dl(j) = one*h
          dd(j) = (4.0E+0, 0.0E+0) *h
-         du(j) = one*h 
-  20  continue 
-      dd(n) = (4.0E+0, 0.0E+0) *h 
+         du(j) = one*h
+  20  continue
+      dd(n) = (4.0E+0, 0.0E+0) *h
 c
-      call cgttrf(n, dl, dd, du, du2, ipiv, ierr) 
+      call cgttrf(n, dl, dd, du, du2, ipiv, ierr)
       if ( ierr .ne. 0 ) then
          print*, ' '
-         print*, ' ERROR with _gttrf. ' 
-         print*, ' ' 
+         print*, ' ERROR with _gttrf. '
+         print*, ' '
          go to 9000
       end if
 c
@@ -177,8 +177,8 @@ c     | Setting INFO=0 indicates that a random vector is    |
 c     | generated in CNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl = 3*ncv**2+5*ncv 
-      tol    = 0.0 
+      lworkl = 3*ncv**2+5*ncv
+      tol    = 0.0
       ido    = 0
       info   = 0
 c
@@ -197,8 +197,8 @@ c
       mode   = 2
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr  
-      iparam(7) = mode 
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %-------------------------------------------%
 c     | M A I N   L O O P (Reverse communication) |
@@ -207,14 +207,14 @@ c
  10   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine CNAUPD and take | 
+c        | Repeatedly call the routine CNAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call cnaupd ( ido, bmat, n, which, nev, tol, resid, ncv, 
-     &        v, ldv, iparam, ipntr, workd, workl, lworkl, 
+         call cnaupd ( ido, bmat, n, which, nev, tol, resid, ncv,
+     &        v, ldv, iparam, ipntr, workd, workl, lworkl,
      &        rwork, info )
 c
          if (ido .eq. -1 .or. ido .eq. 1) then
@@ -233,8 +233,8 @@ c
             call cgttrs('N', n, 1, dl, dd, du, du2, ipiv,
      &                  workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
-               print*, ' ' 
-               print*, ' ERROR with _gttrs. ' 
+               print*, ' '
+               print*, ' ERROR with _gttrs. '
                print*, ' '
                go to 9000
             end if
@@ -268,7 +268,7 @@ c
 c     %-----------------------------------------%
 c     | Either we have convergence, or there is |
 c     | an error.                               |
-c     %-----------------------------------------% 
+c     %-----------------------------------------%
 c
       if ( info .lt. 0 ) then
 c
@@ -280,24 +280,24 @@ c
          print *, ' '
          print *, ' Error with _naupd, info = ',info
          print *, ' Check the documentation of _naupd.'
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using CNEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
 c
          rvec = .true.
 c
-         call cneupd ( rvec, 'A', select, d, v, ldv, sigma, 
-     &        workev, bmat, n, which, nev, tol, resid, ncv, v, 
+         call cneupd ( rvec, 'A', select, d, v, ldv, sigma,
+     &        workev, bmat, n, which, nev, tol, resid, ncv, v,
      &        ldv, iparam, ipntr, workd, workl, lworkl, rwork,
      &        ierr )
 c
@@ -318,8 +318,8 @@ c           %------------------------------------%
 c           | Error condition:                   |
 c           | Check the documentation of CNEUPD. |
 c           %------------------------------------%
-c 
-            print *, ' ' 
+c
+            print *, ' '
             print *, ' Error with _neupd, info = ', ierr
             print *, ' Check the documentation of _neupd'
             print *, ' '
@@ -327,7 +327,7 @@ c
          else
 c
             nconv = iparam(5)
-            do 80 j=1, nconv 
+            do 80 j=1, nconv
 c
 c              %---------------------------%
 c              | Compute the residual norm |
@@ -369,11 +369,11 @@ c
             print *, ' Maximum number of iterations reached.'
             print *, ' '
          else if ( info .eq. 3) then
-            print *, ' ' 
+            print *, ' '
             print *, ' No shifts could be applied during implicit',
      &               ' Arnoldi update, try increasing NCV.'
             print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, '_NDRV3 '
@@ -384,8 +384,8 @@ c
          print *, ' The number of Arnoldi vectors generated ',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -397,21 +397,21 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector multiplication subroutine
 c
       subroutine av (n, v, w)
       integer           n, j
-      Complex             
-     &                  v(n), w(n), one, two, dd, dl, du, s, h, rho 
+      Complex
+     &                  v(n), w(n), one, two, dd, dl, du, s, h, rho
       parameter         (one = (1.0E+0, 0.0E+0) ,
      &                   two = (2.0E+0, 0.0E+0) ,
      &                   rho = (1.0E+1, 0.0E+0) )
 c
 c     Compute the matrix vector multiplication y<---A*x
-c     where A is the stiffness matrix formed by using piecewise linear 
+c     where A is the stiffness matrix formed by using piecewise linear
 c     elements on [0,1].
 c
       h = one / cmplx(n+1)
@@ -422,28 +422,28 @@ c
 c
       w(1) =  dd*v(1) + du*v(2)
       do 10 j = 2,n-1
-         w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1) 
- 10   continue 
-      w(n) =  dl*v(n-1) + dd*v(n) 
+         w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1)
+ 10   continue
+      w(n) =  dl*v(n-1) + dd*v(n)
       return
       end
 c------------------------------------------------------------------------
       subroutine mv (n, v, w)
       integer           n, j
-      Complex  
+      Complex
      &                  v(n), w(n), one, four, h
-      parameter         (one = (1.0E+0, 0.0E+0) , 
+      parameter         (one = (1.0E+0, 0.0E+0) ,
      &                   four = (4.0E+0, 0.0E+0) )
 c
 c     Compute the matrix vector multiplication y<---M*x
-c     where M is the mass matrix formed by using piecewise linear elements 
+c     where M is the mass matrix formed by using piecewise linear elements
 c     on [0,1].
-c 
+c
       w(1) =  four*v(1) + one*v(2)
       do 10 j = 2,n-1
-         w(j) = one*v(j-1) + four*v(j) + one*v(j+1) 
- 10   continue 
-      w(n) =  one*v(n-1) + four*v(n) 
+         w(j) = one*v(j-1) + four*v(j) + one*v(j+1)
+ 10   continue
+      w(n) =  one*v(n-1) + four*v(n)
 c
       h = one / cmplx(n+1)
       call cscal(n, h, w, 1)

EXAMPLES/COMPLEX/cndrv4.f

@@ -1,7 +1,7 @@
       program cndrv4
 c
 c     Simple program to illustrate the idea of reverse communication
-c     in shift and invert mode for a generalized complex nonsymmetric 
+c     in shift and invert mode for a generalized complex nonsymmetric
 c     eigenvalue problem.
 c
 c     We implement example four of ex-complex.doc in DOCUMENTS directory
@@ -11,7 +11,7 @@ c     ... Suppose we want to solve A*x = lambda*B*x in shift-invert mode,
 c         where A and B are derived from a finite element discretization
 c         of a 1-dimensional convection-diffusion operator
 c                         (d^2u/dx^2) + rho*(du/dx)
-c         on the interval [0,1] with zero boundary condition using 
+c         on the interval [0,1] with zero boundary condition using
 c         piecewise linear elements.
 c
 c     ... where the shift sigma is a complex number.
@@ -36,15 +36,15 @@ c     av      Matrix vector multiplication routine that computes A*x.
 c     mv      Matrix vector multiplication routine that computes M*x.
 c
 c\Author
-c     Danny Sorensen               
-c     Richard Lehoucq 
-c     Chao Yang             
-c     Dept. of Computational &     
-c     Applied Mathematics          
-c     Rice University           
-c     Houston, Texas    
+c     Danny Sorensen
+c     Richard Lehoucq
+c     Chao Yang
+c     Dept. of Computational &
+c     Applied Mathematics
+c     Rice University
+c     Houston, Texas
 c
-c\SCCS Information: @(#) 
+c\SCCS Information: @(#)
 c FILE: ndrv4.F   SID: 2.4   DATE OF SID: 10/18/00   RELEASE: 2
 c
 c\Remarks
@@ -63,7 +63,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer           maxn, maxnev, maxncv, ldv
-      parameter         (maxn=256, maxnev=10, maxncv=25, 
+      parameter         (maxn=256, maxnev=10, maxncv=25,
      &                   ldv=maxn )
 c
 c     %--------------%
@@ -72,14 +72,14 @@ c     %--------------%
 c
       integer           iparam(11), ipntr(14), ipiv(maxn)
       logical           select(maxncv)
-      Complex  
-     &                  ax(maxn), mx(maxn), d(maxncv), 
+      Complex
+     &                  ax(maxn), mx(maxn), d(maxncv),
      &                  v(ldv,maxncv), workd(3*maxn), resid(maxn),
      &                  workev(2*maxncv),
      &                  workl(3*maxncv*maxncv+5*maxncv),
      &                  dd(maxn), dl(maxn), du(maxn),
      &                  du2(maxn)
-      Real 
+      Real
      &                  rwork(maxn), rd(maxncv,3)
 c
 c     %---------------%
@@ -89,20 +89,20 @@ c
       character         bmat*1, which*2
       integer           ido, n, nev, ncv, lworkl, info, j, ierr,
      &                  nconv, maxitr, ishfts, mode
-      Complex  
+      Complex
      &                  rho, h, s,
      &                  sigma, s1, s2, s3
       common            /convct/ rho
 c
-      Real 
+      Real
      &                  tol
-      logical           rvec 
-c 
+      logical           rvec
+c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  scnrm2, slapy2
       external          scnrm2, caxpy, ccopy, cgttrf, cgttrs,
      &                  slapy2
@@ -111,10 +111,10 @@ c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Complex  
+      Complex
      &                   one, zero, two, four, six
       parameter         (one = (1.0E+0, 0.0E+0) ,
-     &                   zero = (0.0E+0, 0.0E+0) , 
+     &                   zero = (0.0E+0, 0.0E+0) ,
      &                   two = (2.0E+0, 0.0E+0) ,
      &                   four = (4.0E+0, 0.0E+0) ,
      &                   six = (6.0E+0, 0.0E+0) )
@@ -138,7 +138,7 @@ c     |                   NEV <= MAXNEV,                   |
 c     |               NEV + 2 <= NCV <= MAXNCV             |
 c     %----------------------------------------------------%
 c
-      n     = 100 
+      n     = 100
       nev   = 4
       ncv   = 20
       if ( n .gt. maxn ) then
@@ -153,7 +153,7 @@ c
       end if
       bmat  = 'G'
       which = 'LM'
-      sigma = one 
+      sigma = one
 c
 c     %--------------------------------------------------%
 c     | Construct C = A - SIGMA*M in COMPLEX arithmetic. |
@@ -164,11 +164,11 @@ c     | central difference discretization of the 1-d     |
 c     | convection-diffusion operator u``+ rho*u` on the |
 c     | interval [0, 1] with zero Dirichlet boundary     |
 c     | condition.  The matrix M is chosen to be the     |
-c     | symmetric tridiagonal matrix with 4.0 on the     | 
-c     | diagonal and 1.0 on the off-diagonals.           | 
+c     | symmetric tridiagonal matrix with 4.0 on the     |
+c     | diagonal and 1.0 on the off-diagonals.           |
 c     %--------------------------------------------------%
 c
-      rho = (1.0E+1, 0.0E+0) 
+      rho = (1.0E+1, 0.0E+0)
       h = one / cmplx(n+1)
       s = rho / two
 c
@@ -177,12 +177,12 @@ c
       s3 = -one/h + s - sigma*h/six
 c
       do 10 j = 1, n-1
-	 dl(j) = s1 
+	 dl(j) = s1
 	 dd(j) = s2
 	 du(j) = s3
-  10  continue 
-      dd(n) = s2 
-c 
+  10  continue
+      dd(n) = s2
+c
       call cgttrf(n, dl, dd, du, du2, ipiv, ierr)
       if ( ierr .ne. 0 ) then
          print*, ' '
@@ -202,7 +202,7 @@ c     | Setting INFO=0 indicates that a random vector is    |
 c     | generated in CNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl = 3*ncv**2+5*ncv 
+      lworkl = 3*ncv**2+5*ncv
       tol    = 0.0
       ido    = 0
       info   = 0
@@ -222,11 +222,11 @@ c
       mode   = 3
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %------------------------------------------%
-c     | M A I N   L O O P(Reverse communication) | 
+c     | M A I N   L O O P(Reverse communication) |
 c     %------------------------------------------%
 c
  20   continue
@@ -258,14 +258,14 @@ c           | workd(ipntr(2)).                          |
 c           %-------------------------------------------%
 c
             call mv (n, workd(ipntr(1)), workd(ipntr(2)))
-            call cgttrs('N', n, 1, dl, dd, du, du2, ipiv, 
+            call cgttrs('N', n, 1, dl, dd, du, du2, ipiv,
      &                  workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
                print*, ' ERROR with _gttrs in _NDRV4.'
                print*, ' '
                go to 9000
-            end if 
+            end if
 c
 c           %-----------------------------------------%
 c           | L O O P   B A C K to call CNAUPD again. |
@@ -285,7 +285,7 @@ c           | workd(ipntr(2)).                        |
 c           %-----------------------------------------%
 c
             call ccopy( n, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-            call cgttrs ('N', n, 1, dl, dd, du, du2, ipiv, 
+            call cgttrs ('N', n, 1, dl, dd, du, du2, ipiv,
      &                   workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
@@ -317,8 +317,8 @@ c           %-----------------------------------------%
 c
             go to 20
 c
-         end if 
-c 
+         end if
+c
 c     %-----------------------------------------%
 c     | Either we have convergence, or there is |
 c     | an error.                               |
@@ -334,9 +334,9 @@ c
          print *, ' '
          print *, ' Error with _naupd, info = ', info
          print *, ' Check the documentation of _naupd.'
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
@@ -350,9 +350,9 @@ c        %-------------------------------------------%
 c
          rvec = .true.
 c
-         call cneupd (rvec, 'A', select, d, v, ldv, sigma, 
-     &        workev, bmat, n, which, nev, tol, resid, ncv, v, 
-     &        ldv, iparam, ipntr, workd, workl, lworkl, rwork, 
+         call cneupd (rvec, 'A', select, d, v, ldv, sigma,
+     &        workev, bmat, n, which, nev, tol, resid, ncv, v,
+     &        ldv, iparam, ipntr, workd, workl, lworkl, rwork,
      &        ierr)
 c
 c        %----------------------------------------------%
@@ -367,7 +367,7 @@ c        | returned in V.                               |
 c        %----------------------------------------------%
 c
          if ( ierr .ne. 0) then
-c 
+c
 c           %------------------------------------%
 c           | Error condition:                   |
 c           | Check the documentation of CNEUPD. |
@@ -438,27 +438,27 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector multiplication subroutine
 c
       subroutine mv (n, v, w)
       integer           n, j
-      Complex  
+      Complex
      &                  v(n), w(n), one, four, six, h
       parameter         (one = (1.0E+0, 0.0E+0) ,
      &                   four = (4.0E+0, 0.0E+0) ,
      &                   six = (6.0E+0, 0.0E+0) )
 c
 c     Compute the matrix vector multiplication y<---M*x
-c     where M is a n by n symmetric tridiagonal matrix with 4 on the 
+c     where M is a n by n symmetric tridiagonal matrix with 4 on the
 c     diagonal, 1 on the subdiagonal and superdiagonal.
-c 
+c
       w(1) =  ( four*v(1) + one*v(2) ) / six
       do 40 j = 2,n-1
          w(j) = ( one*v(j-1) + four*v(j) + one*v(j+1) ) / six
- 40   continue 
+ 40   continue
       w(n) =  ( one*v(n-1) + four*v(n) ) / six
 c
       h = one / cmplx(n+1)
@@ -468,9 +468,9 @@ c
 c------------------------------------------------------------------
       subroutine av (n, v, w)
       integer           n, j
-      Complex  
-     &                  v(n), w(n), one, two, dd, dl, du, s, h, rho 
-      parameter         (one = (1.0E+0, 0.0E+0) , 
+      Complex
+     &                  v(n), w(n), one, two, dd, dl, du, s, h, rho
+      parameter         (one = (1.0E+0, 0.0E+0) ,
      &                   two = (2.0E+0, 0.0E+0) )
       common            /convct/ rho
 c

EXAMPLES/COMPLEX/makefile

@@ -1,60 +0,0 @@
-#
-# makefile to run simple examples of the reverse communication
-# protocol.
-#
-# Modify if ALIBS library was built somewhere else.
-#
-# If ALIBS (defined in ../../ARmake.inc) contains the BLAS and LAPACK
-# libraries installed on your system, you DO NOT need to change this
-# makefile. OTHERWISE, you may need to modify the Makefile in the top level
-# ARPACK directory tree to include cdrv and/or zdrv in the
-# definition of the PRECISION variable, and issue 'make lib' from there.
-# For example:
-#
-#         PRECISION = single double sdrv ddrv
-#
-#\SCCS Information: @(#) 
-# FILE: makefile   SID: 2.2   DATE OF SID: 9/24/96   RELEASE: 2 
-#
-include ../../ARmake.inc
-#
-# Issue "complex" to make all 8 complex drivers.
-# Issue "cndrv" to make 4 single precision complex drivers.
-# Issue "zndrv" to make 4 double precision complex drivers.
-#
-
-complex: cndrv zndrv 
-
-#-----------------------------------------------------------------------
-# Complex problem using single complex
-#
-cndrv: cndrv1 cndrv2 cndrv3 cndrv4
-
-cndrv1: cndrv1.o 
-	$(FC) $(FFLAGS) cndrv1.o $(ALIBS) -o cndrv1
-#
-cndrv2: cndrv2.o 
-	$(FC) $(FFLAGS) cndrv2.o $(ALIBS) -o cndrv2
-#
-cndrv3: cndrv3.o 
-	$(FC) $(FFLAGS) cndrv3.o $(ALIBS) -o cndrv3
-#
-cndrv4: cndrv4.o 
-	$(FC) $(FFLAGS) cndrv4.o $(ALIBS) -o cndrv4
-#
-#----------------------------------------------------------------------
-# Complex problem using double complex
-#
-zndrv: zndrv1 zndrv2 zndrv3 zndrv4
-
-zndrv1: zndrv1.o 
-	$(FC) $(FFLAGS) zndrv1.o $(ALIBS) -o zndrv1
-#
-zndrv2: zndrv2.o
-	$(FC) $(FFLAGS) zndrv2.o $(ALIBS) -o zndrv2
-#
-zndrv3: zndrv3.o 
-	$(FC) $(FFLAGS) zndrv3.o $(ALIBS) -o zndrv3
-#
-zndrv4: zndrv4.o 
-	$(FC) $(FFLAGS) zndrv4.o $(ALIBS) -o zndrv4

EXAMPLES/COMPLEX/zndrv1.f

@@ -1,14 +1,14 @@
-      program zndrv1  
+      program zndrv1
 c
 c     Example program to illustrate the idea of reverse communication
-c     for a standard complex nonsymmetric eigenvalue problem. 
+c     for a standard complex nonsymmetric eigenvalue problem.
 c
 c     We implement example one of ex-complex.doc in DOCUMENTS directory
 c
 c\Example-1
 c     ... Suppose we want to solve A*x = lambda*x in regular mode,
 c         where A is obtained from the standard central difference
-c         discretization of the convection-diffusion operator 
+c         discretization of the convection-diffusion operator
 c                 (Laplacian u) + rho*(du / dx)
 c         on the unit squre [0,1]x[0,1] with zero Dirichlet boundary
 c         condition.
@@ -69,12 +69,12 @@ c     %--------------%
 c
       integer           iparam(11), ipntr(14)
       logical           select(maxncv)
-      Complex*16 
-     &                  ax(maxn), d(maxncv), 
-     &                  v(ldv,maxncv), workd(3*maxn), 
-     &                  workev(3*maxncv), resid(maxn), 
+      Complex*16
+     &                  ax(maxn), d(maxncv),
+     &                  v(ldv,maxncv), workd(3*maxn),
+     &                  workev(3*maxncv), resid(maxn),
      &                  workl(3*maxncv*maxncv+5*maxncv)
-      Double precision  
+      Double precision
      &                  rwork(maxncv), rd(maxncv,3)
 c
 c     %---------------%
@@ -84,9 +84,9 @@ c
       character         bmat*1, which*2
       integer           ido, n, nx, nev, ncv, lworkl, info, j,
      &                  ierr, nconv, maxitr, ishfts, mode
-      Complex*16 
+      Complex*16
      &                  sigma
-      Double precision 
+      Double precision
      &                  tol
       logical           rvec
 c
@@ -94,19 +94,19 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dznrm2 , dlapy2 
-      external          dznrm2 , zaxpy , dlapy2  
+      Double precision
+     &                  dznrm2 , dlapy2
+      external          dznrm2 , zaxpy , dlapy2
 c
 c     %-----------------------%
 c     | Executable Statements |
 c     %-----------------------%
-c 
+c
 c     %--------------------------------------------------%
 c     | The number NX is the number of interior points   |
 c     | in the discretization of the 2-dimensional       |
 c     | convection-diffusion operator on the unit        |
-c     | square with zero Dirichlet boundary condition.   | 
+c     | square with zero Dirichlet boundary condition.   |
 c     | The number N(=NX*NX) is the dimension of the     |
 c     | matrix.  A standard eigenvalue problem is        |
 c     | solved (BMAT = 'I').  NEV is the number of       |
@@ -117,13 +117,13 @@ c     | the spectrum.  However, The following            |
 c     | conditions must be satisfied:                    |
 c     |                   N <= MAXN                      |
 c     |                 NEV <= MAXNEV                    |
-c     |           NEV + 2 <= NCV <= MAXNCV               | 
-c     %--------------------------------------------------% 
+c     |           NEV + 2 <= NCV <= MAXNCV               |
+c     %--------------------------------------------------%
 c
-      nx    = 10 
-      n     = nx*nx 
+      nx    = 10
+      n     = nx*nx
       nev   = 4
-      ncv   = 20 
+      ncv   = 20
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NDRV1: N is greater than MAXN '
          go to 9000
@@ -138,18 +138,18 @@ c
       which = 'LM'
 c
 c     %---------------------------------------------------%
-c     | The work array WORKL is used in ZNAUPD  as         | 
+c     | The work array WORKL is used in ZNAUPD  as         |
 c     | workspace.  Its dimension LWORKL is set as        |
 c     | illustrated below.  The parameter TOL determines  |
 c     | the stopping criterion. If TOL<=0, machine        |
 c     | precision is used.  The variable IDO is used for  |
 c     | reverse communication, and is initially set to 0. |
 c     | Setting INFO=0 indicates that a random vector is  |
-c     | generated to start the ARNOLDI iteration.         | 
+c     | generated to start the ARNOLDI iteration.         |
 c     %---------------------------------------------------%
 c
-      lworkl  = 3*ncv**2+5*ncv 
-      tol    = 0.0 
+      lworkl  = 3*ncv**2+5*ncv
+      tol    = 0.0
       ido    = 0
       info   = 0
 c
@@ -168,11 +168,11 @@ c
       mode   = 1
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %-------------------------------------------%
-c     | M A I N   L O O P (Reverse communication) | 
+c     | M A I N   L O O P (Reverse communication) |
 c     %-------------------------------------------%
 c
  10   continue
@@ -197,7 +197,7 @@ c           | The user should supply his/her own        |
 c           | matrix vector multiplication routine here |
 c           | that takes workd(ipntr(1)) as the input   |
 c           | vector, and return the matrix vector      |
-c           | product to workd(ipntr(2)).               | 
+c           | product to workd(ipntr(2)).               |
 c           %-------------------------------------------%
 c
             call av (nx, workd(ipntr(1)), workd(ipntr(2)))
@@ -209,7 +209,7 @@ c
             go to 10
 
          end if
-c 
+c
 c     %----------------------------------------%
 c     | Either we have convergence or there is |
 c     | an error.                              |
@@ -227,7 +227,7 @@ c
          print *, ' Check the documentation of _naupd'
          print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
@@ -241,16 +241,16 @@ c        %-------------------------------------------%
 c
          rvec = .true.
 c
-         call zneupd  (rvec, 'A', select, d, v, ldv, sigma, 
-     &        workev, bmat, n, which, nev, tol, resid, ncv, 
-     &        v, ldv, iparam, ipntr, workd, workl, lworkl, 
+         call zneupd  (rvec, 'A', select, d, v, ldv, sigma,
+     &        workev, bmat, n, which, nev, tol, resid, ncv,
+     &        v, ldv, iparam, ipntr, workd, workl, lworkl,
      &        rwork, ierr)
 c
 c        %----------------------------------------------%
 c        | Eigenvalues are returned in the one          |
 c        | dimensional array D.  The corresponding      |
 c        | eigenvectors are returned in the first NCONV |
-c        | (=IPARAM(5)) columns of the two dimensional  | 
+c        | (=IPARAM(5)) columns of the two dimensional  |
 c        | array V if requested.  Otherwise, an         |
 c        | orthogonal basis for the invariant subspace  |
 c        | corresponding to the eigenvalues in D is     |
@@ -258,7 +258,7 @@ c        | returned in V.                               |
 c        %----------------------------------------------%
 c
          if ( ierr .ne. 0) then
-c 
+c
 c           %------------------------------------%
 c           | Error condition:                   |
 c           | Check the documentation of ZNEUPD . |
@@ -312,11 +312,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, '_NDRV1'
@@ -327,8 +327,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -344,7 +344,7 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector subroutine
@@ -354,21 +354,21 @@ c     discretized using centered difference.
 c
       subroutine av (nx, v, w)
       integer           nx, j, lo
-      Complex*16          
+      Complex*16
      &                  v(nx*nx), w(nx*nx), one, h2
       parameter         (one = (1.0D+0, 0.0D+0) )
       external          zaxpy , tv
 c
-c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block 
+c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block
 c     tridiagonal matrix
 c
-c                  | T -I          | 
+c                  | T -I          |
 c                  |-I  T -I       |
 c             OP = |   -I  T       |
 c                  |        ...  -I|
 c                  |           -I T|
 c
-c     derived from the standard central difference  discretization 
+c     derived from the standard central difference  discretization
 c     of the convection-diffusion operator (Laplacian u) + rho*(du/dx)
 c     with zero boundary condition.
 c
@@ -385,7 +385,7 @@ c
          call tv(nx, v(lo+1), w(lo+1))
          call zaxpy (nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1)
          call zaxpy (nx, -one/h2, v(lo+nx+1), 1, w(lo+1), 1)
-  10  continue 
+  10  continue
 c
       lo = (nx-1)*nx
       call tv(nx, v(lo+1), w(lo+1))
@@ -396,29 +396,29 @@ c
 c=========================================================================
       subroutine tv (nx, x, y)
 c
-      integer           nx, j 
-      Complex*16 
+      integer           nx, j
+      Complex*16
      &                  x(nx), y(nx), h, h2, dd, dl, du
 c
-      Complex*16 
+      Complex*16
      &                  one, rho
       parameter         (one = (1.0D+0, 0.0D+0) ,
      &                   rho = (1.0D+2, 0.0D+0) )
 c
 c     Compute the matrix vector multiplication y<---T*x
-c     where T is a nx by nx tridiagonal matrix with DD on the 
+c     where T is a nx by nx tridiagonal matrix with DD on the
 c     diagonal, DL on the subdiagonal, and DU on the superdiagonal
-c     
+c
       h   = one / dcmplx (nx+1)
       h2  = h*h
       dd  = (4.0D+0, 0.0D+0)  / h2
       dl  = -one/h2 - (5.0D-1, 0.0D+0) *rho/h
       du  = -one/h2 + (5.0D-1, 0.0D+0) *rho/h
-c 
+c
       y(1) =  dd*x(1) + du*x(2)
       do 10 j = 2,nx-1
-         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 
- 10   continue 
-      y(nx) =  dl*x(nx-1) + dd*x(nx) 
+         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1)
+ 10   continue
+      y(nx) =  dl*x(nx-1) + dd*x(nx)
       return
       end

EXAMPLES/COMPLEX/zndrv2.f

@@ -1,7 +1,7 @@
-      program zndrv2 
+      program zndrv2
 c
 c     Simple program to illustrate the idea of reverse communication
-c     in shift-invert mode for a standard complex nonsymmetric eigenvalue 
+c     in shift-invert mode for a standard complex nonsymmetric eigenvalue
 c     problem.
 c
 c     We implement example two of ex-complex.doc in DOCUMENTS directory
@@ -60,7 +60,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer           maxn, maxnev, maxncv, ldv
-      parameter         (maxn=256, maxnev=10, maxncv=25, 
+      parameter         (maxn=256, maxnev=10, maxncv=25,
      &                   ldv=maxn )
 c
 c     %--------------%
@@ -69,14 +69,14 @@ c     %--------------%
 c
       integer           iparam(11), ipntr(14), ipiv(maxn)
       logical           select(maxncv)
-      Complex*16 
+      Complex*16
      &                  ax(maxn), d(maxncv), resid(maxn),
      &                  v(ldv, maxncv), workd(3*maxn),
      &                  workev(2*maxncv),
      &                  workl(3*maxncv*maxncv+5*maxncv),
      &                  dd(maxn), dl(maxn), du(maxn),
      &                  du2(maxn)
-      Double precision 
+      Double precision
      &                  rwork(maxn), rd(maxncv,3)
 c
 c     %---------------%
@@ -86,11 +86,11 @@ c
       character         bmat*1, which*2
       integer           ido, n, nev, ncv, lworkl, info, j, ierr,
      &                  nconv, maxitr, ishfts, mode
-      Complex*16  
+      Complex*16
      &                  h, h2, s, sigma, s1, s2, s3, rho
       common            /convct/ rho
 c
-      Double precision 
+      Double precision
      &                  tol
       logical           rvec
 c
@@ -98,9 +98,9 @@ c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Complex*16  
-     &                   one, zero, two        
-      parameter         (one = (1.0D+0, 0.0D+0) , 
+      Complex*16
+     &                   one, zero, two
+      parameter         (one = (1.0D+0, 0.0D+0) ,
      &                   zero = (0.0D+0, 0.0D+0) ,
      &                   two = (2.0D+0, 0.0D+0) )
 c
@@ -108,10 +108,10 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dznrm2 , dlapy2 
+      Double precision
+     &                  dznrm2 , dlapy2
       external          zgttrf , zgttrs , zaxpy , zcopy , dznrm2 ,
-     &                  dlapy2 
+     &                  dlapy2
 c
 c     %-----------------------%
 c     | Executable statements |
@@ -160,22 +160,22 @@ c     | the interval [0, 1] with zero Dirichlet boundary   |
 c     | condition.                                         |
 c     %----------------------------------------------------%
 c
-      rho = (1.0D+1, 0.0D+0) 
+      rho = (1.0D+1, 0.0D+0)
       h = one / dcmplx (n+1)
       h2 = h*h
       s = rho / two
 c
-      s1 = -one/h2 - s/h 
+      s1 = -one/h2 - s/h
       s2 = two/h2 - sigma
-      s3 = -one/h2 + s/h  
+      s3 = -one/h2 + s/h
 c
       do 10 j = 1, n-1
-         dl(j) = s1 
+         dl(j) = s1
          dd(j) = s2
          du(j) = s3
-  10  continue 
-      dd(n) = s2 
-c 
+  10  continue
+      dd(n) = s2
+c
       call zgttrf (n, dl, dd, du, du2, ipiv, ierr)
       if ( ierr .ne. 0 ) then
          print*, ' '
@@ -195,8 +195,8 @@ c     | Setting INFO=0 indicates that a random vector is    |
 c     | generated in ZNAUPD  to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl = 3*ncv**2+5*ncv 
-      tol    = 0.0 
+      lworkl = 3*ncv**2+5*ncv
+      tol    = 0.0
       ido    = 0
       info   = 0
 c
@@ -214,18 +214,18 @@ c
       maxitr = 300
       mode   = 3
 c
-      iparam(1) = ishfts 
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+      iparam(1) = ishfts
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %-------------------------------------------%
-c     | M A I N   L O O P (Reverse communication) | 
+c     | M A I N   L O O P (Reverse communication) |
 c     %-------------------------------------------%
 c
  20   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine ZNAUPD  and take | 
+c        | Repeatedly call the routine ZNAUPD  and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
@@ -247,8 +247,8 @@ c           %-------------------------------------------%
 c
             call zcopy ( n, workd(ipntr(1)),1, workd(ipntr(2)), 1)
 c
-            call zgttrs ('N', n, 1, dl, dd, du, du2, ipiv, 
-     &                  workd(ipntr(2)), n, ierr) 
+            call zgttrs ('N', n, 1, dl, dd, du, du2, ipiv,
+     &                  workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
                print*, ' ERROR with _gttrs in _NDRV2.'
@@ -279,23 +279,23 @@ c
          print *, ' '
          print *, ' Error with _naupd, info = ',info
          print *, ' Check the documentation in _naupd.'
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using ZNEUPD .                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
-c 
+c
          rvec = .true.
 c
-         call zneupd  (rvec, 'A', select, d, v, ldv, sigma, 
+         call zneupd  (rvec, 'A', select, d, v, ldv, sigma,
      &                workev, bmat, n, which, nev, tol,
      &                resid, ncv, v, ldv, iparam, ipntr, workd,
      &                workl, lworkl, rwork, ierr)
@@ -312,19 +312,19 @@ c        | returned in V.                               |
 c        %----------------------------------------------%
 c
          if ( ierr .ne. 0) then
-c 
+c
 c           %------------------------------------%
-c           | Error condition:                   | 
+c           | Error condition:                   |
 c           | Check the documentation of ZNEUPD . |
 c           %------------------------------------%
-c 
+c
             print *, ' '
             print *, ' Error with _neupd, info = ', ierr
             print *, ' Check the documentation of _neupd. '
             print *, ' '
          else
 c
-            nconv = iparam(5) 
+            nconv = iparam(5)
             do 60 j=1, nconv
 c
 c              %---------------------------%
@@ -366,11 +366,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, '_NDRV2 '
@@ -381,8 +381,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -405,7 +405,7 @@ c     matrix vector multiplication subroutine
 c
       subroutine av (n, v, w)
       integer           n, j
-      Complex*16  
+      Complex*16
      &                   v(n), w(n), rho, two, one, dd, dl, du, s, h,
      &                   h2
       parameter         (one = (1.0D+0, 0.0D+0) ,

EXAMPLES/COMPLEX/zndrv3.f

@@ -1,7 +1,7 @@
-      program zndrv3 
+      program zndrv3
 c
 c     Simple program to illustrate the idea of reverse communication
-c     in inverse mode for a generalized complex nonsymmetric eigenvalue 
+c     in inverse mode for a generalized complex nonsymmetric eigenvalue
 c     problem.
 c
 c     We implement example three of ex-complex.doc in DOCUMENTS directory
@@ -11,8 +11,8 @@ c     ... Suppose we want to solve A*x = lambda*B*x in regular mode,
 c         where A and B are derived from the finite element discretization
 c         of the 1-dimensional convection-diffusion operator
 c                   (d^2u/dx^2) + rho*(du/dx)
-c         on the interval [0,1] with zero boundary condition using 
-c         piecewise linear elements. 
+c         on the interval [0,1] with zero boundary condition using
+c         piecewise linear elements.
 c
 c     ... OP = inv[M]*A  and  B = M.
 c
@@ -60,7 +60,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer           maxn, maxnev, maxncv, ldv
-      parameter         (maxn=256, maxnev=10, maxncv=25, 
+      parameter         (maxn=256, maxnev=10, maxncv=25,
      &                   ldv=maxn )
 c
 c     %--------------%
@@ -69,13 +69,13 @@ c     %--------------%
 c
       integer           iparam(11), ipntr(14), ipiv(maxn)
       logical           select(maxncv)
-      Complex*16 
+      Complex*16
      &                  ax(maxn), mx(maxn), d(maxncv), resid(maxn),
-     &                  v(ldv,maxncv), workd(3*maxn), 
+     &                  v(ldv,maxncv), workd(3*maxn),
      &                  workev(2*maxncv),
      &                  workl(3*maxncv*maxncv+5*maxncv),
      &                  dd(maxn), dl(maxn), du(maxn), du2(maxn)
-      Double precision             
+      Double precision
      &                  rwork(maxn), rd(maxncv,3)
 c
 c     %---------------%
@@ -85,9 +85,9 @@ c
       character         bmat*1, which*2
       integer           ido, n, nev, ncv, lworkl, info, ierr, j,
      &                  nconv, maxitr, ishfts, mode
-      Complex*16            
+      Complex*16
      &                  sigma, h
-      Double precision 
+      Double precision
      &                  tol
       logical           rvec
 c
@@ -95,7 +95,7 @@ c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Complex*16   
+      Complex*16
      &                  zero, one
       parameter         (zero = (0.0D+0, 0.0D+0) ,
      &                   one = (1.0D+0, 0.0D+0) )
@@ -104,10 +104,10 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision  
-     &                  dznrm2 , dlapy2 
+      Double precision
+     &                  dznrm2 , dlapy2
       external          zaxpy , zcopy , dznrm2 , zgttrf , zgttrs ,
-     &                  dlapy2 
+     &                  dlapy2
 c
 c     %-----------------------%
 c     | Executable Statements |
@@ -126,9 +126,9 @@ c     |                  NEV <= MAXNEV,                    |
 c     |              NEV + 2 <= NCV <= MAXNCV              |
 c     %----------------------------------------------------%
 c
-      n     = 100 
-      nev   = 4 
-      ncv   = 20 
+      n     = 100
+      nev   = 4
+      ncv   = 20
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NDRV3: N is greater than MAXN '
          go to 9000
@@ -154,15 +154,15 @@ c
       do 20 j = 1, n-1
          dl(j) = one*h
          dd(j) = (4.0D+0, 0.0D+0) *h
-         du(j) = one*h 
-  20  continue 
-      dd(n) = (4.0D+0, 0.0D+0) *h 
+         du(j) = one*h
+  20  continue
+      dd(n) = (4.0D+0, 0.0D+0) *h
 c
-      call zgttrf (n, dl, dd, du, du2, ipiv, ierr) 
+      call zgttrf (n, dl, dd, du, du2, ipiv, ierr)
       if ( ierr .ne. 0 ) then
          print*, ' '
-         print*, ' ERROR with _gttrf. ' 
-         print*, ' ' 
+         print*, ' ERROR with _gttrf. '
+         print*, ' '
          go to 9000
       end if
 c
@@ -177,8 +177,8 @@ c     | Setting INFO=0 indicates that a random vector is    |
 c     | generated in ZNAUPD  to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl = 3*ncv**2+5*ncv 
-      tol    = 0.0 
+      lworkl = 3*ncv**2+5*ncv
+      tol    = 0.0
       ido    = 0
       info   = 0
 c
@@ -197,8 +197,8 @@ c
       mode   = 2
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr  
-      iparam(7) = mode 
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %-------------------------------------------%
 c     | M A I N   L O O P (Reverse communication) |
@@ -207,14 +207,14 @@ c
  10   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine ZNAUPD  and take | 
+c        | Repeatedly call the routine ZNAUPD  and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call znaupd  ( ido, bmat, n, which, nev, tol, resid, ncv, 
-     &        v, ldv, iparam, ipntr, workd, workl, lworkl, 
+         call znaupd  ( ido, bmat, n, which, nev, tol, resid, ncv,
+     &        v, ldv, iparam, ipntr, workd, workl, lworkl,
      &        rwork, info )
 c
          if (ido .eq. -1 .or. ido .eq. 1) then
@@ -233,8 +233,8 @@ c
             call zgttrs ('N', n, 1, dl, dd, du, du2, ipiv,
      &                  workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
-               print*, ' ' 
-               print*, ' ERROR with _gttrs. ' 
+               print*, ' '
+               print*, ' ERROR with _gttrs. '
                print*, ' '
                go to 9000
             end if
@@ -268,7 +268,7 @@ c
 c     %-----------------------------------------%
 c     | Either we have convergence, or there is |
 c     | an error.                               |
-c     %-----------------------------------------% 
+c     %-----------------------------------------%
 c
       if ( info .lt. 0 ) then
 c
@@ -280,24 +280,24 @@ c
          print *, ' '
          print *, ' Error with _naupd, info = ',info
          print *, ' Check the documentation of _naupd.'
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using ZNEUPD .                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
 c
          rvec = .true.
 c
-         call zneupd  ( rvec, 'A', select, d, v, ldv, sigma, 
-     &        workev, bmat, n, which, nev, tol, resid, ncv, v, 
+         call zneupd  ( rvec, 'A', select, d, v, ldv, sigma,
+     &        workev, bmat, n, which, nev, tol, resid, ncv, v,
      &        ldv, iparam, ipntr, workd, workl, lworkl, rwork,
      &        ierr )
 c
@@ -318,8 +318,8 @@ c           %------------------------------------%
 c           | Error condition:                   |
 c           | Check the documentation of ZNEUPD . |
 c           %------------------------------------%
-c 
-            print *, ' ' 
+c
+            print *, ' '
             print *, ' Error with _neupd, info = ', ierr
             print *, ' Check the documentation of _neupd'
             print *, ' '
@@ -327,7 +327,7 @@ c
          else
 c
             nconv = iparam(5)
-            do 80 j=1, nconv 
+            do 80 j=1, nconv
 c
 c              %---------------------------%
 c              | Compute the residual norm |
@@ -369,11 +369,11 @@ c
             print *, ' Maximum number of iterations reached.'
             print *, ' '
          else if ( info .eq. 3) then
-            print *, ' ' 
+            print *, ' '
             print *, ' No shifts could be applied during implicit',
      &               ' Arnoldi update, try increasing NCV.'
             print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, '_NDRV3 '
@@ -384,8 +384,8 @@ c
          print *, ' The number of Arnoldi vectors generated ',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -397,21 +397,21 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector multiplication subroutine
 c
       subroutine av (n, v, w)
       integer           n, j
-      Complex*16             
-     &                  v(n), w(n), one, two, dd, dl, du, s, h, rho 
+      Complex*16
+     &                  v(n), w(n), one, two, dd, dl, du, s, h, rho
       parameter         (one = (1.0D+0, 0.0D+0) ,
      &                   two = (2.0D+0, 0.0D+0) ,
      &                   rho = (1.0D+1, 0.0D+0) )
 c
 c     Compute the matrix vector multiplication y<---A*x
-c     where A is the stiffness matrix formed by using piecewise linear 
+c     where A is the stiffness matrix formed by using piecewise linear
 c     elements on [0,1].
 c
       h = one / dcmplx (n+1)
@@ -422,28 +422,28 @@ c
 c
       w(1) =  dd*v(1) + du*v(2)
       do 10 j = 2,n-1
-         w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1) 
- 10   continue 
-      w(n) =  dl*v(n-1) + dd*v(n) 
+         w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1)
+ 10   continue
+      w(n) =  dl*v(n-1) + dd*v(n)
       return
       end
 c------------------------------------------------------------------------
       subroutine mv (n, v, w)
       integer           n, j
-      Complex*16  
+      Complex*16
      &                  v(n), w(n), one, four, h
-      parameter         (one = (1.0D+0, 0.0D+0) , 
+      parameter         (one = (1.0D+0, 0.0D+0) ,
      &                   four = (4.0D+0, 0.0D+0) )
 c
 c     Compute the matrix vector multiplication y<---M*x
-c     where M is the mass matrix formed by using piecewise linear elements 
+c     where M is the mass matrix formed by using piecewise linear elements
 c     on [0,1].
-c 
+c
       w(1) =  four*v(1) + one*v(2)
       do 10 j = 2,n-1
-         w(j) = one*v(j-1) + four*v(j) + one*v(j+1) 
- 10   continue 
-      w(n) =  one*v(n-1) + four*v(n) 
+         w(j) = one*v(j-1) + four*v(j) + one*v(j+1)
+ 10   continue
+      w(n) =  one*v(n-1) + four*v(n)
 c
       h = one / dcmplx (n+1)
       call zscal (n, h, w, 1)

EXAMPLES/COMPLEX/zndrv4.f

@@ -1,7 +1,7 @@
-      program zndrv4 
+      program zndrv4
 c
 c     Simple program to illustrate the idea of reverse communication
-c     in shift and invert mode for a generalized complex nonsymmetric 
+c     in shift and invert mode for a generalized complex nonsymmetric
 c     eigenvalue problem.
 c
 c     We implement example four of ex-complex.doc in DOCUMENTS directory
@@ -11,7 +11,7 @@ c     ... Suppose we want to solve A*x = lambda*B*x in shift-invert mode,
 c         where A and B are derived from a finite element discretization
 c         of a 1-dimensional convection-diffusion operator
 c                         (d^2u/dx^2) + rho*(du/dx)
-c         on the interval [0,1] with zero boundary condition using 
+c         on the interval [0,1] with zero boundary condition using
 c         piecewise linear elements.
 c
 c     ... where the shift sigma is a complex number.
@@ -36,15 +36,15 @@ c     av      Matrix vector multiplication routine that computes A*x.
 c     mv      Matrix vector multiplication routine that computes M*x.
 c
 c\Author
-c     Danny Sorensen               
-c     Richard Lehoucq 
-c     Chao Yang             
-c     Dept. of Computational &     
-c     Applied Mathematics          
-c     Rice University           
-c     Houston, Texas    
+c     Danny Sorensen
+c     Richard Lehoucq
+c     Chao Yang
+c     Dept. of Computational &
+c     Applied Mathematics
+c     Rice University
+c     Houston, Texas
 c
-c\SCCS Information: @(#) 
+c\SCCS Information: @(#)
 c FILE: ndrv4.F   SID: 2.4   DATE OF SID: 10/18/00   RELEASE: 2
 c
 c\Remarks
@@ -63,7 +63,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer           maxn, maxnev, maxncv, ldv
-      parameter         (maxn=256, maxnev=10, maxncv=25, 
+      parameter         (maxn=256, maxnev=10, maxncv=25,
      &                   ldv=maxn )
 c
 c     %--------------%
@@ -72,14 +72,14 @@ c     %--------------%
 c
       integer           iparam(11), ipntr(14), ipiv(maxn)
       logical           select(maxncv)
-      Complex*16  
-     &                  ax(maxn), mx(maxn), d(maxncv), 
+      Complex*16
+     &                  ax(maxn), mx(maxn), d(maxncv),
      &                  v(ldv,maxncv), workd(3*maxn), resid(maxn),
      &                  workev(2*maxncv),
      &                  workl(3*maxncv*maxncv+5*maxncv),
      &                  dd(maxn), dl(maxn), du(maxn),
      &                  du2(maxn)
-      Double precision 
+      Double precision
      &                  rwork(maxn), rd(maxncv,3)
 c
 c     %---------------%
@@ -89,32 +89,32 @@ c
       character         bmat*1, which*2
       integer           ido, n, nev, ncv, lworkl, info, j, ierr,
      &                  nconv, maxitr, ishfts, mode
-      Complex*16  
+      Complex*16
      &                  rho, h, s,
      &                  sigma, s1, s2, s3
       common            /convct/ rho
 c
-      Double precision 
+      Double precision
      &                  tol
-      logical           rvec 
-c 
+      logical           rvec
+c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dznrm2 , dlapy2 
+      Double precision
+     &                  dznrm2 , dlapy2
       external          dznrm2 , zaxpy , zcopy , zgttrf , zgttrs ,
-     &                  dlapy2 
+     &                  dlapy2
 c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Complex*16  
+      Complex*16
      &                   one, zero, two, four, six
       parameter         (one = (1.0D+0, 0.0D+0) ,
-     &                   zero = (0.0D+0, 0.0D+0) , 
+     &                   zero = (0.0D+0, 0.0D+0) ,
      &                   two = (2.0D+0, 0.0D+0) ,
      &                   four = (4.0D+0, 0.0D+0) ,
      &                   six = (6.0D+0, 0.0D+0) )
@@ -138,7 +138,7 @@ c     |                   NEV <= MAXNEV,                   |
 c     |               NEV + 2 <= NCV <= MAXNCV             |
 c     %----------------------------------------------------%
 c
-      n     = 100 
+      n     = 100
       nev   = 4
       ncv   = 20
       if ( n .gt. maxn ) then
@@ -153,7 +153,7 @@ c
       end if
       bmat  = 'G'
       which = 'LM'
-      sigma = one 
+      sigma = one
 c
 c     %--------------------------------------------------%
 c     | Construct C = A - SIGMA*M in COMPLEX arithmetic. |
@@ -164,11 +164,11 @@ c     | central difference discretization of the 1-d     |
 c     | convection-diffusion operator u``+ rho*u` on the |
 c     | interval [0, 1] with zero Dirichlet boundary     |
 c     | condition.  The matrix M is chosen to be the     |
-c     | symmetric tridiagonal matrix with 4.0 on the     | 
-c     | diagonal and 1.0 on the off-diagonals.           | 
+c     | symmetric tridiagonal matrix with 4.0 on the     |
+c     | diagonal and 1.0 on the off-diagonals.           |
 c     %--------------------------------------------------%
 c
-      rho = (1.0D+1, 0.0D+0) 
+      rho = (1.0D+1, 0.0D+0)
       h = one / dcmplx (n+1)
       s = rho / two
 c
@@ -177,12 +177,12 @@ c
       s3 = -one/h + s - sigma*h/six
 c
       do 10 j = 1, n-1
-	 dl(j) = s1 
+	 dl(j) = s1
 	 dd(j) = s2
 	 du(j) = s3
-  10  continue 
-      dd(n) = s2 
-c 
+  10  continue
+      dd(n) = s2
+c
       call zgttrf (n, dl, dd, du, du2, ipiv, ierr)
       if ( ierr .ne. 0 ) then
          print*, ' '
@@ -202,7 +202,7 @@ c     | Setting INFO=0 indicates that a random vector is    |
 c     | generated in ZNAUPD  to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl = 3*ncv**2+5*ncv 
+      lworkl = 3*ncv**2+5*ncv
       tol    = 0.0
       ido    = 0
       info   = 0
@@ -222,11 +222,11 @@ c
       mode   = 3
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %------------------------------------------%
-c     | M A I N   L O O P(Reverse communication) | 
+c     | M A I N   L O O P(Reverse communication) |
 c     %------------------------------------------%
 c
  20   continue
@@ -258,14 +258,14 @@ c           | workd(ipntr(2)).                          |
 c           %-------------------------------------------%
 c
             call mv (n, workd(ipntr(1)), workd(ipntr(2)))
-            call zgttrs ('N', n, 1, dl, dd, du, du2, ipiv, 
+            call zgttrs ('N', n, 1, dl, dd, du, du2, ipiv,
      &                  workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
                print*, ' ERROR with _gttrs in _NDRV4.'
                print*, ' '
                go to 9000
-            end if 
+            end if
 c
 c           %-----------------------------------------%
 c           | L O O P   B A C K to call ZNAUPD  again. |
@@ -285,7 +285,7 @@ c           | workd(ipntr(2)).                        |
 c           %-----------------------------------------%
 c
             call zcopy ( n, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-            call zgttrs  ('N', n, 1, dl, dd, du, du2, ipiv, 
+            call zgttrs  ('N', n, 1, dl, dd, du, du2, ipiv,
      &                   workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
@@ -317,8 +317,8 @@ c           %-----------------------------------------%
 c
             go to 20
 c
-         end if 
-c 
+         end if
+c
 c     %-----------------------------------------%
 c     | Either we have convergence, or there is |
 c     | an error.                               |
@@ -334,9 +334,9 @@ c
          print *, ' '
          print *, ' Error with _naupd, info = ', info
          print *, ' Check the documentation of _naupd.'
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
@@ -350,9 +350,9 @@ c        %-------------------------------------------%
 c
          rvec = .true.
 c
-         call zneupd  (rvec, 'A', select, d, v, ldv, sigma, 
-     &        workev, bmat, n, which, nev, tol, resid, ncv, v, 
-     &        ldv, iparam, ipntr, workd, workl, lworkl, rwork, 
+         call zneupd  (rvec, 'A', select, d, v, ldv, sigma,
+     &        workev, bmat, n, which, nev, tol, resid, ncv, v,
+     &        ldv, iparam, ipntr, workd, workl, lworkl, rwork,
      &        ierr)
 c
 c        %----------------------------------------------%
@@ -367,7 +367,7 @@ c        | returned in V.                               |
 c        %----------------------------------------------%
 c
          if ( ierr .ne. 0) then
-c 
+c
 c           %------------------------------------%
 c           | Error condition:                   |
 c           | Check the documentation of ZNEUPD . |
@@ -438,27 +438,27 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector multiplication subroutine
 c
       subroutine mv (n, v, w)
       integer           n, j
-      Complex*16  
+      Complex*16
      &                  v(n), w(n), one, four, six, h
       parameter         (one = (1.0D+0, 0.0D+0) ,
      &                   four = (4.0D+0, 0.0D+0) ,
      &                   six = (6.0D+0, 0.0D+0) )
 c
 c     Compute the matrix vector multiplication y<---M*x
-c     where M is a n by n symmetric tridiagonal matrix with 4 on the 
+c     where M is a n by n symmetric tridiagonal matrix with 4 on the
 c     diagonal, 1 on the subdiagonal and superdiagonal.
-c 
+c
       w(1) =  ( four*v(1) + one*v(2) ) / six
       do 40 j = 2,n-1
          w(j) = ( one*v(j-1) + four*v(j) + one*v(j+1) ) / six
- 40   continue 
+ 40   continue
       w(n) =  ( one*v(n-1) + four*v(n) ) / six
 c
       h = one / dcmplx (n+1)
@@ -468,9 +468,9 @@ c
 c------------------------------------------------------------------
       subroutine av (n, v, w)
       integer           n, j
-      Complex*16  
-     &                  v(n), w(n), one, two, dd, dl, du, s, h, rho 
-      parameter         (one = (1.0D+0, 0.0D+0) , 
+      Complex*16
+     &                  v(n), w(n), one, two, dd, dl, du, s, h, rho
+      parameter         (one = (1.0D+0, 0.0D+0) ,
      &                   two = (2.0D+0, 0.0D+0) )
       common            /convct/ rho
 c

EXAMPLES/Makefile.am

@@ -0,0 +1,2 @@
+SUBDIRS = BAND COMPLEX NONSYM SIMPLE SVD SYM
+EXTRA_DIST = README

EXAMPLES/NONSYM/Makefile.am

@@ -0,0 +1,26 @@
+LDADD = $(top_builddir)/SRC/libarpack$(LIBSUFFIX).la $(LAPACK_LIBS) $(BLAS_LIBS)
+
+SNDRV = sndrv1 sndrv2 sndrv3 sndrv4 sndrv5 sndrv6
+DNDRV = dndrv1 dndrv2 dndrv3 dndrv4 dndrv5 dndrv6
+NONSYM = $(SNDRV) $(DNDRV)
+
+check_PROGRAMS = $(NONSYM)
+TESTS = $(check_PROGRAMS)
+
+EXTRA_DIST = README
+
+# Simple nonsymmetric problem using single precision
+sndrv1_SOURCES = sndrv1.f
+sndrv2_SOURCES = sndrv2.f
+sndrv3_SOURCES = sndrv3.f
+sndrv4_SOURCES = sndrv4.f
+sndrv5_SOURCES = sndrv5.f
+sndrv6_SOURCES = sndrv6.f
+
+# Simple nonsymmetric problem using double precision
+dndrv1_SOURCES = dndrv1.f
+dndrv2_SOURCES = dndrv2.f
+dndrv3_SOURCES = dndrv3.f
+dndrv4_SOURCES = dndrv4.f
+dndrv5_SOURCES = dndrv5.f
+dndrv6_SOURCES = dndrv6.f

EXAMPLES/NONSYM/dndrv1.f

@@ -1,4 +1,4 @@
-      program dndrv1 
+      program dndrv1
 c
 c
 c     Example program to illustrate the idea of reverse communication
@@ -9,9 +9,9 @@ c
 c\Example-1
 c     ... Suppose we want to solve A*x = lambda*x in regular mode,
 c         where A is obtained from the standard central difference
-c         discretization of the convection-diffusion operator 
+c         discretization of the convection-diffusion operator
 c                 (Laplacian u) + rho*(du / dx)
-c         on the unit square [0,1]x[0,1] with zero Dirichlet boundary 
+c         on the unit square [0,1]x[0,1] with zero Dirichlet boundary
 c         condition.
 c
 c     ... OP = A  and  B = I.
@@ -30,7 +30,7 @@ c     dlapy2  LAPACK routine to compute sqrt(x**2+y**2) carefully.
 c     daxpy   Level 1 BLAS that computes y <- alpha*x+y.
 c     dnrm2   Level 1 BLAS that computes the norm of a vector.
 c     av      Matrix vector multiplication routine that computes A*x.
-c     tv      Matrix vector multiplication routine that computes T*x, 
+c     tv      Matrix vector multiplication routine that computes T*x,
 c             where T is a tridiagonal matrix.  It is used in routine
 c             av.
 c
@@ -71,9 +71,9 @@ c
       integer           iparam(11), ipntr(14)
       logical           select(maxncv)
       Double precision
-     &                  ax(maxn), d(maxncv,3), resid(maxn), 
-     &                  v(ldv,maxncv), workd(3*maxn), 
-     &                  workev(3*maxncv), 
+     &                  ax(maxn), d(maxncv,3), resid(maxn),
+     &                  v(ldv,maxncv), workd(3*maxn),
+     &                  workev(3*maxncv),
      &                  workl(3*maxncv*maxncv+6*maxncv)
 c
 c     %---------------%
@@ -112,12 +112,12 @@ c
 c     %-----------------------%
 c     | Executable Statements |
 c     %-----------------------%
-c 
+c
 c     %--------------------------------------------------%
 c     | The number NX is the number of interior points   |
 c     | in the discretization of the 2-dimensional       |
 c     | convection-diffusion operator on the unit        |
-c     | square with zero Dirichlet boundary condition.   | 
+c     | square with zero Dirichlet boundary condition.   |
 c     | The number N(=NX*NX) is the dimension of the     |
 c     | matrix.  A standard eigenvalue problem is        |
 c     | solved (BMAT = 'I').  NEV is the number of       |
@@ -128,13 +128,13 @@ c     | the spectrum.  However, The following            |
 c     | conditions must be satisfied:                    |
 c     |                   N <= MAXN                      |
 c     |                 NEV <= MAXNEV                    |
-c     |           NEV + 2 <= NCV <= MAXNCV               | 
-c     %--------------------------------------------------% 
+c     |           NEV + 2 <= NCV <= MAXNCV               |
+c     %--------------------------------------------------%
 c
-      nx    = 10 
-      n     = nx*nx 
+      nx    = 10
+      n     = nx*nx
       nev   = 4
-      ncv   = 20 
+      ncv   = 20
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NDRV1: N is greater than MAXN '
          go to 9000
@@ -149,18 +149,18 @@ c
       which = 'SM'
 c
 c     %-----------------------------------------------------%
-c     | The work array WORKL is used in DNAUPD as           |  
+c     | The work array WORKL is used in DNAUPD as           |
 c     | workspace.  Its dimension LWORKL is set as          |
 c     | illustrated below.  The parameter TOL determines    |
 c     | the stopping criterion. If TOL<=0, machine          |
 c     | precision is used.  The variable IDO is used for    |
 c     | reverse communication, and is initially set to 0.   |
 c     | Setting INFO=0 indicates that a random vector is    |
-c     | generated in DNAUPD to start the Arnoldi iteration. | 
+c     | generated in DNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl  = 3*ncv**2+6*ncv 
-      tol    = zero 
+      lworkl  = 3*ncv**2+6*ncv
+      tol    = zero
       ido    = 0
       info   = 0
 c
@@ -179,11 +179,11 @@ c
       mode   = 1
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr 
+      iparam(3) = maxitr
       iparam(7) = mode
 c
 c     %-------------------------------------------%
-c     | M A I N   L O O P (Reverse communication) | 
+c     | M A I N   L O O P (Reverse communication) |
 c     %-------------------------------------------%
 c
  10   continue
@@ -195,8 +195,8 @@ c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call dnaupd ( ido, bmat, n, which, nev, tol, resid, 
-     &        ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, 
+         call dnaupd ( ido, bmat, n, which, nev, tol, resid,
+     &        ncv, v, ldv, iparam, ipntr, workd, workl, lworkl,
      &        info )
 c
          if (ido .eq. -1 .or. ido .eq. 1) then
@@ -208,7 +208,7 @@ c           | The user should supply his/her own        |
 c           | matrix vector multiplication routine here |
 c           | that takes workd(ipntr(1)) as the input   |
 c           | vector, and return the matrix vector      |
-c           | product to workd(ipntr(2)).               | 
+c           | product to workd(ipntr(2)).               |
 c           %-------------------------------------------%
 c
             call av (nx, workd(ipntr(1)), workd(ipntr(2)))
@@ -219,8 +219,8 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-      end if 
-c 
+      end if
+c
 c     %----------------------------------------%
 c     | Either we have convergence or there is |
 c     | an error.                              |
@@ -238,7 +238,7 @@ c
          print *, ' Check the documentation of _naupd'
          print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
@@ -252,8 +252,8 @@ c        %-------------------------------------------%
 c
          rvec = .true.
 c
-         call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv, 
-     &        sigmar, sigmai, workev, bmat, n, which, nev, tol, 
+         call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv,
+     &        sigmar, sigmai, workev, bmat, n, which, nev, tol,
      &        resid, ncv, v, ldv, iparam, ipntr, workd, workl,
      &        lworkl, ierr )
 c
@@ -281,7 +281,7 @@ c
              print *, ' Check the documentation of _neupd. '
              print *, ' '
 c
-         else 
+         else
 c
              first  = .true.
              nconv  = iparam(5)
@@ -317,9 +317,9 @@ c                  %------------------------%
 c                  | Ritz value is complex. |
 c                  | Residual of one Ritz   |
 c                  | value of the conjugate |
-c                  | pair is computed.      | 
+c                  | pair is computed.      |
 c                  %------------------------%
-c        
+c
                    call av(nx, v(1,j), ax)
                    call daxpy(n, -d(j,1), v(1,j), 1, ax, 1)
                    call daxpy(n, d(j,2), v(1,j+1), 1, ax, 1)
@@ -354,23 +354,23 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _NDRV1 '
          print *, ' ====== '
-         print *, ' ' 
+         print *, ' '
          print *, ' Size of the matrix is ', n
          print *, ' The number of Ritz values requested is ', nev
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -386,37 +386,37 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector subroutine
 c
-c     The matrix used is the 2 dimensional convection-diffusion 
+c     The matrix used is the 2 dimensional convection-diffusion
 c     operator discretized using central difference.
 c
       subroutine av (nx, v, w)
       integer           nx, j, lo
-      Double precision         
+      Double precision
      &                  v(nx*nx), w(nx*nx), one, h2
       parameter         (one = 1.0D+0)
       external          daxpy
 c
-c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block 
+c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block
 c     tridiagonal matrix
 c
-c                  | T -I          | 
+c                  | T -I          |
 c                  |-I  T -I       |
 c             OP = |   -I  T       |
 c                  |        ...  -I|
 c                  |           -I T|
 c
-c     derived from the standard central difference discretization 
-c     of the 2 dimensional convection-diffusion operator 
-c     (Laplacian u) + rho*(du/dx) on a unit square with zero boundary 
+c     derived from the standard central difference discretization
+c     of the 2 dimensional convection-diffusion operator
+c     (Laplacian u) + rho*(du/dx) on a unit square with zero boundary
 c     condition.
 c
-c     When rho*h/2 <= 1, the discrete convection-diffusion operator 
-c     has real eigenvalues.  When rho*h/2 > 1, it has COMPLEX 
+c     When rho*h/2 <= 1, the discrete convection-diffusion operator
+c     has real eigenvalues.  When rho*h/2 > 1, it has COMPLEX
 c     eigenvalues.
 c
 c     The subroutine TV is called to compute y<---T*x.
@@ -432,7 +432,7 @@ c
          call tv(nx, v(lo+1), w(lo+1))
          call daxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1)
          call daxpy(nx, -one/h2, v(lo+nx+1), 1, w(lo+1), 1)
-  10  continue 
+  10  continue
 c
       lo = (nx-1)*nx
       call tv(nx, v(lo+1), w(lo+1))
@@ -443,21 +443,21 @@ c
 c=========================================================================
       subroutine tv (nx, x, y)
 c
-      integer           nx, j 
+      integer           nx, j
       Double precision
      &                  x(nx), y(nx), h, h2, dd, dl, du
 c
       Double precision
      &                  one, zero, rho
-      parameter         (one = 1.0D+0, zero = 0.0D+0, 
+      parameter         (one = 1.0D+0, zero = 0.0D+0,
      &                   rho = 0.0D+0)
 c
 c     Compute the matrix vector multiplication y<---T*x
-c     where T is a nx by nx tridiagonal matrix with DD on the 
+c     where T is a nx by nx tridiagonal matrix with DD on the
 c     diagonal, DL on the subdiagonal, and DU on the superdiagonal.
 c
-c     When rho*h/2 <= 1, the discrete convection-diffusion operator 
-c     has real eigenvalues.  When rho*h/2 > 1, it has COMPLEX 
+c     When rho*h/2 <= 1, the discrete convection-diffusion operator
+c     has real eigenvalues.  When rho*h/2 > 1, it has COMPLEX
 c     eigenvalues.
 c
       h   = one / dble(nx+1)
@@ -465,11 +465,11 @@ c
       dd  = 4.0D+0 / h2
       dl  = -one / h2 - 5.0D-1*rho / h
       du  = -one / h2 + 5.0D-1*rho / h
-c 
+c
       y(1) =  dd*x(1) + du*x(2)
       do 10 j = 2,nx-1
-         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 
- 10   continue 
-      y(nx) =  dl*x(nx-1) + dd*x(nx) 
+         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1)
+ 10   continue
+      y(nx) =  dl*x(nx-1) + dd*x(nx)
       return
       end

EXAMPLES/NONSYM/dndrv2.f

@@ -9,7 +9,7 @@ c\Example-2
 c     ... Suppose we want to solve A*x = lambda*x in shift-invert mode,
 c         where A is derived from the centered difference discretization
 c         of the 1-dimensional convection-diffusion operator
-c                          (d^2u / dx^2) + rho*(du/dx) 
+c                          (d^2u / dx^2) + rho*(du/dx)
 c         on the interval [0,1] with zero Dirichlet boundary condition.
 c
 c     ... The shift sigma is a real number.
@@ -61,7 +61,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer           maxn, maxnev, maxncv, ldv
-      parameter         (maxn=256, maxnev=10, maxncv=25, 
+      parameter         (maxn=256, maxnev=10, maxncv=25,
      &                   ldv=maxn )
 c
 c     %--------------%
@@ -97,7 +97,7 @@ c
       Double precision
      &                   one, zero, two, rho
       common            /convct/ rho
-      parameter         (one = 1.0D+0, zero = 0.0D+0, 
+      parameter         (one = 1.0D+0, zero = 0.0D+0,
      &                   two = 2.0D+0)
 c
 c     %-----------------------------%
@@ -128,14 +128,14 @@ c     | 'LM'.  The user can modify NEV, NCV, SIGMAR to   |
 c     | solve problems of different sizes, and to get    |
 c     | different parts of the spectrum.  However, The   |
 c     | following conditions must be satisfied:          |
-c     |                 N <= MAXN,                       | 
+c     |                 N <= MAXN,                       |
 c     |               NEV <= MAXNEV,                     |
-c     |           NEV + 2 <= NCV <= MAXNCV               | 
+c     |           NEV + 2 <= NCV <= MAXNCV               |
 c     %--------------------------------------------------%
 c
       n     = 100
-      nev   = 4 
-      ncv   = 20 
+      nev   = 4
+      ncv   = 20
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NDRV2: N is greater than MAXN '
          go to 9000
@@ -148,8 +148,8 @@ c
       end if
       bmat  = 'I'
       which = 'LM'
-      sigmar = 1.0D+0 
-      sigmai = 0.0D+0 
+      sigmar = 1.0D+0
+      sigmai = 0.0D+0
 c
 c     %----------------------------------------------------%
 c     | Construct C = A - SIGMA*I in real arithmetic, and  |
@@ -157,7 +157,7 @@ c     | factor C in real arithmetic using LAPACK           |
 c     | subroutine dgttrf. The matrix A is chosen to be    |
 c     | the tridiagonal matrix derived from standard       |
 c     | central difference of the 1-d convection diffusion |
-c     | operator u" + rho*u' on the interval [0, 1] with   | 
+c     | operator u" + rho*u' on the interval [0, 1] with   |
 c     | zero Dirichlet boundary condition.                 |
 c     %----------------------------------------------------%
 c
@@ -165,25 +165,25 @@ c
       h = one / dble(n+1)
       s = rho*h / two
 c
-      s1 = -one-s 
+      s1 = -one-s
       s2 = two - sigmar
-      s3 = -one+s  
+      s3 = -one+s
 c
       do 10 j = 1, n-1
-         dl(j) = s1 
+         dl(j) = s1
          dd(j) = s2
          du(j) = s3
-  10  continue 
-      dd(n) = s2 
-c 
+  10  continue
+      dd(n) = s2
+c
       call dgttrf(n, dl, dd, du, du2, ipiv, ierr)
       if ( ierr .ne. 0 ) then
-         print*, ' ' 
+         print*, ' '
          print*, ' ERROR with _gttrf in _NDRV2.'
          print*, ' '
          go to 9000
       end if
-c        
+c
 c     %-----------------------------------------------------%
 c     | The work array WORKL is used in DNAUPD as           |
 c     | workspace.  Its dimension LWORKL is set as          |
@@ -195,8 +195,8 @@ c     | Setting INFO=0 indicates that a random vector is    |
 c     | generated in DNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl = 3*ncv**2+6*ncv 
-      tol    = zero 
+      lworkl = 3*ncv**2+6*ncv
+      tol    = zero
       ido    = 0
       info   = 0
 c
@@ -213,26 +213,26 @@ c
       ishfts = 1
       maxitr = 300
       mode   = 3
- 
-      iparam(1) = ishfts 
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+
+      iparam(1) = ishfts
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %-------------------------------------------%
-c     | M A I N   L O O P (Reverse communication) | 
+c     | M A I N   L O O P (Reverse communication) |
 c     %-------------------------------------------%
 c
  20   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine DNAUPD and take | 
+c        | Repeatedly call the routine DNAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call dnaupd ( ido, bmat, n, which, nev, tol, resid, 
-     &        ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, 
+         call dnaupd ( ido, bmat, n, which, nev, tol, resid,
+     &        ncv, v, ldv, iparam, ipntr, workd, workl, lworkl,
      &        info )
 c
          if ( ido .eq. -1 .or. ido .eq. 1) then
@@ -247,10 +247,10 @@ c           %-------------------------------------------%
 c
             call dcopy( n, workd(ipntr(1)), 1, workd(ipntr(2)), 1)
 c
-            call dgttrs('N', n, 1, dl, dd, du, du2, ipiv, 
-     &                  workd(ipntr(2)), n, ierr) 
+            call dgttrs('N', n, 1, dl, dd, du, du2, ipiv,
+     &                  workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
-               print*, ' ' 
+               print*, ' '
                print*, ' ERROR with _gttrs in _NDRV2.'
                print*, ' '
                go to 9000
@@ -279,26 +279,26 @@ c
          print *, ' '
          print *, ' Error with _naupd, info = ', info
          print *, ' Check the documentation in _naupd.'
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using DNEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
-c 
+c
          rvec = .true.
 c
-         call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv,  
-     &        sigmar, sigmai, workev, bmat, n, which, nev, tol, 
-     &        resid, ncv, v, ldv, iparam, ipntr, workd, 
-     &        workl, lworkl, ierr )            
+         call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv,
+     &        sigmar, sigmai, workev, bmat, n, which, nev, tol,
+     &        resid, ncv, v, ldv, iparam, ipntr, workd,
+     &        workl, lworkl, ierr )
 c
 c        %-----------------------------------------------%
 c        | The real part of the eigenvalue is returned   |
@@ -319,11 +319,11 @@ c           | Error condition:                   |
 c           | Check the documentation of DNEUPD. |
 c           %------------------------------------%
 c
-            print *, ' ' 
+            print *, ' '
             print *, ' Error with _neupd, info = ', ierr
             print *, ' Check the documentation of _neupd. '
-            print *, ' ' 
-c 
+            print *, ' '
+c
          else
 c
             first  = .true.
@@ -360,9 +360,9 @@ c                 %------------------------%
 c                 | Ritz value is complex  |
 c                 | Residual of one Ritz   |
 c                 | value of the conjugate |
-c                 | pair is computed.      | 
+c                 | pair is computed.      |
 c                 %------------------------%
-c 
+c
                   call av(n, v(1,j), ax)
                   call daxpy(n, -d(j,1), v(1,j), 1, ax, 1)
                   call daxpy(n, d(j,2), v(1,j+1), 1, ax, 1)
@@ -397,11 +397,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _NDRV2 '
@@ -412,8 +412,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)

EXAMPLES/NONSYM/dndrv3.f

@@ -15,7 +15,7 @@ c         using linear elements.
 c
 c     ... So OP = inv[M]*A  and  B = M.
 c
-c     ... Use mode 2 of DNAUPD. 
+c     ... Use mode 2 of DNAUPD.
 c
 c\BeginLib
 c
@@ -60,7 +60,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer           maxn, maxnev, maxncv, ldv
-      parameter         (maxn=256, maxnev=10, maxncv=25, 
+      parameter         (maxn=256, maxnev=10, maxncv=25,
      &                   ldv=maxn )
 c
 c     %--------------%
@@ -71,7 +71,7 @@ c
       logical           select(maxncv)
       Double precision
      &                  ax(maxn), mx(maxn), d(maxncv, 3), resid(maxn),
-     &                  v(ldv,maxncv), workd(3*maxn), 
+     &                  v(ldv,maxncv), workd(3*maxn),
      &                  workev(3*maxncv),
      &                  workl(3*maxncv*maxncv+6*maxncv),
      &                  md(maxn), me(maxn-1)
@@ -83,7 +83,7 @@ c
       character         bmat*1, which*2
       integer           ido, n, nev, ncv, lworkl, info, ierr, j,
      &                  nconv, maxitr, ishfts, mode
-      Double precision           
+      Double precision
      &                  tol, sigmar, sigmai, h
       logical           first, rvec
 c
@@ -91,14 +91,14 @@ c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Double precision  
+      Double precision
      &                  zero, one
       parameter         (zero = 0.0D+0, one = 1.0D+0)
 c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
-      Double precision 
+      Double precision
      &                  dnrm2, dlapy2
       external          daxpy, dnrm2, dpttrf, dpttrs, dlapy2
 c
@@ -125,9 +125,9 @@ c     |                  NEV <= MAXNEV,                    |
 c     |              NEV + 2 <= NCV <= MAXNCV              |
 c     %----------------------------------------------------%
 c
-      n     = 100 
-      nev   = 4 
-      ncv   = 20 
+      n     = 100
+      nev   = 4
+      ncv   = 20
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NDRV3: N is greater than MAXN '
          go to 9000
@@ -148,16 +148,16 @@ c     %------------------------------------------------%
 c
       h = one / dble(n+1)
       do 20 j = 1, n-1
-         md(j) = 4.0D+0*h 
-         me(j) = one*h 
-  20  continue 
+         md(j) = 4.0D+0*h
+         me(j) = one*h
+  20  continue
       md(n) = 4.0D+0*h
-c 
+c
       call dpttrf(n, md, me, ierr)
       if ( ierr .ne. 0 ) then
          print*, ' '
-         print*, ' ERROR with _pttrf. ' 
-         print*, ' ' 
+         print*, ' ERROR with _pttrf. '
+         print*, ' '
          go to 9000
       end if
 c
@@ -172,8 +172,8 @@ c     | Setting INFO=0 indicates that a random vector is    |
 c     | generated in DNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl = 3*ncv**2+6*ncv 
-      tol    = 0.0 
+      lworkl = 3*ncv**2+6*ncv
+      tol    = 0.0
       ido    = 0
       info   = 0
 c
@@ -191,9 +191,9 @@ c
       maxitr = 300
       mode   = 2
 c
-      iparam(1) = ishfts 
-      iparam(3) = maxitr  
-      iparam(7) = mode 
+      iparam(1) = ishfts
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %-------------------------------------------%
 c     | M A I N   L O O P (Reverse communication) |
@@ -202,14 +202,14 @@ c
  10   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine DNAUPD and take | 
+c        | Repeatedly call the routine DNAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call dnaupd ( ido, bmat, n, which, nev, tol, resid, 
-     &                 ncv, v, ldv, iparam, ipntr, workd, 
+         call dnaupd ( ido, bmat, n, which, nev, tol, resid,
+     &                 ncv, v, ldv, iparam, ipntr, workd,
      &                 workl, lworkl, info )
 c
          if (ido .eq. -1 .or. ido .eq. 1) then
@@ -228,8 +228,8 @@ c
             call dpttrs(n, 1, md, me, workd(ipntr(2)), n,
      &                  ierr)
             if ( ierr .ne. 0 ) then
-               print*, ' ' 
-               print*, ' ERROR with _pttrs. ' 
+               print*, ' '
+               print*, ' ERROR with _pttrs. '
                print*, ' '
                go to 9000
             end if
@@ -264,7 +264,7 @@ c
 c     %-----------------------------------------%
 c     | Either we have convergence, or there is |
 c     | an error.                               |
-c     %-----------------------------------------% 
+c     %-----------------------------------------%
 c
       if ( info .lt. 0 ) then
 c
@@ -276,22 +276,22 @@ c
          print *, ' '
          print *, ' Error with _naupd, info = ', info
          print *, ' Check the documentation of _naupd.'
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using DNEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
 c
          rvec = .true.
-         call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv, 
+         call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv,
      &        sigmar, sigmai, workev, bmat, n, which, nev, tol,
      &        resid, ncv, v, ldv, iparam, ipntr, workd,
      &        workl, lworkl, ierr )
@@ -314,13 +314,13 @@ c           %------------------------------------%
 c           | Error condition:                   |
 c           | Check the documentation of DNEUPD. |
 c           %------------------------------------%
-c 
-            print *, ' ' 
+c
+            print *, ' '
             print *, ' Error with _neupd, info = ', ierr
             print *, ' Check the documentation of _neupd'
             print *, ' '
 c
-         else 
+         else
 c
             first = .true.
             nconv = iparam(5)
@@ -399,11 +399,11 @@ c
             print *, ' Maximum number of iterations reached.'
             print *, ' '
          else if ( info .eq. 3) then
-            print *, ' ' 
+            print *, ' '
             print *, ' No shifts could be applied during implicit',
      &               ' Arnoldi update, try increasing NCV.'
             print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _NDRV3 '
@@ -414,8 +414,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -431,16 +431,16 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector multiplication subroutine
 c
       subroutine av (n, v, w)
       integer           n, j
-      Double precision            
-     &                  v(n), w(n), one, two, dd, dl, du, s, h, rho 
-      parameter         ( rho = 1.0D+1, one = 1.0D+0, 
+      Double precision
+     &                  v(n), w(n), one, two, dd, dl, du, s, h, rho
+      parameter         ( rho = 1.0D+1, one = 1.0D+0,
      &                    two = 2.0D+0)
 c
 c     Compute the matrix vector multiplication y<---A*x
@@ -458,27 +458,27 @@ c
 c
       w(1) =  dd*v(1) + du*v(2)
       do 10 j = 2,n-1
-         w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1) 
- 10   continue 
-      w(n) =  dl*v(n-1) + dd*v(n) 
+         w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1)
+ 10   continue
+      w(n) =  dl*v(n-1) + dd*v(n)
       return
       end
 c------------------------------------------------------------------------
       subroutine mv (n, v, w)
       integer           n, j
-      Double precision 
+      Double precision
      &                  v(n), w(n), one, four, h
       parameter         ( one = 1.0D+0, four = 4.0D+0)
 c
 c     Compute the matrix vector multiplication y<---M*x
-c     where M is the mass matrix formed by using piecewise linear 
+c     where M is the mass matrix formed by using piecewise linear
 c     elements on [0,1].
-c 
+c
       w(1) =  four*v(1) + one*v(2)
       do 10 j = 2,n-1
-         w(j) = one*v(j-1) + four*v(j) + one*v(j+1) 
- 10   continue 
-      w(n) =  one*v(n-1) + four*v(n) 
+         w(j) = one*v(j-1) + four*v(j) + one*v(j+1)
+ 10   continue
+      w(n) =  one*v(n-1) + four*v(n)
 c
       h = one / dble(n+1)
       call dscal(n, h, w, 1)

EXAMPLES/NONSYM/dndrv4.f

@@ -1,7 +1,7 @@
       program dndrv4
 c
 c     Simple program to illustrate the idea of reverse communication
-c     in shift-invert mode for a generalized nonsymmetric eigenvalue 
+c     in shift-invert mode for a generalized nonsymmetric eigenvalue
 c     problem.
 c
 c     We implement example four of ex-nonsym.doc in DOCUMENTS directory
@@ -25,7 +25,7 @@ c
 c\Routines called:
 c     dnaupd  ARPACK reverse communication interface routine.
 c     dneupd  ARPACK routine that returns Ritz values and (optionally)
-c             Ritz vectors. 
+c             Ritz vectors.
 c     dgttrf  LAPACK tridiagonal factorization routine.
 c     dgttrs  LAPACK tridiagonal linear system solve routine.
 c     dlapy2  LAPACK routine to compute sqrt(x**2+y**2) carefully.
@@ -37,15 +37,15 @@ c     av      Matrix vector multiplication routine that computes A*x.
 c     mv      Matrix vector multiplication routine that computes M*x.
 c
 c\Author
-c     Richard Lehoucq 
-c     Danny Sorensen               
-c     Chao Yang             
-c     Dept. of Computational &     
-c     Applied Mathematics          
-c     Rice University           
-c     Houston, Texas    
+c     Richard Lehoucq
+c     Danny Sorensen
+c     Chao Yang
+c     Dept. of Computational &
+c     Applied Mathematics
+c     Rice University
+c     Houston, Texas
 c
-c\SCCS Information: @(#) 
+c\SCCS Information: @(#)
 c FILE: ndrv4.F   SID: 2.5   DATE OF SID: 10/17/00   RELEASE: 2
 c
 c\Remarks
@@ -64,7 +64,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer           maxn, maxnev, maxncv, ldv
-      parameter         (maxn=256, maxnev=10, maxncv=25, 
+      parameter         (maxn=256, maxnev=10, maxncv=25,
      &                   ldv=maxn )
 c
 c     %--------------%
@@ -90,13 +90,13 @@ c
       Double precision
      &                  tol, h, s,
      &                  sigmar, sigmai, s1, s2, s3
-      logical           first, rvec 
-c 
+      logical           first, rvec
+c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision   
+      Double precision
      &                  ddot, dnrm2, dlapy2
       external          ddot, dnrm2, dlapy2, dgttrf, dgttrs
 c
@@ -113,7 +113,7 @@ c
       Double precision
      &                   one, zero, two, six, rho
       common            /convct/ rho
-      parameter         (one = 1.0D+0, zero = 0.0D+0, 
+      parameter         (one = 1.0D+0, zero = 0.0D+0,
      &                   two = 2.0D+0, six = 6.0D+0)
 c
 c     %-----------------------%
@@ -130,14 +130,14 @@ c     | The user can modify NEV, NCV, SIGMAR to solve      |
 c     | problems of different sizes, and to get different  |
 c     | parts of the spectrum.  However, The following     |
 c     | conditions must be satisfied:                      |
-c     |                     N <= MAXN,                     | 
+c     |                     N <= MAXN,                     |
 c     |                   NEV <= MAXNEV,                   |
-c     |               NEV + 2 <= NCV <= MAXNCV             | 
+c     |               NEV + 2 <= NCV <= MAXNCV             |
 c     %----------------------------------------------------%
 c
-      n     = 100 
-      nev   = 4 
-      ncv   = 10 
+      n     = 100
+      nev   = 4
+      ncv   = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NDRV4: N is greater than MAXN '
          go to 9000
@@ -150,7 +150,7 @@ c
       end if
       bmat  = 'G'
       which = 'LM'
-      sigmar = one 
+      sigmar = one
       sigmai = zero
 c
 c     %--------------------------------------------------%
@@ -175,12 +175,12 @@ c
       s3 = -one/h + s - sigmar*h/six
 c
       do 10 j = 1, n-1
-         dl(j) = s1 
+         dl(j) = s1
          dd(j) = s2
          du(j) = s3
-  10  continue 
-      dd(n) = s2 
-c 
+  10  continue
+      dd(n) = s2
+c
       call dgttrf(n, dl, dd, du, du2, ipiv, ierr)
       if ( ierr .ne. 0 ) then
          print*, ' '
@@ -200,7 +200,7 @@ c     | Setting INFO=0 indicates that a random vector is    |
 c     | generated in DNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl = 3*ncv**2+6*ncv 
+      lworkl = 3*ncv**2+6*ncv
       tol    = zero
       ido    = 0
       info   = 0
@@ -224,20 +224,20 @@ c
       iparam(7) = mode
 c
 c     %------------------------------------------%
-c     | M A I N   L O O P(Reverse communication) | 
+c     | M A I N   L O O P(Reverse communication) |
 c     %------------------------------------------%
 c
  20   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine DNAUPD and take | 
+c        | Repeatedly call the routine DNAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call dnaupd ( ido, bmat, n, which, nev, tol, resid, 
-     &                 ncv, v, ldv, iparam, ipntr, workd, 
+         call dnaupd ( ido, bmat, n, which, nev, tol, resid,
+     &                 ncv, v, ldv, iparam, ipntr, workd,
      &                 workl, lworkl, info )
 c
          if (ido .eq. -1) then
@@ -255,8 +255,8 @@ c           | workd(ipntr(2)).                          |
 c           %-------------------------------------------%
 c
             call mv (n, workd(ipntr(1)), workd(ipntr(2)))
-            call dgttrs('N', n, 1, dl, dd, du, du2, ipiv, 
-     &                  workd(ipntr(2)), n, ierr) 
+            call dgttrs('N', n, 1, dl, dd, du, du2, ipiv,
+     &                  workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
                print*, ' ERROR with _gttrs in _NDRV4.'
@@ -282,7 +282,7 @@ c           | workd(ipntr(2)).                        |
 c           %-----------------------------------------%
 c
             call dcopy( n, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-            call dgttrs ('N', n, 1, dl, dd, du, du2, ipiv, 
+            call dgttrs ('N', n, 1, dl, dd, du, du2, ipiv,
      &                  workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
@@ -314,8 +314,8 @@ c           %-----------------------------------------%
 c
             go to 20
 c
-         end if 
-c 
+         end if
+c
 c
 c     %-----------------------------------------%
 c     | Either we have convergence, or there is |
@@ -334,23 +334,23 @@ c
          print *, ' Check the documentation in _naupd.'
          print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using DNEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
 c
          rvec = .true.
-         call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv,  
-     &        sigmar, sigmai, workev, bmat, n, which, nev, tol, 
-     &        resid, ncv, v, ldv, iparam, ipntr, workd, 
-     &        workl, lworkl, ierr )            
+         call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv,
+     &        sigmar, sigmai, workev, bmat, n, which, nev, tol,
+     &        resid, ncv, v, ldv, iparam, ipntr, workd,
+     &        workl, lworkl, ierr )
 c
 c        %-----------------------------------------------%
 c        | The real part of the eigenvalue is returned   |
@@ -365,16 +365,16 @@ c        | the eigenvalues in D is returned in V.        |
 c        %-----------------------------------------------%
 c
          if ( ierr .ne. 0) then
-c 
+c
 c            %------------------------------------%
 c            | Error condition:                   |
 c            | Check the documentation of DNEUPD. |
 c            %------------------------------------%
 c
-             print *, ' ' 
+             print *, ' '
              print *, ' Error with _neupd, info = ', ierr
              print *, ' Check the documentation of _neupd. '
-             print *, ' ' 
+             print *, ' '
 c
          else
 c
@@ -413,9 +413,9 @@ c                    %------------------------%
 c                    | Ritz value is complex. |
 c                    | Residual of one Ritz   |
 c                    | value of the conjugate |
-c                    | pair is computed.      | 
+c                    | pair is computed.      |
 c                    %------------------------%
-c     
+c
                      call av(n, v(1,j), ax)
                      call mv(n, v(1,j), mx)
                      call daxpy(n, -d(j,1), mx, 1, ax, 1)
@@ -455,11 +455,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _NDRV4 '
@@ -470,8 +470,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -487,7 +487,7 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector multiplication subroutine
@@ -495,17 +495,17 @@ c
       subroutine mv (n, v, w)
       integer           n, j
       Double precision
-     &                  v(n), w(n), one, four, six, h 
+     &                  v(n), w(n), one, four, six, h
       parameter         (one = 1.0D+0, four = 4.0D+0, six = 6.0D+0)
 c
 c     Compute the matrix vector multiplication y<---M*x
-c     where M is mass matrix formed by using piecewise linear elements 
+c     where M is mass matrix formed by using piecewise linear elements
 c     on [0,1].
-c 
+c
       w(1) =  ( four*v(1) + one*v(2) ) / six
       do 10 j = 2,n-1
          w(j) = ( one*v(j-1) + four*v(j) + one*v(j+1) ) / six
- 10   continue 
+ 10   continue
       w(n) =  ( one*v(n-1) + four*v(n) ) / six
 c
       h = one / dble(n+1)
@@ -516,7 +516,7 @@ c------------------------------------------------------------------
       subroutine av (n, v, w)
       integer           n, j
       Double precision
-     &                  v(n), w(n), one, two, dd, dl, du, s, h, rho 
+     &                  v(n), w(n), one, two, dd, dl, du, s, h, rho
       common            /convct/ rho
       parameter         (one = 1.0D+0, two = 2.0D+0)
 c
@@ -530,7 +530,7 @@ c     This routine is only used in residual calculation.
 c
       h = one / dble(n+1)
       s = rho / two
-      dd = two / h 
+      dd = two / h
       dl = -one/h - s
       du = -one/h + s
 c

EXAMPLES/NONSYM/dndrv5.f

@@ -8,9 +8,9 @@ c
 c\Example-5
 c
 c     ... Suppose we want to solve A*x = lambda*B*x in shift-invert mode
-c         The matrix A is the tridiagonal matrix with 2 on the diagonal, 
-c         -2 on the subdiagonal and 3 on the superdiagonal.  The matrix M 
-c         is the tridiagonal matrix with 4 on the diagonal and 1 on the 
+c         The matrix A is the tridiagonal matrix with 2 on the diagonal,
+c         -2 on the subdiagonal and 3 on the superdiagonal.  The matrix M
+c         is the tridiagonal matrix with 4 on the diagonal and 1 on the
 c         off-diagonals.
 c     ... The shift sigma is a complex number (sigmar, sigmai).
 c     ... OP = Real_Part{inv[A-(SIGMAR,SIGMAI)*M]*M and  B = M.
@@ -32,15 +32,15 @@ c     av      Matrix vector subroutine that computes A*x.
 c     mv      Matrix vector subroutine that computes M*x.
 c
 c\Author
-c     Richard Lehoucq 
-c     Danny Sorensen               
-c     Chao Yang             
-c     Dept. of Computational &     
-c     Applied Mathematics          
-c     Rice University           
-c     Houston, Texas    
+c     Richard Lehoucq
+c     Danny Sorensen
+c     Chao Yang
+c     Dept. of Computational &
+c     Applied Mathematics
+c     Rice University
+c     Houston, Texas
 c
-c\SCCS Information: @(#) 
+c\SCCS Information: @(#)
 c FILE: ndrv5.F   SID: 2.5   DATE OF SID: 10/17/00   RELEASE: 2
 c
 c\Remarks
@@ -59,7 +59,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer           maxn, maxnev, maxncv, ldv
-      parameter         (maxn=256, maxnev=10, maxncv=25, 
+      parameter         (maxn=256, maxnev=10, maxncv=25,
      &                   ldv=maxn )
 c
 c     %--------------%
@@ -73,7 +73,7 @@ c
      &                  v(ldv,maxncv), workd(3*maxn),
      &                  workev(3*maxncv),
      &                  workl(3*maxncv*maxncv+6*maxncv)
-      Complex*16         
+      Complex*16
      &                  cdd(maxn), cdl(maxn), cdu(maxn),
      &                  cdu2(maxn), ctemp(maxn)
 c
@@ -86,16 +86,16 @@ c
      &                  nconv, maxitr, ishfts, mode
       Double precision
      &                  tol, numr, numi, denr, deni, sigmar, sigmai
-      Complex*16         
+      Complex*16
      &                  c1, c2, c3
-      logical           first, rvec 
-c 
+      logical           first, rvec
+c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
       external          zgttrf, zgttrs
-      Double precision   
+      Double precision
      &                  ddot, dnrm2, dlapy2
       external          ddot, dnrm2, dlapy2
 c
@@ -128,14 +128,14 @@ c     | to 'LM'.  The user can modify NEV, NCV, SIGMAR,    |
 c     | SIGMAI to solve problems of different sizes, and   |
 c     | to get different parts of the spectrum. However,   |
 c     | The following conditions must be satisfied:        |
-c     |                     N <= MAXN,                     | 
+c     |                     N <= MAXN,                     |
 c     |                   NEV <= MAXNEV,                   |
-c     |               NEV + 2 <= NCV <= MAXNCV             | 
+c     |               NEV + 2 <= NCV <= MAXNCV             |
 c     %----------------------------------------------------%
 c
-      n     = 100 
-      nev   = 4 
-      ncv   = 20 
+      n     = 100
+      nev   = 4
+      ncv   = 20
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NDRV5: N is greater than MAXN '
          go to 9000
@@ -167,12 +167,12 @@ c
       c3 = dcmplx( 3.0D+0-sigmar, -sigmai)
 c
       do 10 j = 1, n-1
-         cdl(j) = c1 
+         cdl(j) = c1
          cdd(j) = c2
          cdu(j) = c3
-  10  continue 
-      cdd(n) = c2 
-c 
+  10  continue
+      cdd(n) = c2
+c
       call zgttrf(n, cdl, cdd, cdu, cdu2, ipiv, ierr)
       if ( ierr .ne. 0 ) then
          print*, ' '
@@ -192,8 +192,8 @@ c     | Setting INFO=0 indicates that a random vector is    |
 c     | generated in DNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl = 3*ncv**2+6*ncv 
-      tol    = zero 
+      lworkl = 3*ncv**2+6*ncv
+      tol    = zero
       ido    = 0
       info   = 0
 c
@@ -212,30 +212,30 @@ c
       mode   = 3
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr  
-      iparam(7) = mode 
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %------------------------------------------%
-c     | M A I N   L O O P(Reverse communication) | 
+c     | M A I N   L O O P(Reverse communication) |
 c     %------------------------------------------%
 c
  20   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine DNAUPD and take | 
+c        | Repeatedly call the routine DNAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call dnaupd ( ido, bmat, n, which, nev, tol, resid, 
-     &                 ncv, v, ldv, iparam, ipntr, workd, 
+         call dnaupd ( ido, bmat, n, which, nev, tol, resid,
+     &                 ncv, v, ldv, iparam, ipntr, workd,
      &                 workl, lworkl, info )
 c
          if (ido .eq. -1) then
 c
 c           %-------------------------------------------------------%
-c           |                       Perform                         | 
+c           |                       Perform                         |
 c           | y <--- OP*x = Real_Part{inv[A-(SIGMAR,SIGMAI)*M]*M*x} |
 c           | to force starting vector into the range of OP. The    |
 c           | user should supply his/her own matrix vector          |
@@ -251,14 +251,14 @@ c
                ctemp(j) = dcmplx(workd(ipntr(2)+j-1))
   30        continue
 c
-            call zgttrs('N', n, 1, cdl, cdd, cdu, cdu2, ipiv, 
+            call zgttrs('N', n, 1, cdl, cdd, cdu, cdu2, ipiv,
      &                  ctemp, n, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
                print*, ' ERROR with _gttrs in _NDRV5.'
                print*, ' '
                go to 9000
-            end if 
+            end if
             do  40 j = 1, n
                workd(ipntr(2)+j-1) = dble(ctemp(j))
   40        continue
@@ -283,14 +283,14 @@ c
             do 50 j = 1,n
                ctemp(j) = dcmplx(workd(ipntr(3)+j-1))
   50        continue
-            call zgttrs ('N', n, 1, cdl, cdd, cdu, cdu2, ipiv, 
+            call zgttrs ('N', n, 1, cdl, cdd, cdu, cdu2, ipiv,
      &                   ctemp, n, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
                print*, ' ERROR with _gttrs in _NDRV5.'
                print*, ' '
                go to 9000
-            end if 
+            end if
             do  60 j = 1, n
                workd(ipntr(2)+j-1) = dble(ctemp(j))
   60        continue
@@ -320,7 +320,7 @@ c
 c
          end if
 c
-c 
+c
 c     %------------------------------------------%
 c     | Either we have convergence, or there is  |
 c     | an error.                                |
@@ -336,25 +336,25 @@ c
          print *, ' '
          print *, ' Error with _naupd info = ',info
          print *, ' Check the documentation of _naupd.'
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using DNEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
 c
          rvec = .true.
-         call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv, 
-     &        sigmar, sigmai, workev, bmat, n, which, nev, tol, 
-     &        resid, ncv, v, ldv, iparam, ipntr, workd, 
-     &        workl, lworkl, ierr ) 
+         call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv,
+     &        sigmar, sigmai, workev, bmat, n, which, nev, tol,
+     &        resid, ncv, v, ldv, iparam, ipntr, workd,
+     &        workl, lworkl, ierr )
 c
 c        %-----------------------------------------------%
 c        | The real part of the eigenvalue is returned   |
@@ -375,14 +375,14 @@ c           | Error condition:                   |
 c           | Check the documentation of DNEUPD. |
 c           %------------------------------------%
 c
-            print *, ' ' 
+            print *, ' '
             print *, ' Error with _neupd = ', ierr
             print *, ' Check the documentation of _neupd. '
-            print *, ' ' 
+            print *, ' '
 c
-         else 
+         else
 c
-            first = .true. 
+            first = .true.
             nconv =  iparam(5)
             do 70 j=1,nconv
 c
@@ -394,7 +394,7 @@ c
                if ( d(j,2) .eq. zero ) then
 c
 c                 %---------------------------%
-c                 |    Eigenvalue is real.    | 
+c                 |    Eigenvalue is real.    |
 c                 | Compute d = x'(Ax)/x'(Mx).|
 c                 %---------------------------%
 c
@@ -402,7 +402,7 @@ c
                   numr = ddot(n, v(1,j), 1, ax, 1)
                   call mv(n, v(1,j), ax )
                   denr = ddot(n, v(1,j), 1, ax, 1)
-                  d(j,1) =  numr / denr 
+                  d(j,1) =  numr / denr
 c
                else if (first) then
 c
@@ -420,7 +420,7 @@ c                 %----------------%
                   numr = ddot(n, v(1,j), 1, ax, 1)
                   numi = ddot(n, v(1,j+1), 1, ax, 1)
                   call av(n, v(1,j+1), ax)
-                  numr = numr + ddot(n,v(1,j+1),1,ax,1) 
+                  numr = numr + ddot(n,v(1,j+1),1,ax,1)
                   numi = -numi + ddot(n,v(1,j),1,ax,1)
 c
 c                 %----------------%
@@ -431,7 +431,7 @@ c
                   denr = ddot(n, v(1,j), 1, ax, 1)
                   deni = ddot(n, v(1,j+1), 1, ax, 1)
                   call mv(n, v(1,j+1), ax)
-                  denr = denr + ddot(n,v(1,j+1),1,ax,1) 
+                  denr = denr + ddot(n,v(1,j+1),1,ax,1)
                   deni = -deni + ddot(n,v(1,j),1, ax,1)
 c
 c                 %----------------%
@@ -452,7 +452,7 @@ c                 | the conjugate pair by taking |
 c                 | the conjugate of the last    |
 c                 | eigenvalue computed.         |
 c                 %------------------------------%
-c 
+c
                   d(j,1) = d(j-1,1)
                   d(j,2) = -d(j-1,2)
                   first = .true.
@@ -475,7 +475,7 @@ c           | tolerance)                |
 c           %---------------------------%
 c
             first  = .true.
-            do 80 j=1, nconv 
+            do 80 j=1, nconv
 c
                if (d(j,2) .eq. zero)  then
 c
@@ -495,9 +495,9 @@ c                 %------------------------%
 c                 | Ritz value is complex  |
 c                 | Residual of one Ritz   |
 c                 | value of the conjugate |
-c                 | pair is computed.      | 
+c                 | pair is computed.      |
 c                 %------------------------%
-c        
+c
                   call av(n, v(1,j), ax)
                   call mv(n, v(1,j), mx)
                   call daxpy(n, -d(j,1), mx, 1, ax, 1)
@@ -527,7 +527,7 @@ c
              call dmout(6, nconv, 3, d, maxncv, -6,
      &            'Ritz values (Real,Imag) and relative residuals')
 c
-         end if 
+         end if
 c
 c        %-------------------------------------------%
 c        | Print additional convergence information. |
@@ -538,11 +538,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _NDRV5 '
@@ -553,8 +553,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -570,7 +570,7 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector multiplication subroutine
@@ -578,25 +578,25 @@ c
       subroutine mv (n, v, w)
       integer           n, j
       Double precision
-     &                  v(n), w(n), one, four 
+     &                  v(n), w(n), one, four
       parameter         (one = 1.0D+0, four = 4.0D+0)
 c
 c     Compute the matrix vector multiplication y<---M*x
-c     where M is a n by n symmetric tridiagonal matrix with 4 on the 
+c     where M is a n by n symmetric tridiagonal matrix with 4 on the
 c     diagonal, 1 on the subdiagonal and superdiagonal.
-c 
+c
       w(1) =  four*v(1) + one*v(2)
       do 10 j = 2,n-1
-         w(j) = one*v(j-1) + four*v(j) + one*v(j+1) 
- 10   continue 
-      w(n) =  one*v(n-1) + four*v(n) 
+         w(j) = one*v(j-1) + four*v(j) + one*v(j+1)
+ 10   continue
+      w(n) =  one*v(n-1) + four*v(n)
       return
       end
 c------------------------------------------------------------------
       subroutine av (n, v, w)
       integer           n, j
-      Double precision            
-     &                  v(n), w(n), three, two 
+      Double precision
+     &                  v(n), w(n), three, two
       parameter         (three = 3.0D+0, two = 2.0D+0)
 c
 c     Compute the matrix vector multiplication y<---A*x

EXAMPLES/NONSYM/dndrv6.f

@@ -8,9 +8,9 @@ c
 c\Example-6
 c
 c     ... Suppose we want to solve A*x = lambda*B*x in shift-invert mode
-c         The matrix A is the tridiagonal matrix with 2 on the diagonal, 
-c         -2 on the subdiagonal and 3 on the superdiagonal.  The matrix M 
-c         is the tridiagonal matrix with 4 on the diagonal and 1 on the 
+c         The matrix A is the tridiagonal matrix with 2 on the diagonal,
+c         -2 on the subdiagonal and 3 on the superdiagonal.  The matrix M
+c         is the tridiagonal matrix with 4 on the diagonal and 1 on the
 c         off-diagonals.
 c     ... The shift sigma is a complex number (sigmar, sigmai).
 c     ... OP = Imaginary_Part{inv[A-(SIGMAR,SIGMAI)*M]*M  and  B = M.
@@ -32,15 +32,15 @@ c     av      Matrix vector subroutine that computes A*x.
 c     mv      Matrix vector subroutine that computes M*x.
 c
 c\Author
-c     Richard Lehoucq 
-c     Danny Sorensen               
-c     Chao Yang             
-c     Dept. of Computational &     
-c     Applied Mathematics          
-c     Rice University           
-c     Houston, Texas    
+c     Richard Lehoucq
+c     Danny Sorensen
+c     Chao Yang
+c     Dept. of Computational &
+c     Applied Mathematics
+c     Rice University
+c     Houston, Texas
 c
-c\SCCS Information: @(#) 
+c\SCCS Information: @(#)
 c FILE: ndrv6.F   SID: 2.5   DATE OF SID: 10/17/00   RELEASE: 2
 c
 c\Remarks
@@ -59,7 +59,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer           maxn, maxnev, maxncv, ldv
-      parameter         (maxn=256, maxnev=10, maxncv=25, 
+      parameter         (maxn=256, maxnev=10, maxncv=25,
      &                   ldv=maxn )
 c
 c     %--------------%
@@ -73,7 +73,7 @@ c
      &                  v(ldv,maxncv), workd(3*maxn),
      &                  workev(3*maxncv),
      &                  workl(3*maxncv*maxncv+6*maxncv)
-      Complex*16         
+      Complex*16
      &                  cdd(maxn), cdl(maxn), cdu(maxn),
      &                  cdu2(maxn), ctemp(maxn)
 c
@@ -86,16 +86,16 @@ c
      &                  nconv, maxitr, ishfts, mode
       Double precision
      &                  tol, numr, numi, denr, deni, sigmar, sigmai
-      Complex*16         
+      Complex*16
      &                  c1, c2, c3
-      logical           first, rvec 
-c 
+      logical           first, rvec
+c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
       external          zgttrf, zgttrs
-      Double precision   
+      Double precision
      &                  ddot, dnrm2, dlapy2
       external          ddot, dnrm2, dlapy2
 c
@@ -127,14 +127,14 @@ c     | to 'LM'.  The user can modify NEV, NCV, SIGMA to   |
 c     | solve problems of different sizes, and to get      |
 c     | different parts of the spectrum. However, The      |
 c     | following conditions must be satisfied:            |
-c     |                     N <= MAXN,                     | 
+c     |                     N <= MAXN,                     |
 c     |                   NEV <= MAXNEV,                   |
-c     |               NEV + 2 <= NCV <= MAXNCV             | 
+c     |               NEV + 2 <= NCV <= MAXNCV             |
 c     %----------------------------------------------------%
 c
-      n     = 100 
-      nev   = 4 
-      ncv   = 20 
+      n     = 100
+      nev   = 4
+      ncv   = 20
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NDRV6: N is greater than MAXN '
          go to 9000
@@ -148,7 +148,7 @@ c
       bmat  = 'G'
       which = 'LM'
       sigmar = 4.0D-1
-      sigmai = 6.0D-1 
+      sigmai = 6.0D-1
 c
 c     %----------------------------------------------------%
 c     | Construct C = A - (SIGMAR,SIGMAI)*M in complex     |
@@ -166,12 +166,12 @@ c
       c3 = dcmplx( 3.0D+0-sigmar, -sigmai)
 c
       do 10 j = 1, n-1
-         cdl(j) = c1 
+         cdl(j) = c1
          cdd(j) = c2
          cdu(j) = c3
-  10  continue 
-      cdd(n) = c2 
-c 
+  10  continue
+      cdd(n) = c2
+c
       call zgttrf(n, cdl, cdd, cdu, cdu2, ipiv, ierr)
       if ( ierr .ne. 0 ) then
          print*, ' '
@@ -191,8 +191,8 @@ c     | Setting INFO=0 indicates that a random vector is    |
 c     | generated in DNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl = 3*ncv**2+6*ncv 
-      tol    = zero 
+      lworkl = 3*ncv**2+6*ncv
+      tol    = zero
       ido    = 0
       info   = 0
 c
@@ -211,31 +211,31 @@ c
       mode   = 3
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr  
+      iparam(3) = maxitr
       iparam(7) = mode
 c
 c     %------------------------------------------%
-c     | M A I N   L O O P(Reverse communication) | 
+c     | M A I N   L O O P(Reverse communication) |
 c     %------------------------------------------%
 c
  20   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine DNAUPD and take | 
+c        | Repeatedly call the routine DNAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call dnaupd ( ido, bmat, n, which, nev, tol, resid, 
-     &                 ncv, v, ldv, iparam, ipntr, workd, 
+         call dnaupd ( ido, bmat, n, which, nev, tol, resid,
+     &                 ncv, v, ldv, iparam, ipntr, workd,
      &                 workl, lworkl, info )
 c
 
          if (ido .eq. -1) then
 c
 c           %------------------------------------------------------------%
-c           |                           Perform                          | 
+c           |                           Perform                          |
 c           | y <--- OP*x = Imaginary_Part{inv[A-(SIGMAR,SIGMAI)*M]*M*x} |
 c           | to force starting vector into the range of OP. The user    |
 c           | should supply his/her own matrix vector multiplication     |
@@ -250,14 +250,14 @@ c
                ctemp(j) = dcmplx(workd(ipntr(2)+j-1))
   30        continue
 c
-            call zgttrs('N', n, 1, cdl, cdd, cdu, cdu2, ipiv, 
+            call zgttrs('N', n, 1, cdl, cdd, cdu, cdu2, ipiv,
      &                  ctemp, maxn, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
                print*, ' ERROR with _gttrs in _NDRV6.'
                print*, ' '
                go to 9000
-            end if 
+            end if
             do  40 j = 1, n
                workd(ipntr(2)+j-1) = dimag(ctemp(j))
   40        continue
@@ -282,14 +282,14 @@ c
             do 50 j = 1,n
                ctemp(j) = dcmplx(workd(ipntr(3)+j-1))
   50        continue
-            call zgttrs ('N', n, 1, cdl, cdd, cdu, cdu2, ipiv, 
+            call zgttrs ('N', n, 1, cdl, cdd, cdu, cdu2, ipiv,
      &                   ctemp, maxn, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
                print*, ' ERROR with _gttrs in _NDRV6.'
                print*, ' '
                go to 9000
-            end if 
+            end if
             do  60 j = 1, n
                workd(ipntr(2)+j-1) = dimag(ctemp(j))
   60        continue
@@ -335,24 +335,24 @@ c
          print *, ' '
          print *, ' Error with _naupd, info = ',info
          print *, ' Check the documentation of _naupd.'
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using DNEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
 c
          rvec = .true.
-         call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv,  
-     &        sigmar, sigmai, workev, bmat, n, which, nev, tol, 
-     &        resid, ncv, v, ldv, iparam, ipntr, workd, 
+         call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv,
+     &        sigmar, sigmai, workev, bmat, n, which, nev, tol,
+     &        resid, ncv, v, ldv, iparam, ipntr, workd,
      &        workl, lworkl, ierr )
 c
 c        %-----------------------------------------------%
@@ -368,16 +368,16 @@ c        | the eigenvalues in D is returned in V.        |
 c        %-----------------------------------------------%
 c
          if ( ierr .ne. 0) then
-c 
+c
 c           %------------------------------------%
 c           | Error condition:                   |
 c           | Check the documentation of DNEUPD. |
 c           %------------------------------------%
 c
-            print *, ' ' 
+            print *, ' '
             print *, ' Error with _neupd, info = ', ierr
             print *, ' Check the documentation of _neupd. '
-            print *, ' ' 
+            print *, ' '
 c
          else
 c
@@ -393,7 +393,7 @@ c
                 if ( d(j,2) .eq. zero) then
 c
 c                  %----------------------------%
-c                  | Eigenvalue is real.        | 
+c                  | Eigenvalue is real.        |
 c                  | Compute d = x'(Ax)/x'(Mx). |
 c                  %----------------------------%
 c
@@ -401,7 +401,7 @@ c
                    numr = ddot(n, v(1,j), 1, ax, 1)
                    call mv(n, v(1,j), ax )
                    denr = ddot(n, v(1,j), 1, ax, 1)
-                   d(j,1) =  numr / denr 
+                   d(j,1) =  numr / denr
 c
                 else if (first) then
 c
@@ -419,7 +419,7 @@ c
                    numr = ddot(n, v(1,j), 1, ax, 1)
                    numi = ddot(n, v(1,j+1), 1, ax, 1)
                    call av(n, v(1,j+1), ax)
-                   numr = numr + ddot(n,v(1,j+1),1,ax,1) 
+                   numr = numr + ddot(n,v(1,j+1),1,ax,1)
                    numi = -numi + ddot(n,v(1,j),1,ax,1)
 c
 c                  %----------------%
@@ -430,7 +430,7 @@ c
                    denr = ddot(n, v(1,j), 1, ax, 1)
                    deni = ddot(n, v(1,j+1), 1, ax, 1)
                    call mv(n, v(1,j+1), ax)
-                   denr = denr + ddot(n,v(1,j+1),1,ax,1) 
+                   denr = denr + ddot(n,v(1,j+1),1,ax,1)
                    deni = -deni + ddot(n,v(1,j),1, ax,1)
 c
 c                  %----------------%
@@ -451,7 +451,7 @@ c                  | the conjugate pair by taking |
 c                  | the conjugate of the last    |
 c                  | eigenvalue computed.         |
 c                  %------------------------------%
-c 
+c
                    d(j,1) = d(j-1,1)
                    d(j,2) = -d(j-1,2)
                    first = .true.
@@ -475,7 +475,7 @@ c           %---------------------------%
 c
             first = .true.
             nconv = iparam(5)
-            do 80 j=1, nconv 
+            do 80 j=1, nconv
 c
                if (d(j,2) .eq. zero)  then
 c
@@ -495,9 +495,9 @@ c                 %------------------------%
 c                 | Ritz value is complex  |
 c                 | Residual of one Ritz   |
 c                 | value of the conjugate |
-c                 | pair is computed.      | 
+c                 | pair is computed.      |
 c                 %------------------------%
-c        
+c
                   call av(n, v(1,j), ax)
                   call mv(n, v(1,j), mx)
                   call daxpy(n, -d(j,1), mx, 1, ax, 1)
@@ -510,7 +510,7 @@ c
                   call mv(n, v(1,j), mx)
                   call daxpy(n, -d(j,2), mx, 1, ax, 1)
                   d(j,3) = dlapy2( d(j,3), dnrm2(n, ax, 1) )
-                  d(j,3) = d(j,3) / dlapy2(d(j,1),d(j,2)) 
+                  d(j,3) = d(j,3) / dlapy2(d(j,1),d(j,2))
                   d(j+1,3) = d(j,3)
                   first = .false.
                else
@@ -537,11 +537,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _NDRV6 '
@@ -552,8 +552,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -569,7 +569,7 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector multiplication subroutine
@@ -577,25 +577,25 @@ c
       subroutine mv (n, v, w)
       integer           n, j
       Double precision
-     &                  v(n), w(n), one, four 
+     &                  v(n), w(n), one, four
       parameter         (one = 1.0D+0, four = 4.0D+0)
 c
 c     Compute the matrix vector multiplication y<---M*x
-c     where M is a n by n symmetric tridiagonal matrix with 4 on the 
+c     where M is a n by n symmetric tridiagonal matrix with 4 on the
 c     diagonal, 1 on the subdiagonal and superdiagonal.
-c 
+c
       w(1) =  four*v(1) + one*v(2)
       do 10 j = 2,n-1
-         w(j) = one*v(j-1) + four*v(j) + one*v(j+1) 
- 10   continue 
-      w(n) =  one*v(n-1) + four*v(n) 
+         w(j) = one*v(j-1) + four*v(j) + one*v(j+1)
+ 10   continue
+      w(n) =  one*v(n-1) + four*v(n)
       return
       end
 c------------------------------------------------------------------
       subroutine av (n, v, w)
       integer           n, j
-      Double precision            
-     &                  v(n), w(n), three, two 
+      Double precision
+     &                  v(n), w(n), three, two
       parameter         (three = 3.0D+0, two = 2.0D+0)
 c
 c     Compute the matrix vector multiplication y<---A*x

EXAMPLES/NONSYM/makefile

@@ -1,71 +0,0 @@
-#
-# makefile to run simple examples of the reverse communication
-# protocol.
-#
-# Modify if ARPACK library was built somewhere else.
-#
-# If ALIBS (defined in ../../ARmake.inc) contains the BLAS and LAPACK
-# libraries installed on your system, you DO NOT need to change this
-# makefile. OTHERWISE, you may need to modify the Makefile in the top level
-# ARPACK directory tree to include sdrv and/or ddrv in the
-# definition of the PRECISION variable, and issue 'make lib' from there.
-# For example:
-#
-#         PRECISION = single double sdrv ddrv
-#
-#\SCCS Information: @(#) 
-# FILE: makefile   SID: 2.2   DATE OF SID: 9/24/96   RELEASE: 2
-#
-include ../../ARmake.inc
-#
-# Issue "make nonsym" to make all 12 nonsymmetric drivers.
-# Issue "make sndrv" to make 6 single precision nonsymmetric drivers.
-# Issue "make dndrv" to make 6 double precision nonsymmetric drivers.
-#
-nonsym: sndrv dndrv 
-#
-#-----------------------------------------------------------------------
-# Simple nonsymmetric problem using single precision
-#
-sndrv: sndrv1 sndrv2 sndrv3 sndrv4 sndrv5 sndrv6
-
-sndrv1: sndrv1.o  
-	$(FC) $(FFLAGS) sndrv1.o $(ALIBS)  -o sndrv1
-#
-sndrv2: sndrv2.o 
-	$(FC) $(FFLAGS) sndrv2.o $(ALIBS) -o sndrv2
-#
-sndrv3: sndrv3.o 
-	$(FC) $(FFLAGS) sndrv3.o $(ALIBS) -o sndrv3
-#
-sndrv4: sndrv4.o 
-	$(FC) $(FFLAGS) sndrv4.o $(ALIBS) -o sndrv4
-#
-sndrv5: sndrv5.o 
-	$(FC) $(FFLAGS) sndrv5.o $(ALIBS) -o sndrv5
-#
-sndrv6: sndrv6.o 
-	$(FC) $(FFLAGS) sndrv6.o $(ALIBS) -o sndrv6
-#
-#------------------------------------------------------
-# Simple nonsymmetric problem using double precision
-#
-dndrv: dndrv1 dndrv2 dndrv3 dndrv4 dndrv5 dndrv6
-
-dndrv1: dndrv1.o 
-	$(FC) $(FFLAGS) dndrv1.o $(ALIBS) -o dndrv1 
-#
-dndrv2: dndrv2.o 
-	$(FC) $(FFLAGS) dndrv2.o $(ALIBS) -o dndrv2
-#
-dndrv3: dndrv3.o 
-	$(FC) $(FFLAGS) dndrv3.o $(ALIBS) -o dndrv3
-#
-dndrv4: dndrv4.o 
-	$(FC) $(FFLAGS) dndrv4.o $(ALIBS) -o dndrv4
-#
-dndrv5: dndrv5.o 
-	$(FC) $(FFLAGS) dndrv5.o $(ALIBS) -o dndrv5
-#
-dndrv6: dndrv6.o 
-	$(FC) $(FFLAGS) dndrv6.o $(ALIBS) -o dndrv6

EXAMPLES/NONSYM/sndrv1.f

@@ -1,4 +1,4 @@
-      program sndrv1 
+      program sndrv1
 c
 c
 c     Example program to illustrate the idea of reverse communication
@@ -9,9 +9,9 @@ c
 c\Example-1
 c     ... Suppose we want to solve A*x = lambda*x in regular mode,
 c         where A is obtained from the standard central difference
-c         discretization of the convection-diffusion operator 
+c         discretization of the convection-diffusion operator
 c                 (Laplacian u) + rho*(du / dx)
-c         on the unit square [0,1]x[0,1] with zero Dirichlet boundary 
+c         on the unit square [0,1]x[0,1] with zero Dirichlet boundary
 c         condition.
 c
 c     ... OP = A  and  B = I.
@@ -30,7 +30,7 @@ c     slapy2  LAPACK routine to compute sqrt(x**2+y**2) carefully.
 c     saxpy   Level 1 BLAS that computes y <- alpha*x+y.
 c     snrm2   Level 1 BLAS that computes the norm of a vector.
 c     av      Matrix vector multiplication routine that computes A*x.
-c     tv      Matrix vector multiplication routine that computes T*x, 
+c     tv      Matrix vector multiplication routine that computes T*x,
 c             where T is a tridiagonal matrix.  It is used in routine
 c             av.
 c
@@ -71,9 +71,9 @@ c
       integer           iparam(11), ipntr(14)
       logical           select(maxncv)
       Real
-     &                  ax(maxn), d(maxncv,3), resid(maxn), 
-     &                  v(ldv,maxncv), workd(3*maxn), 
-     &                  workev(3*maxncv), 
+     &                  ax(maxn), d(maxncv,3), resid(maxn),
+     &                  v(ldv,maxncv), workd(3*maxn),
+     &                  workev(3*maxncv),
      &                  workl(3*maxncv*maxncv+6*maxncv)
 c
 c     %---------------%
@@ -112,12 +112,12 @@ c
 c     %-----------------------%
 c     | Executable Statements |
 c     %-----------------------%
-c 
+c
 c     %--------------------------------------------------%
 c     | The number NX is the number of interior points   |
 c     | in the discretization of the 2-dimensional       |
 c     | convection-diffusion operator on the unit        |
-c     | square with zero Dirichlet boundary condition.   | 
+c     | square with zero Dirichlet boundary condition.   |
 c     | The number N(=NX*NX) is the dimension of the     |
 c     | matrix.  A standard eigenvalue problem is        |
 c     | solved (BMAT = 'I').  NEV is the number of       |
@@ -128,13 +128,13 @@ c     | the spectrum.  However, The following            |
 c     | conditions must be satisfied:                    |
 c     |                   N <= MAXN                      |
 c     |                 NEV <= MAXNEV                    |
-c     |           NEV + 2 <= NCV <= MAXNCV               | 
-c     %--------------------------------------------------% 
+c     |           NEV + 2 <= NCV <= MAXNCV               |
+c     %--------------------------------------------------%
 c
-      nx    = 10 
-      n     = nx*nx 
+      nx    = 10
+      n     = nx*nx
       nev   = 4
-      ncv   = 20 
+      ncv   = 20
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NDRV1: N is greater than MAXN '
          go to 9000
@@ -149,18 +149,18 @@ c
       which = 'SM'
 c
 c     %-----------------------------------------------------%
-c     | The work array WORKL is used in SNAUPD as           |  
+c     | The work array WORKL is used in SNAUPD as           |
 c     | workspace.  Its dimension LWORKL is set as          |
 c     | illustrated below.  The parameter TOL determines    |
 c     | the stopping criterion. If TOL<=0, machine          |
 c     | precision is used.  The variable IDO is used for    |
 c     | reverse communication, and is initially set to 0.   |
 c     | Setting INFO=0 indicates that a random vector is    |
-c     | generated in SNAUPD to start the Arnoldi iteration. | 
+c     | generated in SNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl  = 3*ncv**2+6*ncv 
-      tol    = zero 
+      lworkl  = 3*ncv**2+6*ncv
+      tol    = zero
       ido    = 0
       info   = 0
 c
@@ -179,11 +179,11 @@ c
       mode   = 1
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr 
+      iparam(3) = maxitr
       iparam(7) = mode
 c
 c     %-------------------------------------------%
-c     | M A I N   L O O P (Reverse communication) | 
+c     | M A I N   L O O P (Reverse communication) |
 c     %-------------------------------------------%
 c
  10   continue
@@ -195,8 +195,8 @@ c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call snaupd ( ido, bmat, n, which, nev, tol, resid, 
-     &        ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, 
+         call snaupd ( ido, bmat, n, which, nev, tol, resid,
+     &        ncv, v, ldv, iparam, ipntr, workd, workl, lworkl,
      &        info )
 c
          if (ido .eq. -1 .or. ido .eq. 1) then
@@ -208,7 +208,7 @@ c           | The user should supply his/her own        |
 c           | matrix vector multiplication routine here |
 c           | that takes workd(ipntr(1)) as the input   |
 c           | vector, and return the matrix vector      |
-c           | product to workd(ipntr(2)).               | 
+c           | product to workd(ipntr(2)).               |
 c           %-------------------------------------------%
 c
             call av (nx, workd(ipntr(1)), workd(ipntr(2)))
@@ -219,8 +219,8 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-      end if 
-c 
+      end if
+c
 c     %----------------------------------------%
 c     | Either we have convergence or there is |
 c     | an error.                              |
@@ -238,7 +238,7 @@ c
          print *, ' Check the documentation of _naupd'
          print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
@@ -252,8 +252,8 @@ c        %-------------------------------------------%
 c
          rvec = .true.
 c
-         call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv, 
-     &        sigmar, sigmai, workev, bmat, n, which, nev, tol, 
+         call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv,
+     &        sigmar, sigmai, workev, bmat, n, which, nev, tol,
      &        resid, ncv, v, ldv, iparam, ipntr, workd, workl,
      &        lworkl, ierr )
 c
@@ -281,7 +281,7 @@ c
              print *, ' Check the documentation of _neupd. '
              print *, ' '
 c
-         else 
+         else
 c
              first  = .true.
              nconv  = iparam(5)
@@ -317,9 +317,9 @@ c                  %------------------------%
 c                  | Ritz value is complex. |
 c                  | Residual of one Ritz   |
 c                  | value of the conjugate |
-c                  | pair is computed.      | 
+c                  | pair is computed.      |
 c                  %------------------------%
-c        
+c
                    call av(nx, v(1,j), ax)
                    call saxpy(n, -d(j,1), v(1,j), 1, ax, 1)
                    call saxpy(n, d(j,2), v(1,j+1), 1, ax, 1)
@@ -354,23 +354,23 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _NDRV1 '
          print *, ' ====== '
-         print *, ' ' 
+         print *, ' '
          print *, ' Size of the matrix is ', n
          print *, ' The number of Ritz values requested is ', nev
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -386,37 +386,37 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector subroutine
 c
-c     The matrix used is the 2 dimensional convection-diffusion 
+c     The matrix used is the 2 dimensional convection-diffusion
 c     operator discretized using central difference.
 c
       subroutine av (nx, v, w)
       integer           nx, j, lo
-      Real         
+      Real
      &                  v(nx*nx), w(nx*nx), one, h2
       parameter         (one = 1.0E+0)
       external          saxpy
 c
-c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block 
+c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block
 c     tridiagonal matrix
 c
-c                  | T -I          | 
+c                  | T -I          |
 c                  |-I  T -I       |
 c             OP = |   -I  T       |
 c                  |        ...  -I|
 c                  |           -I T|
 c
-c     derived from the standard central difference discretization 
-c     of the 2 dimensional convection-diffusion operator 
-c     (Laplacian u) + rho*(du/dx) on a unit square with zero boundary 
+c     derived from the standard central difference discretization
+c     of the 2 dimensional convection-diffusion operator
+c     (Laplacian u) + rho*(du/dx) on a unit square with zero boundary
 c     condition.
 c
-c     When rho*h/2 <= 1, the discrete convection-diffusion operator 
-c     has real eigenvalues.  When rho*h/2 > 1, it has COMPLEX 
+c     When rho*h/2 <= 1, the discrete convection-diffusion operator
+c     has real eigenvalues.  When rho*h/2 > 1, it has COMPLEX
 c     eigenvalues.
 c
 c     The subroutine TV is called to compute y<---T*x.
@@ -432,7 +432,7 @@ c
          call tv(nx, v(lo+1), w(lo+1))
          call saxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1)
          call saxpy(nx, -one/h2, v(lo+nx+1), 1, w(lo+1), 1)
-  10  continue 
+  10  continue
 c
       lo = (nx-1)*nx
       call tv(nx, v(lo+1), w(lo+1))
@@ -443,21 +443,21 @@ c
 c=========================================================================
       subroutine tv (nx, x, y)
 c
-      integer           nx, j 
+      integer           nx, j
       Real
      &                  x(nx), y(nx), h, h2, dd, dl, du
 c
       Real
      &                  one, zero, rho
-      parameter         (one = 1.0E+0, zero = 0.0E+0, 
+      parameter         (one = 1.0E+0, zero = 0.0E+0,
      &                   rho = 0.0E+0)
 c
 c     Compute the matrix vector multiplication y<---T*x
-c     where T is a nx by nx tridiagonal matrix with DD on the 
+c     where T is a nx by nx tridiagonal matrix with DD on the
 c     diagonal, DL on the subdiagonal, and DU on the superdiagonal.
 c
-c     When rho*h/2 <= 1, the discrete convection-diffusion operator 
-c     has real eigenvalues.  When rho*h/2 > 1, it has COMPLEX 
+c     When rho*h/2 <= 1, the discrete convection-diffusion operator
+c     has real eigenvalues.  When rho*h/2 > 1, it has COMPLEX
 c     eigenvalues.
 c
       h   = one / real(nx+1)
@@ -465,11 +465,11 @@ c
       dd  = 4.0E+0 / h2
       dl  = -one / h2 - 5.0E-1*rho / h
       du  = -one / h2 + 5.0E-1*rho / h
-c 
+c
       y(1) =  dd*x(1) + du*x(2)
       do 10 j = 2,nx-1
-         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 
- 10   continue 
-      y(nx) =  dl*x(nx-1) + dd*x(nx) 
+         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1)
+ 10   continue
+      y(nx) =  dl*x(nx-1) + dd*x(nx)
       return
       end

EXAMPLES/NONSYM/sndrv2.f

@@ -9,7 +9,7 @@ c\Example-2
 c     ... Suppose we want to solve A*x = lambda*x in shift-invert mode,
 c         where A is derived from the centered difference discretization
 c         of the 1-dimensional convection-diffusion operator
-c                          (d^2u / dx^2) + rho*(du/dx) 
+c                          (d^2u / dx^2) + rho*(du/dx)
 c         on the interval [0,1] with zero Dirichlet boundary condition.
 c
 c     ... The shift sigma is a real number.
@@ -61,7 +61,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer           maxn, maxnev, maxncv, ldv
-      parameter         (maxn=256, maxnev=10, maxncv=25, 
+      parameter         (maxn=256, maxnev=10, maxncv=25,
      &                   ldv=maxn )
 c
 c     %--------------%
@@ -97,7 +97,7 @@ c
       Real
      &                   one, zero, two, rho
       common            /convct/ rho
-      parameter         (one = 1.0E+0, zero = 0.0E+0, 
+      parameter         (one = 1.0E+0, zero = 0.0E+0,
      &                   two = 2.0E+0)
 c
 c     %-----------------------------%
@@ -128,14 +128,14 @@ c     | 'LM'.  The user can modify NEV, NCV, SIGMAR to   |
 c     | solve problems of different sizes, and to get    |
 c     | different parts of the spectrum.  However, The   |
 c     | following conditions must be satisfied:          |
-c     |                 N <= MAXN,                       | 
+c     |                 N <= MAXN,                       |
 c     |               NEV <= MAXNEV,                     |
-c     |           NEV + 2 <= NCV <= MAXNCV               | 
+c     |           NEV + 2 <= NCV <= MAXNCV               |
 c     %--------------------------------------------------%
 c
       n     = 100
-      nev   = 4 
-      ncv   = 20 
+      nev   = 4
+      ncv   = 20
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NDRV2: N is greater than MAXN '
          go to 9000
@@ -148,8 +148,8 @@ c
       end if
       bmat  = 'I'
       which = 'LM'
-      sigmar = 1.0E+0 
-      sigmai = 0.0E+0 
+      sigmar = 1.0E+0
+      sigmai = 0.0E+0
 c
 c     %----------------------------------------------------%
 c     | Construct C = A - SIGMA*I in real arithmetic, and  |
@@ -157,7 +157,7 @@ c     | factor C in real arithmetic using LAPACK           |
 c     | subroutine sgttrf. The matrix A is chosen to be    |
 c     | the tridiagonal matrix derived from standard       |
 c     | central difference of the 1-d convection diffusion |
-c     | operator u" + rho*u' on the interval [0, 1] with   | 
+c     | operator u" + rho*u' on the interval [0, 1] with   |
 c     | zero Dirichlet boundary condition.                 |
 c     %----------------------------------------------------%
 c
@@ -165,25 +165,25 @@ c
       h = one / real(n+1)
       s = rho*h / two
 c
-      s1 = -one-s 
+      s1 = -one-s
       s2 = two - sigmar
-      s3 = -one+s  
+      s3 = -one+s
 c
       do 10 j = 1, n-1
-         dl(j) = s1 
+         dl(j) = s1
          dd(j) = s2
          du(j) = s3
-  10  continue 
-      dd(n) = s2 
-c 
+  10  continue
+      dd(n) = s2
+c
       call sgttrf(n, dl, dd, du, du2, ipiv, ierr)
       if ( ierr .ne. 0 ) then
-         print*, ' ' 
+         print*, ' '
          print*, ' ERROR with _gttrf in _NDRV2.'
          print*, ' '
          go to 9000
       end if
-c        
+c
 c     %-----------------------------------------------------%
 c     | The work array WORKL is used in SNAUPD as           |
 c     | workspace.  Its dimension LWORKL is set as          |
@@ -195,8 +195,8 @@ c     | Setting INFO=0 indicates that a random vector is    |
 c     | generated in SNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl = 3*ncv**2+6*ncv 
-      tol    = zero 
+      lworkl = 3*ncv**2+6*ncv
+      tol    = zero
       ido    = 0
       info   = 0
 c
@@ -213,26 +213,26 @@ c
       ishfts = 1
       maxitr = 300
       mode   = 3
- 
-      iparam(1) = ishfts 
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+
+      iparam(1) = ishfts
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %-------------------------------------------%
-c     | M A I N   L O O P (Reverse communication) | 
+c     | M A I N   L O O P (Reverse communication) |
 c     %-------------------------------------------%
 c
  20   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine SNAUPD and take | 
+c        | Repeatedly call the routine SNAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call snaupd ( ido, bmat, n, which, nev, tol, resid, 
-     &        ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, 
+         call snaupd ( ido, bmat, n, which, nev, tol, resid,
+     &        ncv, v, ldv, iparam, ipntr, workd, workl, lworkl,
      &        info )
 c
          if ( ido .eq. -1 .or. ido .eq. 1) then
@@ -247,10 +247,10 @@ c           %-------------------------------------------%
 c
             call scopy( n, workd(ipntr(1)), 1, workd(ipntr(2)), 1)
 c
-            call sgttrs('N', n, 1, dl, dd, du, du2, ipiv, 
-     &                  workd(ipntr(2)), n, ierr) 
+            call sgttrs('N', n, 1, dl, dd, du, du2, ipiv,
+     &                  workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
-               print*, ' ' 
+               print*, ' '
                print*, ' ERROR with _gttrs in _NDRV2.'
                print*, ' '
                go to 9000
@@ -279,26 +279,26 @@ c
          print *, ' '
          print *, ' Error with _naupd, info = ', info
          print *, ' Check the documentation in _naupd.'
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using SNEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
-c 
+c
          rvec = .true.
 c
-         call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv,  
-     &        sigmar, sigmai, workev, bmat, n, which, nev, tol, 
-     &        resid, ncv, v, ldv, iparam, ipntr, workd, 
-     &        workl, lworkl, ierr )            
+         call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv,
+     &        sigmar, sigmai, workev, bmat, n, which, nev, tol,
+     &        resid, ncv, v, ldv, iparam, ipntr, workd,
+     &        workl, lworkl, ierr )
 c
 c        %-----------------------------------------------%
 c        | The real part of the eigenvalue is returned   |
@@ -319,11 +319,11 @@ c           | Error condition:                   |
 c           | Check the documentation of SNEUPD. |
 c           %------------------------------------%
 c
-            print *, ' ' 
+            print *, ' '
             print *, ' Error with _neupd, info = ', ierr
             print *, ' Check the documentation of _neupd. '
-            print *, ' ' 
-c 
+            print *, ' '
+c
          else
 c
             first  = .true.
@@ -360,9 +360,9 @@ c                 %------------------------%
 c                 | Ritz value is complex  |
 c                 | Residual of one Ritz   |
 c                 | value of the conjugate |
-c                 | pair is computed.      | 
+c                 | pair is computed.      |
 c                 %------------------------%
-c 
+c
                   call av(n, v(1,j), ax)
                   call saxpy(n, -d(j,1), v(1,j), 1, ax, 1)
                   call saxpy(n, d(j,2), v(1,j+1), 1, ax, 1)
@@ -397,11 +397,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _NDRV2 '
@@ -412,8 +412,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)

EXAMPLES/NONSYM/sndrv3.f

@@ -15,7 +15,7 @@ c         using linear elements.
 c
 c     ... So OP = inv[M]*A  and  B = M.
 c
-c     ... Use mode 2 of SNAUPD. 
+c     ... Use mode 2 of SNAUPD.
 c
 c\BeginLib
 c
@@ -60,7 +60,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer           maxn, maxnev, maxncv, ldv
-      parameter         (maxn=256, maxnev=10, maxncv=25, 
+      parameter         (maxn=256, maxnev=10, maxncv=25,
      &                   ldv=maxn )
 c
 c     %--------------%
@@ -71,7 +71,7 @@ c
       logical           select(maxncv)
       Real
      &                  ax(maxn), mx(maxn), d(maxncv, 3), resid(maxn),
-     &                  v(ldv,maxncv), workd(3*maxn), 
+     &                  v(ldv,maxncv), workd(3*maxn),
      &                  workev(3*maxncv),
      &                  workl(3*maxncv*maxncv+6*maxncv),
      &                  md(maxn), me(maxn-1)
@@ -83,7 +83,7 @@ c
       character         bmat*1, which*2
       integer           ido, n, nev, ncv, lworkl, info, ierr, j,
      &                  nconv, maxitr, ishfts, mode
-      Real           
+      Real
      &                  tol, sigmar, sigmai, h
       logical           first, rvec
 c
@@ -91,14 +91,14 @@ c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Real  
+      Real
      &                  zero, one
       parameter         (zero = 0.0E+0, one = 1.0E+0)
 c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
-      Real 
+      Real
      &                  snrm2, slapy2
       external          saxpy, snrm2, spttrf, spttrs, slapy2
 c
@@ -125,9 +125,9 @@ c     |                  NEV <= MAXNEV,                    |
 c     |              NEV + 2 <= NCV <= MAXNCV              |
 c     %----------------------------------------------------%
 c
-      n     = 100 
-      nev   = 4 
-      ncv   = 20 
+      n     = 100
+      nev   = 4
+      ncv   = 20
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NDRV3: N is greater than MAXN '
          go to 9000
@@ -148,16 +148,16 @@ c     %------------------------------------------------%
 c
       h = one / real(n+1)
       do 20 j = 1, n-1
-         md(j) = 4.0E+0*h 
-         me(j) = one*h 
-  20  continue 
+         md(j) = 4.0E+0*h
+         me(j) = one*h
+  20  continue
       md(n) = 4.0E+0*h
-c 
+c
       call spttrf(n, md, me, ierr)
       if ( ierr .ne. 0 ) then
          print*, ' '
-         print*, ' ERROR with _pttrf. ' 
-         print*, ' ' 
+         print*, ' ERROR with _pttrf. '
+         print*, ' '
          go to 9000
       end if
 c
@@ -172,8 +172,8 @@ c     | Setting INFO=0 indicates that a random vector is    |
 c     | generated in SNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl = 3*ncv**2+6*ncv 
-      tol    = 0.0 
+      lworkl = 3*ncv**2+6*ncv
+      tol    = 0.0
       ido    = 0
       info   = 0
 c
@@ -191,9 +191,9 @@ c
       maxitr = 300
       mode   = 2
 c
-      iparam(1) = ishfts 
-      iparam(3) = maxitr  
-      iparam(7) = mode 
+      iparam(1) = ishfts
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %-------------------------------------------%
 c     | M A I N   L O O P (Reverse communication) |
@@ -202,14 +202,14 @@ c
  10   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine SNAUPD and take | 
+c        | Repeatedly call the routine SNAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call snaupd ( ido, bmat, n, which, nev, tol, resid, 
-     &                 ncv, v, ldv, iparam, ipntr, workd, 
+         call snaupd ( ido, bmat, n, which, nev, tol, resid,
+     &                 ncv, v, ldv, iparam, ipntr, workd,
      &                 workl, lworkl, info )
 c
          if (ido .eq. -1 .or. ido .eq. 1) then
@@ -228,8 +228,8 @@ c
             call spttrs(n, 1, md, me, workd(ipntr(2)), n,
      &                  ierr)
             if ( ierr .ne. 0 ) then
-               print*, ' ' 
-               print*, ' ERROR with _pttrs. ' 
+               print*, ' '
+               print*, ' ERROR with _pttrs. '
                print*, ' '
                go to 9000
             end if
@@ -264,7 +264,7 @@ c
 c     %-----------------------------------------%
 c     | Either we have convergence, or there is |
 c     | an error.                               |
-c     %-----------------------------------------% 
+c     %-----------------------------------------%
 c
       if ( info .lt. 0 ) then
 c
@@ -276,22 +276,22 @@ c
          print *, ' '
          print *, ' Error with _naupd, info = ', info
          print *, ' Check the documentation of _naupd.'
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using SNEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
 c
          rvec = .true.
-         call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv, 
+         call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv,
      &        sigmar, sigmai, workev, bmat, n, which, nev, tol,
      &        resid, ncv, v, ldv, iparam, ipntr, workd,
      &        workl, lworkl, ierr )
@@ -314,13 +314,13 @@ c           %------------------------------------%
 c           | Error condition:                   |
 c           | Check the documentation of SNEUPD. |
 c           %------------------------------------%
-c 
-            print *, ' ' 
+c
+            print *, ' '
             print *, ' Error with _neupd, info = ', ierr
             print *, ' Check the documentation of _neupd'
             print *, ' '
 c
-         else 
+         else
 c
             first = .true.
             nconv = iparam(5)
@@ -399,11 +399,11 @@ c
             print *, ' Maximum number of iterations reached.'
             print *, ' '
          else if ( info .eq. 3) then
-            print *, ' ' 
+            print *, ' '
             print *, ' No shifts could be applied during implicit',
      &               ' Arnoldi update, try increasing NCV.'
             print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _NDRV3 '
@@ -414,8 +414,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -431,16 +431,16 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector multiplication subroutine
 c
       subroutine av (n, v, w)
       integer           n, j
-      Real            
-     &                  v(n), w(n), one, two, dd, dl, du, s, h, rho 
-      parameter         ( rho = 1.0E+1, one = 1.0E+0, 
+      Real
+     &                  v(n), w(n), one, two, dd, dl, du, s, h, rho
+      parameter         ( rho = 1.0E+1, one = 1.0E+0,
      &                    two = 2.0E+0)
 c
 c     Compute the matrix vector multiplication y<---A*x
@@ -458,27 +458,27 @@ c
 c
       w(1) =  dd*v(1) + du*v(2)
       do 10 j = 2,n-1
-         w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1) 
- 10   continue 
-      w(n) =  dl*v(n-1) + dd*v(n) 
+         w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1)
+ 10   continue
+      w(n) =  dl*v(n-1) + dd*v(n)
       return
       end
 c------------------------------------------------------------------------
       subroutine mv (n, v, w)
       integer           n, j
-      Real 
+      Real
      &                  v(n), w(n), one, four, h
       parameter         ( one = 1.0E+0, four = 4.0E+0)
 c
 c     Compute the matrix vector multiplication y<---M*x
-c     where M is the mass matrix formed by using piecewise linear 
+c     where M is the mass matrix formed by using piecewise linear
 c     elements on [0,1].
-c 
+c
       w(1) =  four*v(1) + one*v(2)
       do 10 j = 2,n-1
-         w(j) = one*v(j-1) + four*v(j) + one*v(j+1) 
- 10   continue 
-      w(n) =  one*v(n-1) + four*v(n) 
+         w(j) = one*v(j-1) + four*v(j) + one*v(j+1)
+ 10   continue
+      w(n) =  one*v(n-1) + four*v(n)
 c
       h = one / real(n+1)
       call sscal(n, h, w, 1)

EXAMPLES/NONSYM/sndrv4.f

@@ -1,7 +1,7 @@
       program sndrv4
 c
 c     Simple program to illustrate the idea of reverse communication
-c     in shift-invert mode for a generalized nonsymmetric eigenvalue 
+c     in shift-invert mode for a generalized nonsymmetric eigenvalue
 c     problem.
 c
 c     We implement example four of ex-nonsym.doc in DOCUMENTS directory
@@ -25,7 +25,7 @@ c
 c\Routines called:
 c     snaupd  ARPACK reverse communication interface routine.
 c     sneupd  ARPACK routine that returns Ritz values and (optionally)
-c             Ritz vectors. 
+c             Ritz vectors.
 c     sgttrf  LAPACK tridiagonal factorization routine.
 c     sgttrs  LAPACK tridiagonal linear system solve routine.
 c     slapy2  LAPACK routine to compute sqrt(x**2+y**2) carefully.
@@ -37,15 +37,15 @@ c     av      Matrix vector multiplication routine that computes A*x.
 c     mv      Matrix vector multiplication routine that computes M*x.
 c
 c\Author
-c     Richard Lehoucq 
-c     Danny Sorensen               
-c     Chao Yang             
-c     Dept. of Computational &     
-c     Applied Mathematics          
-c     Rice University           
-c     Houston, Texas    
+c     Richard Lehoucq
+c     Danny Sorensen
+c     Chao Yang
+c     Dept. of Computational &
+c     Applied Mathematics
+c     Rice University
+c     Houston, Texas
 c
-c\SCCS Information: @(#) 
+c\SCCS Information: @(#)
 c FILE: ndrv4.F   SID: 2.5   DATE OF SID: 10/17/00   RELEASE: 2
 c
 c\Remarks
@@ -64,7 +64,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer           maxn, maxnev, maxncv, ldv
-      parameter         (maxn=256, maxnev=10, maxncv=25, 
+      parameter         (maxn=256, maxnev=10, maxncv=25,
      &                   ldv=maxn )
 c
 c     %--------------%
@@ -90,13 +90,13 @@ c
       Real
      &                  tol, h, s,
      &                  sigmar, sigmai, s1, s2, s3
-      logical           first, rvec 
-c 
+      logical           first, rvec
+c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real   
+      Real
      &                  sdot, snrm2, slapy2
       external          sdot, snrm2, slapy2, sgttrf, sgttrs
 c
@@ -113,7 +113,7 @@ c
       Real
      &                   one, zero, two, six, rho
       common            /convct/ rho
-      parameter         (one = 1.0E+0, zero = 0.0E+0, 
+      parameter         (one = 1.0E+0, zero = 0.0E+0,
      &                   two = 2.0E+0, six = 6.0E+0)
 c
 c     %-----------------------%
@@ -130,14 +130,14 @@ c     | The user can modify NEV, NCV, SIGMAR to solve      |
 c     | problems of different sizes, and to get different  |
 c     | parts of the spectrum.  However, The following     |
 c     | conditions must be satisfied:                      |
-c     |                     N <= MAXN,                     | 
+c     |                     N <= MAXN,                     |
 c     |                   NEV <= MAXNEV,                   |
-c     |               NEV + 2 <= NCV <= MAXNCV             | 
+c     |               NEV + 2 <= NCV <= MAXNCV             |
 c     %----------------------------------------------------%
 c
-      n     = 100 
-      nev   = 4 
-      ncv   = 10 
+      n     = 100
+      nev   = 4
+      ncv   = 10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NDRV4: N is greater than MAXN '
          go to 9000
@@ -150,7 +150,7 @@ c
       end if
       bmat  = 'G'
       which = 'LM'
-      sigmar = one 
+      sigmar = one
       sigmai = zero
 c
 c     %--------------------------------------------------%
@@ -175,12 +175,12 @@ c
       s3 = -one/h + s - sigmar*h/six
 c
       do 10 j = 1, n-1
-         dl(j) = s1 
+         dl(j) = s1
          dd(j) = s2
          du(j) = s3
-  10  continue 
-      dd(n) = s2 
-c 
+  10  continue
+      dd(n) = s2
+c
       call sgttrf(n, dl, dd, du, du2, ipiv, ierr)
       if ( ierr .ne. 0 ) then
          print*, ' '
@@ -200,7 +200,7 @@ c     | Setting INFO=0 indicates that a random vector is    |
 c     | generated in SNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl = 3*ncv**2+6*ncv 
+      lworkl = 3*ncv**2+6*ncv
       tol    = zero
       ido    = 0
       info   = 0
@@ -224,20 +224,20 @@ c
       iparam(7) = mode
 c
 c     %------------------------------------------%
-c     | M A I N   L O O P(Reverse communication) | 
+c     | M A I N   L O O P(Reverse communication) |
 c     %------------------------------------------%
 c
  20   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine SNAUPD and take | 
+c        | Repeatedly call the routine SNAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call snaupd ( ido, bmat, n, which, nev, tol, resid, 
-     &                 ncv, v, ldv, iparam, ipntr, workd, 
+         call snaupd ( ido, bmat, n, which, nev, tol, resid,
+     &                 ncv, v, ldv, iparam, ipntr, workd,
      &                 workl, lworkl, info )
 c
          if (ido .eq. -1) then
@@ -255,8 +255,8 @@ c           | workd(ipntr(2)).                          |
 c           %-------------------------------------------%
 c
             call mv (n, workd(ipntr(1)), workd(ipntr(2)))
-            call sgttrs('N', n, 1, dl, dd, du, du2, ipiv, 
-     &                  workd(ipntr(2)), n, ierr) 
+            call sgttrs('N', n, 1, dl, dd, du, du2, ipiv,
+     &                  workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
                print*, ' ERROR with _gttrs in _NDRV4.'
@@ -282,7 +282,7 @@ c           | workd(ipntr(2)).                        |
 c           %-----------------------------------------%
 c
             call scopy( n, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-            call sgttrs ('N', n, 1, dl, dd, du, du2, ipiv, 
+            call sgttrs ('N', n, 1, dl, dd, du, du2, ipiv,
      &                  workd(ipntr(2)), n, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
@@ -314,8 +314,8 @@ c           %-----------------------------------------%
 c
             go to 20
 c
-         end if 
-c 
+         end if
+c
 c
 c     %-----------------------------------------%
 c     | Either we have convergence, or there is |
@@ -334,23 +334,23 @@ c
          print *, ' Check the documentation in _naupd.'
          print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using SNEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
 c
          rvec = .true.
-         call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv,  
-     &        sigmar, sigmai, workev, bmat, n, which, nev, tol, 
-     &        resid, ncv, v, ldv, iparam, ipntr, workd, 
-     &        workl, lworkl, ierr )            
+         call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv,
+     &        sigmar, sigmai, workev, bmat, n, which, nev, tol,
+     &        resid, ncv, v, ldv, iparam, ipntr, workd,
+     &        workl, lworkl, ierr )
 c
 c        %-----------------------------------------------%
 c        | The real part of the eigenvalue is returned   |
@@ -365,16 +365,16 @@ c        | the eigenvalues in D is returned in V.        |
 c        %-----------------------------------------------%
 c
          if ( ierr .ne. 0) then
-c 
+c
 c            %------------------------------------%
 c            | Error condition:                   |
 c            | Check the documentation of SNEUPD. |
 c            %------------------------------------%
 c
-             print *, ' ' 
+             print *, ' '
              print *, ' Error with _neupd, info = ', ierr
              print *, ' Check the documentation of _neupd. '
-             print *, ' ' 
+             print *, ' '
 c
          else
 c
@@ -413,9 +413,9 @@ c                    %------------------------%
 c                    | Ritz value is complex. |
 c                    | Residual of one Ritz   |
 c                    | value of the conjugate |
-c                    | pair is computed.      | 
+c                    | pair is computed.      |
 c                    %------------------------%
-c     
+c
                      call av(n, v(1,j), ax)
                      call mv(n, v(1,j), mx)
                      call saxpy(n, -d(j,1), mx, 1, ax, 1)
@@ -455,11 +455,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _NDRV4 '
@@ -470,8 +470,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -487,7 +487,7 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector multiplication subroutine
@@ -495,17 +495,17 @@ c
       subroutine mv (n, v, w)
       integer           n, j
       Real
-     &                  v(n), w(n), one, four, six, h 
+     &                  v(n), w(n), one, four, six, h
       parameter         (one = 1.0E+0, four = 4.0E+0, six = 6.0E+0)
 c
 c     Compute the matrix vector multiplication y<---M*x
-c     where M is mass matrix formed by using piecewise linear elements 
+c     where M is mass matrix formed by using piecewise linear elements
 c     on [0,1].
-c 
+c
       w(1) =  ( four*v(1) + one*v(2) ) / six
       do 10 j = 2,n-1
          w(j) = ( one*v(j-1) + four*v(j) + one*v(j+1) ) / six
- 10   continue 
+ 10   continue
       w(n) =  ( one*v(n-1) + four*v(n) ) / six
 c
       h = one / real(n+1)
@@ -516,7 +516,7 @@ c------------------------------------------------------------------
       subroutine av (n, v, w)
       integer           n, j
       Real
-     &                  v(n), w(n), one, two, dd, dl, du, s, h, rho 
+     &                  v(n), w(n), one, two, dd, dl, du, s, h, rho
       common            /convct/ rho
       parameter         (one = 1.0E+0, two = 2.0E+0)
 c
@@ -530,7 +530,7 @@ c     This routine is only used in residual calculation.
 c
       h = one / real(n+1)
       s = rho / two
-      dd = two / h 
+      dd = two / h
       dl = -one/h - s
       du = -one/h + s
 c

EXAMPLES/NONSYM/sndrv5.f

@@ -8,9 +8,9 @@ c
 c\Example-5
 c
 c     ... Suppose we want to solve A*x = lambda*B*x in shift-invert mode
-c         The matrix A is the tridiagonal matrix with 2 on the diagonal, 
-c         -2 on the subdiagonal and 3 on the superdiagonal.  The matrix M 
-c         is the tridiagonal matrix with 4 on the diagonal and 1 on the 
+c         The matrix A is the tridiagonal matrix with 2 on the diagonal,
+c         -2 on the subdiagonal and 3 on the superdiagonal.  The matrix M
+c         is the tridiagonal matrix with 4 on the diagonal and 1 on the
 c         off-diagonals.
 c     ... The shift sigma is a complex number (sigmar, sigmai).
 c     ... OP = Real_Part{inv[A-(SIGMAR,SIGMAI)*M]*M and  B = M.
@@ -32,15 +32,15 @@ c     av      Matrix vector subroutine that computes A*x.
 c     mv      Matrix vector subroutine that computes M*x.
 c
 c\Author
-c     Richard Lehoucq 
-c     Danny Sorensen               
-c     Chao Yang             
-c     Dept. of Computational &     
-c     Applied Mathematics          
-c     Rice University           
-c     Houston, Texas    
+c     Richard Lehoucq
+c     Danny Sorensen
+c     Chao Yang
+c     Dept. of Computational &
+c     Applied Mathematics
+c     Rice University
+c     Houston, Texas
 c
-c\SCCS Information: @(#) 
+c\SCCS Information: @(#)
 c FILE: ndrv5.F   SID: 2.5   DATE OF SID: 10/17/00   RELEASE: 2
 c
 c\Remarks
@@ -59,7 +59,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer           maxn, maxnev, maxncv, ldv
-      parameter         (maxn=256, maxnev=10, maxncv=25, 
+      parameter         (maxn=256, maxnev=10, maxncv=25,
      &                   ldv=maxn )
 c
 c     %--------------%
@@ -73,7 +73,7 @@ c
      &                  v(ldv,maxncv), workd(3*maxn),
      &                  workev(3*maxncv),
      &                  workl(3*maxncv*maxncv+6*maxncv)
-      Complex         
+      Complex
      &                  cdd(maxn), cdl(maxn), cdu(maxn),
      &                  cdu2(maxn), ctemp(maxn)
 c
@@ -86,16 +86,16 @@ c
      &                  nconv, maxitr, ishfts, mode
       Real
      &                  tol, numr, numi, denr, deni, sigmar, sigmai
-      Complex         
+      Complex
      &                  c1, c2, c3
-      logical           first, rvec 
-c 
+      logical           first, rvec
+c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
       external          cgttrf, cgttrs
-      Real   
+      Real
      &                  sdot, snrm2, slapy2
       external          sdot, snrm2, slapy2
 c
@@ -128,14 +128,14 @@ c     | to 'LM'.  The user can modify NEV, NCV, SIGMAR,    |
 c     | SIGMAI to solve problems of different sizes, and   |
 c     | to get different parts of the spectrum. However,   |
 c     | The following conditions must be satisfied:        |
-c     |                     N <= MAXN,                     | 
+c     |                     N <= MAXN,                     |
 c     |                   NEV <= MAXNEV,                   |
-c     |               NEV + 2 <= NCV <= MAXNCV             | 
+c     |               NEV + 2 <= NCV <= MAXNCV             |
 c     %----------------------------------------------------%
 c
-      n     = 100 
-      nev   = 4 
-      ncv   = 20 
+      n     = 100
+      nev   = 4
+      ncv   = 20
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NDRV5: N is greater than MAXN '
          go to 9000
@@ -167,12 +167,12 @@ c
       c3 = cmplx( 3.0E+0-sigmar, -sigmai)
 c
       do 10 j = 1, n-1
-         cdl(j) = c1 
+         cdl(j) = c1
          cdd(j) = c2
          cdu(j) = c3
-  10  continue 
-      cdd(n) = c2 
-c 
+  10  continue
+      cdd(n) = c2
+c
       call cgttrf(n, cdl, cdd, cdu, cdu2, ipiv, ierr)
       if ( ierr .ne. 0 ) then
          print*, ' '
@@ -192,8 +192,8 @@ c     | Setting INFO=0 indicates that a random vector is    |
 c     | generated in SNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl = 3*ncv**2+6*ncv 
-      tol    = zero 
+      lworkl = 3*ncv**2+6*ncv
+      tol    = zero
       ido    = 0
       info   = 0
 c
@@ -212,30 +212,30 @@ c
       mode   = 3
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr  
-      iparam(7) = mode 
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %------------------------------------------%
-c     | M A I N   L O O P(Reverse communication) | 
+c     | M A I N   L O O P(Reverse communication) |
 c     %------------------------------------------%
 c
  20   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine SNAUPD and take | 
+c        | Repeatedly call the routine SNAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call snaupd ( ido, bmat, n, which, nev, tol, resid, 
-     &                 ncv, v, ldv, iparam, ipntr, workd, 
+         call snaupd ( ido, bmat, n, which, nev, tol, resid,
+     &                 ncv, v, ldv, iparam, ipntr, workd,
      &                 workl, lworkl, info )
 c
          if (ido .eq. -1) then
 c
 c           %-------------------------------------------------------%
-c           |                       Perform                         | 
+c           |                       Perform                         |
 c           | y <--- OP*x = Real_Part{inv[A-(SIGMAR,SIGMAI)*M]*M*x} |
 c           | to force starting vector into the range of OP. The    |
 c           | user should supply his/her own matrix vector          |
@@ -251,14 +251,14 @@ c
                ctemp(j) = cmplx(workd(ipntr(2)+j-1))
   30        continue
 c
-            call cgttrs('N', n, 1, cdl, cdd, cdu, cdu2, ipiv, 
+            call cgttrs('N', n, 1, cdl, cdd, cdu, cdu2, ipiv,
      &                  ctemp, n, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
                print*, ' ERROR with _gttrs in _NDRV5.'
                print*, ' '
                go to 9000
-            end if 
+            end if
             do  40 j = 1, n
                workd(ipntr(2)+j-1) = real(ctemp(j))
   40        continue
@@ -283,14 +283,14 @@ c
             do 50 j = 1,n
                ctemp(j) = cmplx(workd(ipntr(3)+j-1))
   50        continue
-            call cgttrs ('N', n, 1, cdl, cdd, cdu, cdu2, ipiv, 
+            call cgttrs ('N', n, 1, cdl, cdd, cdu, cdu2, ipiv,
      &                   ctemp, n, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
                print*, ' ERROR with _gttrs in _NDRV5.'
                print*, ' '
                go to 9000
-            end if 
+            end if
             do  60 j = 1, n
                workd(ipntr(2)+j-1) = real(ctemp(j))
   60        continue
@@ -320,7 +320,7 @@ c
 c
          end if
 c
-c 
+c
 c     %------------------------------------------%
 c     | Either we have convergence, or there is  |
 c     | an error.                                |
@@ -336,25 +336,25 @@ c
          print *, ' '
          print *, ' Error with _naupd info = ',info
          print *, ' Check the documentation of _naupd.'
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using SNEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
 c
          rvec = .true.
-         call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv, 
-     &        sigmar, sigmai, workev, bmat, n, which, nev, tol, 
-     &        resid, ncv, v, ldv, iparam, ipntr, workd, 
-     &        workl, lworkl, ierr ) 
+         call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv,
+     &        sigmar, sigmai, workev, bmat, n, which, nev, tol,
+     &        resid, ncv, v, ldv, iparam, ipntr, workd,
+     &        workl, lworkl, ierr )
 c
 c        %-----------------------------------------------%
 c        | The real part of the eigenvalue is returned   |
@@ -375,14 +375,14 @@ c           | Error condition:                   |
 c           | Check the documentation of SNEUPD. |
 c           %------------------------------------%
 c
-            print *, ' ' 
+            print *, ' '
             print *, ' Error with _neupd = ', ierr
             print *, ' Check the documentation of _neupd. '
-            print *, ' ' 
+            print *, ' '
 c
-         else 
+         else
 c
-            first = .true. 
+            first = .true.
             nconv =  iparam(5)
             do 70 j=1,nconv
 c
@@ -394,7 +394,7 @@ c
                if ( d(j,2) .eq. zero ) then
 c
 c                 %---------------------------%
-c                 |    Eigenvalue is real.    | 
+c                 |    Eigenvalue is real.    |
 c                 | Compute d = x'(Ax)/x'(Mx).|
 c                 %---------------------------%
 c
@@ -402,7 +402,7 @@ c
                   numr = sdot(n, v(1,j), 1, ax, 1)
                   call mv(n, v(1,j), ax )
                   denr = sdot(n, v(1,j), 1, ax, 1)
-                  d(j,1) =  numr / denr 
+                  d(j,1) =  numr / denr
 c
                else if (first) then
 c
@@ -420,7 +420,7 @@ c                 %----------------%
                   numr = sdot(n, v(1,j), 1, ax, 1)
                   numi = sdot(n, v(1,j+1), 1, ax, 1)
                   call av(n, v(1,j+1), ax)
-                  numr = numr + sdot(n,v(1,j+1),1,ax,1) 
+                  numr = numr + sdot(n,v(1,j+1),1,ax,1)
                   numi = -numi + sdot(n,v(1,j),1,ax,1)
 c
 c                 %----------------%
@@ -431,7 +431,7 @@ c
                   denr = sdot(n, v(1,j), 1, ax, 1)
                   deni = sdot(n, v(1,j+1), 1, ax, 1)
                   call mv(n, v(1,j+1), ax)
-                  denr = denr + sdot(n,v(1,j+1),1,ax,1) 
+                  denr = denr + sdot(n,v(1,j+1),1,ax,1)
                   deni = -deni + sdot(n,v(1,j),1, ax,1)
 c
 c                 %----------------%
@@ -452,7 +452,7 @@ c                 | the conjugate pair by taking |
 c                 | the conjugate of the last    |
 c                 | eigenvalue computed.         |
 c                 %------------------------------%
-c 
+c
                   d(j,1) = d(j-1,1)
                   d(j,2) = -d(j-1,2)
                   first = .true.
@@ -475,7 +475,7 @@ c           | tolerance)                |
 c           %---------------------------%
 c
             first  = .true.
-            do 80 j=1, nconv 
+            do 80 j=1, nconv
 c
                if (d(j,2) .eq. zero)  then
 c
@@ -495,9 +495,9 @@ c                 %------------------------%
 c                 | Ritz value is complex  |
 c                 | Residual of one Ritz   |
 c                 | value of the conjugate |
-c                 | pair is computed.      | 
+c                 | pair is computed.      |
 c                 %------------------------%
-c        
+c
                   call av(n, v(1,j), ax)
                   call mv(n, v(1,j), mx)
                   call saxpy(n, -d(j,1), mx, 1, ax, 1)
@@ -527,7 +527,7 @@ c
              call smout(6, nconv, 3, d, maxncv, -6,
      &            'Ritz values (Real,Imag) and relative residuals')
 c
-         end if 
+         end if
 c
 c        %-------------------------------------------%
 c        | Print additional convergence information. |
@@ -538,11 +538,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _NDRV5 '
@@ -553,8 +553,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -570,7 +570,7 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector multiplication subroutine
@@ -578,25 +578,25 @@ c
       subroutine mv (n, v, w)
       integer           n, j
       Real
-     &                  v(n), w(n), one, four 
+     &                  v(n), w(n), one, four
       parameter         (one = 1.0E+0, four = 4.0E+0)
 c
 c     Compute the matrix vector multiplication y<---M*x
-c     where M is a n by n symmetric tridiagonal matrix with 4 on the 
+c     where M is a n by n symmetric tridiagonal matrix with 4 on the
 c     diagonal, 1 on the subdiagonal and superdiagonal.
-c 
+c
       w(1) =  four*v(1) + one*v(2)
       do 10 j = 2,n-1
-         w(j) = one*v(j-1) + four*v(j) + one*v(j+1) 
- 10   continue 
-      w(n) =  one*v(n-1) + four*v(n) 
+         w(j) = one*v(j-1) + four*v(j) + one*v(j+1)
+ 10   continue
+      w(n) =  one*v(n-1) + four*v(n)
       return
       end
 c------------------------------------------------------------------
       subroutine av (n, v, w)
       integer           n, j
-      Real            
-     &                  v(n), w(n), three, two 
+      Real
+     &                  v(n), w(n), three, two
       parameter         (three = 3.0E+0, two = 2.0E+0)
 c
 c     Compute the matrix vector multiplication y<---A*x

EXAMPLES/NONSYM/sndrv6.f

@@ -8,9 +8,9 @@ c
 c\Example-6
 c
 c     ... Suppose we want to solve A*x = lambda*B*x in shift-invert mode
-c         The matrix A is the tridiagonal matrix with 2 on the diagonal, 
-c         -2 on the subdiagonal and 3 on the superdiagonal.  The matrix M 
-c         is the tridiagonal matrix with 4 on the diagonal and 1 on the 
+c         The matrix A is the tridiagonal matrix with 2 on the diagonal,
+c         -2 on the subdiagonal and 3 on the superdiagonal.  The matrix M
+c         is the tridiagonal matrix with 4 on the diagonal and 1 on the
 c         off-diagonals.
 c     ... The shift sigma is a complex number (sigmar, sigmai).
 c     ... OP = Imaginary_Part{inv[A-(SIGMAR,SIGMAI)*M]*M  and  B = M.
@@ -32,15 +32,15 @@ c     av      Matrix vector subroutine that computes A*x.
 c     mv      Matrix vector subroutine that computes M*x.
 c
 c\Author
-c     Richard Lehoucq 
-c     Danny Sorensen               
-c     Chao Yang             
-c     Dept. of Computational &     
-c     Applied Mathematics          
-c     Rice University           
-c     Houston, Texas    
+c     Richard Lehoucq
+c     Danny Sorensen
+c     Chao Yang
+c     Dept. of Computational &
+c     Applied Mathematics
+c     Rice University
+c     Houston, Texas
 c
-c\SCCS Information: @(#) 
+c\SCCS Information: @(#)
 c FILE: ndrv6.F   SID: 2.5   DATE OF SID: 10/17/00   RELEASE: 2
 c
 c\Remarks
@@ -59,7 +59,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer           maxn, maxnev, maxncv, ldv
-      parameter         (maxn=256, maxnev=10, maxncv=25, 
+      parameter         (maxn=256, maxnev=10, maxncv=25,
      &                   ldv=maxn )
 c
 c     %--------------%
@@ -73,7 +73,7 @@ c
      &                  v(ldv,maxncv), workd(3*maxn),
      &                  workev(3*maxncv),
      &                  workl(3*maxncv*maxncv+6*maxncv)
-      Complex         
+      Complex
      &                  cdd(maxn), cdl(maxn), cdu(maxn),
      &                  cdu2(maxn), ctemp(maxn)
 c
@@ -86,16 +86,16 @@ c
      &                  nconv, maxitr, ishfts, mode
       Real
      &                  tol, numr, numi, denr, deni, sigmar, sigmai
-      Complex         
+      Complex
      &                  c1, c2, c3
-      logical           first, rvec 
-c 
+      logical           first, rvec
+c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
       external          cgttrf, cgttrs
-      Real   
+      Real
      &                  sdot, snrm2, slapy2
       external          sdot, snrm2, slapy2
 c
@@ -127,14 +127,14 @@ c     | to 'LM'.  The user can modify NEV, NCV, SIGMA to   |
 c     | solve problems of different sizes, and to get      |
 c     | different parts of the spectrum. However, The      |
 c     | following conditions must be satisfied:            |
-c     |                     N <= MAXN,                     | 
+c     |                     N <= MAXN,                     |
 c     |                   NEV <= MAXNEV,                   |
-c     |               NEV + 2 <= NCV <= MAXNCV             | 
+c     |               NEV + 2 <= NCV <= MAXNCV             |
 c     %----------------------------------------------------%
 c
-      n     = 100 
-      nev   = 4 
-      ncv   = 20 
+      n     = 100
+      nev   = 4
+      ncv   = 20
       if ( n .gt. maxn ) then
          print *, ' ERROR with _NDRV6: N is greater than MAXN '
          go to 9000
@@ -148,7 +148,7 @@ c
       bmat  = 'G'
       which = 'LM'
       sigmar = 4.0E-1
-      sigmai = 6.0E-1 
+      sigmai = 6.0E-1
 c
 c     %----------------------------------------------------%
 c     | Construct C = A - (SIGMAR,SIGMAI)*M in complex     |
@@ -166,12 +166,12 @@ c
       c3 = cmplx( 3.0E+0-sigmar, -sigmai)
 c
       do 10 j = 1, n-1
-         cdl(j) = c1 
+         cdl(j) = c1
          cdd(j) = c2
          cdu(j) = c3
-  10  continue 
-      cdd(n) = c2 
-c 
+  10  continue
+      cdd(n) = c2
+c
       call cgttrf(n, cdl, cdd, cdu, cdu2, ipiv, ierr)
       if ( ierr .ne. 0 ) then
          print*, ' '
@@ -191,8 +191,8 @@ c     | Setting INFO=0 indicates that a random vector is    |
 c     | generated in SNAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
-      lworkl = 3*ncv**2+6*ncv 
-      tol    = zero 
+      lworkl = 3*ncv**2+6*ncv
+      tol    = zero
       ido    = 0
       info   = 0
 c
@@ -211,31 +211,31 @@ c
       mode   = 3
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr  
+      iparam(3) = maxitr
       iparam(7) = mode
 c
 c     %------------------------------------------%
-c     | M A I N   L O O P(Reverse communication) | 
+c     | M A I N   L O O P(Reverse communication) |
 c     %------------------------------------------%
 c
  20   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine SNAUPD and take | 
+c        | Repeatedly call the routine SNAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call snaupd ( ido, bmat, n, which, nev, tol, resid, 
-     &                 ncv, v, ldv, iparam, ipntr, workd, 
+         call snaupd ( ido, bmat, n, which, nev, tol, resid,
+     &                 ncv, v, ldv, iparam, ipntr, workd,
      &                 workl, lworkl, info )
 c
 
          if (ido .eq. -1) then
 c
 c           %------------------------------------------------------------%
-c           |                           Perform                          | 
+c           |                           Perform                          |
 c           | y <--- OP*x = Imaginary_Part{inv[A-(SIGMAR,SIGMAI)*M]*M*x} |
 c           | to force starting vector into the range of OP. The user    |
 c           | should supply his/her own matrix vector multiplication     |
@@ -250,14 +250,14 @@ c
                ctemp(j) = cmplx(workd(ipntr(2)+j-1))
   30        continue
 c
-            call cgttrs('N', n, 1, cdl, cdd, cdu, cdu2, ipiv, 
+            call cgttrs('N', n, 1, cdl, cdd, cdu, cdu2, ipiv,
      &                  ctemp, maxn, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
                print*, ' ERROR with _gttrs in _NDRV6.'
                print*, ' '
                go to 9000
-            end if 
+            end if
             do  40 j = 1, n
                workd(ipntr(2)+j-1) = aimag(ctemp(j))
   40        continue
@@ -282,14 +282,14 @@ c
             do 50 j = 1,n
                ctemp(j) = cmplx(workd(ipntr(3)+j-1))
   50        continue
-            call cgttrs ('N', n, 1, cdl, cdd, cdu, cdu2, ipiv, 
+            call cgttrs ('N', n, 1, cdl, cdd, cdu, cdu2, ipiv,
      &                   ctemp, maxn, ierr)
             if ( ierr .ne. 0 ) then
                print*, ' '
                print*, ' ERROR with _gttrs in _NDRV6.'
                print*, ' '
                go to 9000
-            end if 
+            end if
             do  60 j = 1, n
                workd(ipntr(2)+j-1) = aimag(ctemp(j))
   60        continue
@@ -335,24 +335,24 @@ c
          print *, ' '
          print *, ' Error with _naupd, info = ',info
          print *, ' Check the documentation of _naupd.'
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using SNEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
 c
          rvec = .true.
-         call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv,  
-     &        sigmar, sigmai, workev, bmat, n, which, nev, tol, 
-     &        resid, ncv, v, ldv, iparam, ipntr, workd, 
+         call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv,
+     &        sigmar, sigmai, workev, bmat, n, which, nev, tol,
+     &        resid, ncv, v, ldv, iparam, ipntr, workd,
      &        workl, lworkl, ierr )
 c
 c        %-----------------------------------------------%
@@ -368,16 +368,16 @@ c        | the eigenvalues in D is returned in V.        |
 c        %-----------------------------------------------%
 c
          if ( ierr .ne. 0) then
-c 
+c
 c           %------------------------------------%
 c           | Error condition:                   |
 c           | Check the documentation of SNEUPD. |
 c           %------------------------------------%
 c
-            print *, ' ' 
+            print *, ' '
             print *, ' Error with _neupd, info = ', ierr
             print *, ' Check the documentation of _neupd. '
-            print *, ' ' 
+            print *, ' '
 c
          else
 c
@@ -393,7 +393,7 @@ c
                 if ( d(j,2) .eq. zero) then
 c
 c                  %----------------------------%
-c                  | Eigenvalue is real.        | 
+c                  | Eigenvalue is real.        |
 c                  | Compute d = x'(Ax)/x'(Mx). |
 c                  %----------------------------%
 c
@@ -401,7 +401,7 @@ c
                    numr = sdot(n, v(1,j), 1, ax, 1)
                    call mv(n, v(1,j), ax )
                    denr = sdot(n, v(1,j), 1, ax, 1)
-                   d(j,1) =  numr / denr 
+                   d(j,1) =  numr / denr
 c
                 else if (first) then
 c
@@ -419,7 +419,7 @@ c
                    numr = sdot(n, v(1,j), 1, ax, 1)
                    numi = sdot(n, v(1,j+1), 1, ax, 1)
                    call av(n, v(1,j+1), ax)
-                   numr = numr + sdot(n,v(1,j+1),1,ax,1) 
+                   numr = numr + sdot(n,v(1,j+1),1,ax,1)
                    numi = -numi + sdot(n,v(1,j),1,ax,1)
 c
 c                  %----------------%
@@ -430,7 +430,7 @@ c
                    denr = sdot(n, v(1,j), 1, ax, 1)
                    deni = sdot(n, v(1,j+1), 1, ax, 1)
                    call mv(n, v(1,j+1), ax)
-                   denr = denr + sdot(n,v(1,j+1),1,ax,1) 
+                   denr = denr + sdot(n,v(1,j+1),1,ax,1)
                    deni = -deni + sdot(n,v(1,j),1, ax,1)
 c
 c                  %----------------%
@@ -451,7 +451,7 @@ c                  | the conjugate pair by taking |
 c                  | the conjugate of the last    |
 c                  | eigenvalue computed.         |
 c                  %------------------------------%
-c 
+c
                    d(j,1) = d(j-1,1)
                    d(j,2) = -d(j-1,2)
                    first = .true.
@@ -475,7 +475,7 @@ c           %---------------------------%
 c
             first = .true.
             nconv = iparam(5)
-            do 80 j=1, nconv 
+            do 80 j=1, nconv
 c
                if (d(j,2) .eq. zero)  then
 c
@@ -495,9 +495,9 @@ c                 %------------------------%
 c                 | Ritz value is complex  |
 c                 | Residual of one Ritz   |
 c                 | value of the conjugate |
-c                 | pair is computed.      | 
+c                 | pair is computed.      |
 c                 %------------------------%
-c        
+c
                   call av(n, v(1,j), ax)
                   call mv(n, v(1,j), mx)
                   call saxpy(n, -d(j,1), mx, 1, ax, 1)
@@ -510,7 +510,7 @@ c
                   call mv(n, v(1,j), mx)
                   call saxpy(n, -d(j,2), mx, 1, ax, 1)
                   d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) )
-                  d(j,3) = d(j,3) / slapy2(d(j,1),d(j,2)) 
+                  d(j,3) = d(j,3) / slapy2(d(j,1),d(j,2))
                   d(j+1,3) = d(j,3)
                   first = .false.
                else
@@ -537,11 +537,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _NDRV6 '
@@ -552,8 +552,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -569,7 +569,7 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector multiplication subroutine
@@ -577,25 +577,25 @@ c
       subroutine mv (n, v, w)
       integer           n, j
       Real
-     &                  v(n), w(n), one, four 
+     &                  v(n), w(n), one, four
       parameter         (one = 1.0E+0, four = 4.0E+0)
 c
 c     Compute the matrix vector multiplication y<---M*x
-c     where M is a n by n symmetric tridiagonal matrix with 4 on the 
+c     where M is a n by n symmetric tridiagonal matrix with 4 on the
 c     diagonal, 1 on the subdiagonal and superdiagonal.
-c 
+c
       w(1) =  four*v(1) + one*v(2)
       do 10 j = 2,n-1
-         w(j) = one*v(j-1) + four*v(j) + one*v(j+1) 
- 10   continue 
-      w(n) =  one*v(n-1) + four*v(n) 
+         w(j) = one*v(j-1) + four*v(j) + one*v(j+1)
+ 10   continue
+      w(n) =  one*v(n-1) + four*v(n)
       return
       end
 c------------------------------------------------------------------
       subroutine av (n, v, w)
       integer           n, j
-      Real            
-     &                  v(n), w(n), three, two 
+      Real
+     &                  v(n), w(n), three, two
       parameter         (three = 3.0E+0, two = 2.0E+0)
 c
 c     Compute the matrix vector multiplication y<---A*x

EXAMPLES/README.CALLING-ARPACK-FROM-C-OR-CPP

@@ -0,0 +1,2 @@
+In ../TESTS, the file icb_arpack_c.c     is an example of how to call arpack from C.
+In ../TESTS, the file icb_arpack_cpp.cpp is an example of how to call arpack from C++.

EXAMPLES/SIMPLE/Makefile.am

@@ -0,0 +1,15 @@
+LDADD = $(top_builddir)/SRC/libarpack$(LIBSUFFIX).la $(LAPACK_LIBS) $(BLAS_LIBS)
+
+SIMPLE = sssimp dssimp snsimp dnsimp cnsimp znsimp
+
+check_PROGRAMS = $(SIMPLE)
+TESTS = $(check_PROGRAMS)
+
+EXTRA_DIST = README debug.h
+
+sssimp_SOURCES = sssimp.f
+dssimp_SOURCES = dssimp.f
+snsimp_SOURCES = snsimp.f
+dnsimp_SOURCES = dnsimp.f
+cnsimp_SOURCES = cnsimp.f
+znsimp_SOURCES = znsimp.f

EXAMPLES/SIMPLE/cnsimp.f

@@ -1,26 +1,26 @@
-      program cnsimp 
+      program cnsimp
 c
-c     This example program is intended to illustrate the 
-c     simplest case of using ARPACK in considerable detail.  
+c     This example program is intended to illustrate the
+c     simplest case of using ARPACK in considerable detail.
 c     This code may be used to understand basic usage of ARPACK
-c     and as a template for creating an interface to ARPACK.  
-c   
-c     This code shows how to use ARPACK to find a few eigenvalues 
-c     (lambda) and corresponding eigenvectors (x) for the standard 
+c     and as a template for creating an interface to ARPACK.
+c
+c     This code shows how to use ARPACK to find a few eigenvalues
+c     (lambda) and corresponding eigenvectors (x) for the standard
 c     eigenvalue problem:
-c          
+c
 c                        A*x = lambda*x
-c 
+c
 c     where A is a general n by n complex matrix.
 c
-c     The main points illustrated here are 
+c     The main points illustrated here are
 c
-c        1) How to declare sufficient memory to find NEV 
+c        1) How to declare sufficient memory to find NEV
 c           eigenvalues of largest magnitude.  Other options
 c           are available.
 c
-c        2) Illustration of the reverse communication interface 
-c           needed to utilize the top level ARPACK routine CNAUPD 
+c        2) Illustration of the reverse communication interface
+c           needed to utilize the top level ARPACK routine CNAUPD
 c           that computes the quantities needed to construct
 c           the desired eigenvalues and eigenvectors(if requested).
 c
@@ -28,8 +28,8 @@ c        3) How to extract the desired eigenvalues and eigenvectors
 c           using the ARPACK routine CNEUPD.
 c
 c     The only thing that must be supplied in order to use this
-c     routine on your problem is to change the array dimensions 
-c     appropriately, to specify WHICH eigenvalues you want to compute 
+c     routine on your problem is to change the array dimensions
+c     appropriately, to specify WHICH eigenvalues you want to compute
 c     and to supply a matrix-vector product
 c
 c                         w <-  Av
@@ -40,7 +40,7 @@ c
 c     Once usage of this routine is understood, you may wish to explore
 c     the other available options to improve convergence, to solve generalized
 c     problems, etc.  Look at the file ex-complex.doc in DOCUMENTS directory.
-c     This codes implements  
+c     This codes implements
 c
 c
 c\Example-1
@@ -65,11 +65,11 @@ c             av.
 c
 c\Author
 c     Richard Lehoucq
-c     Danny Sorensen 
-c     Chao Yang 
-c     Dept. of Computational & 
-c     Applied Mathematics 
-c     Rice University 
+c     Danny Sorensen
+c     Chao Yang
+c     Dept. of Computational &
+c     Applied Mathematics
+c     Rice University
 c     Houston, Texas
 c
 c\SCCS Information: @(#)
@@ -112,12 +112,12 @@ c     %--------------%
 c
       integer           iparam(11), ipntr(14)
       logical           select(maxncv)
-      Complex 
-     &                  ax(maxn), d(maxncv), 
-     &                  v(ldv,maxncv), workd(3*maxn), 
-     &                  workev(2*maxncv), resid(maxn), 
+      Complex
+     &                  ax(maxn), d(maxncv),
+     &                  v(ldv,maxncv), workd(3*maxn),
+     &                  workev(2*maxncv), resid(maxn),
      &                  workl(3*maxncv*maxncv+5*maxncv)
-      Real  
+      Real
      &                  rwork(maxncv), rd(maxncv,3)
 c
 c     %---------------%
@@ -127,9 +127,9 @@ c
       character         bmat*1, which*2
       integer           ido, n, nx, nev, ncv, lworkl, info, ierr,
      &                  j, ishfts, maxitr, mode1, nconv
-      Complex 
+      Complex
      &                  sigma
-      Real 
+      Real
      &                  tol
       logical           rvec
 c
@@ -137,9 +137,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                  scnrm2, slapy2
-      external          scnrm2, caxpy, slapy2 
+      external          scnrm2, caxpy, slapy2
 c
 c     %-----------------------%
 c     | Executable Statements |
@@ -158,7 +158,7 @@ c
       include 'debug.h'
       ndigit = -3
       logfil = 6
-      mcaitr = 0 
+      mcaitr = 0
       mcapps = 0
       mcaupd = 1
       mcaup2 = 0
@@ -169,16 +169,16 @@ c     %-------------------------------------------------%
 c     | The following sets dimensions for this problem. |
 c     %-------------------------------------------------%
 c
-      nx    = 10 
-      n     = nx*nx 
+      nx    = 10
+      n     = nx*nx
 c
 c     %-----------------------------------------------%
-c     |                                               | 
-c     | Specifications for ARPACK usage are set       | 
+c     |                                               |
+c     | Specifications for ARPACK usage are set       |
 c     | below:                                        |
 c     |                                               |
-c     |    1) NEV = 4  asks for 4 eigenvalues to be   |  
-c     |       computed.                               | 
+c     |    1) NEV = 4  asks for 4 eigenvalues to be   |
+c     |       computed.                               |
 c     |                                               |
 c     |    2) NCV = 20 sets the length of the Arnoldi |
 c     |       factorization                           |
@@ -190,7 +190,7 @@ c     |    4) Ask for the NEV eigenvalues of          |
 c     |       largest magnitude                       |
 c     |         (indicated by which = 'LM')           |
 c     |       See documentation in CNAUPD for the     |
-c     |       other options SM, LR, SR, LI, SI.       | 
+c     |       other options SM, LR, SR, LI, SI.       |
 c     |                                               |
 c     | Note: NEV and NCV must satisfy the following  |
 c     | conditions:                                   |
@@ -200,7 +200,7 @@ c     |                                               |
 c     %-----------------------------------------------%
 c
       nev   = 4
-      ncv   = 20 
+      ncv   = 20
       bmat  = 'I'
       which = 'LM'
 c
@@ -234,26 +234,26 @@ c     |      used to specify actions to be taken on return  |
 c     |      from CNAUPD. (see usage below)                 |
 c     |                                                     |
 c     |      It MUST initially be set to 0 before the first |
-c     |      call to CNAUPD.                                | 
+c     |      call to CNAUPD.                                |
 c     |                                                     |
 c     | INFO on entry specifies starting vector information |
 c     |      and on return indicates error codes            |
 c     |                                                     |
-c     |      Initially, setting INFO=0 indicates that a     | 
+c     |      Initially, setting INFO=0 indicates that a     |
 c     |      random starting vector is requested to         |
 c     |      start the ARNOLDI iteration.  Setting INFO to  |
 c     |      a nonzero value on the initial call is used    |
 c     |      if you want to specify your own starting       |
-c     |      vector (This vector must be placed in RESID).  | 
+c     |      vector (This vector must be placed in RESID).  |
 c     |                                                     |
-c     | The work array WORKL is used in CNAUPD as           | 
+c     | The work array WORKL is used in CNAUPD as           |
 c     | workspace.  Its dimension LWORKL is set as          |
 c     | illustrated below.                                  |
 c     |                                                     |
 c     %-----------------------------------------------------%
 c
-      lworkl  = 3*ncv**2+5*ncv 
-      tol    = 0.0 
+      lworkl  = 3*ncv**2+5*ncv
+      tol    = 0.0
       ido    = 0
       info   = 0
 c
@@ -274,19 +274,19 @@ c
       mode1 = 1
 c
       iparam(1) = ishfts
-c                
+c
       iparam(3) = maxitr
-c                  
+c
       iparam(7) = mode1
 c
 c     %------------------------------------------------%
-c     | M A I N   L O O P (Reverse Communication Loop) | 
+c     | M A I N   L O O P (Reverse Communication Loop) |
 c     %------------------------------------------------%
 c
  10   continue
-c   
+c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine CNAUPD and take | 
+c        | Repeatedly call the routine CNAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
@@ -308,11 +308,11 @@ c           | matrix vector multiplication routine here |
 c           | that takes workd(ipntr(1)) as the input   |
 c           | vector x , and returns the resulting      |
 c           | matrix-vector product y = A*x in the      |
-c           | array workd(ipntr(2)).                    | 
+c           | array workd(ipntr(2)).                    |
 c           %-------------------------------------------%
 c
             call av (nx, workd(ipntr(1)), workd(ipntr(2)))
-c 
+c
 c           %-----------------------------------------%
 c           | L O O P   B A C K to call CNAUPD again. |
 c           %-----------------------------------------%
@@ -320,7 +320,7 @@ c
             go to 10
 c
          endif
-c 
+c
 c     %----------------------------------------%
 c     | Either we have convergence or there is |
 c     | an error.                              |
@@ -338,16 +338,16 @@ c
          print *, ' Check the documentation of _naupd'
          print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using CNEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may be also computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        |                                           |
 c        | The routine CNEUPD now called to do this  |
 c        | post processing (Other modes may require  |
@@ -355,7 +355,7 @@ c        | more complicated post processing than     |
 c        | mode1.)                                   |
 c        |                                           |
 c        %-------------------------------------------%
-c           
+c
          rvec = .true.
 c
          call cneupd (rvec, 'A', select, D, V, ldv, sigma,
@@ -429,11 +429,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, '_NSIMP '
@@ -444,8 +444,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -461,7 +461,7 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector subroutine
@@ -471,22 +471,22 @@ c     discretized using centered difference.
 c
       subroutine av (nx, v, w)
       integer           nx, j, lo
-      Complex          
+      Complex
      &                  v(nx*nx), w(nx*nx), one, h2
       parameter         (one = (1.0E+0, 0.0E+0) )
       external          caxpy
 c
-c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block 
+c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block
 c     tridiagonal matrix
 c
-c                  | T -I          | 
+c                  | T -I          |
 c                  |-I  T -I       |
 c             OP = |   -I  T       |
 c                  |        ...  -I|
 c                  |           -I T|
 c
-c     derived from the standard central difference discretization 
-c     of the 2-dimensional convection-diffusion operator 
+c     derived from the standard central difference discretization
+c     of the 2-dimensional convection-diffusion operator
 c                  (Laplacian u) + rho*(du/dx)
 c     on the unit squqre with zero boundary condition.
 c
@@ -503,7 +503,7 @@ c
          call tv(nx, v(lo+1), w(lo+1))
          call caxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1)
          call caxpy(nx, -one/h2, v(lo+nx+1), 1, w(lo+1), 1)
-  10  continue 
+  10  continue
 c
       lo = (nx-1)*nx
       call tv(nx, v(lo+1), w(lo+1))
@@ -514,29 +514,29 @@ c
 c=========================================================================
       subroutine tv (nx, x, y)
 c
-      integer           nx, j 
-      Complex 
+      integer           nx, j
+      Complex
      &                  x(nx), y(nx), h, h2, dd, dl, du
 c
-      Complex 
+      Complex
      &                  one, rho
-      parameter         (one = (1.0E+0, 0.0E+0) , 
+      parameter         (one = (1.0E+0, 0.0E+0) ,
      &                   rho = (1.0E+2, 0.0E+0) )
 c
 c     Compute the matrix vector multiplication y<---T*x
-c     where T is a nx by nx tridiagonal matrix with DD on the 
+c     where T is a nx by nx tridiagonal matrix with DD on the
 c     diagonal, DL on the subdiagonal, and DU on the superdiagonal
-c     
+c
       h   = one / cmplx(nx+1)
       h2  = h*h
       dd  = (4.0E+0, 0.0E+0)  / h2
       dl  = -one/h2 - (5.0E-1, 0.0E+0) *rho/h
       du  = -one/h2 + (5.0E-1, 0.0E+0) *rho/h
-c 
+c
       y(1) =  dd*x(1) + du*x(2)
       do 10 j = 2,nx-1
-         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 
- 10   continue 
-      y(nx) =  dl*x(nx-1) + dd*x(nx) 
+         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1)
+ 10   continue
+      y(nx) =  dl*x(nx-1) + dd*x(nx)
       return
       end

EXAMPLES/SIMPLE/dnsimp.f

@@ -45,7 +45,7 @@ c
 c\Example-1
 c     ... Suppose we want to solve A*x = lambda*x in regular mode,
 c         where A is obtained from the standard central difference
-c         discretization of the convection-diffusion operator 
+c         discretization of the convection-diffusion operator
 c                 (Laplacian u) + rho*(du / dx)
 c         on the unit square, with zero Dirichlet boundary condition.
 c
@@ -63,7 +63,7 @@ c     dlapy2  LAPACK routine to compute sqrt(x**2+y**2) carefully.
 c     daxpy   Level 1 BLAS that computes y <- alpha*x+y.
 c     dnrm2   Level 1 BLAS that computes the norm of a vector.
 c     av      Matrix vector multiplication routine that computes A*x.
-c     tv      Matrix vector multiplication routine that computes T*x, 
+c     tv      Matrix vector multiplication routine that computes T*x,
 c             where T is a tridiagonal matrix.  It is used in routine
 c             av.
 c
@@ -117,9 +117,9 @@ c
       integer           iparam(11), ipntr(14)
       logical           select(maxncv)
       Double precision
-     &                  ax(maxn), d(maxncv,3), resid(maxn), 
-     &                  v(ldv,maxncv), workd(3*maxn), 
-     &                  workev(3*maxncv), 
+     &                  ax(maxn), d(maxncv,3), resid(maxn),
+     &                  v(ldv,maxncv), workd(3*maxn),
+     &                  workev(3*maxncv),
      &                  workl(3*maxncv*maxncv+6*maxncv)
 c
 c     %---------------%
@@ -147,7 +147,7 @@ c     %-----------------------------%
 c
       Double precision
      &                  dlapy2, dnrm2
-      external          dlapy2, dnrm2, daxpy 
+      external          dlapy2, dnrm2, daxpy
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -183,8 +183,8 @@ c     %-------------------------------------------------%
 c     | The following sets dimensions for this problem. |
 c     %-------------------------------------------------%
 c
-      nx    = 10 
-      n     = nx*nx 
+      nx    = 10
+      n     = nx*nx
 c
 c     %-----------------------------------------------%
 c     |                                               |
@@ -266,8 +266,8 @@ c     | illustrated below.                                  |
 c     |                                                     |
 c     %-----------------------------------------------------%
 c
-      lworkl  = 3*ncv**2+6*ncv 
-      tol    = zero 
+      lworkl  = 3*ncv**2+6*ncv
+      tol    = zero
       ido    = 0
       info   = 0
 c
@@ -294,7 +294,7 @@ c
       iparam(7) = mode1
 c
 c     %-------------------------------------------%
-c     | M A I N   L O O P (Reverse communication) | 
+c     | M A I N   L O O P (Reverse communication) |
 c     %-------------------------------------------%
 c
  10   continue
@@ -306,8 +306,8 @@ c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call dnaupd ( ido, bmat, n, which, nev, tol, resid, ncv, 
-     &                 v, ldv, iparam, ipntr, workd, workl, lworkl, 
+         call dnaupd ( ido, bmat, n, which, nev, tol, resid, ncv,
+     &                 v, ldv, iparam, ipntr, workd, workl, lworkl,
      &                 info )
 c
          if (ido .eq. -1 .or. ido .eq. 1) then
@@ -319,7 +319,7 @@ c           | The user should supply his/her own        |
 c           | matrix vector multiplication routine here |
 c           | that takes workd(ipntr(1)) as the input   |
 c           | vector, and return the matrix vector      |
-c           | product to workd(ipntr(2)).               | 
+c           | product to workd(ipntr(2)).               |
 c           %-------------------------------------------%
 c
             call av (nx, workd(ipntr(1)), workd(ipntr(2)))
@@ -349,7 +349,7 @@ c
          print *, ' Check the documentation of _naupd'
          print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
@@ -369,8 +369,8 @@ c        %-------------------------------------------%
 c
          rvec = .true.
 c
-         call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv, 
-     &        sigmar, sigmai, workev, bmat, n, which, nev, tol, 
+         call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv,
+     &        sigmar, sigmai, workev, bmat, n, which, nev, tol,
      &        resid, ncv, v, ldv, iparam, ipntr, workd, workl,
      &        lworkl, ierr )
 c
@@ -472,11 +472,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _NSIMP '
@@ -487,8 +487,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -504,37 +504,37 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector subroutine
 c
-c     The matrix used is the 2 dimensional convection-diffusion 
+c     The matrix used is the 2 dimensional convection-diffusion
 c     operator discretized using central difference.
 c
       subroutine av (nx, v, w)
       integer           nx, j, lo
-      Double precision         
+      Double precision
      &                  v(nx*nx), w(nx*nx), one, h2
       parameter         (one = 1.0D+0)
       external          daxpy, tv
 c
-c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block 
+c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block
 c     tridiagonal matrix
 c
-c                  | T -I          | 
+c                  | T -I          |
 c                  |-I  T -I       |
 c             OP = |   -I  T       |
 c                  |        ...  -I|
 c                  |           -I T|
 c
-c     derived from the standard central difference discretization 
-c     of the 2 dimensional convection-diffusion operator 
-c     (Laplacian u) + rho*(du/dx) on a unit square with zero boundary 
+c     derived from the standard central difference discretization
+c     of the 2 dimensional convection-diffusion operator
+c     (Laplacian u) + rho*(du/dx) on a unit square with zero boundary
 c     condition.
 c
-c     When rho*h/2 <= 1, the discrete convection-diffusion operator 
-c     has real eigenvalues.  When rho*h/2 > 1, it has complex 
+c     When rho*h/2 <= 1, the discrete convection-diffusion operator
+c     has real eigenvalues.  When rho*h/2 > 1, it has complex
 c     eigenvalues.
 c
 c     The subroutine TV is called to computed y<---T*x.
@@ -550,7 +550,7 @@ c
          call tv(nx, v(lo+1), w(lo+1))
          call daxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1)
          call daxpy(nx, -one/h2, v(lo+nx+1), 1, w(lo+1), 1)
-  10  continue 
+  10  continue
 c
       lo = (nx-1)*nx
       call tv(nx, v(lo+1), w(lo+1))
@@ -561,7 +561,7 @@ c
 c=========================================================================
       subroutine tv (nx, x, y)
 c
-      integer           nx, j 
+      integer           nx, j
       Double precision
      &                  x(nx), y(nx), h, dd, dl, du, h2
 c
@@ -570,23 +570,23 @@ c
       parameter         (one = 1.0D+0, rho = 1.0D+2)
 c
 c     Compute the matrix vector multiplication y<---T*x
-c     where T is a nx by nx tridiagonal matrix with DD on the 
+c     where T is a nx by nx tridiagonal matrix with DD on the
 c     diagonal, DL on the subdiagonal, and DU on the superdiagonal.
 c
-c     When rho*h/2 <= 1, the discrete convection-diffusion operator 
-c     has real eigenvalues.  When rho*h/2 > 1, it has complex 
+c     When rho*h/2 <= 1, the discrete convection-diffusion operator
+c     has real eigenvalues.  When rho*h/2 > 1, it has complex
 c     eigenvalues.
 c
       h   = one / dble(nx+1)
       h2  = h*h
-      dd  = 4.0D+0 / h2 
+      dd  = 4.0D+0 / h2
       dl  = -one/h2 - 5.0D-1*rho/h
       du  = -one/h2 + 5.0D-1*rho/h
-c 
+c
       y(1) =  dd*x(1) + du*x(2)
       do 10 j = 2,nx-1
-         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 
- 10   continue 
-      y(nx) =  dl*x(nx-1) + dd*x(nx) 
+         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1)
+ 10   continue
+      y(nx) =  dl*x(nx-1) + dd*x(nx)
       return
       end

EXAMPLES/SIMPLE/dssimp.f

@@ -1,26 +1,26 @@
       program dssimp
 c
-c     This example program is intended to illustrate the 
-c     simplest case of using ARPACK in considerable detail.  
+c     This example program is intended to illustrate the
+c     simplest case of using ARPACK in considerable detail.
 c     This code may be used to understand basic usage of ARPACK
-c     and as a template for creating an interface to ARPACK.  
-c   
-c     This code shows how to use ARPACK to find a few eigenvalues 
-c     (lambda) and corresponding eigenvectors (x) for the standard 
+c     and as a template for creating an interface to ARPACK.
+c
+c     This code shows how to use ARPACK to find a few eigenvalues
+c     (lambda) and corresponding eigenvectors (x) for the standard
 c     eigenvalue problem:
-c          
+c
 c                        A*x = lambda*x
-c 
+c
 c     where A is an n by n real symmetric matrix.
 c
-c     The main points illustrated here are 
+c     The main points illustrated here are
 c
-c        1) How to declare sufficient memory to find NEV 
+c        1) How to declare sufficient memory to find NEV
 c           eigenvalues of largest magnitude.  Other options
 c           are available.
 c
-c        2) Illustration of the reverse communication interface 
-c           needed to utilize the top level ARPACK routine DSAUPD 
+c        2) Illustration of the reverse communication interface
+c           needed to utilize the top level ARPACK routine DSAUPD
 c           that computes the quantities needed to construct
 c           the desired eigenvalues and eigenvectors(if requested).
 c
@@ -28,8 +28,8 @@ c        3) How to extract the desired eigenvalues and eigenvectors
 c           using the ARPACK routine DSEUPD.
 c
 c     The only thing that must be supplied in order to use this
-c     routine on your problem is to change the array dimensions 
-c     appropriately, to specify WHICH eigenvalues you want to compute 
+c     routine on your problem is to change the array dimensions
+c     appropriately, to specify WHICH eigenvalues you want to compute
 c     and to supply a matrix-vector product
 c
 c                         w <-  Av
@@ -39,7 +39,7 @@ c
 c     Once usage of this routine is understood, you may wish to explore
 c     the other available options to improve convergence, to solve generalized
 c     problems, etc.  Look at the file ex-sym.doc in DOCUMENTS directory.
-c     This codes implements  
+c     This codes implements
 c
 c\Example-1
 c     ... Suppose we want to solve A*x = lambda*x in regular mode,
@@ -101,7 +101,7 @@ c     | MAXNCV: Maximum NCV allowed.                         |
 c     %------------------------------------------------------%
 c
       integer          maxn, maxnev, maxncv, ldv
-      parameter       (maxn=256, maxnev=10, maxncv=25, 
+      parameter       (maxn=256, maxnev=10, maxncv=25,
      $                 ldv=maxn )
 c
 c     %--------------%
@@ -123,7 +123,7 @@ c
       integer          ido, n, nev, ncv, lworkl, info, ierr,
      &                 j, nx, ishfts, maxitr, mode1, nconv
       logical          rvec
-      Double precision      
+      Double precision
      &                 tol, sigma
 c
 c     %------------%
@@ -133,12 +133,12 @@ c
       Double precision
      &                 zero
       parameter        (zero = 0.0D+0)
-c  
+c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision           
+      Double precision
      &                 dnrm2
       external         dnrm2, daxpy
 c
@@ -166,13 +166,13 @@ c
       ndigit = -3
       logfil = 6
       msgets = 0
-      msaitr = 0 
+      msaitr = 0
       msapps = 0
       msaupd = 1
       msaup2 = 0
       mseigt = 0
       mseupd = 0
-c     
+c
 c     %-------------------------------------------------%
 c     | The following sets dimensions for this problem. |
 c     %-------------------------------------------------%
@@ -181,12 +181,12 @@ c
       n = nx*nx
 c
 c     %-----------------------------------------------%
-c     |                                               | 
-c     | Specifications for ARPACK usage are set       | 
+c     |                                               |
+c     | Specifications for ARPACK usage are set       |
 c     | below:                                        |
 c     |                                               |
-c     |    1) NEV = 4  asks for 4 eigenvalues to be   |  
-c     |       computed.                               | 
+c     |    1) NEV = 4  asks for 4 eigenvalues to be   |
+c     |       computed.                               |
 c     |                                               |
 c     |    2) NCV = 20 sets the length of the Arnoldi |
 c     |       factorization                           |
@@ -198,7 +198,7 @@ c     |    4) Ask for the NEV eigenvalues of          |
 c     |       largest magnitude                       |
 c     |         (indicated by which = 'LM')           |
 c     |       See documentation in DSAUPD for the     |
-c     |       other options SM, LA, SA, LI, SI.       | 
+c     |       other options SM, LA, SA, LI, SI.       |
 c     |                                               |
 c     | Note: NEV and NCV must satisfy the following  |
 c     | conditions:                                   |
@@ -207,7 +207,7 @@ c     |          NEV + 1 <= NCV <= MAXNCV             |
 c     %-----------------------------------------------%
 c
       nev   = 4
-      ncv   = 20 
+      ncv   = 20
       bmat  = 'I'
       which = 'LM'
 c
@@ -241,26 +241,26 @@ c     |      used to specify actions to be taken on return  |
 c     |      from DSAUPD. (See usage below.)                |
 c     |                                                     |
 c     |      It MUST initially be set to 0 before the first |
-c     |      call to DSAUPD.                                | 
+c     |      call to DSAUPD.                                |
 c     |                                                     |
 c     | INFO on entry specifies starting vector information |
 c     |      and on return indicates error codes            |
 c     |                                                     |
-c     |      Initially, setting INFO=0 indicates that a     | 
+c     |      Initially, setting INFO=0 indicates that a     |
 c     |      random starting vector is requested to         |
 c     |      start the ARNOLDI iteration.  Setting INFO to  |
 c     |      a nonzero value on the initial call is used    |
 c     |      if you want to specify your own starting       |
-c     |      vector (This vector must be placed in RESID.)  | 
+c     |      vector (This vector must be placed in RESID.)  |
 c     |                                                     |
-c     | The work array WORKL is used in DSAUPD as           | 
+c     | The work array WORKL is used in DSAUPD as           |
 c     | workspace.  Its dimension LWORKL is set as          |
 c     | illustrated below.                                  |
 c     |                                                     |
 c     %-----------------------------------------------------%
 c
       lworkl = ncv*(ncv+8)
-      tol = zero 
+      tol = zero
       info = 0
       ido = 0
 c
@@ -277,13 +277,13 @@ c     | DSAUPD.                                           |
 c     %---------------------------------------------------%
 c
       ishfts = 1
-      maxitr = 300 
+      maxitr = 300
       mode1 = 1
 c
       iparam(1) = ishfts
-c                
+c
       iparam(3) = maxitr
-c                  
+c
       iparam(7) = mode1
 c
 c     %------------------------------------------------%
@@ -293,13 +293,13 @@ c
  10   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine DSAUPD and take | 
+c        | Repeatedly call the routine DSAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call dsaupd ( ido, bmat, n, which, nev, tol, resid, 
+         call dsaupd ( ido, bmat, n, which, nev, tol, resid,
      &                 ncv, v, ldv, iparam, ipntr, workd, workl,
      &                 lworkl, info )
 c
@@ -323,7 +323,7 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-         end if 
+         end if
 c
 c     %----------------------------------------%
 c     | Either we have convergence or there is |
@@ -342,16 +342,16 @@ c
          print *, ' Check documentation in _saupd '
          print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using DSEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may be also computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        |                                           |
 c        | The routine DSEUPD now called to do this  |
 c        | post processing (Other modes may require  |
@@ -359,11 +359,11 @@ c        | more complicated post processing than     |
 c        | mode1.)                                   |
 c        |                                           |
 c        %-------------------------------------------%
-c           
+c
           rvec = .true.
 c
-          call dseupd ( rvec, 'All', select, d, v, ldv, sigma, 
-     &         bmat, n, which, nev, tol, resid, ncv, v, ldv, 
+          call dseupd ( rvec, 'All', select, d, v, ldv, sigma,
+     &         bmat, n, which, nev, tol, resid, ncv, v, ldv,
      &         iparam, ipntr, workd, workl, lworkl, ierr )
 c
 c         %----------------------------------------------%
@@ -431,11 +431,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
           else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-          end if      
+          end if
 c
           print *, ' '
           print *, ' _SSIMP '
@@ -446,8 +446,8 @@ c
           print *, ' The number of Arnoldi vectors generated',
      &             ' (NCV) is ', ncv
           print *, ' What portion of the spectrum: ', which
-          print *, ' The number of converged Ritz values is ', 
-     &               nconv 
+          print *, ' The number of converged Ritz values is ',
+     &               nconv
           print *, ' The number of Implicit Arnoldi update',
      &             ' iterations taken is ', iparam(3)
           print *, ' The number of OP*x is ', iparam(9)
@@ -463,17 +463,17 @@ c
  9000 continue
 c
       end
-c 
+c
 c ------------------------------------------------------------------
 c     matrix vector subroutine
 c
 c     The matrix used is the 2 dimensional discrete Laplacian on unit
 c     square with zero Dirichlet boundary condition.
 c
-c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block 
+c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block
 c     tridiagonal matrix
 c
-c                  | T -I          | 
+c                  | T -I          |
 c                  |-I  T -I       |
 c             OP = |   -I  T       |
 c                  |        ...  -I|
@@ -485,7 +485,7 @@ c
       integer           nx, j, lo, n2
       Double precision
      &                  v(nx*nx), w(nx*nx), one, h2
-      parameter         ( one = 1.0D+0 ) 
+      parameter         ( one = 1.0D+0 )
 c
       call tv(nx,v(1),w(1))
       call daxpy(nx, -one, v(nx+1), 1, w(1), 1)
@@ -495,7 +495,7 @@ c
          call tv(nx, v(lo+1), w(lo+1))
          call daxpy(nx, -one, v(lo-nx+1), 1, w(lo+1), 1)
          call daxpy(nx, -one, v(lo+nx+1), 1, w(lo+1), 1)
-  10  continue 
+  10  continue
 c
       lo = (nx-1)*nx
       call tv(nx, v(lo+1), w(lo+1))
@@ -512,7 +512,7 @@ c
 c-------------------------------------------------------------------
       subroutine tv (nx, x, y)
 c
-      integer           nx, j 
+      integer           nx, j
       Double precision
      &                  x(nx), y(nx), dd, dl, du
 c
@@ -521,19 +521,19 @@ c
       parameter         (one = 1.0D+0, four = 4.0D+0)
 c
 c     Compute the matrix vector multiplication y<---T*x
-c     where T is a nx by nx tridiagonal matrix with DD on the 
+c     where T is a nx by nx tridiagonal matrix with DD on the
 c     diagonal, DL on the subdiagonal, and DU on the superdiagonal.
-c     
 c
-      dd  = four 
-      dl  = -one 
+c
+      dd  = four
+      dl  = -one
       du  = -one
-c 
+c
       y(1) =  dd*x(1) + du*x(2)
       do 10 j = 2,nx-1
-         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 
- 10   continue 
-      y(nx) =  dl*x(nx-1) + dd*x(nx) 
+         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1)
+ 10   continue
+      y(nx) =  dl*x(nx-1) + dd*x(nx)
       return
       end
 

EXAMPLES/SIMPLE/makefile

@@ -1,27 +0,0 @@
-#
-# makefile to run simple examples of the reverse communication
-# protocol.
-#
-# Modify if ARPACK library was built somewhere else.
-#
-#\SCCS Information: @(#) 
-# FILE: makefile   SID: 2.2   DATE OF SID: 9/24/96   RELEASE: 2
-#
-include ../../ARmake.inc
-#
-# simple drivers
-#
-simple: sssimp dssimp snsimp dnsimp cnsimp znsimp
-#
-sssimp: sssimp.o
-	$(FC) $(FFLAGS) sssimp.o $(ALIBS) -o sssimp
-dssimp: dssimp.o
-	$(FC) $(FFLAGS) dssimp.o $(ALIBS) -o dssimp
-snsimp: snsimp.o
-	$(FC) $(FFLAGS) snsimp.o $(ALIBS) -o snsimp
-dnsimp: dnsimp.o
-	$(FC) $(FFLAGS) dnsimp.o $(ALIBS) -o dnsimp
-cnsimp: cnsimp.o
-	$(FC) $(FFLAGS) cnsimp.o $(ALIBS) -o cnsimp 
-znsimp: znsimp.o
-	$(FC) $(FFLAGS) znsimp.o $(ALIBS) -o znsimp  

EXAMPLES/SIMPLE/snsimp.f

@@ -45,7 +45,7 @@ c
 c\Example-1
 c     ... Suppose we want to solve A*x = lambda*x in regular mode,
 c         where A is obtained from the standard central difference
-c         discretization of the convection-diffusion operator 
+c         discretization of the convection-diffusion operator
 c                 (Laplacian u) + rho*(du / dx)
 c         on the unit square, with zero Dirichlet boundary condition.
 c
@@ -63,7 +63,7 @@ c     slapy2  LAPACK routine to compute sqrt(x**2+y**2) carefully.
 c     saxpy   Level 1 BLAS that computes y <- alpha*x+y.
 c     snrm2   Level 1 BLAS that computes the norm of a vector.
 c     av      Matrix vector multiplication routine that computes A*x.
-c     tv      Matrix vector multiplication routine that computes T*x, 
+c     tv      Matrix vector multiplication routine that computes T*x,
 c             where T is a tridiagonal matrix.  It is used in routine
 c             av.
 c
@@ -117,9 +117,9 @@ c
       integer           iparam(11), ipntr(14)
       logical           select(maxncv)
       Real
-     &                  ax(maxn), d(maxncv,3), resid(maxn), 
-     &                  v(ldv,maxncv), workd(3*maxn), 
-     &                  workev(3*maxncv), 
+     &                  ax(maxn), d(maxncv,3), resid(maxn),
+     &                  v(ldv,maxncv), workd(3*maxn),
+     &                  workev(3*maxncv),
      &                  workl(3*maxncv*maxncv+6*maxncv)
 c
 c     %---------------%
@@ -147,7 +147,7 @@ c     %-----------------------------%
 c
       Real
      &                  slapy2, snrm2
-      external          slapy2, snrm2, saxpy 
+      external          slapy2, snrm2, saxpy
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -183,8 +183,8 @@ c     %-------------------------------------------------%
 c     | The following sets dimensions for this problem. |
 c     %-------------------------------------------------%
 c
-      nx    = 10 
-      n     = nx*nx 
+      nx    = 10
+      n     = nx*nx
 c
 c     %-----------------------------------------------%
 c     |                                               |
@@ -266,8 +266,8 @@ c     | illustrated below.                                  |
 c     |                                                     |
 c     %-----------------------------------------------------%
 c
-      lworkl  = 3*ncv**2+6*ncv 
-      tol    = zero 
+      lworkl  = 3*ncv**2+6*ncv
+      tol    = zero
       ido    = 0
       info   = 0
 c
@@ -294,7 +294,7 @@ c
       iparam(7) = mode1
 c
 c     %-------------------------------------------%
-c     | M A I N   L O O P (Reverse communication) | 
+c     | M A I N   L O O P (Reverse communication) |
 c     %-------------------------------------------%
 c
  10   continue
@@ -306,8 +306,8 @@ c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call snaupd ( ido, bmat, n, which, nev, tol, resid, ncv, 
-     &                 v, ldv, iparam, ipntr, workd, workl, lworkl, 
+         call snaupd ( ido, bmat, n, which, nev, tol, resid, ncv,
+     &                 v, ldv, iparam, ipntr, workd, workl, lworkl,
      &                 info )
 c
          if (ido .eq. -1 .or. ido .eq. 1) then
@@ -319,7 +319,7 @@ c           | The user should supply his/her own        |
 c           | matrix vector multiplication routine here |
 c           | that takes workd(ipntr(1)) as the input   |
 c           | vector, and return the matrix vector      |
-c           | product to workd(ipntr(2)).               | 
+c           | product to workd(ipntr(2)).               |
 c           %-------------------------------------------%
 c
             call av (nx, workd(ipntr(1)), workd(ipntr(2)))
@@ -349,7 +349,7 @@ c
          print *, ' Check the documentation of _naupd'
          print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
@@ -369,8 +369,8 @@ c        %-------------------------------------------%
 c
          rvec = .true.
 c
-         call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv, 
-     &        sigmar, sigmai, workev, bmat, n, which, nev, tol, 
+         call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv,
+     &        sigmar, sigmai, workev, bmat, n, which, nev, tol,
      &        resid, ncv, v, ldv, iparam, ipntr, workd, workl,
      &        lworkl, ierr )
 c
@@ -472,11 +472,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _NSIMP '
@@ -487,8 +487,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -504,37 +504,37 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector subroutine
 c
-c     The matrix used is the 2 dimensional convection-diffusion 
+c     The matrix used is the 2 dimensional convection-diffusion
 c     operator discretized using central difference.
 c
       subroutine av (nx, v, w)
       integer           nx, j, lo
-      Real         
+      Real
      &                  v(nx*nx), w(nx*nx), one, h2
       parameter         (one = 1.0E+0)
       external          saxpy, tv
 c
-c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block 
+c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block
 c     tridiagonal matrix
 c
-c                  | T -I          | 
+c                  | T -I          |
 c                  |-I  T -I       |
 c             OP = |   -I  T       |
 c                  |        ...  -I|
 c                  |           -I T|
 c
-c     derived from the standard central difference discretization 
-c     of the 2 dimensional convection-diffusion operator 
-c     (Laplacian u) + rho*(du/dx) on a unit square with zero boundary 
+c     derived from the standard central difference discretization
+c     of the 2 dimensional convection-diffusion operator
+c     (Laplacian u) + rho*(du/dx) on a unit square with zero boundary
 c     condition.
 c
-c     When rho*h/2 <= 1, the discrete convection-diffusion operator 
-c     has real eigenvalues.  When rho*h/2 > 1, it has complex 
+c     When rho*h/2 <= 1, the discrete convection-diffusion operator
+c     has real eigenvalues.  When rho*h/2 > 1, it has complex
 c     eigenvalues.
 c
 c     The subroutine TV is called to computed y<---T*x.
@@ -550,7 +550,7 @@ c
          call tv(nx, v(lo+1), w(lo+1))
          call saxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1)
          call saxpy(nx, -one/h2, v(lo+nx+1), 1, w(lo+1), 1)
-  10  continue 
+  10  continue
 c
       lo = (nx-1)*nx
       call tv(nx, v(lo+1), w(lo+1))
@@ -561,7 +561,7 @@ c
 c=========================================================================
       subroutine tv (nx, x, y)
 c
-      integer           nx, j 
+      integer           nx, j
       Real
      &                  x(nx), y(nx), h, dd, dl, du, h2
 c
@@ -570,23 +570,23 @@ c
       parameter         (one = 1.0E+0, rho = 1.0E+2)
 c
 c     Compute the matrix vector multiplication y<---T*x
-c     where T is a nx by nx tridiagonal matrix with DD on the 
+c     where T is a nx by nx tridiagonal matrix with DD on the
 c     diagonal, DL on the subdiagonal, and DU on the superdiagonal.
 c
-c     When rho*h/2 <= 1, the discrete convection-diffusion operator 
-c     has real eigenvalues.  When rho*h/2 > 1, it has complex 
+c     When rho*h/2 <= 1, the discrete convection-diffusion operator
+c     has real eigenvalues.  When rho*h/2 > 1, it has complex
 c     eigenvalues.
 c
       h   = one / real(nx+1)
       h2  = h*h
-      dd  = 4.0E+0 / h2 
+      dd  = 4.0E+0 / h2
       dl  = -one/h2 - 5.0E-1*rho/h
       du  = -one/h2 + 5.0E-1*rho/h
-c 
+c
       y(1) =  dd*x(1) + du*x(2)
       do 10 j = 2,nx-1
-         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 
- 10   continue 
-      y(nx) =  dl*x(nx-1) + dd*x(nx) 
+         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1)
+ 10   continue
+      y(nx) =  dl*x(nx-1) + dd*x(nx)
       return
       end

EXAMPLES/SIMPLE/sssimp.f

@@ -1,26 +1,26 @@
       program sssimp
 c
-c     This example program is intended to illustrate the 
-c     simplest case of using ARPACK in considerable detail.  
+c     This example program is intended to illustrate the
+c     simplest case of using ARPACK in considerable detail.
 c     This code may be used to understand basic usage of ARPACK
-c     and as a template for creating an interface to ARPACK.  
-c   
-c     This code shows how to use ARPACK to find a few eigenvalues 
-c     (lambda) and corresponding eigenvectors (x) for the standard 
+c     and as a template for creating an interface to ARPACK.
+c
+c     This code shows how to use ARPACK to find a few eigenvalues
+c     (lambda) and corresponding eigenvectors (x) for the standard
 c     eigenvalue problem:
-c          
+c
 c                        A*x = lambda*x
-c 
+c
 c     where A is an n by n real symmetric matrix.
 c
-c     The main points illustrated here are 
+c     The main points illustrated here are
 c
-c        1) How to declare sufficient memory to find NEV 
+c        1) How to declare sufficient memory to find NEV
 c           eigenvalues of largest magnitude.  Other options
 c           are available.
 c
-c        2) Illustration of the reverse communication interface 
-c           needed to utilize the top level ARPACK routine SSAUPD 
+c        2) Illustration of the reverse communication interface
+c           needed to utilize the top level ARPACK routine SSAUPD
 c           that computes the quantities needed to construct
 c           the desired eigenvalues and eigenvectors(if requested).
 c
@@ -28,8 +28,8 @@ c        3) How to extract the desired eigenvalues and eigenvectors
 c           using the ARPACK routine SSEUPD.
 c
 c     The only thing that must be supplied in order to use this
-c     routine on your problem is to change the array dimensions 
-c     appropriately, to specify WHICH eigenvalues you want to compute 
+c     routine on your problem is to change the array dimensions
+c     appropriately, to specify WHICH eigenvalues you want to compute
 c     and to supply a matrix-vector product
 c
 c                         w <-  Av
@@ -39,7 +39,7 @@ c
 c     Once usage of this routine is understood, you may wish to explore
 c     the other available options to improve convergence, to solve generalized
 c     problems, etc.  Look at the file ex-sym.doc in DOCUMENTS directory.
-c     This codes implements  
+c     This codes implements
 c
 c\Example-1
 c     ... Suppose we want to solve A*x = lambda*x in regular mode,
@@ -101,7 +101,7 @@ c     | MAXNCV: Maximum NCV allowed.                         |
 c     %------------------------------------------------------%
 c
       integer          maxn, maxnev, maxncv, ldv
-      parameter       (maxn=256, maxnev=10, maxncv=25, 
+      parameter       (maxn=256, maxnev=10, maxncv=25,
      $                 ldv=maxn )
 c
 c     %--------------%
@@ -123,7 +123,7 @@ c
       integer          ido, n, nev, ncv, lworkl, info, ierr,
      &                 j, nx, ishfts, maxitr, mode1, nconv
       logical          rvec
-      Real      
+      Real
      &                 tol, sigma
 c
 c     %------------%
@@ -133,12 +133,12 @@ c
       Real
      &                 zero
       parameter        (zero = 0.0E+0)
-c  
+c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real           
+      Real
      &                 snrm2
       external         snrm2, saxpy
 c
@@ -166,13 +166,13 @@ c
       ndigit = -3
       logfil = 6
       msgets = 0
-      msaitr = 0 
+      msaitr = 0
       msapps = 0
       msaupd = 1
       msaup2 = 0
       mseigt = 0
       mseupd = 0
-c     
+c
 c     %-------------------------------------------------%
 c     | The following sets dimensions for this problem. |
 c     %-------------------------------------------------%
@@ -181,12 +181,12 @@ c
       n = nx*nx
 c
 c     %-----------------------------------------------%
-c     |                                               | 
-c     | Specifications for ARPACK usage are set       | 
+c     |                                               |
+c     | Specifications for ARPACK usage are set       |
 c     | below:                                        |
 c     |                                               |
-c     |    1) NEV = 4  asks for 4 eigenvalues to be   |  
-c     |       computed.                               | 
+c     |    1) NEV = 4  asks for 4 eigenvalues to be   |
+c     |       computed.                               |
 c     |                                               |
 c     |    2) NCV = 20 sets the length of the Arnoldi |
 c     |       factorization                           |
@@ -198,7 +198,7 @@ c     |    4) Ask for the NEV eigenvalues of          |
 c     |       largest magnitude                       |
 c     |         (indicated by which = 'LM')           |
 c     |       See documentation in SSAUPD for the     |
-c     |       other options SM, LA, SA, LI, SI.       | 
+c     |       other options SM, LA, SA, LI, SI.       |
 c     |                                               |
 c     | Note: NEV and NCV must satisfy the following  |
 c     | conditions:                                   |
@@ -207,7 +207,7 @@ c     |          NEV + 1 <= NCV <= MAXNCV             |
 c     %-----------------------------------------------%
 c
       nev   = 4
-      ncv   = 20 
+      ncv   = 20
       bmat  = 'I'
       which = 'LM'
 c
@@ -241,26 +241,26 @@ c     |      used to specify actions to be taken on return  |
 c     |      from SSAUPD. (See usage below.)                |
 c     |                                                     |
 c     |      It MUST initially be set to 0 before the first |
-c     |      call to SSAUPD.                                | 
+c     |      call to SSAUPD.                                |
 c     |                                                     |
 c     | INFO on entry specifies starting vector information |
 c     |      and on return indicates error codes            |
 c     |                                                     |
-c     |      Initially, setting INFO=0 indicates that a     | 
+c     |      Initially, setting INFO=0 indicates that a     |
 c     |      random starting vector is requested to         |
 c     |      start the ARNOLDI iteration.  Setting INFO to  |
 c     |      a nonzero value on the initial call is used    |
 c     |      if you want to specify your own starting       |
-c     |      vector (This vector must be placed in RESID.)  | 
+c     |      vector (This vector must be placed in RESID.)  |
 c     |                                                     |
-c     | The work array WORKL is used in SSAUPD as           | 
+c     | The work array WORKL is used in SSAUPD as           |
 c     | workspace.  Its dimension LWORKL is set as          |
 c     | illustrated below.                                  |
 c     |                                                     |
 c     %-----------------------------------------------------%
 c
       lworkl = ncv*(ncv+8)
-      tol = zero 
+      tol = zero
       info = 0
       ido = 0
 c
@@ -277,13 +277,13 @@ c     | SSAUPD.                                           |
 c     %---------------------------------------------------%
 c
       ishfts = 1
-      maxitr = 300 
+      maxitr = 300
       mode1 = 1
 c
       iparam(1) = ishfts
-c                
+c
       iparam(3) = maxitr
-c                  
+c
       iparam(7) = mode1
 c
 c     %------------------------------------------------%
@@ -293,13 +293,13 @@ c
  10   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine SSAUPD and take | 
+c        | Repeatedly call the routine SSAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call ssaupd ( ido, bmat, n, which, nev, tol, resid, 
+         call ssaupd ( ido, bmat, n, which, nev, tol, resid,
      &                 ncv, v, ldv, iparam, ipntr, workd, workl,
      &                 lworkl, info )
 c
@@ -323,7 +323,7 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-         end if 
+         end if
 c
 c     %----------------------------------------%
 c     | Either we have convergence or there is |
@@ -342,16 +342,16 @@ c
          print *, ' Check documentation in _saupd '
          print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using SSEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may be also computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        |                                           |
 c        | The routine SSEUPD now called to do this  |
 c        | post processing (Other modes may require  |
@@ -359,11 +359,11 @@ c        | more complicated post processing than     |
 c        | mode1.)                                   |
 c        |                                           |
 c        %-------------------------------------------%
-c           
+c
           rvec = .true.
 c
-          call sseupd ( rvec, 'All', select, d, v, ldv, sigma, 
-     &         bmat, n, which, nev, tol, resid, ncv, v, ldv, 
+          call sseupd ( rvec, 'All', select, d, v, ldv, sigma,
+     &         bmat, n, which, nev, tol, resid, ncv, v, ldv,
      &         iparam, ipntr, workd, workl, lworkl, ierr )
 c
 c         %----------------------------------------------%
@@ -431,11 +431,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
           else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-          end if      
+          end if
 c
           print *, ' '
           print *, ' _SSIMP '
@@ -446,8 +446,8 @@ c
           print *, ' The number of Arnoldi vectors generated',
      &             ' (NCV) is ', ncv
           print *, ' What portion of the spectrum: ', which
-          print *, ' The number of converged Ritz values is ', 
-     &               nconv 
+          print *, ' The number of converged Ritz values is ',
+     &               nconv
           print *, ' The number of Implicit Arnoldi update',
      &             ' iterations taken is ', iparam(3)
           print *, ' The number of OP*x is ', iparam(9)
@@ -463,17 +463,17 @@ c
  9000 continue
 c
       end
-c 
+c
 c ------------------------------------------------------------------
 c     matrix vector subroutine
 c
 c     The matrix used is the 2 dimensional discrete Laplacian on unit
 c     square with zero Dirichlet boundary condition.
 c
-c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block 
+c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block
 c     tridiagonal matrix
 c
-c                  | T -I          | 
+c                  | T -I          |
 c                  |-I  T -I       |
 c             OP = |   -I  T       |
 c                  |        ...  -I|
@@ -485,7 +485,7 @@ c
       integer           nx, j, lo, n2
       Real
      &                  v(nx*nx), w(nx*nx), one, h2
-      parameter         ( one = 1.0E+0 ) 
+      parameter         ( one = 1.0E+0 )
 c
       call tv(nx,v(1),w(1))
       call saxpy(nx, -one, v(nx+1), 1, w(1), 1)
@@ -495,7 +495,7 @@ c
          call tv(nx, v(lo+1), w(lo+1))
          call saxpy(nx, -one, v(lo-nx+1), 1, w(lo+1), 1)
          call saxpy(nx, -one, v(lo+nx+1), 1, w(lo+1), 1)
-  10  continue 
+  10  continue
 c
       lo = (nx-1)*nx
       call tv(nx, v(lo+1), w(lo+1))
@@ -512,7 +512,7 @@ c
 c-------------------------------------------------------------------
       subroutine tv (nx, x, y)
 c
-      integer           nx, j 
+      integer           nx, j
       Real
      &                  x(nx), y(nx), dd, dl, du
 c
@@ -521,19 +521,19 @@ c
       parameter         (one = 1.0E+0, four = 4.0E+0)
 c
 c     Compute the matrix vector multiplication y<---T*x
-c     where T is a nx by nx tridiagonal matrix with DD on the 
+c     where T is a nx by nx tridiagonal matrix with DD on the
 c     diagonal, DL on the subdiagonal, and DU on the superdiagonal.
-c     
 c
-      dd  = four 
-      dl  = -one 
+c
+      dd  = four
+      dl  = -one
       du  = -one
-c 
+c
       y(1) =  dd*x(1) + du*x(2)
       do 10 j = 2,nx-1
-         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 
- 10   continue 
-      y(nx) =  dl*x(nx-1) + dd*x(nx) 
+         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1)
+ 10   continue
+      y(nx) =  dl*x(nx-1) + dd*x(nx)
       return
       end
 

EXAMPLES/SIMPLE/znsimp.f

@@ -1,26 +1,26 @@
-      program znsimp  
+      program znsimp
 c
-c     This example program is intended to illustrate the 
-c     simplest case of using ARPACK in considerable detail.  
+c     This example program is intended to illustrate the
+c     simplest case of using ARPACK in considerable detail.
 c     This code may be used to understand basic usage of ARPACK
-c     and as a template for creating an interface to ARPACK.  
-c   
-c     This code shows how to use ARPACK to find a few eigenvalues 
-c     (lambda) and corresponding eigenvectors (x) for the standard 
+c     and as a template for creating an interface to ARPACK.
+c
+c     This code shows how to use ARPACK to find a few eigenvalues
+c     (lambda) and corresponding eigenvectors (x) for the standard
 c     eigenvalue problem:
-c          
+c
 c                        A*x = lambda*x
-c 
+c
 c     where A is a general n by n complex matrix.
 c
-c     The main points illustrated here are 
+c     The main points illustrated here are
 c
-c        1) How to declare sufficient memory to find NEV 
+c        1) How to declare sufficient memory to find NEV
 c           eigenvalues of largest magnitude.  Other options
 c           are available.
 c
-c        2) Illustration of the reverse communication interface 
-c           needed to utilize the top level ARPACK routine ZNAUPD  
+c        2) Illustration of the reverse communication interface
+c           needed to utilize the top level ARPACK routine ZNAUPD
 c           that computes the quantities needed to construct
 c           the desired eigenvalues and eigenvectors(if requested).
 c
@@ -28,8 +28,8 @@ c        3) How to extract the desired eigenvalues and eigenvectors
 c           using the ARPACK routine ZNEUPD .
 c
 c     The only thing that must be supplied in order to use this
-c     routine on your problem is to change the array dimensions 
-c     appropriately, to specify WHICH eigenvalues you want to compute 
+c     routine on your problem is to change the array dimensions
+c     appropriately, to specify WHICH eigenvalues you want to compute
 c     and to supply a matrix-vector product
 c
 c                         w <-  Av
@@ -40,7 +40,7 @@ c
 c     Once usage of this routine is understood, you may wish to explore
 c     the other available options to improve convergence, to solve generalized
 c     problems, etc.  Look at the file ex-complex.doc in DOCUMENTS directory.
-c     This codes implements  
+c     This codes implements
 c
 c
 c\Example-1
@@ -65,11 +65,11 @@ c             av.
 c
 c\Author
 c     Richard Lehoucq
-c     Danny Sorensen 
-c     Chao Yang 
-c     Dept. of Computational & 
-c     Applied Mathematics 
-c     Rice University 
+c     Danny Sorensen
+c     Chao Yang
+c     Dept. of Computational &
+c     Applied Mathematics
+c     Rice University
 c     Houston, Texas
 c
 c\SCCS Information: @(#)
@@ -112,12 +112,12 @@ c     %--------------%
 c
       integer           iparam(11), ipntr(14)
       logical           select(maxncv)
-      Complex*16 
-     &                  ax(maxn), d(maxncv), 
-     &                  v(ldv,maxncv), workd(3*maxn), 
-     &                  workev(2*maxncv), resid(maxn), 
+      Complex*16
+     &                  ax(maxn), d(maxncv),
+     &                  v(ldv,maxncv), workd(3*maxn),
+     &                  workev(2*maxncv), resid(maxn),
      &                  workl(3*maxncv*maxncv+5*maxncv)
-      Double precision  
+      Double precision
      &                  rwork(maxncv), rd(maxncv,3)
 c
 c     %---------------%
@@ -127,9 +127,9 @@ c
       character         bmat*1, which*2
       integer           ido, n, nx, nev, ncv, lworkl, info, ierr,
      &                  j, ishfts, maxitr, mode1, nconv
-      Complex*16 
+      Complex*16
      &                  sigma
-      Double precision 
+      Double precision
      &                  tol
       logical           rvec
 c
@@ -137,9 +137,9 @@ c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                  dznrm2 , dlapy2 
-      external          dznrm2 , zaxpy , dlapy2  
+      Double precision
+     &                  dznrm2 , dlapy2
+      external          dznrm2 , zaxpy , dlapy2
 c
 c     %-----------------------%
 c     | Executable Statements |
@@ -158,7 +158,7 @@ c
       include 'debug.h'
       ndigit = -3
       logfil = 6
-      mcaitr = 0 
+      mcaitr = 0
       mcapps = 0
       mcaupd = 1
       mcaup2 = 0
@@ -169,16 +169,16 @@ c     %-------------------------------------------------%
 c     | The following sets dimensions for this problem. |
 c     %-------------------------------------------------%
 c
-      nx    = 10 
-      n     = nx*nx 
+      nx    = 10
+      n     = nx*nx
 c
 c     %-----------------------------------------------%
-c     |                                               | 
-c     | Specifications for ARPACK usage are set       | 
+c     |                                               |
+c     | Specifications for ARPACK usage are set       |
 c     | below:                                        |
 c     |                                               |
-c     |    1) NEV = 4  asks for 4 eigenvalues to be   |  
-c     |       computed.                               | 
+c     |    1) NEV = 4  asks for 4 eigenvalues to be   |
+c     |       computed.                               |
 c     |                                               |
 c     |    2) NCV = 20 sets the length of the Arnoldi |
 c     |       factorization                           |
@@ -190,7 +190,7 @@ c     |    4) Ask for the NEV eigenvalues of          |
 c     |       largest magnitude                       |
 c     |         (indicated by which = 'LM')           |
 c     |       See documentation in ZNAUPD  for the     |
-c     |       other options SM, LR, SR, LI, SI.       | 
+c     |       other options SM, LR, SR, LI, SI.       |
 c     |                                               |
 c     | Note: NEV and NCV must satisfy the following  |
 c     | conditions:                                   |
@@ -200,7 +200,7 @@ c     |                                               |
 c     %-----------------------------------------------%
 c
       nev   = 4
-      ncv   = 20 
+      ncv   = 20
       bmat  = 'I'
       which = 'LM'
 c
@@ -234,26 +234,26 @@ c     |      used to specify actions to be taken on return  |
 c     |      from ZNAUPD . (see usage below)                 |
 c     |                                                     |
 c     |      It MUST initially be set to 0 before the first |
-c     |      call to ZNAUPD .                                | 
+c     |      call to ZNAUPD .                                |
 c     |                                                     |
 c     | INFO on entry specifies starting vector information |
 c     |      and on return indicates error codes            |
 c     |                                                     |
-c     |      Initially, setting INFO=0 indicates that a     | 
+c     |      Initially, setting INFO=0 indicates that a     |
 c     |      random starting vector is requested to         |
 c     |      start the ARNOLDI iteration.  Setting INFO to  |
 c     |      a nonzero value on the initial call is used    |
 c     |      if you want to specify your own starting       |
-c     |      vector (This vector must be placed in RESID).  | 
+c     |      vector (This vector must be placed in RESID).  |
 c     |                                                     |
-c     | The work array WORKL is used in ZNAUPD  as           | 
+c     | The work array WORKL is used in ZNAUPD  as           |
 c     | workspace.  Its dimension LWORKL is set as          |
 c     | illustrated below.                                  |
 c     |                                                     |
 c     %-----------------------------------------------------%
 c
-      lworkl  = 3*ncv**2+5*ncv 
-      tol    = 0.0 
+      lworkl  = 3*ncv**2+5*ncv
+      tol    = 0.0
       ido    = 0
       info   = 0
 c
@@ -274,19 +274,19 @@ c
       mode1 = 1
 c
       iparam(1) = ishfts
-c                
+c
       iparam(3) = maxitr
-c                  
+c
       iparam(7) = mode1
 c
 c     %------------------------------------------------%
-c     | M A I N   L O O P (Reverse Communication Loop) | 
+c     | M A I N   L O O P (Reverse Communication Loop) |
 c     %------------------------------------------------%
 c
  10   continue
-c   
+c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine ZNAUPD  and take | 
+c        | Repeatedly call the routine ZNAUPD  and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
@@ -308,11 +308,11 @@ c           | matrix vector multiplication routine here |
 c           | that takes workd(ipntr(1)) as the input   |
 c           | vector x , and returns the resulting      |
 c           | matrix-vector product y = A*x in the      |
-c           | array workd(ipntr(2)).                    | 
+c           | array workd(ipntr(2)).                    |
 c           %-------------------------------------------%
 c
             call av (nx, workd(ipntr(1)), workd(ipntr(2)))
-c 
+c
 c           %-----------------------------------------%
 c           | L O O P   B A C K to call ZNAUPD  again. |
 c           %-----------------------------------------%
@@ -320,7 +320,7 @@ c
             go to 10
 c
          endif
-c 
+c
 c     %----------------------------------------%
 c     | Either we have convergence or there is |
 c     | an error.                              |
@@ -338,16 +338,16 @@ c
          print *, ' Check the documentation of _naupd'
          print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using ZNEUPD .                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may be also computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        |                                           |
 c        | The routine ZNEUPD  now called to do this  |
 c        | post processing (Other modes may require  |
@@ -355,7 +355,7 @@ c        | more complicated post processing than     |
 c        | mode1.)                                   |
 c        |                                           |
 c        %-------------------------------------------%
-c           
+c
          rvec = .true.
 c
          call zneupd  (rvec, 'A', select, D, V, ldv, sigma,
@@ -429,11 +429,11 @@ c
              print *, ' Maximum number of iterations reached.'
              print *, ' '
          else if ( info .eq. 3) then
-             print *, ' ' 
+             print *, ' '
              print *, ' No shifts could be applied during implicit',
      &                ' Arnoldi update, try increasing NCV.'
              print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, '_NSIMP '
@@ -444,8 +444,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -461,7 +461,7 @@ c
  9000 continue
 c
       end
-c 
+c
 c==========================================================================
 c
 c     matrix vector subroutine
@@ -471,22 +471,22 @@ c     discretized using centered difference.
 c
       subroutine av (nx, v, w)
       integer           nx, j, lo
-      Complex*16          
+      Complex*16
      &                  v(nx*nx), w(nx*nx), one, h2
       parameter         (one = (1.0D+0, 0.0D+0) )
-      external          zaxpy 
+      external          zaxpy
 c
-c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block 
+c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block
 c     tridiagonal matrix
 c
-c                  | T -I          | 
+c                  | T -I          |
 c                  |-I  T -I       |
 c             OP = |   -I  T       |
 c                  |        ...  -I|
 c                  |           -I T|
 c
-c     derived from the standard central difference discretization 
-c     of the 2-dimensional convection-diffusion operator 
+c     derived from the standard central difference discretization
+c     of the 2-dimensional convection-diffusion operator
 c                  (Laplacian u) + rho*(du/dx)
 c     on the unit squqre with zero boundary condition.
 c
@@ -503,7 +503,7 @@ c
          call tv(nx, v(lo+1), w(lo+1))
          call zaxpy (nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1)
          call zaxpy (nx, -one/h2, v(lo+nx+1), 1, w(lo+1), 1)
-  10  continue 
+  10  continue
 c
       lo = (nx-1)*nx
       call tv(nx, v(lo+1), w(lo+1))
@@ -514,29 +514,29 @@ c
 c=========================================================================
       subroutine tv (nx, x, y)
 c
-      integer           nx, j 
-      Complex*16 
+      integer           nx, j
+      Complex*16
      &                  x(nx), y(nx), h, h2, dd, dl, du
 c
-      Complex*16 
+      Complex*16
      &                  one, rho
-      parameter         (one = (1.0D+0, 0.0D+0) , 
+      parameter         (one = (1.0D+0, 0.0D+0) ,
      &                   rho = (1.0D+2, 0.0D+0) )
 c
 c     Compute the matrix vector multiplication y<---T*x
-c     where T is a nx by nx tridiagonal matrix with DD on the 
+c     where T is a nx by nx tridiagonal matrix with DD on the
 c     diagonal, DL on the subdiagonal, and DU on the superdiagonal
-c     
+c
       h   = one / dcmplx (nx+1)
       h2  = h*h
       dd  = (4.0D+0, 0.0D+0)  / h2
       dl  = -one/h2 - (5.0D-1, 0.0D+0) *rho/h
       du  = -one/h2 + (5.0D-1, 0.0D+0) *rho/h
-c 
+c
       y(1) =  dd*x(1) + du*x(2)
       do 10 j = 2,nx-1
-         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 
- 10   continue 
-      y(nx) =  dl*x(nx-1) + dd*x(nx) 
+         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1)
+ 10   continue
+      y(nx) =  dl*x(nx-1) + dd*x(nx)
       return
       end

EXAMPLES/SVD/Makefile.am

@@ -0,0 +1,11 @@
+LDADD = $(top_builddir)/SRC/libarpack$(LIBSUFFIX).la $(LAPACK_LIBS) $(BLAS_LIBS)
+
+SVD = ssvd dsvd
+
+check_PROGRAMS = $(SVD)
+TESTS = $(check_PROGRAMS)
+
+EXTRA_DIST = README debug.h
+
+ssvd_SOURCES = ssvd.f
+dsvd_SOURCES = dsvd.f

EXAMPLES/SVD/dsvd.f

@@ -1,14 +1,14 @@
       program dsvd
 c
-c     This example program is intended to illustrate the 
+c     This example program is intended to illustrate the
 c     the use of ARPACK to compute the Singular Value Decomposition.
-c   
+c
 c     This code shows how to use ARPACK to find a few of the
-c     largest singular values(sigma) and corresponding right singular 
+c     largest singular values(sigma) and corresponding right singular
 c     vectors (v) for the the matrix A by solving the symmetric problem:
-c          
+c
 c                        (A'*A)*v = sigma*v
-c 
+c
 c     where A is an m by n real matrix.
 c
 c     This code may be easily modified to estimate the 2-norm
@@ -21,20 +21,20 @@ c
 c     This formulation is appropriate when  m  .ge.  n.
 c     Reverse the roles of A and A' in the case that  m .le. n.
 c
-c     The main points illustrated here are 
+c     The main points illustrated here are
 c
-c        1) How to declare sufficient memory to find NEV 
-c           largest singular values of A .  
+c        1) How to declare sufficient memory to find NEV
+c           largest singular values of A .
 c
-c        2) Illustration of the reverse communication interface 
-c           needed to utilize the top level ARPACK routine DSAUPD 
+c        2) Illustration of the reverse communication interface
+c           needed to utilize the top level ARPACK routine DSAUPD
 c           that computes the quantities needed to construct
 c           the desired singular values and vectors(if requested).
 c
 c        3) How to extract the desired singular values and vectors
 c           using the ARPACK routine DSEUPD.
 c
-c        4) How to construct the left singular vectors U from the 
+c        4) How to construct the left singular vectors U from the
 c           right singular vectors V to obtain the decomposition
 c
 c                        A*V = U*S
@@ -42,14 +42,14 @@ c
 c           where S = diag(sigma_1, sigma_2, ..., sigma_k).
 c
 c     The only thing that must be supplied in order to use this
-c     routine on your problem is to change the array dimensions 
-c     appropriately, to specify WHICH singular values you want to 
-c     compute and to supply a the matrix-vector products 
+c     routine on your problem is to change the array dimensions
+c     appropriately, to specify WHICH singular values you want to
+c     compute and to supply a the matrix-vector products
 c
 c                         w <-  Ax
 c                         y <-  A'w
 c
-c     in place of the calls  to AV( ) and ATV( ) respectively below.  
+c     in place of the calls  to AV( ) and ATV( ) respectively below.
 c
 c     Further documentation is available in the header of DSAUPD
 c     which may be found in the SRC directory.
@@ -58,11 +58,11 @@ c     This codes implements
 c
 c\Example-1
 c     ... Suppose we want to solve A'A*v = sigma*v in regular mode,
-c         where A is derived from the simplest finite difference 
+c         where A is derived from the simplest finite difference
 c         discretization of the 2-dimensional kernel  K(s,t)dt  where
 c
 c                 K(s,t) =  s(t-1)   if 0 .le. s .le. t .le. 1,
-c                           t(s-1)   if 0 .le. t .lt. s .le. 1. 
+c                           t(s-1)   if 0 .le. t .lt. s .le. 1.
 c
 c         See subroutines AV  and ATV for details.
 c     ... OP = A'*A  and  B = I.
@@ -133,7 +133,7 @@ c     | MAXNCV: Maximum NCV allowed                          |
 c     %------------------------------------------------------%
 c
       integer          maxm, maxn, maxnev, maxncv, ldv, ldu
-      parameter       (maxm = 500, maxn=250, maxnev=10, maxncv=25, 
+      parameter       (maxm = 500, maxn=250, maxnev=10, maxncv=25,
      &                 ldu = maxm, ldv=maxn )
 c
 c     %--------------%
@@ -141,8 +141,8 @@ c     | Local Arrays |
 c     %--------------%
 c
       Double precision
-     &                 v(ldv,maxncv), u(ldu, maxnev), 
-     &                 workl(maxncv*(maxncv+8)), workd(3*maxn), 
+     &                 v(ldv,maxncv), u(ldu, maxnev),
+     &                 workl(maxncv*(maxncv+8)), workd(3*maxn),
      &                 s(maxncv,2), resid(maxn), ax(maxm)
       logical          select(maxncv)
       integer          iparam(11), ipntr(11)
@@ -155,7 +155,7 @@ c
       integer          ido, m, n, nev, ncv, lworkl, info, ierr,
      &                 j, ishfts, maxitr, mode1, nconv
       logical          rvec
-      Double precision      
+      Double precision
      &                 tol, sigma, temp
 c
 c     %------------%
@@ -165,12 +165,12 @@ c
       Double precision
      &                 one, zero
       parameter        (one = 1.0D+0, zero = 0.0D+0)
-c  
+c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision           
+      Double precision
      &                 dnrm2
       external         dnrm2, daxpy, dcopy, dscal
 c
@@ -192,7 +192,7 @@ c
       ndigit = -3
       logfil = 6
       msgets = 0
-      msaitr = 0 
+      msaitr = 0
       msapps = 0
       msaupd = 1
       msaup2 = 0
@@ -207,11 +207,11 @@ c
       n = 100
 c
 c     %------------------------------------------------%
-c     | Specifications for ARPACK usage are set        | 
+c     | Specifications for ARPACK usage are set        |
 c     | below:                                         |
 c     |                                                |
-c     |    1) NEV = 4 asks for 4 singular values to be |  
-c     |       computed.                                | 
+c     |    1) NEV = 4 asks for 4 singular values to be |
+c     |       computed.                                |
 c     |                                                |
 c     |    2) NCV = 20 sets the length of the Arnoldi  |
 c     |       factorization                            |
@@ -223,7 +223,7 @@ c     |    4) Ask for the NEV singular values of       |
 c     |       largest magnitude                        |
 c     |         (indicated by which = 'LM')            |
 c     |       See documentation in DSAUPD for the      |
-c     |       other options SM, BE.                    | 
+c     |       other options SM, BE.                    |
 c     |                                                |
 c     | Note: NEV and NCV must satisfy the following   |
 c     |       conditions:                              |
@@ -232,7 +232,7 @@ c     |             NEV + 1 <= NCV <= MAXNCV           |
 c     %------------------------------------------------%
 c
       nev   = 4
-      ncv   = 10 
+      ncv   = 10
       bmat  = 'I'
       which = 'LM'
 c
@@ -265,25 +265,25 @@ c     |      used to specify actions to be taken on return  |
 c     |      from DSAUPD. (See usage below.)                |
 c     |                                                     |
 c     |      It MUST initially be set to 0 before the first |
-c     |      call to DSAUPD.                                | 
+c     |      call to DSAUPD.                                |
 c     |                                                     |
 c     | INFO on entry specifies starting vector information |
 c     |      and on return indicates error codes            |
 c     |                                                     |
-c     |      Initially, setting INFO=0 indicates that a     | 
+c     |      Initially, setting INFO=0 indicates that a     |
 c     |      random starting vector is requested to         |
 c     |      start the ARNOLDI iteration.  Setting INFO to  |
 c     |      a nonzero value on the initial call is used    |
 c     |      if you want to specify your own starting       |
-c     |      vector (This vector must be placed in RESID.)  | 
+c     |      vector (This vector must be placed in RESID.)  |
 c     |                                                     |
-c     | The work array WORKL is used in DSAUPD as           | 
+c     | The work array WORKL is used in DSAUPD as           |
 c     | workspace.  Its dimension LWORKL is set as          |
 c     | illustrated below.                                  |
 c     %-----------------------------------------------------%
 c
       lworkl = ncv*(ncv+8)
-      tol = zero 
+      tol = zero
       info = 0
       ido = 0
 c
@@ -304,9 +304,9 @@ c
       mode1 = 1
 c
       iparam(1) = ishfts
-c                
+c
       iparam(3) = maxitr
-c                  
+c
       iparam(7) = mode1
 c
 c     %------------------------------------------------%
@@ -316,13 +316,13 @@ c
  10   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine DSAUPD and take | 
+c        | Repeatedly call the routine DSAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call dsaupd ( ido, bmat, n, which, nev, tol, resid, 
+         call dsaupd ( ido, bmat, n, which, nev, tol, resid,
      &                 ncv, v, ldv, iparam, ipntr, workd, workl,
      &                 lworkl, info )
 c
@@ -339,7 +339,7 @@ c           | the input, and returns the result in  |
 c           | workd(ipntr(2)).                      |
 c           %---------------------------------------%
 c
-            call av (m, n, workd(ipntr(1)), ax) 
+            call av (m, n, workd(ipntr(1)), ax)
             call atv (m, n, ax, workd(ipntr(2)))
 c
 c           %-----------------------------------------%
@@ -348,7 +348,7 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-         end if 
+         end if
 c
 c     %----------------------------------------%
 c     | Either we have convergence or there is |
@@ -367,31 +367,31 @@ c
          print *, ' Check documentation in _saupd '
          print *, ' '
 c
-      else 
+      else
 c
 c        %--------------------------------------------%
 c        | No fatal errors occurred.                  |
 c        | Post-Process using DSEUPD.                 |
 c        |                                            |
-c        | Computed singular values may be extracted. |  
+c        | Computed singular values may be extracted. |
 c        |                                            |
 c        | Singular vectors may also be computed now  |
-c        | if desired.  (indicated by rvec = .true.)  | 
+c        | if desired.  (indicated by rvec = .true.)  |
 c        |                                            |
 c        | The routine DSEUPD now called to do this   |
-c        | post processing                            | 
+c        | post processing                            |
 c        %--------------------------------------------%
-c           
+c
          rvec = .true.
 c
-         call dseupd ( rvec, 'All', select, s, v, ldv, sigma, 
-     &        bmat, n, which, nev, tol, resid, ncv, v, ldv, 
+         call dseupd ( rvec, 'All', select, s, v, ldv, sigma,
+     &        bmat, n, which, nev, tol, resid, ncv, v, ldv,
      &        iparam, ipntr, workd, workl, lworkl, ierr )
 c
 c        %-----------------------------------------------%
 c        | Singular values are returned in the first     |
 c        | column of the two dimensional array S         |
-c        | and the corresponding right singular vectors  | 
+c        | and the corresponding right singular vectors  |
 c        | are returned in the first NEV columns of the  |
 c        | two dimensional array V as requested here.    |
 c        %-----------------------------------------------%
@@ -468,11 +468,11 @@ c
             print *, ' Maximum number of iterations reached.'
             print *, ' '
          else if ( info .eq. 3) then
-            print *, ' ' 
+            print *, ' '
             print *, ' No shifts could be applied during implicit',
      &               ' Arnoldi update, try increasing NCV.'
             print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _SVD '
@@ -483,8 +483,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -500,16 +500,16 @@ c
  9000 continue
 c
       end
-c 
+c
 c ------------------------------------------------------------------
 c     matrix vector subroutines
 c
-c     The matrix A is derived from the simplest finite difference 
-c     discretization of the integral operator 
+c     The matrix A is derived from the simplest finite difference
+c     discretization of the integral operator
 c
 c                     f(s) = integral(K(s,t)x(t)dt).
-c      
-c     Thus, the matrix A is a discretization of the 2-dimensional kernel 
+c
+c     Thus, the matrix A is a discretization of the 2-dimensional kernel
 c     K(s,t)dt, where
 c
 c                 K(s,t) =  s(t-1)   if 0 .le. s .le. t .le. 1,
@@ -521,7 +521,7 @@ c                 A(i,j) = k*(si)*(tj - 1)  if i .le. j,
 c                          k*(tj)*(si - 1)  if i .gt. j
 c
 c     where si = i/(m+1)  and  tj = j/(n+1)  and k = 1/(n+1).
-c      
+c
 c-------------------------------------------------------------------
 c
       subroutine av (m, n, x, w)
@@ -531,7 +531,7 @@ c
       integer          m, n, i, j
       Double precision
      &                 x(n), w(m), one, zero, h, k, s, t
-      parameter        ( one = 1.0D+0, zero = 0.0D+0 ) 
+      parameter        ( one = 1.0D+0, zero = 0.0D+0 )
 c
       h = one / dble(m+1)
       k = one / dble(n+1)
@@ -539,19 +539,19 @@ c
          w(i) = zero
  5    continue
       t = zero
-c      
+c
       do 30 j = 1,n
          t = t+k
          s = zero
          do 10 i = 1,j
            s = s+h
            w(i) = w(i) + k*s*(t-one)*x(j)
- 10      continue 
+ 10      continue
          do 20 i = j+1,m
            s = s+h
-           w(i) = w(i) + k*t*(s-one)*x(j) 
+           w(i) = w(i) + k*t*(s-one)*x(j)
  20      continue
- 30   continue      
+ 30   continue
 c
       return
       end
@@ -588,7 +588,7 @@ c
  30   continue
 c
       return
-      end 
+      end
 c
 
 

EXAMPLES/SVD/makefile

@@ -1,15 +0,0 @@
-#
-# makefile to run simple examples of the reverse communication
-# protocol.
-#
-# Modify if ARPACK library was built somewhere else.
-#
-#\SCCS Information: @(#) 
-# FILE: makefile   SID: 2.2   DATE OF SID: 9/24/96   RELEASE: 2
-#
-include ../../ARmake.inc
-
-ssvd: ssvd.o
-	$(FC) $(FFLAGS) ssvd.o $(ALIBS) -o ssvd
-dsvd: dsvd.o
-	$(FC) $(FFLAGS) dsvd.o $(ALIBS) -o dsvd

EXAMPLES/SVD/ssvd.f

@@ -1,14 +1,14 @@
       program ssvd
 c
-c     This example program is intended to illustrate the 
+c     This example program is intended to illustrate the
 c     the use of ARPACK to compute the Singular Value Decomposition.
-c   
+c
 c     This code shows how to use ARPACK to find a few of the
-c     largest singular values(sigma) and corresponding right singular 
+c     largest singular values(sigma) and corresponding right singular
 c     vectors (v) for the the matrix A by solving the symmetric problem:
-c          
+c
 c                        (A'*A)*v = sigma*v
-c 
+c
 c     where A is an m by n real matrix.
 c
 c     This code may be easily modified to estimate the 2-norm
@@ -21,20 +21,20 @@ c
 c     This formulation is appropriate when  m  .ge.  n.
 c     Reverse the roles of A and A' in the case that  m .le. n.
 c
-c     The main points illustrated here are 
+c     The main points illustrated here are
 c
-c        1) How to declare sufficient memory to find NEV 
-c           largest singular values of A .  
+c        1) How to declare sufficient memory to find NEV
+c           largest singular values of A .
 c
-c        2) Illustration of the reverse communication interface 
-c           needed to utilize the top level ARPACK routine SSAUPD 
+c        2) Illustration of the reverse communication interface
+c           needed to utilize the top level ARPACK routine SSAUPD
 c           that computes the quantities needed to construct
 c           the desired singular values and vectors(if requested).
 c
 c        3) How to extract the desired singular values and vectors
 c           using the ARPACK routine SSEUPD.
 c
-c        4) How to construct the left singular vectors U from the 
+c        4) How to construct the left singular vectors U from the
 c           right singular vectors V to obtain the decomposition
 c
 c                        A*V = U*S
@@ -42,14 +42,14 @@ c
 c           where S = diag(sigma_1, sigma_2, ..., sigma_k).
 c
 c     The only thing that must be supplied in order to use this
-c     routine on your problem is to change the array dimensions 
-c     appropriately, to specify WHICH singular values you want to 
-c     compute and to supply a the matrix-vector products 
+c     routine on your problem is to change the array dimensions
+c     appropriately, to specify WHICH singular values you want to
+c     compute and to supply a the matrix-vector products
 c
 c                         w <-  Ax
 c                         y <-  A'w
 c
-c     in place of the calls  to AV( ) and ATV( ) respectively below.  
+c     in place of the calls  to AV( ) and ATV( ) respectively below.
 c
 c     Further documentation is available in the header of DSAUPD
 c     which may be found in the SRC directory.
@@ -58,11 +58,11 @@ c     This codes implements
 c
 c\Example-1
 c     ... Suppose we want to solve A'A*v = sigma*v in regular mode,
-c         where A is derived from the simplest finite difference 
+c         where A is derived from the simplest finite difference
 c         discretization of the 2-dimensional kernel  K(s,t)dt  where
 c
 c                 K(s,t) =  s(t-1)   if 0 .le. s .le. t .le. 1,
-c                           t(s-1)   if 0 .le. t .lt. s .le. 1. 
+c                           t(s-1)   if 0 .le. t .lt. s .le. 1.
 c
 c         See subroutines AV  and ATV for details.
 c     ... OP = A'*A  and  B = I.
@@ -133,7 +133,7 @@ c     | MAXNCV: Maximum NCV allowed                          |
 c     %------------------------------------------------------%
 c
       integer          maxm, maxn, maxnev, maxncv, ldv, ldu
-      parameter       (maxm = 500, maxn=250, maxnev=10, maxncv=25, 
+      parameter       (maxm = 500, maxn=250, maxnev=10, maxncv=25,
      &                 ldu = maxm, ldv=maxn )
 c
 c     %--------------%
@@ -141,8 +141,8 @@ c     | Local Arrays |
 c     %--------------%
 c
       Real
-     &                 v(ldv,maxncv), u(ldu, maxnev), 
-     &                 workl(maxncv*(maxncv+8)), workd(3*maxn), 
+     &                 v(ldv,maxncv), u(ldu, maxnev),
+     &                 workl(maxncv*(maxncv+8)), workd(3*maxn),
      &                 s(maxncv,2), resid(maxn), ax(maxm)
       logical          select(maxncv)
       integer          iparam(11), ipntr(11)
@@ -155,7 +155,7 @@ c
       integer          ido, m, n, nev, ncv, lworkl, info, ierr,
      &                 j, ishfts, maxitr, mode1, nconv
       logical          rvec
-      Real      
+      Real
      &                 tol, sigma, temp
 c
 c     %------------%
@@ -165,12 +165,12 @@ c
       Real
      &                 one, zero
       parameter        (one = 1.0E+0, zero = 0.0E+0)
-c  
+c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real           
+      Real
      &                 snrm2
       external         snrm2, saxpy, scopy, sscal
 c
@@ -192,7 +192,7 @@ c
       ndigit = -3
       logfil = 6
       msgets = 0
-      msaitr = 0 
+      msaitr = 0
       msapps = 0
       msaupd = 1
       msaup2 = 0
@@ -207,11 +207,11 @@ c
       n = 100
 c
 c     %------------------------------------------------%
-c     | Specifications for ARPACK usage are set        | 
+c     | Specifications for ARPACK usage are set        |
 c     | below:                                         |
 c     |                                                |
-c     |    1) NEV = 4 asks for 4 singular values to be |  
-c     |       computed.                                | 
+c     |    1) NEV = 4 asks for 4 singular values to be |
+c     |       computed.                                |
 c     |                                                |
 c     |    2) NCV = 20 sets the length of the Arnoldi  |
 c     |       factorization                            |
@@ -223,7 +223,7 @@ c     |    4) Ask for the NEV singular values of       |
 c     |       largest magnitude                        |
 c     |         (indicated by which = 'LM')            |
 c     |       See documentation in SSAUPD for the      |
-c     |       other options SM, BE.                    | 
+c     |       other options SM, BE.                    |
 c     |                                                |
 c     | Note: NEV and NCV must satisfy the following   |
 c     |       conditions:                              |
@@ -232,7 +232,7 @@ c     |             NEV + 1 <= NCV <= MAXNCV           |
 c     %------------------------------------------------%
 c
       nev   = 4
-      ncv   = 10 
+      ncv   = 10
       bmat  = 'I'
       which = 'LM'
 c
@@ -265,25 +265,25 @@ c     |      used to specify actions to be taken on return  |
 c     |      from SSAUPD. (See usage below.)                |
 c     |                                                     |
 c     |      It MUST initially be set to 0 before the first |
-c     |      call to SSAUPD.                                | 
+c     |      call to SSAUPD.                                |
 c     |                                                     |
 c     | INFO on entry specifies starting vector information |
 c     |      and on return indicates error codes            |
 c     |                                                     |
-c     |      Initially, setting INFO=0 indicates that a     | 
+c     |      Initially, setting INFO=0 indicates that a     |
 c     |      random starting vector is requested to         |
 c     |      start the ARNOLDI iteration.  Setting INFO to  |
 c     |      a nonzero value on the initial call is used    |
 c     |      if you want to specify your own starting       |
-c     |      vector (This vector must be placed in RESID.)  | 
+c     |      vector (This vector must be placed in RESID.)  |
 c     |                                                     |
-c     | The work array WORKL is used in SSAUPD as           | 
+c     | The work array WORKL is used in SSAUPD as           |
 c     | workspace.  Its dimension LWORKL is set as          |
 c     | illustrated below.                                  |
 c     %-----------------------------------------------------%
 c
       lworkl = ncv*(ncv+8)
-      tol = zero 
+      tol = zero
       info = 0
       ido = 0
 c
@@ -304,9 +304,9 @@ c
       mode1 = 1
 c
       iparam(1) = ishfts
-c                
+c
       iparam(3) = maxitr
-c                  
+c
       iparam(7) = mode1
 c
 c     %------------------------------------------------%
@@ -316,13 +316,13 @@ c
  10   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine SSAUPD and take | 
+c        | Repeatedly call the routine SSAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call ssaupd ( ido, bmat, n, which, nev, tol, resid, 
+         call ssaupd ( ido, bmat, n, which, nev, tol, resid,
      &                 ncv, v, ldv, iparam, ipntr, workd, workl,
      &                 lworkl, info )
 c
@@ -339,7 +339,7 @@ c           | the input, and returns the result in  |
 c           | workd(ipntr(2)).                      |
 c           %---------------------------------------%
 c
-            call av (m, n, workd(ipntr(1)), ax) 
+            call av (m, n, workd(ipntr(1)), ax)
             call atv (m, n, ax, workd(ipntr(2)))
 c
 c           %-----------------------------------------%
@@ -348,7 +348,7 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-         end if 
+         end if
 c
 c     %----------------------------------------%
 c     | Either we have convergence or there is |
@@ -367,31 +367,31 @@ c
          print *, ' Check documentation in _saupd '
          print *, ' '
 c
-      else 
+      else
 c
 c        %--------------------------------------------%
 c        | No fatal errors occurred.                  |
 c        | Post-Process using SSEUPD.                 |
 c        |                                            |
-c        | Computed singular values may be extracted. |  
+c        | Computed singular values may be extracted. |
 c        |                                            |
 c        | Singular vectors may also be computed now  |
-c        | if desired.  (indicated by rvec = .true.)  | 
+c        | if desired.  (indicated by rvec = .true.)  |
 c        |                                            |
 c        | The routine SSEUPD now called to do this   |
-c        | post processing                            | 
+c        | post processing                            |
 c        %--------------------------------------------%
-c           
+c
          rvec = .true.
 c
-         call sseupd ( rvec, 'All', select, s, v, ldv, sigma, 
-     &        bmat, n, which, nev, tol, resid, ncv, v, ldv, 
+         call sseupd ( rvec, 'All', select, s, v, ldv, sigma,
+     &        bmat, n, which, nev, tol, resid, ncv, v, ldv,
      &        iparam, ipntr, workd, workl, lworkl, ierr )
 c
 c        %-----------------------------------------------%
 c        | Singular values are returned in the first     |
 c        | column of the two dimensional array S         |
-c        | and the corresponding right singular vectors  | 
+c        | and the corresponding right singular vectors  |
 c        | are returned in the first NEV columns of the  |
 c        | two dimensional array V as requested here.    |
 c        %-----------------------------------------------%
@@ -468,11 +468,11 @@ c
             print *, ' Maximum number of iterations reached.'
             print *, ' '
          else if ( info .eq. 3) then
-            print *, ' ' 
+            print *, ' '
             print *, ' No shifts could be applied during implicit',
      &               ' Arnoldi update, try increasing NCV.'
             print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _SVD '
@@ -483,8 +483,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -500,16 +500,16 @@ c
  9000 continue
 c
       end
-c 
+c
 c ------------------------------------------------------------------
 c     matrix vector subroutines
 c
-c     The matrix A is derived from the simplest finite difference 
-c     discretization of the integral operator 
+c     The matrix A is derived from the simplest finite difference
+c     discretization of the integral operator
 c
 c                     f(s) = integral(K(s,t)x(t)dt).
-c      
-c     Thus, the matrix A is a discretization of the 2-dimensional kernel 
+c
+c     Thus, the matrix A is a discretization of the 2-dimensional kernel
 c     K(s,t)dt, where
 c
 c                 K(s,t) =  s(t-1)   if 0 .le. s .le. t .le. 1,
@@ -521,7 +521,7 @@ c                 A(i,j) = k*(si)*(tj - 1)  if i .le. j,
 c                          k*(tj)*(si - 1)  if i .gt. j
 c
 c     where si = i/(m+1)  and  tj = j/(n+1)  and k = 1/(n+1).
-c      
+c
 c-------------------------------------------------------------------
 c
       subroutine av (m, n, x, w)
@@ -531,7 +531,7 @@ c
       integer          m, n, i, j
       Real
      &                 x(n), w(m), one, zero, h, k, s, t
-      parameter        ( one = 1.0E+0, zero = 0.0E+0 ) 
+      parameter        ( one = 1.0E+0, zero = 0.0E+0 )
 c
       h = one / real(m+1)
       k = one / real(n+1)
@@ -539,19 +539,19 @@ c
          w(i) = zero
  5    continue
       t = zero
-c      
+c
       do 30 j = 1,n
          t = t+k
          s = zero
          do 10 i = 1,j
            s = s+h
            w(i) = w(i) + k*s*(t-one)*x(j)
- 10      continue 
+ 10      continue
          do 20 i = j+1,m
            s = s+h
-           w(i) = w(i) + k*t*(s-one)*x(j) 
+           w(i) = w(i) + k*t*(s-one)*x(j)
  20      continue
- 30   continue      
+ 30   continue
 c
       return
       end
@@ -588,7 +588,7 @@ c
  30   continue
 c
       return
-      end 
+      end
 c
 
 

EXAMPLES/SYM/Makefile.am

@@ -0,0 +1,26 @@
+LDADD = $(top_builddir)/SRC/libarpack$(LIBSUFFIX).la $(LAPACK_LIBS) $(BLAS_LIBS)
+
+SSDRV = ssdrv1 ssdrv2 ssdrv3 ssdrv4 ssdrv5 ssdrv6
+DSDRV = dsdrv1 dsdrv2 dsdrv3 dsdrv4 dsdrv5 dsdrv6
+SYM = $(SSDRV) $(DSDRV)
+
+check_PROGRAMS = $(SYM)
+TESTS = $(check_PROGRAMS)
+
+EXTRA_DIST = README
+
+# simple symmetric problem using single precision
+ssdrv1_SOURCES = ssdrv1.f
+ssdrv2_SOURCES = ssdrv2.f
+ssdrv3_SOURCES = ssdrv3.f
+ssdrv4_SOURCES = ssdrv4.f
+ssdrv5_SOURCES = ssdrv5.f
+ssdrv6_SOURCES = ssdrv6.f
+
+# simple symmetric problem using double precision
+dsdrv1_SOURCES = dsdrv1.f
+dsdrv2_SOURCES = dsdrv2.f
+dsdrv3_SOURCES = dsdrv3.f
+dsdrv4_SOURCES = dsdrv4.f
+dsdrv5_SOURCES = dsdrv5.f
+dsdrv6_SOURCES = dsdrv6.f

EXAMPLES/SYM/dsdrv1.f

@@ -1,4 +1,4 @@
-      program dsdrv1 
+      program dsdrv1
 c
 c     Simple program to illustrate the idea of reverse communication
 c     in regular mode for a standard symmetric eigenvalue problem.
@@ -26,7 +26,7 @@ c             Ritz vectors.
 c     dnrm2   Level 1 BLAS that computes the norm of a vector.
 c     daxpy   Level 1 BLAS that computes y <- alpha*x+y.
 c     av      Matrix vector multiplication routine that computes A*x.
-c     tv      Matrix vector multiplication routine that computes T*x, 
+c     tv      Matrix vector multiplication routine that computes T*x,
 c             where T is a tridiagonal matrix.  It is used in routine
 c             av.
 c
@@ -59,7 +59,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer          maxn, maxnev, maxncv, ldv
-      parameter       (maxn=256, maxnev=10, maxncv=25, 
+      parameter       (maxn=256, maxnev=10, maxncv=25,
      $                 ldv=maxn )
 c
 c     %--------------%
@@ -78,10 +78,10 @@ c     | Local Scalars |
 c     %---------------%
 c
       character        bmat*1, which*2
-      integer          ido, n, nev, ncv, lworkl, info, ierr, j, 
+      integer          ido, n, nev, ncv, lworkl, info, ierr, j,
      &                 nx, nconv, maxitr, mode, ishfts
       logical          rvec
-      Double precision      
+      Double precision
      &                 tol, sigma
 c
 c     %------------%
@@ -91,12 +91,12 @@ c
       Double precision
      &                 zero
       parameter        (zero = 0.0D+0)
-c  
+c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision           
+      Double precision
      &                 dnrm2
       external         dnrm2, daxpy
 c
@@ -122,15 +122,15 @@ c     | modify NEV, NCV, WHICH to solve problems of        |
 c     | different sizes, and to get different parts of the |
 c     | spectrum.  However, The following conditions must  |
 c     | be satisfied:                                      |
-c     |                   N <= MAXN,                       | 
+c     |                   N <= MAXN,                       |
 c     |                 NEV <= MAXNEV,                     |
-c     |             NEV + 1 <= NCV <= MAXNCV               | 
-c     %----------------------------------------------------% 
+c     |             NEV + 1 <= NCV <= MAXNCV               |
+c     %----------------------------------------------------%
 c
       nx = 10
       n = nx*nx
-      nev =  4 
-      ncv =  10 
+      nev =  4
+      ncv =  10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _SDRV1: N is greater than MAXN '
          go to 9000
@@ -157,7 +157,7 @@ c     | iteration.                                       |
 c     %--------------------------------------------------%
 c
       lworkl = ncv*(ncv+8)
-      tol = zero 
+      tol = zero
       info = 0
       ido = 0
 c
@@ -174,10 +174,10 @@ c
       ishfts = 1
       maxitr = 300
       mode   = 1
-c      
-      iparam(1) = ishfts 
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+c
+      iparam(1) = ishfts
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %-------------------------------------------%
 c     | M A I N   L O O P (Reverse communication) |
@@ -186,13 +186,13 @@ c
  10   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine DSAUPD and take | 
+c        | Repeatedly call the routine DSAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call dsaupd ( ido, bmat, n, which, nev, tol, resid, 
+         call dsaupd ( ido, bmat, n, which, nev, tol, resid,
      &                 ncv, v, ldv, iparam, ipntr, workd, workl,
      &                 lworkl, info )
 c
@@ -216,7 +216,7 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-         end if 
+         end if
 c
 c     %----------------------------------------%
 c     | Either we have convergence or there is |
@@ -235,22 +235,22 @@ c
          print *, ' Check documentation in _saupd '
          print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using DSEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
-c           
+c
          rvec = .true.
 c
-         call dseupd ( rvec, 'All', select, d, v, ldv, sigma, 
-     &        bmat, n, which, nev, tol, resid, ncv, v, ldv, 
+         call dseupd ( rvec, 'All', select, d, v, ldv, sigma,
+     &        bmat, n, which, nev, tol, resid, ncv, v, ldv,
      &        iparam, ipntr, workd, workl, lworkl, ierr )
 
 c        %----------------------------------------------%
@@ -318,11 +318,11 @@ c
             print *, ' Maximum number of iterations reached.'
             print *, ' '
          else if ( info .eq. 3) then
-            print *, ' ' 
+            print *, ' '
             print *, ' No shifts could be applied during implicit',
      &               ' Arnoldi update, try increasing NCV.'
             print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _SDRV1 '
@@ -333,8 +333,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -350,17 +350,17 @@ c
  9000 continue
 c
       end
-c 
+c
 c ------------------------------------------------------------------
 c     matrix vector subroutine
 c
 c     The matrix used is the 2 dimensional discrete Laplacian on unit
 c     square with zero Dirichlet boundary condition.
 c
-c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block 
+c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block
 c     tridiagonal matrix
 c
-c                  | T -I          | 
+c                  | T -I          |
 c                  |-I  T -I       |
 c             OP = |   -I  T       |
 c                  |        ...  -I|
@@ -372,7 +372,7 @@ c
       integer           nx, j, lo, n2
       Double precision
      &                  v(nx*nx), w(nx*nx), one, h2
-      parameter         ( one = 1.0D+0 ) 
+      parameter         ( one = 1.0D+0 )
 c
       call tv(nx,v(1),w(1))
       call daxpy(nx, -one, v(nx+1), 1, w(1), 1)
@@ -382,7 +382,7 @@ c
          call tv(nx, v(lo+1), w(lo+1))
          call daxpy(nx, -one, v(lo-nx+1), 1, w(lo+1), 1)
          call daxpy(nx, -one, v(lo+nx+1), 1, w(lo+1), 1)
-  10  continue 
+  10  continue
 c
       lo = (nx-1)*nx
       call tv(nx, v(lo+1), w(lo+1))
@@ -392,14 +392,14 @@ c     Scale the vector w by (1/h^2), where h is the mesh size
 c
       n2 = nx*nx
       h2 = one / dble((nx+1)*(nx+1))
-      call dscal(n2, one/h2, w, 1) 
+      call dscal(n2, one/h2, w, 1)
       return
       end
 c
 c-------------------------------------------------------------------
       subroutine tv (nx, x, y)
 c
-      integer           nx, j 
+      integer           nx, j
       Double precision
      &                  x(nx), y(nx), dd, dl, du
 c
@@ -408,19 +408,19 @@ c
       parameter        (one = 1.0D+0 )
 c
 c     Compute the matrix vector multiplication y<---T*x
-c     where T is a nx by nx tridiagonal matrix with DD on the 
+c     where T is a nx by nx tridiagonal matrix with DD on the
 c     diagonal, DL on the subdiagonal, and DU on the superdiagonal.
-c     
+c
 c
       dd  = 4.0D+0
-      dl  = -one 
+      dl  = -one
       du  = -one
-c 
+c
       y(1) =  dd*x(1) + du*x(2)
       do 10 j = 2,nx-1
-         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 
- 10   continue 
-      y(nx) =  dl*x(nx-1) + dd*x(nx) 
+         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1)
+ 10   continue
+      y(nx) =  dl*x(nx-1) + dd*x(nx)
       return
       end
 

EXAMPLES/SYM/dsdrv2.f

@@ -1,9 +1,9 @@
-      program dsdrv2 
+      program dsdrv2
 c
 c     Program to illustrate the idea of reverse communication
 c     in shift and invert mode for a standard symmetric eigenvalue
-c     problem.  The following program uses the two LAPACK subroutines 
-c     dgttrf.f and dgttrs.f to factor and solve a tridiagonal system of 
+c     problem.  The following program uses the two LAPACK subroutines
+c     dgttrf.f and dgttrs.f to factor and solve a tridiagonal system of
 c     equations.
 c
 c     We implement example two of ex-sym.doc in DOCUMENTS directory
@@ -25,7 +25,7 @@ c             Ritz vectors.
 c     dgttrf  LAPACK tridiagonal factorization routine.
 c     dgttrs  LAPACK tridiagonal solve routine.
 c     daxpy   daxpy   Level 1 BLAS that computes y <- alpha*x+y.
-c     dnrm2   Level 1 BLAS that computes the norm of a vector.     
+c     dnrm2   Level 1 BLAS that computes the norm of a vector.
 c     av      Matrix vector multiplication routine that computes A*x.
 c
 c\Author
@@ -56,7 +56,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer          maxn, maxnev, maxncv, ldv
-      parameter        (maxn=256, maxnev=10, maxncv=25, 
+      parameter        (maxn=256, maxnev=10, maxncv=25,
      &                 ldv=maxn )
 c
 c     %--------------%
@@ -65,7 +65,7 @@ c     %--------------%
 c
       Double precision
      &                 v(ldv,maxncv), workl(maxncv*(maxncv+8)),
-     &                 workd(3*maxn), d(maxncv,2), resid(maxn), 
+     &                 workd(3*maxn), d(maxncv,2), resid(maxn),
      &                 ad(maxn), adl(maxn), adu(maxn), adu2(maxn),
      &                 ax(maxn)
       logical          select(maxncv)
@@ -86,9 +86,9 @@ c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Double precision           
-     &                 zero, one, two 
-      parameter        (zero = 0.0D+0, one = 1.0D+0, 
+      Double precision
+     &                 zero, one, two
+      parameter        (zero = 0.0D+0, one = 1.0D+0,
      &                  two = 2.0D+0)
 c
 c     %-----------------------------%
@@ -115,14 +115,14 @@ c     | standard eigenvalue problem is solved (BMAT = 'I'. |
 c     | NEV is the number of eigenvalues (closest to       |
 c     | SIGMA) to be approximated.  Since the shift-invert |
 c     | mode is used, WHICH is set to 'LM'.  The user can  |
-c     | modify NEV, NCV, SIGMA to solve problems of        | 
+c     | modify NEV, NCV, SIGMA to solve problems of        |
 c     | different sizes, and to get different parts of the |
 c     | spectrum.  However, The following conditions must  |
 c     | be satisfied:                                      |
-c     |                   N <= MAXN,                       | 
+c     |                   N <= MAXN,                       |
 c     |                 NEV <= MAXNEV,                     |
-c     |             NEV + 1 <= NCV <= MAXNCV               | 
-c     %----------------------------------------------------% 
+c     |             NEV + 1 <= NCV <= MAXNCV               |
+c     %----------------------------------------------------%
 c
       n = 100
       nev = 4
@@ -140,7 +140,7 @@ c
 c
       bmat = 'I'
       which = 'LM'
-      sigma = zero 
+      sigma = zero
 c
 c     %--------------------------------------------------%
 c     | The work array WORKL is used in DSAUPD as        |
@@ -155,7 +155,7 @@ c     | iteration.                                       |
 c     %--------------------------------------------------%
 c
       lworkl = ncv*(ncv+8)
-      tol = zero 
+      tol = zero
       ido = 0
       info = 0
 c
@@ -173,24 +173,24 @@ c
       maxitr = 300
       mode   = 3
 c
-      iparam(1) = ishfts 
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+      iparam(1) = ishfts
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %-----------------------------------------------------%
 c     | Call LAPACK routine to factor (A-SIGMA*I), where A  |
-c     | is the 1-d Laplacian.                               | 
+c     | is the 1-d Laplacian.                               |
 c     %-----------------------------------------------------%
 c
       h2 = one / dble((n+1)*(n+1))
       do 20 j=1,n
          ad(j) = two / h2 - sigma
          adl(j) = -one / h2
- 20   continue 
+ 20   continue
       call dcopy (n, adl, 1, adu, 1)
       call dgttrf (n, adl, ad, adu, adu2, ipiv, ierr)
-      if (ierr .ne. 0) then 
-         print *, ' ' 
+      if (ierr .ne. 0) then
+         print *, ' '
          print *, ' Error with _gttrf in SDRV2.'
          print *, ' '
          go to 9000
@@ -230,7 +230,7 @@ c
             if (ierr .ne. 0) then
                print *, ' '
                print *, ' Error with _gttrs in _SDRV2. '
-               print *, ' ' 
+               print *, ' '
                go to 9000
             end if
 c
@@ -240,7 +240,7 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-         end if 
+         end if
 c
 c     %----------------------------------------%
 c     | Either we have convergence or there is |
@@ -257,9 +257,9 @@ c
          print *, ' '
          print *, ' Error with _saupd, info = ',info
          print *, ' Check documentation of _saupd '
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
@@ -288,7 +288,7 @@ c        | corresponding to the eigenvalues in D is     |
 c        | returned in V.                               |
 c        %----------------------------------------------%
 
-         if ( ierr .ne. 0 ) then 
+         if ( ierr .ne. 0 ) then
 c
 c           %------------------------------------%
 c           | Error condition:                   |
@@ -300,7 +300,7 @@ c
             print *, ' Check the documentation of _seupd '
             print *, ' '
 c
-         else 
+         else
 c
             nconv =  iparam(5)
             do 30 j=1, nconv
@@ -351,14 +351,14 @@ c
          print *, ' '
          print *, ' _SDRV2 '
          print *, ' ====== '
-         print *, ' ' 
+         print *, ' '
          print *, ' Size of the matrix is ', n
          print *, ' The number of Ritz values requested is ', nev
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
          print *, ' The number of converged Ritz values is ',
-     &              nconv 
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -389,10 +389,10 @@ c
 c
       w(1) =  two*v(1) - v(2)
       do 100 j = 2,n-1
-         w(j) = - v(j-1) + two*v(j) - v(j+1) 
+         w(j) = - v(j-1) + two*v(j) - v(j+1)
   100 continue
       j = n
-      w(j) = - v(j-1) + two*v(j) 
+      w(j) = - v(j-1) + two*v(j)
 c
 c     Scale the vector w by (1 / h^2).
 c

EXAMPLES/SYM/dsdrv3.f

@@ -1,15 +1,15 @@
-      program dsdrv3  
+      program dsdrv3
 c
 c     Program to illustrate the idea of reverse communication in
 c     inverse mode for a generalized symmetric eigenvalue problem.
-c     The following program uses the two LAPACK subroutines dgttrf .f 
+c     The following program uses the two LAPACK subroutines dgttrf .f
 c     and dgttrs .f to factor and solve a tridiagonal system of equations.
 c
 c     We implement example three of ex-sym.doc in DOCUMENTS directory
 c
 c\Example-3
 c     ... Suppose we want to solve A*x = lambda*M*x in inverse mode,
-c         where A and M are obtained by the finite element of the 
+c         where A and M are obtained by the finite element of the
 c         1-dimensional discrete Laplacian
 c                             d^2u / dx^2
 c         on the interval [0,1] with zero Dirichlet boundary condition
@@ -17,7 +17,7 @@ c         using piecewise linear elements.
 c
 c     ... OP = inv[M]*A  and  B = M.
 c
-c     ... Use mode 2 of DSAUPD .    
+c     ... Use mode 2 of DSAUPD .
 c
 c\BeginLib
 c
@@ -30,7 +30,7 @@ c     dgttrs   LAPACK tridiagonal solve routine.
 c     daxpy    Level 1 BLAS that computes y <- alpha*x+y.
 c     dscal    Level 1 BLAS that scales a vector by a scalar.
 c     dcopy    Level 1 BLAS that copies one vector to another.
-c     dnrm2    Level 1 BLAS that computes the norm of a vector.     
+c     dnrm2    Level 1 BLAS that computes the norm of a vector.
 c     av      Matrix vector multiplication routine that computes A*x.
 c     mv      Matrix vector multiplication routine that computes M*x.
 c
@@ -62,16 +62,16 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer          maxn, maxnev, maxncv, ldv
-      parameter        (maxn=256, maxnev=10, maxncv=25, 
+      parameter        (maxn=256, maxnev=10, maxncv=25,
      &                 ldv=maxn )
 c
 c     %--------------%
 c     | Local Arrays |
 c     %--------------%
 c
-      Double precision 
+      Double precision
      &                 v(ldv,maxncv), workl(maxncv*(maxncv+8)),
-     &                 workd(3*maxn), d(maxncv,2), resid(maxn), 
+     &                 workd(3*maxn), d(maxncv,2), resid(maxn),
      &                 ad(maxn), adl(maxn), adu(maxn), adu2(maxn),
      &                 ax(maxn), mx(maxn)
       logical          select(maxncv)
@@ -85,25 +85,25 @@ c
       integer          ido, n, nev, ncv, lworkl, info, j, ierr,
      &                 nconv, maxitr, ishfts, mode
       logical          rvec
-      Double precision 
+      Double precision
      &                 sigma, r1, r2, tol, h
 c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Double precision  
+      Double precision
      &                 zero, one, four, six
-      parameter        ( zero = 0.0D+0 , one = 1.0D+0 , 
+      parameter        ( zero = 0.0D+0 , one = 1.0D+0 ,
      &                   four = 4.0D+0 , six = 6.0D+0  )
 c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Double precision 
-     &                 dnrm2 
-      external         daxpy , dcopy , dscal , dnrm2 , dgttrf , dgttrs 
+      Double precision
+     &                 dnrm2
+      external         daxpy , dcopy , dscal , dnrm2 , dgttrf , dgttrs
 c
 c     %--------------------%
 c     | Intrinsic function |
@@ -123,9 +123,9 @@ c     | approximated.  The user can modify NEV, NCV, WHICH |
 c     | to solve problems of different sizes, and to get   |
 c     | different parts of the spectrum.  However, The     |
 c     | following conditions must be satisfied:            |
-c     |                     N <= MAXN,                     | 
+c     |                     N <= MAXN,                     |
 c     |                   NEV <= MAXNEV,                   |
-c     |               NEV + 1 <= NCV <= MAXNCV             | 
+c     |               NEV + 1 <= NCV <= MAXNCV             |
 c     %----------------------------------------------------%
 c
       n = 100
@@ -157,7 +157,7 @@ c     | iteration.                                       |
 c     %--------------------------------------------------%
 c
       lworkl = ncv*(ncv+8)
-      tol = zero 
+      tol = zero
       ido = 0
       info = 0
 c
@@ -176,7 +176,7 @@ c
       mode   = 2
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr 
+      iparam(3) = maxitr
       iparam(7) = mode
 c
 c     %------------------------------------------------%
@@ -188,18 +188,18 @@ c     %------------------------------------------------%
 c
       h = one / dble (n+1)
 c
-      r1 = (four / six) * h 
+      r1 = (four / six) * h
       r2 = (one / six) * h
       do 20 j=1,n
          ad(j) =  r1
          adl(j) = r2
- 20   continue 
+ 20   continue
       call dcopy  (n, adl, 1, adu, 1)
       call dgttrf  (n, adl, ad, adu, adu2, ipiv, ierr)
-      if (ierr .ne. 0) then 
+      if (ierr .ne. 0) then
          print *, ' '
          print *, ' Error with _gttrf in _SDRV3. '
-         print *, ' ' 
+         print *, ' '
          go to 9000
       end if
 c
@@ -210,13 +210,13 @@ c
  10   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine DSAUPD  and take | 
+c        | Repeatedly call the routine DSAUPD  and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call dsaupd  ( ido, bmat, n, which, nev, tol, resid, 
+         call dsaupd  ( ido, bmat, n, which, nev, tol, resid,
      &                 ncv, v, ldv, iparam, ipntr, workd, workl,
      &                 lworkl, info )
 c
@@ -229,7 +229,7 @@ c           | matrix vector multiplication (A*x)   |
 c           | routine and a linear system solver   |
 c           | here.  The matrix vector             |
 c           | multiplication routine takes         |
-c           | workd(ipntr(1)) as the input vector. | 
+c           | workd(ipntr(1)) as the input vector. |
 c           | The final result is returned to      |
 c           | workd(ipntr(2)). The result of A*x   |
 c           | overwrites workd(ipntr(1)).          |
@@ -237,12 +237,12 @@ c           %--------------------------------------%
 c
             call av (n, workd(ipntr(1)), workd(ipntr(2)))
             call dcopy (n, workd(ipntr(2)),  1, workd(ipntr(1)), 1)
-            call dgttrs  ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, 
+            call dgttrs  ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv,
      &                  workd(ipntr(2)), n, ierr)
-            if (ierr .ne. 0) then 
+            if (ierr .ne. 0) then
                print *, ' '
                print *, ' Error with _gttrs in _SDRV3.'
-               print *, ' '  
+               print *, ' '
                go to 9000
             end if
 c
@@ -271,7 +271,7 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-         end if 
+         end if
 c
 c
 c
@@ -290,24 +290,24 @@ c
          print *, ' '
          print *, ' Error with _saupd, info = ',info
          print *, ' Check the documentation of _saupd '
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using DSEUPD .                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
-c           
+c
          rvec = .true.
 c
-         call dseupd  ( rvec, 'All', select, d, v, ldv, sigma, 
-     &        bmat, n, which, nev, tol, resid, ncv, v, ldv, 
+         call dseupd  ( rvec, 'All', select, d, v, ldv, sigma,
+     &        bmat, n, which, nev, tol, resid, ncv, v, ldv,
      &        iparam, ipntr, workd, workl, lworkl, ierr )
 c
 c        %----------------------------------------------%
@@ -321,19 +321,19 @@ c        | corresponding to the eigenvalues in D is     |
 c        | returned in V.                               |
 c        %----------------------------------------------%
 c
-         if (ierr .ne. 0) then 
+         if (ierr .ne. 0) then
 c
 c           %------------------------------------%
 c           | Error condition:                   |
 c           | Check the documentation of DSEUPD . |
 c           %------------------------------------%
-c 
-            print *, ' ' 
+c
+            print *, ' '
             print *, ' Error with _seupd, info = ', ierr
             print *, ' Check the documentation of _seupd'
             print *, ' '
 c
-         else 
+         else
 c
             nconv =  iparam(5)
             do 30 j=1, nconv
@@ -376,23 +376,23 @@ c
             print *, ' Maximum number of iterations reached.'
             print *, ' '
          else if ( info .eq. 3) then
-            print *, ' ' 
+            print *, ' '
             print *, ' No shifts could be applied during implicit',
      &               ' Arnoldi update, try increasing NCV.'
             print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _SDRV3 '
          print *, ' ====== '
-         print *, ' ' 
+         print *, ' '
          print *, ' Size of the matrix is ', n
          print *, ' The number of Ritz values requested is ', nev
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -416,17 +416,17 @@ c     on the interval [0,1].
 c
       subroutine mv (n, v, w)
       integer           n, j
-      Double precision 
+      Double precision
      &                  v(n),w(n), one, four, six, h
-      parameter         (one = 1.0D+0 , four = 4.0D+0 , 
+      parameter         (one = 1.0D+0 , four = 4.0D+0 ,
      &                   six = 6.0D+0 )
 c
       w(1) = four*v(1) + v(2)
       do 100 j = 2,n-1
-         w(j) = v(j-1) + four*v(j) + v(j+1) 
+         w(j) = v(j-1) + four*v(j) + v(j+1)
   100 continue
       j = n
-      w(j) = v(j-1) + four*v(j) 
+      w(j) = v(j-1) + four*v(j)
 c
 c     Scale the vector w by h.
 c
@@ -438,23 +438,23 @@ c
 c--------------------------------------------------------------------
 c     matrix vector subroutine
 c
-c     The matrix used is the stiffness matrix obtained from the finite 
+c     The matrix used is the stiffness matrix obtained from the finite
 c     element discretization of the 1-dimensional discrete Laplacian
 c     on the interval [0,1] with zero Dirichlet boundary condition using
 c     piecewise linear elements.
 c
       subroutine av (n, v, w)
       integer           n, j
-      Double precision 
+      Double precision
      &                  v(n),w(n), two, one, h
       parameter         ( one = 1.0D+0 , two = 2.0D+0  )
 c
       w(1) =  two*v(1) - v(2)
       do 100 j = 2,n-1
-         w(j) = - v(j-1) + two*v(j) - v(j+1) 
+         w(j) = - v(j-1) + two*v(j) - v(j+1)
   100 continue
       j = n
-      w(j) = - v(j-1) + two*v(j) 
+      w(j) = - v(j-1) + two*v(j)
 c
 c     Scale the vector w by (1 / h).
 c

EXAMPLES/SYM/dsdrv4.f

@@ -1,9 +1,9 @@
-      program dsdrv4 
+      program dsdrv4
 c
 c     Program to illustrate the idea of reverse communication
 c     in shift and invert mode for a generalized symmetric eigenvalue
-c     problem.  The following program uses the two LAPACK subroutines 
-c     dgttrf.f and dgttrs to factor and solve a tridiagonal system of 
+c     problem.  The following program uses the two LAPACK subroutines
+c     dgttrf.f and dgttrs to factor and solve a tridiagonal system of
 c     equations.
 c
 c     We implement example four of ex-sym.doc in DOCUMENTS directory
@@ -34,7 +34,7 @@ c     dscal   Level 1 BLAS that scales a vector by a scalar.
 c     dnrm2   Level 1 BLAS that computes the norm of a vector.
 c     av      Matrix vector multiplication routine that computes A*x.
 c     mv      Matrix vector multiplication routine that computes M*x.
-c 
+c
 c\Author
 c     Richard Lehoucq
 c     Danny Sorensen
@@ -51,7 +51,7 @@ c\Remarks
 c     1. None
 c
 c\EndLib
-c----------------------------------------------------------------------     
+c----------------------------------------------------------------------
 c
 c     %-----------------------------%
 c     | Define leading dimensions   |
@@ -63,7 +63,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer          maxn, maxnev, maxncv, ldv
-      parameter        (maxn=256, maxnev=10, maxncv=25, 
+      parameter        (maxn=256, maxnev=10, maxncv=25,
      &                 ldv=maxn)
 c
 c     %--------------%
@@ -72,7 +72,7 @@ c     %--------------%
 c
       Double precision
      &                 v(ldv,maxncv), workl(maxncv*(maxncv+8)),
-     &                 workd(3*maxn), d(maxncv,2), resid(maxn), 
+     &                 workd(3*maxn), d(maxncv,2), resid(maxn),
      &                 ad(maxn), adl(maxn), adu(maxn), adu2(maxn)
       logical          select(maxncv)
       integer          iparam(11), ipntr(11), ipiv(maxn)
@@ -85,7 +85,7 @@ c
       integer          ido, n, nev, ncv, lworkl, info, j, ierr,
      &                 nconv, maxitr, ishfts, mode
       logical          rvec
-      Double precision    
+      Double precision
      &                 sigma, r1, r2, tol, h
 c
 c     %------------%
@@ -126,10 +126,10 @@ c     | The user can modify NEV, NCV, SIGMA to solve       |
 c     | problems of different sizes, and to get different  |
 c     | parts of the spectrum. However, The following      |
 c     | conditions must be satisfied:                      |
-c     |                   N <= MAXN,                       | 
+c     |                   N <= MAXN,                       |
 c     |                 NEV <= MAXNEV,                     |
-c     |             NEV + 1 <= NCV <= MAXNCV               | 
-c     %----------------------------------------------------% 
+c     |             NEV + 1 <= NCV <= MAXNCV               |
+c     %----------------------------------------------------%
 c
       n = 100
       nev = 4
@@ -146,7 +146,7 @@ c
       end if
       bmat = 'G'
       which = 'LM'
-      sigma = zero 
+      sigma = zero
 c
 c     %--------------------------------------------------%
 c     | The work array WORKL is used in DSAUPD as        |
@@ -161,7 +161,7 @@ c     | iteration.                                       |
 c     %--------------------------------------------------%
 c
       lworkl = ncv*(ncv+8)
-      tol = zero 
+      tol = zero
       ido = 0
       info = 0
 c
@@ -180,8 +180,8 @@ c
       mode   = 3
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %-------------------------------------------------------%
 c     | Call LAPACK routine to factor the tridiagonal matrix  |
@@ -197,10 +197,10 @@ c
       do 20 j=1,n
          ad(j) = two/h - sigma * r1
          adl(j) = -one/h - sigma * r2
- 20   continue 
+ 20   continue
       call dcopy (n, adl, 1, adu, 1)
       call dgttrf (n, adl, ad, adu, adu2, ipiv, ierr)
-      if (ierr .ne. 0) then 
+      if (ierr .ne. 0) then
          print *, ' Error with _gttrf in _SDRV4.'
          go to 9000
       end if
@@ -238,12 +238,12 @@ c           %--------------------------------------------%
 c
             call mv (n, workd(ipntr(1)), workd(ipntr(2)))
 c
-            call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, 
-     &                   workd(ipntr(2)), n, ierr) 
-            if (ierr .ne. 0) then 
+            call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv,
+     &                   workd(ipntr(2)), n, ierr)
+            if (ierr .ne. 0) then
                print *, ' '
                print *, ' Error with _gttrs in _SDRV4. '
-               print *, ' ' 
+               print *, ' '
                go to 9000
             end if
 c
@@ -261,16 +261,16 @@ c           | M*x has been saved in workd(ipntr(3)).  |
 c           | the user only needs the linear system   |
 c           | solver here that takes workd(ipntr(3)   |
 c           | as input, and returns the result to     |
-c           | workd(ipntr(2)).                        | 
+c           | workd(ipntr(2)).                        |
 c           %-----------------------------------------%
 c
             call dcopy ( n, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-            call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, 
+            call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv,
      &                   workd(ipntr(2)), n, ierr)
-            if (ierr .ne. 0) then 
+            if (ierr .ne. 0) then
                print *, ' '
                print *, ' Error with _gttrs in _SDRV4.'
-               print *, ' ' 
+               print *, ' '
                go to 9000
             end if
 c
@@ -298,7 +298,7 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-        end if 
+        end if
 c
 c     %-----------------------------------------%
 c     | Either we have convergence, or there is |
@@ -315,9 +315,9 @@ c
          print *, ' '
          print *, ' Error with _saupd, info = ',info
          print *, ' Check the documentation of _saupd '
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
@@ -332,7 +332,7 @@ c
          rvec = .true.
 c
          call dseupd ( rvec, 'All', select, d, v, ldv, sigma,
-     &        bmat, n, which, nev, tol, resid, ncv, v, ldv, 
+     &        bmat, n, which, nev, tol, resid, ncv, v, ldv,
      &        iparam, ipntr, workd, workl, lworkl, ierr )
 c
 c        %----------------------------------------------%
@@ -346,7 +346,7 @@ c        | corresponding to the eigenvalues in D is     |
 c        | returned in V.                               |
 c        %----------------------------------------------%
 c
-         if ( ierr .ne. 0 ) then 
+         if ( ierr .ne. 0 ) then
 c
 c           %------------------------------------%
 c           | Error condition:                   |
@@ -358,7 +358,7 @@ c
             print *, ' Check the documentation of _seupd '
             print *, ' '
 c
-         else 
+         else
 c
             nconv =  iparam(5)
             do 30 j=1, nconv
@@ -375,7 +375,7 @@ c              | indicates how many are    |
 c              | accurate to the requested |
 c              | tolerance)                |
 c              %---------------------------%
-c  
+c
                call av(n, v(1,j), workd)
                call mv(n, v(1,j), workd(n+1))
                call daxpy (n, -d(j,1), workd(n+1), 1, workd, 1)
@@ -414,7 +414,7 @@ c
      &               ' (NCV) is ', ncv
         print *, ' What portion of the spectrum: ', which
         print *, ' The number of converged Ritz values is ',
-     &             nconv 
+     &             nconv
         print *, ' The number of Implicit Arnoldi update',
      &           ' iterations taken is ', iparam(3)
         print *, ' The number of OP*x is ', iparam(9)
@@ -440,15 +440,15 @@ c
       integer         n, j
       Double precision
      &                v(n),w(n), one, four, six, h
-      parameter       (one = 1.0D+0, four = 4.0D+0, 
+      parameter       (one = 1.0D+0, four = 4.0D+0,
      &                 six = 6.0D+0)
 c
       w(1) =  four*v(1) + v(2)
       do 100 j = 2,n-1
-         w(j) = v(j-1) + four*v(j) + v(j+1) 
+         w(j) = v(j-1) + four*v(j) + v(j+1)
   100 continue
       j = n
-      w(j) = v(j-1) + four*v(j) 
+      w(j) = v(j-1) + four*v(j)
 c
 c     Scale the vector w by h.
 c
@@ -458,8 +458,8 @@ c
       end
 c------------------------------------------------------------------------
 c     matrix vector subroutine
-c     where the matrix is the finite element discretization of the 
-c     1 dimensional discrete Laplacian on [0,1] with zero Dirichlet 
+c     where the matrix is the finite element discretization of the
+c     1 dimensional discrete Laplacian on [0,1] with zero Dirichlet
 c     boundary condition using piecewise linear elements.
 c
       subroutine av (n, v, w)
@@ -470,10 +470,10 @@ c
 c
       w(1) =  two*v(1) - v(2)
       do 100 j = 2,n-1
-         w(j) = - v(j-1) + two*v(j) - v(j+1) 
+         w(j) = - v(j-1) + two*v(j) - v(j+1)
   100 continue
       j = n
-      w(j) = - v(j-1) + two*v(j) 
+      w(j) = - v(j-1) + two*v(j)
 c
 c     Scale the vector w by (1/h)
 c

EXAMPLES/SYM/dsdrv5.f

@@ -1,9 +1,9 @@
-      program dsdrv5 
+      program dsdrv5
 c
 c     Program to illustrate the idea of reverse communication
 c     in Buckling mode for a generalized symmetric eigenvalue
-c     problem.  The following program uses the two LAPACK subroutines 
-c     dgttrf.f and dgttrs.f to factor and solve a tridiagonal system of 
+c     problem.  The following program uses the two LAPACK subroutines
+c     dgttrf.f and dgttrs.f to factor and solve a tridiagonal system of
 c     equations.
 c
 c     We implement example five of ex-sym.doc in DOCUMENTS directory
@@ -21,8 +21,8 @@ c
 c\BeginLib
 c
 c\References:
-c  1. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos 
-c     Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", 
+c  1. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos
+c     Algorithm for Solving Sparse Symmetric Generalized Eigenproblems",
 c     SIAM J. Matr. Anal. Apps.,  January (1993).
 c
 c\Routines called:
@@ -34,7 +34,7 @@ c     dgttrs  LAPACK tridiagonal solve routine.
 c     daxpy   Level 1 BLAS that computes y <- alpha*x+y.
 c     dcopy   Level 1 BLAS that copies one vector to another.
 c     dscal   Level 1 BLAS that scales a vector by a scalar.
-c     dnrm2   Level 1 BLAS that computes the norm of a vector.   
+c     dnrm2   Level 1 BLAS that computes the norm of a vector.
 c     av      Matrix vector multiplication routine that computes A*x.
 c     mv      Matrix vector multiplication routine that computes M*x.
 c
@@ -54,7 +54,7 @@ c\Remarks
 c     1. None
 c
 c\EndLib
-c----------------------------------------------------------------------     
+c----------------------------------------------------------------------
 c
 c     %-----------------------------%
 c     | Define leading dimensions   |
@@ -66,7 +66,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer          maxn, maxnev, maxncv, ldv
-      parameter        (maxn=256, maxnev=10, maxncv=25, 
+      parameter        (maxn=256, maxnev=10, maxncv=25,
      &                 ldv=maxn)
 c
 c     %--------------%
@@ -75,7 +75,7 @@ c     %--------------%
 c
       Double precision
      &                 v(ldv,maxncv), workl(maxncv*(maxncv+8)),
-     &                 workd(3*maxn), d(maxncv,2), resid(maxn), 
+     &                 workd(3*maxn), d(maxncv,2), resid(maxn),
      &                 ad(maxn), adl(maxn), adu(maxn), adu2(maxn),
      &                 ax(maxn), mx(maxn)
       logical          select(maxncv)
@@ -89,7 +89,7 @@ c
       integer          ido, n, nev, ncv, lworkl, info, j, ierr,
      &                 nconv, maxitr, ishfts, mode
       logical          rvec
-      Double precision    
+      Double precision
      &                 h, sigma, r1, r2, tol
 c
 c     %------------%
@@ -130,12 +130,12 @@ c     | NCV, SIGMA to solve problems of different sizes, |
 c     | and to get different parts of the spectrum.      |
 c     | However, The following conditions must be        |
 c     | satisfied:                                       |
-c     |                 N <= MAXN,                       | 
+c     |                 N <= MAXN,                       |
 c     |               NEV <= MAXNEV,                     |
 c     |           NEV + 1 <= NCV <= MAXNCV               |
-c     |                                                  | 
+c     |                                                  |
 c     | The  shift SIGMA cannot be zero!!!               |
-c     %--------------------------------------------------% 
+c     %--------------------------------------------------%
 c
       n = 100
       nev = 4
@@ -152,7 +152,7 @@ c
       end if
       bmat = 'G'
       which = 'LM'
-      sigma = one 
+      sigma = one
 c
 c     %-----------------------------------------------------%
 c     | The work array WORKL is used in DSAUPD as           |
@@ -166,7 +166,7 @@ c     | generated in DSAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl = ncv*(ncv+8)
-      tol = zero 
+      tol = zero
       ido = 0
       info = 0
 c
@@ -185,8 +185,8 @@ c
       mode   = 4
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %------------------------------------------------------%
 c     | Call LAPACK routine to factor the tridiagonal matrix |
@@ -203,10 +203,10 @@ c
       do 20 j=1,n
          ad(j) = two / h - sigma * r1
          adl(j) = -one / h- sigma * r2
- 20   continue 
+ 20   continue
       call dcopy (n, adl, 1, adu, 1)
       call dgttrf (n, adl, ad, adu, adu2, ipiv, ierr)
-      if (ierr .ne. 0) then 
+      if (ierr .ne. 0) then
          print *, ' '
          print *, ' Error with _gttrf in _SDRV5.'
          print *, ' '
@@ -226,8 +226,8 @@ c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call dsaupd ( ido, bmat, n, which, nev, tol, resid, 
-     &        ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, 
+         call dsaupd ( ido, bmat, n, which, nev, tol, resid,
+     &        ncv, v, ldv, iparam, ipntr, workd, workl, lworkl,
      &        info )
 c
          if (ido .eq. -1) then
@@ -246,10 +246,10 @@ c           %-------------------------------------------%
 c
             call av (n, workd(ipntr(1)), workd(ipntr(2)))
 c
-            call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, 
+            call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv,
      &                   workd(ipntr(2)), n, ierr)
-            if (ierr .ne. 0) then 
-               print *, ' ' 
+            if (ierr .ne. 0) then
+               print *, ' '
                print *, ' Error with _gttrs in SDRV5.'
                print *, ' '
                go to 9000
@@ -273,9 +273,9 @@ c           | workd(ipntr(2)).                         |
 c           %------------------------------------------%
 c
             call dcopy ( n, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-            call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, 
+            call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv,
      &                   workd(ipntr(2)), n, ierr)
-            if (ierr .ne. 0) then 
+            if (ierr .ne. 0) then
                print *, ' '
                print *, ' Error with _gttrs in _SDRV5.'
                print *, ' '
@@ -306,7 +306,7 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-         end if 
+         end if
 c
 c     %-----------------------------------------%
 c     | Either we have convergence, or there is |
@@ -323,9 +323,9 @@ c
          print *, ' '
          print *, ' Error with _saupd, info = ',info
          print *, ' Check the documentation of _saupd '
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
@@ -339,11 +339,11 @@ c        %-------------------------------------------%
 c
          rvec = .true.
 c
-         call dseupd ( rvec, 'All', select, d, v, ldv, sigma, 
-     &        bmat, n, which, nev, tol, resid, ncv, v, ldv, 
+         call dseupd ( rvec, 'All', select, d, v, ldv, sigma,
+     &        bmat, n, which, nev, tol, resid, ncv, v, ldv,
      &        iparam, ipntr, workd, workl, lworkl, ierr )
 c
-         if (ierr .ne. 0) then 
+         if (ierr .ne. 0) then
 c
 c           %------------------------------------%
 c           | Error condition:                   |
@@ -357,7 +357,7 @@ c
 c
          else
 c
-            nconv =  iparam(5) 
+            nconv =  iparam(5)
             do 30 j=1, nconv
 c
 c              %---------------------------%
@@ -412,7 +412,7 @@ c
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
          print *, ' The number of converged Ritz values is ',
-     &              nconv 
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -432,7 +432,7 @@ c
 c------------------------------------------------------------------------
 c     Matrix vector subroutine
 c     where the matrix is the 1-dimensional mass matrix
-c     arising from using piecewise linear finite elements on the 
+c     arising from using piecewise linear finite elements on the
 c     interval [0,1].
 c
       subroutine mv (n, v, w)
@@ -444,10 +444,10 @@ c
 c
       w(1) =  four*v(1) + v(2)
       do 100 j = 2,n-1
-         w(j) = v(j-1) + four*v(j) + v(j+1) 
+         w(j) = v(j-1) + four*v(j) + v(j+1)
   100 continue
       j = n
-      w(j) = v(j-1) + four*v(j) 
+      w(j) = v(j-1) + four*v(j)
 c
 c     Scale the vector w by h.
 c
@@ -470,10 +470,10 @@ c
 c
       w(1) =  two*v(1) - v(2)
       do 100 j = 2,n-1
-         w(j) = - v(j-1) + two*v(j) - v(j+1) 
+         w(j) = - v(j-1) + two*v(j) - v(j+1)
   100 continue
       j = n
-      w(j) = - v(j-1) + two*v(j) 
+      w(j) = - v(j-1) + two*v(j)
 c
 c     Scale the vector w by (1/h)
 c

EXAMPLES/SYM/dsdrv6.f

@@ -1,9 +1,9 @@
-      program dsdrv6 
+      program dsdrv6
 c
 c     Program to illustrate the idea of reverse communication
-c     in Cayley mode for a generalized symmetric eigenvalue 
-c     problem.  The following program uses the two LAPACK subroutines 
-c     dgttrf.f and dgttrs.f to factor and solve a tridiagonal system of 
+c     in Cayley mode for a generalized symmetric eigenvalue
+c     problem.  The following program uses the two LAPACK subroutines
+c     dgttrf.f and dgttrs.f to factor and solve a tridiagonal system of
 c     equations.
 c
 c     We implement example six of ex-sym.doc in DOCUMENTS directory
@@ -23,8 +23,8 @@ c
 c\BeginLib
 c
 c\References:
-c  1. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos 
-c     Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", 
+c  1. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos
+c     Algorithm for Solving Sparse Symmetric Generalized Eigenproblems",
 c     SIAM J. Matr. Anal. Apps.,  January (1993).
 c
 c\Routines called:
@@ -36,7 +36,7 @@ c     dgttrs  LAPACK tridiagonal solve routine.
 c     daxpy   Level 1 BLAS that computes y <- alpha*x+y.
 c     dcopy   Level 1 BLAS that copies one vector to another.
 c     dscal   Level 1 BLAS that scales a vector by a scalar.
-c     dnrm2   Level 1 BLAS that computes the norm of a vector. 
+c     dnrm2   Level 1 BLAS that computes the norm of a vector.
 c     av      Matrix vector multiplication routine that computes A*x.
 c     mv      Matrix vector multiplication routine that computes M*x.
 c
@@ -46,9 +46,9 @@ c     Richard Lehoucq
 c     Chao Yang
 c     Dept. of Computational &
 c     Applied Mathematics
-c     Rice University 
-c     Houston, Texas 
-c 
+c     Rice University
+c     Houston, Texas
+c
 c\SCCS Information: @(#)
 c FILE: sdrv6.F   SID: 2.5   DATE OF SID: 10/17/00   RELEASE: 2
 c
@@ -68,7 +68,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer          maxn, maxnev, maxncv, ldv
-      parameter        (maxn=256, maxnev=10, maxncv=25, 
+      parameter        (maxn=256, maxnev=10, maxncv=25,
      &                 ldv=maxn)
 c
 c     %--------------%
@@ -77,7 +77,7 @@ c     %--------------%
 c
       Double precision
      &                 v(ldv,maxncv), workl(maxncv*(maxncv+8)),
-     &                 workd(3*maxn), d(maxncv,2), resid(maxn), 
+     &                 workd(3*maxn), d(maxncv,2), resid(maxn),
      &                 ad(maxn), adl(maxn), adu(maxn), adu2(maxn),
      &                 temp(maxn), ax(maxn), mx(maxn)
       logical          select(maxncv)
@@ -100,9 +100,9 @@ c     %------------%
 c
       Double precision
      &                 zero, one, two, four, six
-      parameter        (zero = 0.0D+0, one = 1.0D+0, 
+      parameter        (zero = 0.0D+0, one = 1.0D+0,
      &                  four = 4.0D+0, six = 6.0D+0,
-     &                  two = 2.0D+0 ) 
+     &                  two = 2.0D+0 )
 c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
@@ -132,9 +132,9 @@ c     | NCV, SIGMA to solve problems of different sizes, |
 c     | and to get different parts of the spectrum.      |
 c     | However, The following conditions must be        |
 c     | satisfied:                                       |
-c     |                 N <= MAXN,                       | 
+c     |                 N <= MAXN,                       |
 c     |               NEV <= MAXNEV,                     |
-c     |           NEV + 1 <= NCV <= MAXNCV               | 
+c     |           NEV + 1 <= NCV <= MAXNCV               |
 c     %--------------------------------------------------%
 c
       n = 100
@@ -186,8 +186,8 @@ c
       mode   = 5
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %------------------------------------------------------%
 c     | Call LAPACK routine to factor (A-sigma*M).  The      |
@@ -203,10 +203,10 @@ c
       do 20 j=1,n
          ad(j) = two / h - sigma * r1
          adl(j) = -one / h - sigma * r2
- 20   continue 
+ 20   continue
       call dcopy (n, adl, 1, adu, 1)
       call dgttrf (n, adl, ad, adu, adu2, ipiv, ierr)
-      if (ierr .ne. 0) then 
+      if (ierr .ne. 0) then
          print *, ' '
          print *, ' Error with _gttrf in _SDRV6.'
          print *, ' '
@@ -226,8 +226,8 @@ c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call dsaupd ( ido, bmat, n, which, nev, tol, resid, ncv, 
-     &                 v, ldv, iparam, ipntr, workd, workl, lworkl, 
+         call dsaupd ( ido, bmat, n, which, nev, tol, resid, ncv,
+     &                 v, ldv, iparam, ipntr, workd, workl, lworkl,
      &                 info )
 c
          if (ido .eq. -1) then
@@ -239,19 +239,19 @@ c           | user should provide his/her matrix vector (A*x, M*x)  |
 c           | multiplication routines and a linear system solver    |
 c           | here.  The matrix vector multiplication routine takes |
 c           | workd(ipntr(1)) as the input vector.  The final       |
-c           | result is returned to workd(ipntr(2)).                | 
+c           | result is returned to workd(ipntr(2)).                |
 c           %-------------------------------------------------------%
 c
             call av (n, workd(ipntr(1)), workd(ipntr(2)))
             call mv (n, workd(ipntr(1)), temp)
-            call daxpy(n, sigma, temp, 1, workd(ipntr(2)), 1) 
+            call daxpy(n, sigma, temp, 1, workd(ipntr(2)), 1)
 c
-            call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, 
+            call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv,
      &                workd(ipntr(2)), n, ierr)
-            if (ierr .ne. 0) then 
+            if (ierr .ne. 0) then
                print *, ' '
                print *, ' Error with _gttrs in _SDRV6.'
-               print *, ' ' 
+               print *, ' '
                go to 9000
             end if
 c
@@ -272,15 +272,15 @@ c           | matrix vector multiplication routine takes         |
 c           | workd(ipntr(1)) as the input, and the result is    |
 c           | combined with workd(ipntr(3)) to form the input    |
 c           | for the linear system solver.  The final result is |
-c           | returned to workd(ipntr(2)).                       | 
+c           | returned to workd(ipntr(2)).                       |
 c           %----------------------------------------------------%
 c
             call av (n, workd(ipntr(1)), workd(ipntr(2)))
             call daxpy(n, sigma, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-            call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, 
+            call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv,
      &                   workd(ipntr(2)), n, ierr)
-            if (ierr .ne. 0) then 
-               print *, ' ' 
+            if (ierr .ne. 0) then
+               print *, ' '
                print *, ' Error with _gttrs in _SDRV6. '
                print *, ' '
                go to 9000
@@ -309,7 +309,7 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-         end if 
+         end if
 c
 c     %-----------------------------------------%
 c     | Either we have convergence, or there is |
@@ -328,7 +328,7 @@ c
            print *, ' Check the documentation of _saupd. '
            print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
@@ -342,8 +342,8 @@ c        %-------------------------------------------%
 c
          rvec = .true.
 c
-         call dseupd ( rvec, 'All', select, d, v, ldv, sigma, 
-     &        bmat, n, which, nev, tol, resid, ncv, v, ldv, 
+         call dseupd ( rvec, 'All', select, d, v, ldv, sigma,
+     &        bmat, n, which, nev, tol, resid, ncv, v, ldv,
      &        iparam, ipntr, workd, workl, lworkl, ierr )
 c
 c        %----------------------------------------------%
@@ -357,7 +357,7 @@ c        | corresponding to the eigenvalues in D is     |
 c        | returned in V.                               |
 c        %----------------------------------------------%
 c
-         if ( ierr .ne. 0 ) then 
+         if ( ierr .ne. 0 ) then
 c
 c           %------------------------------------%
 c           | Error condition:                   |
@@ -383,7 +383,7 @@ c           | indicates how many are    |
 c           | accurate to the requested |
 c           | tolerance)                |
 c           %---------------------------%
-c  
+c
             nconv = iparam(5)
             do 30 j=1, nconv
                call av(n, v(1,j), ax)
@@ -423,7 +423,7 @@ c
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
          print *, ' The number of converged Ritz values is ',
-     &              nconv 
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &           ' iterations taken is', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -448,17 +448,17 @@ c     on the interval [0,1].
 c
       subroutine mv (n, v, w)
       integer           n, j
-      Double precision 
+      Double precision
      &                  v(n), w(n), one, four, six, h
-      parameter         (one = 1.0D+0, four = 4.0D+0, 
-     &                   six = 6.0D+0) 
+      parameter         (one = 1.0D+0, four = 4.0D+0,
+     &                   six = 6.0D+0)
 c
       w(1) =  four*v(1) + v(2)
       do 100 j = 2,n-1
-         w(j) = v(j-1) + four*v(j) + v(j+1) 
+         w(j) = v(j-1) + four*v(j) + v(j+1)
   100 continue
       j = n
-      w(j) = v(j-1) + four*v(j) 
+      w(j) = v(j-1) + four*v(j)
 c
 c     Scale the vector w by h.
 c
@@ -469,7 +469,7 @@ c
 c
 c------------------------------------------------------------------------
 c     Matrix vector subroutine
-c     where the matrix is the stiffness matrix obtained from the 
+c     where the matrix is the stiffness matrix obtained from the
 c     finite element discretization of the 1-dimensional discrete Laplacian
 c     on the interval [0,1] with zero Dirichlet boundary condition
 c     using piecewise linear elements.
@@ -482,14 +482,14 @@ c
 c
       w(1) =  two*v(1) - v(2)
       do 100 j = 2,n-1
-         w(j) = - v(j-1) + two*v(j) - v(j+1) 
+         w(j) = - v(j-1) + two*v(j) - v(j+1)
   100 continue
       j = n
       w(j) = - v(j-1) + two*v(j)
-c     
+c
 c     Scale the vector w by (1/h).
 c
       h = one / dble(n+1)
-      call dscal(n, one/h, w, 1) 
+      call dscal(n, one/h, w, 1)
       return
       end

EXAMPLES/SYM/makefile

@@ -1,64 +0,0 @@
-#
-# makefile to run simple examples of the reverse communication
-# protocol.
-#
-# Modify if ARPACK library was built somewhere else.
-# We assume that the required BLAS and LAPACK routines
-# are in the version of libarpack.a built. If not, you
-# will need to modify the link step below and link to them.
-#
-#\SCCS Information: @(#) 
-# FILE: makefile   SID: 2.1   DATE OF SID: 11/19/95   RELEASE: 2
-#
-include ../../ARmake.inc
-#
-# Issue "make sym" to make all 12 symmetric drivers
-# Issue "make ssdrv" to make 6 single precision symmetric drivers
-# Issue "make dsdrv" to make 6 double precision symmetric drivers
-#
-sym: ssdrv dsdrv 
-#
-# simple symmetric problem using single precision
-#
-ssdrv: ssdrv1 ssdrv2 ssdrv3 ssdrv4 ssdrv5 ssdrv6
-
-ssdrv1: ssdrv1.o 
-	$(FC) $(FFLAGS) ssdrv1.o $(ALIBS) -o ssdrv1
-#
-ssdrv2: ssdrv2.o 
-	$(FC) $(FFLAGS) ssdrv2.o $(ALIBS) -o ssdrv2
-#
-ssdrv3: ssdrv3.o 
-	$(FC) $(FFLAGS) ssdrv3.o $(ALIBS) -o ssdrv3
-#
-ssdrv4: ssdrv4.o 
-	$(FC) $(FFLAGS) ssdrv4.o $(ALIBS) -o ssdrv4
-#
-ssdrv5: ssdrv5.o 
-	$(FC) $(FFLAGS) ssdrv5.o $(ALIBS) -o ssdrv5
-#
-ssdrv6: ssdrv6.o
-	$(FC) $(FFLAGS) ssdrv6.o $(ALIBS) -o ssdrv6
-#
-#-----------------------------------------------------------------------
-# simple symmetric problem using double precision
-#
-dsdrv: dsdrv1 dsdrv2 dsdrv3 dsdrv4 dsdrv5 dsdrv6
-
-dsdrv1: dsdrv1.o
-	$(FC) $(FFLAGS) dsdrv1.o $(ALIBS) -o dsdrv1
-#
-dsdrv2: dsdrv2.o 
-	$(FC) $(FFLAGS) dsdrv2.o $(ALIBS) -o dsdrv2
-#
-dsdrv3: dsdrv3.o
-	$(FC) $(FFLAGS) dsdrv3.o $(ALIBS) -o dsdrv3
-#
-dsdrv4: dsdrv4.o
-	$(FC) $(FFLAGS) dsdrv4.o $(ALIBS) -o dsdrv4
-#
-dsdrv5: dsdrv5.o
-	$(FC) $(FFLAGS) dsdrv5.o $(ALIBS) -o dsdrv5
-#
-dsdrv6: dsdrv6.o
-	$(FC) $(FFLAGS) dsdrv6.o $(ALIBS) -o dsdrv6 

EXAMPLES/SYM/ssdrv1.f

@@ -1,4 +1,4 @@
-      program ssdrv1 
+      program ssdrv1
 c
 c     Simple program to illustrate the idea of reverse communication
 c     in regular mode for a standard symmetric eigenvalue problem.
@@ -26,7 +26,7 @@ c             Ritz vectors.
 c     snrm2   Level 1 BLAS that computes the norm of a vector.
 c     saxpy   Level 1 BLAS that computes y <- alpha*x+y.
 c     av      Matrix vector multiplication routine that computes A*x.
-c     tv      Matrix vector multiplication routine that computes T*x, 
+c     tv      Matrix vector multiplication routine that computes T*x,
 c             where T is a tridiagonal matrix.  It is used in routine
 c             av.
 c
@@ -59,7 +59,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer          maxn, maxnev, maxncv, ldv
-      parameter       (maxn=256, maxnev=10, maxncv=25, 
+      parameter       (maxn=256, maxnev=10, maxncv=25,
      $                 ldv=maxn )
 c
 c     %--------------%
@@ -78,10 +78,10 @@ c     | Local Scalars |
 c     %---------------%
 c
       character        bmat*1, which*2
-      integer          ido, n, nev, ncv, lworkl, info, ierr, j, 
+      integer          ido, n, nev, ncv, lworkl, info, ierr, j,
      &                 nx, nconv, maxitr, mode, ishfts
       logical          rvec
-      Real      
+      Real
      &                 tol, sigma
 c
 c     %------------%
@@ -91,12 +91,12 @@ c
       Real
      &                 zero
       parameter        (zero = 0.0E+0)
-c  
+c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real           
+      Real
      &                 snrm2
       external         snrm2, saxpy
 c
@@ -122,15 +122,15 @@ c     | modify NEV, NCV, WHICH to solve problems of        |
 c     | different sizes, and to get different parts of the |
 c     | spectrum.  However, The following conditions must  |
 c     | be satisfied:                                      |
-c     |                   N <= MAXN,                       | 
+c     |                   N <= MAXN,                       |
 c     |                 NEV <= MAXNEV,                     |
-c     |             NEV + 1 <= NCV <= MAXNCV               | 
-c     %----------------------------------------------------% 
+c     |             NEV + 1 <= NCV <= MAXNCV               |
+c     %----------------------------------------------------%
 c
       nx = 10
       n = nx*nx
-      nev =  4 
-      ncv =  10 
+      nev =  4
+      ncv =  10
       if ( n .gt. maxn ) then
          print *, ' ERROR with _SDRV1: N is greater than MAXN '
          go to 9000
@@ -157,7 +157,7 @@ c     | iteration.                                       |
 c     %--------------------------------------------------%
 c
       lworkl = ncv*(ncv+8)
-      tol = zero 
+      tol = zero
       info = 0
       ido = 0
 c
@@ -174,10 +174,10 @@ c
       ishfts = 1
       maxitr = 300
       mode   = 1
-c      
-      iparam(1) = ishfts 
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+c
+      iparam(1) = ishfts
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %-------------------------------------------%
 c     | M A I N   L O O P (Reverse communication) |
@@ -186,13 +186,13 @@ c
  10   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine SSAUPD and take | 
+c        | Repeatedly call the routine SSAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call ssaupd ( ido, bmat, n, which, nev, tol, resid, 
+         call ssaupd ( ido, bmat, n, which, nev, tol, resid,
      &                 ncv, v, ldv, iparam, ipntr, workd, workl,
      &                 lworkl, info )
 c
@@ -216,7 +216,7 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-         end if 
+         end if
 c
 c     %----------------------------------------%
 c     | Either we have convergence or there is |
@@ -235,22 +235,22 @@ c
          print *, ' Check documentation in _saupd '
          print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using SSEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
-c           
+c
          rvec = .true.
 c
-         call sseupd ( rvec, 'All', select, d, v, ldv, sigma, 
-     &        bmat, n, which, nev, tol, resid, ncv, v, ldv, 
+         call sseupd ( rvec, 'All', select, d, v, ldv, sigma,
+     &        bmat, n, which, nev, tol, resid, ncv, v, ldv,
      &        iparam, ipntr, workd, workl, lworkl, ierr )
 
 c        %----------------------------------------------%
@@ -318,11 +318,11 @@ c
             print *, ' Maximum number of iterations reached.'
             print *, ' '
          else if ( info .eq. 3) then
-            print *, ' ' 
+            print *, ' '
             print *, ' No shifts could be applied during implicit',
      &               ' Arnoldi update, try increasing NCV.'
             print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _SDRV1 '
@@ -333,8 +333,8 @@ c
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -350,17 +350,17 @@ c
  9000 continue
 c
       end
-c 
+c
 c ------------------------------------------------------------------
 c     matrix vector subroutine
 c
 c     The matrix used is the 2 dimensional discrete Laplacian on unit
 c     square with zero Dirichlet boundary condition.
 c
-c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block 
+c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block
 c     tridiagonal matrix
 c
-c                  | T -I          | 
+c                  | T -I          |
 c                  |-I  T -I       |
 c             OP = |   -I  T       |
 c                  |        ...  -I|
@@ -372,7 +372,7 @@ c
       integer           nx, j, lo, n2
       Real
      &                  v(nx*nx), w(nx*nx), one, h2
-      parameter         ( one = 1.0E+0 ) 
+      parameter         ( one = 1.0E+0 )
 c
       call tv(nx,v(1),w(1))
       call saxpy(nx, -one, v(nx+1), 1, w(1), 1)
@@ -382,7 +382,7 @@ c
          call tv(nx, v(lo+1), w(lo+1))
          call saxpy(nx, -one, v(lo-nx+1), 1, w(lo+1), 1)
          call saxpy(nx, -one, v(lo+nx+1), 1, w(lo+1), 1)
-  10  continue 
+  10  continue
 c
       lo = (nx-1)*nx
       call tv(nx, v(lo+1), w(lo+1))
@@ -392,14 +392,14 @@ c     Scale the vector w by (1/h^2), where h is the mesh size
 c
       n2 = nx*nx
       h2 = one / real((nx+1)*(nx+1))
-      call sscal(n2, one/h2, w, 1) 
+      call sscal(n2, one/h2, w, 1)
       return
       end
 c
 c-------------------------------------------------------------------
       subroutine tv (nx, x, y)
 c
-      integer           nx, j 
+      integer           nx, j
       Real
      &                  x(nx), y(nx), dd, dl, du
 c
@@ -408,19 +408,19 @@ c
       parameter        (one = 1.0E+0 )
 c
 c     Compute the matrix vector multiplication y<---T*x
-c     where T is a nx by nx tridiagonal matrix with DD on the 
+c     where T is a nx by nx tridiagonal matrix with DD on the
 c     diagonal, DL on the subdiagonal, and DU on the superdiagonal.
-c     
+c
 c
       dd  = 4.0E+0
-      dl  = -one 
+      dl  = -one
       du  = -one
-c 
+c
       y(1) =  dd*x(1) + du*x(2)
       do 10 j = 2,nx-1
-         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 
- 10   continue 
-      y(nx) =  dl*x(nx-1) + dd*x(nx) 
+         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1)
+ 10   continue
+      y(nx) =  dl*x(nx-1) + dd*x(nx)
       return
       end
 

EXAMPLES/SYM/ssdrv2.f

@@ -1,9 +1,9 @@
-      program ssdrv2 
+      program ssdrv2
 c
 c     Program to illustrate the idea of reverse communication
 c     in shift and invert mode for a standard symmetric eigenvalue
-c     problem.  The following program uses the two LAPACK subroutines 
-c     sgttrf.f and sgttrs.f to factor and solve a tridiagonal system of 
+c     problem.  The following program uses the two LAPACK subroutines
+c     sgttrf.f and sgttrs.f to factor and solve a tridiagonal system of
 c     equations.
 c
 c     We implement example two of ex-sym.doc in DOCUMENTS directory
@@ -25,7 +25,7 @@ c             Ritz vectors.
 c     sgttrf  LAPACK tridiagonal factorization routine.
 c     sgttrs  LAPACK tridiagonal solve routine.
 c     saxpy   saxpy   Level 1 BLAS that computes y <- alpha*x+y.
-c     snrm2   Level 1 BLAS that computes the norm of a vector.     
+c     snrm2   Level 1 BLAS that computes the norm of a vector.
 c     av      Matrix vector multiplication routine that computes A*x.
 c
 c\Author
@@ -56,7 +56,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer          maxn, maxnev, maxncv, ldv
-      parameter        (maxn=256, maxnev=10, maxncv=25, 
+      parameter        (maxn=256, maxnev=10, maxncv=25,
      &                 ldv=maxn )
 c
 c     %--------------%
@@ -65,7 +65,7 @@ c     %--------------%
 c
       Real
      &                 v(ldv,maxncv), workl(maxncv*(maxncv+8)),
-     &                 workd(3*maxn), d(maxncv,2), resid(maxn), 
+     &                 workd(3*maxn), d(maxncv,2), resid(maxn),
      &                 ad(maxn), adl(maxn), adu(maxn), adu2(maxn),
      &                 ax(maxn)
       logical          select(maxncv)
@@ -86,9 +86,9 @@ c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Real           
-     &                 zero, one, two 
-      parameter        (zero = 0.0E+0, one = 1.0E+0, 
+      Real
+     &                 zero, one, two
+      parameter        (zero = 0.0E+0, one = 1.0E+0,
      &                  two = 2.0E+0)
 c
 c     %-----------------------------%
@@ -115,14 +115,14 @@ c     | standard eigenvalue problem is solved (BMAT = 'I'. |
 c     | NEV is the number of eigenvalues (closest to       |
 c     | SIGMA) to be approximated.  Since the shift-invert |
 c     | mode is used, WHICH is set to 'LM'.  The user can  |
-c     | modify NEV, NCV, SIGMA to solve problems of        | 
+c     | modify NEV, NCV, SIGMA to solve problems of        |
 c     | different sizes, and to get different parts of the |
 c     | spectrum.  However, The following conditions must  |
 c     | be satisfied:                                      |
-c     |                   N <= MAXN,                       | 
+c     |                   N <= MAXN,                       |
 c     |                 NEV <= MAXNEV,                     |
-c     |             NEV + 1 <= NCV <= MAXNCV               | 
-c     %----------------------------------------------------% 
+c     |             NEV + 1 <= NCV <= MAXNCV               |
+c     %----------------------------------------------------%
 c
       n = 100
       nev = 4
@@ -140,7 +140,7 @@ c
 c
       bmat = 'I'
       which = 'LM'
-      sigma = zero 
+      sigma = zero
 c
 c     %--------------------------------------------------%
 c     | The work array WORKL is used in SSAUPD as        |
@@ -155,7 +155,7 @@ c     | iteration.                                       |
 c     %--------------------------------------------------%
 c
       lworkl = ncv*(ncv+8)
-      tol = zero 
+      tol = zero
       ido = 0
       info = 0
 c
@@ -173,24 +173,24 @@ c
       maxitr = 300
       mode   = 3
 c
-      iparam(1) = ishfts 
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+      iparam(1) = ishfts
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %-----------------------------------------------------%
 c     | Call LAPACK routine to factor (A-SIGMA*I), where A  |
-c     | is the 1-d Laplacian.                               | 
+c     | is the 1-d Laplacian.                               |
 c     %-----------------------------------------------------%
 c
       h2 = one / real((n+1)*(n+1))
       do 20 j=1,n
          ad(j) = two / h2 - sigma
          adl(j) = -one / h2
- 20   continue 
+ 20   continue
       call scopy (n, adl, 1, adu, 1)
       call sgttrf (n, adl, ad, adu, adu2, ipiv, ierr)
-      if (ierr .ne. 0) then 
-         print *, ' ' 
+      if (ierr .ne. 0) then
+         print *, ' '
          print *, ' Error with _gttrf in SDRV2.'
          print *, ' '
          go to 9000
@@ -230,7 +230,7 @@ c
             if (ierr .ne. 0) then
                print *, ' '
                print *, ' Error with _gttrs in _SDRV2. '
-               print *, ' ' 
+               print *, ' '
                go to 9000
             end if
 c
@@ -240,7 +240,7 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-         end if 
+         end if
 c
 c     %----------------------------------------%
 c     | Either we have convergence or there is |
@@ -257,9 +257,9 @@ c
          print *, ' '
          print *, ' Error with _saupd, info = ',info
          print *, ' Check documentation of _saupd '
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
@@ -288,7 +288,7 @@ c        | corresponding to the eigenvalues in D is     |
 c        | returned in V.                               |
 c        %----------------------------------------------%
 
-         if ( ierr .ne. 0 ) then 
+         if ( ierr .ne. 0 ) then
 c
 c           %------------------------------------%
 c           | Error condition:                   |
@@ -300,7 +300,7 @@ c
             print *, ' Check the documentation of _seupd '
             print *, ' '
 c
-         else 
+         else
 c
             nconv =  iparam(5)
             do 30 j=1, nconv
@@ -351,14 +351,14 @@ c
          print *, ' '
          print *, ' _SDRV2 '
          print *, ' ====== '
-         print *, ' ' 
+         print *, ' '
          print *, ' Size of the matrix is ', n
          print *, ' The number of Ritz values requested is ', nev
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
          print *, ' The number of converged Ritz values is ',
-     &              nconv 
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -389,10 +389,10 @@ c
 c
       w(1) =  two*v(1) - v(2)
       do 100 j = 2,n-1
-         w(j) = - v(j-1) + two*v(j) - v(j+1) 
+         w(j) = - v(j-1) + two*v(j) - v(j+1)
   100 continue
       j = n
-      w(j) = - v(j-1) + two*v(j) 
+      w(j) = - v(j-1) + two*v(j)
 c
 c     Scale the vector w by (1 / h^2).
 c

EXAMPLES/SYM/ssdrv3.f

@@ -1,15 +1,15 @@
-      program ssdrv3 
+      program ssdrv3
 c
 c     Program to illustrate the idea of reverse communication in
 c     inverse mode for a generalized symmetric eigenvalue problem.
-c     The following program uses the two LAPACK subroutines sgttrf.f 
+c     The following program uses the two LAPACK subroutines sgttrf.f
 c     and sgttrs.f to factor and solve a tridiagonal system of equations.
 c
 c     We implement example three of ex-sym.doc in DOCUMENTS directory
 c
 c\Example-3
 c     ... Suppose we want to solve A*x = lambda*M*x in inverse mode,
-c         where A and M are obtained by the finite element of the 
+c         where A and M are obtained by the finite element of the
 c         1-dimensional discrete Laplacian
 c                             d^2u / dx^2
 c         on the interval [0,1] with zero Dirichlet boundary condition
@@ -17,7 +17,7 @@ c         using piecewise linear elements.
 c
 c     ... OP = inv[M]*A  and  B = M.
 c
-c     ... Use mode 2 of SSAUPD.    
+c     ... Use mode 2 of SSAUPD.
 c
 c\BeginLib
 c
@@ -30,7 +30,7 @@ c     sgttrs  LAPACK tridiagonal solve routine.
 c     saxpy   Level 1 BLAS that computes y <- alpha*x+y.
 c     sscal   Level 1 BLAS that scales a vector by a scalar.
 c     scopy   Level 1 BLAS that copies one vector to another.
-c     snrm2   Level 1 BLAS that computes the norm of a vector.     
+c     snrm2   Level 1 BLAS that computes the norm of a vector.
 c     av      Matrix vector multiplication routine that computes A*x.
 c     mv      Matrix vector multiplication routine that computes M*x.
 c
@@ -62,16 +62,16 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer          maxn, maxnev, maxncv, ldv
-      parameter        (maxn=256, maxnev=10, maxncv=25, 
+      parameter        (maxn=256, maxnev=10, maxncv=25,
      &                 ldv=maxn )
 c
 c     %--------------%
 c     | Local Arrays |
 c     %--------------%
 c
-      Real 
+      Real
      &                 v(ldv,maxncv), workl(maxncv*(maxncv+8)),
-     &                 workd(3*maxn), d(maxncv,2), resid(maxn), 
+     &                 workd(3*maxn), d(maxncv,2), resid(maxn),
      &                 ad(maxn), adl(maxn), adu(maxn), adu2(maxn),
      &                 ax(maxn), mx(maxn)
       logical          select(maxncv)
@@ -85,23 +85,23 @@ c
       integer          ido, n, nev, ncv, lworkl, info, j, ierr,
      &                 nconv, maxitr, ishfts, mode
       logical          rvec
-      Real 
+      Real
      &                 sigma, r1, r2, tol, h
 c
 c     %------------%
 c     | Parameters |
 c     %------------%
 c
-      Real  
+      Real
      &                 zero, one, four, six
-      parameter        ( zero = 0.0E+0 , one = 1.0E+0 , 
+      parameter        ( zero = 0.0E+0 , one = 1.0E+0 ,
      &                   four = 4.0E+0 , six = 6.0E+0  )
 c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
 c     %-----------------------------%
 c
-      Real 
+      Real
      &                 snrm2
       external         saxpy, scopy, sscal, snrm2, sgttrf, sgttrs
 c
@@ -123,9 +123,9 @@ c     | approximated.  The user can modify NEV, NCV, WHICH |
 c     | to solve problems of different sizes, and to get   |
 c     | different parts of the spectrum.  However, The     |
 c     | following conditions must be satisfied:            |
-c     |                     N <= MAXN,                     | 
+c     |                     N <= MAXN,                     |
 c     |                   NEV <= MAXNEV,                   |
-c     |               NEV + 1 <= NCV <= MAXNCV             | 
+c     |               NEV + 1 <= NCV <= MAXNCV             |
 c     %----------------------------------------------------%
 c
       n = 100
@@ -157,7 +157,7 @@ c     | iteration.                                       |
 c     %--------------------------------------------------%
 c
       lworkl = ncv*(ncv+8)
-      tol = zero 
+      tol = zero
       ido = 0
       info = 0
 c
@@ -176,7 +176,7 @@ c
       mode   = 2
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr 
+      iparam(3) = maxitr
       iparam(7) = mode
 c
 c     %------------------------------------------------%
@@ -188,18 +188,18 @@ c     %------------------------------------------------%
 c
       h = one / real (n+1)
 c
-      r1 = (four / six) * h 
+      r1 = (four / six) * h
       r2 = (one / six) * h
       do 20 j=1,n
          ad(j) =  r1
          adl(j) = r2
- 20   continue 
+ 20   continue
       call scopy (n, adl, 1, adu, 1)
       call sgttrf (n, adl, ad, adu, adu2, ipiv, ierr)
-      if (ierr .ne. 0) then 
+      if (ierr .ne. 0) then
          print *, ' '
          print *, ' Error with _gttrf in _SDRV3. '
-         print *, ' ' 
+         print *, ' '
          go to 9000
       end if
 c
@@ -210,13 +210,13 @@ c
  10   continue
 c
 c        %---------------------------------------------%
-c        | Repeatedly call the routine SSAUPD and take | 
+c        | Repeatedly call the routine SSAUPD and take |
 c        | actions indicated by parameter IDO until    |
 c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call ssaupd ( ido, bmat, n, which, nev, tol, resid, 
+         call ssaupd ( ido, bmat, n, which, nev, tol, resid,
      &                 ncv, v, ldv, iparam, ipntr, workd, workl,
      &                 lworkl, info )
 c
@@ -229,7 +229,7 @@ c           | matrix vector multiplication (A*x)   |
 c           | routine and a linear system solver   |
 c           | here.  The matrix vector             |
 c           | multiplication routine takes         |
-c           | workd(ipntr(1)) as the input vector. | 
+c           | workd(ipntr(1)) as the input vector. |
 c           | The final result is returned to      |
 c           | workd(ipntr(2)). The result of A*x   |
 c           | overwrites workd(ipntr(1)).          |
@@ -237,12 +237,12 @@ c           %--------------------------------------%
 c
             call av (n, workd(ipntr(1)), workd(ipntr(2)))
             call scopy(n, workd(ipntr(2)),  1, workd(ipntr(1)), 1)
-            call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, 
+            call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv,
      &                  workd(ipntr(2)), n, ierr)
-            if (ierr .ne. 0) then 
+            if (ierr .ne. 0) then
                print *, ' '
                print *, ' Error with _gttrs in _SDRV3.'
-               print *, ' '  
+               print *, ' '
                go to 9000
             end if
 c
@@ -271,7 +271,7 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-         end if 
+         end if
 c
 c
 c
@@ -290,24 +290,24 @@ c
          print *, ' '
          print *, ' Error with _saupd, info = ',info
          print *, ' Check the documentation of _saupd '
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
 c        | Post-Process using SSEUPD.                |
 c        |                                           |
-c        | Computed eigenvalues may be extracted.    |  
+c        | Computed eigenvalues may be extracted.    |
 c        |                                           |
 c        | Eigenvectors may also be computed now if  |
-c        | desired.  (indicated by rvec = .true.)    | 
+c        | desired.  (indicated by rvec = .true.)    |
 c        %-------------------------------------------%
-c           
+c
          rvec = .true.
 c
-         call sseupd ( rvec, 'All', select, d, v, ldv, sigma, 
-     &        bmat, n, which, nev, tol, resid, ncv, v, ldv, 
+         call sseupd ( rvec, 'All', select, d, v, ldv, sigma,
+     &        bmat, n, which, nev, tol, resid, ncv, v, ldv,
      &        iparam, ipntr, workd, workl, lworkl, ierr )
 c
 c        %----------------------------------------------%
@@ -321,19 +321,19 @@ c        | corresponding to the eigenvalues in D is     |
 c        | returned in V.                               |
 c        %----------------------------------------------%
 c
-         if (ierr .ne. 0) then 
+         if (ierr .ne. 0) then
 c
 c           %------------------------------------%
 c           | Error condition:                   |
 c           | Check the documentation of SSEUPD. |
 c           %------------------------------------%
-c 
-            print *, ' ' 
+c
+            print *, ' '
             print *, ' Error with _seupd, info = ', ierr
             print *, ' Check the documentation of _seupd'
             print *, ' '
 c
-         else 
+         else
 c
             nconv =  iparam(5)
             do 30 j=1, nconv
@@ -376,23 +376,23 @@ c
             print *, ' Maximum number of iterations reached.'
             print *, ' '
          else if ( info .eq. 3) then
-            print *, ' ' 
+            print *, ' '
             print *, ' No shifts could be applied during implicit',
      &               ' Arnoldi update, try increasing NCV.'
             print *, ' '
-         end if      
+         end if
 c
          print *, ' '
          print *, ' _SDRV3 '
          print *, ' ====== '
-         print *, ' ' 
+         print *, ' '
          print *, ' Size of the matrix is ', n
          print *, ' The number of Ritz values requested is ', nev
          print *, ' The number of Arnoldi vectors generated',
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
-         print *, ' The number of converged Ritz values is ', 
-     &              nconv 
+         print *, ' The number of converged Ritz values is ',
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is ', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -416,17 +416,17 @@ c     on the interval [0,1].
 c
       subroutine mv (n, v, w)
       integer           n, j
-      Real 
+      Real
      &                  v(n),w(n), one, four, six, h
-      parameter         (one = 1.0E+0 , four = 4.0E+0 , 
+      parameter         (one = 1.0E+0 , four = 4.0E+0 ,
      &                   six = 6.0E+0 )
 c
       w(1) = four*v(1) + v(2)
       do 100 j = 2,n-1
-         w(j) = v(j-1) + four*v(j) + v(j+1) 
+         w(j) = v(j-1) + four*v(j) + v(j+1)
   100 continue
       j = n
-      w(j) = v(j-1) + four*v(j) 
+      w(j) = v(j-1) + four*v(j)
 c
 c     Scale the vector w by h.
 c
@@ -438,23 +438,23 @@ c
 c--------------------------------------------------------------------
 c     matrix vector subroutine
 c
-c     The matrix used is the stiffness matrix obtained from the finite 
+c     The matrix used is the stiffness matrix obtained from the finite
 c     element discretization of the 1-dimensional discrete Laplacian
 c     on the interval [0,1] with zero Dirichlet boundary condition using
 c     piecewise linear elements.
 c
       subroutine av (n, v, w)
       integer           n, j
-      Real 
+      Real
      &                  v(n),w(n), two, one, h
       parameter         ( one = 1.0E+0 , two = 2.0E+0  )
 c
       w(1) =  two*v(1) - v(2)
       do 100 j = 2,n-1
-         w(j) = - v(j-1) + two*v(j) - v(j+1) 
+         w(j) = - v(j-1) + two*v(j) - v(j+1)
   100 continue
       j = n
-      w(j) = - v(j-1) + two*v(j) 
+      w(j) = - v(j-1) + two*v(j)
 c
 c     Scale the vector w by (1 / h).
 c

EXAMPLES/SYM/ssdrv4.f

@@ -1,9 +1,9 @@
-      program ssdrv4 
+      program ssdrv4
 c
 c     Program to illustrate the idea of reverse communication
 c     in shift and invert mode for a generalized symmetric eigenvalue
-c     problem.  The following program uses the two LAPACK subroutines 
-c     sgttrf.f and sgttrs to factor and solve a tridiagonal system of 
+c     problem.  The following program uses the two LAPACK subroutines
+c     sgttrf.f and sgttrs to factor and solve a tridiagonal system of
 c     equations.
 c
 c     We implement example four of ex-sym.doc in DOCUMENTS directory
@@ -34,7 +34,7 @@ c     sscal   Level 1 BLAS that scales a vector by a scalar.
 c     snrm2   Level 1 BLAS that computes the norm of a vector.
 c     av      Matrix vector multiplication routine that computes A*x.
 c     mv      Matrix vector multiplication routine that computes M*x.
-c 
+c
 c\Author
 c     Richard Lehoucq
 c     Danny Sorensen
@@ -51,7 +51,7 @@ c\Remarks
 c     1. None
 c
 c\EndLib
-c----------------------------------------------------------------------     
+c----------------------------------------------------------------------
 c
 c     %-----------------------------%
 c     | Define leading dimensions   |
@@ -63,7 +63,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer          maxn, maxnev, maxncv, ldv
-      parameter        (maxn=256, maxnev=10, maxncv=25, 
+      parameter        (maxn=256, maxnev=10, maxncv=25,
      &                 ldv=maxn)
 c
 c     %--------------%
@@ -72,7 +72,7 @@ c     %--------------%
 c
       Real
      &                 v(ldv,maxncv), workl(maxncv*(maxncv+8)),
-     &                 workd(3*maxn), d(maxncv,2), resid(maxn), 
+     &                 workd(3*maxn), d(maxncv,2), resid(maxn),
      &                 ad(maxn), adl(maxn), adu(maxn), adu2(maxn)
       logical          select(maxncv)
       integer          iparam(11), ipntr(11), ipiv(maxn)
@@ -85,7 +85,7 @@ c
       integer          ido, n, nev, ncv, lworkl, info, j, ierr,
      &                 nconv, maxitr, ishfts, mode
       logical          rvec
-      Real    
+      Real
      &                 sigma, r1, r2, tol, h
 c
 c     %------------%
@@ -126,10 +126,10 @@ c     | The user can modify NEV, NCV, SIGMA to solve       |
 c     | problems of different sizes, and to get different  |
 c     | parts of the spectrum. However, The following      |
 c     | conditions must be satisfied:                      |
-c     |                   N <= MAXN,                       | 
+c     |                   N <= MAXN,                       |
 c     |                 NEV <= MAXNEV,                     |
-c     |             NEV + 1 <= NCV <= MAXNCV               | 
-c     %----------------------------------------------------% 
+c     |             NEV + 1 <= NCV <= MAXNCV               |
+c     %----------------------------------------------------%
 c
       n = 100
       nev = 4
@@ -146,7 +146,7 @@ c
       end if
       bmat = 'G'
       which = 'LM'
-      sigma = zero 
+      sigma = zero
 c
 c     %--------------------------------------------------%
 c     | The work array WORKL is used in SSAUPD as        |
@@ -161,7 +161,7 @@ c     | iteration.                                       |
 c     %--------------------------------------------------%
 c
       lworkl = ncv*(ncv+8)
-      tol = zero 
+      tol = zero
       ido = 0
       info = 0
 c
@@ -180,8 +180,8 @@ c
       mode   = 3
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %-------------------------------------------------------%
 c     | Call LAPACK routine to factor the tridiagonal matrix  |
@@ -197,10 +197,10 @@ c
       do 20 j=1,n
          ad(j) = two/h - sigma * r1
          adl(j) = -one/h - sigma * r2
- 20   continue 
+ 20   continue
       call scopy (n, adl, 1, adu, 1)
       call sgttrf (n, adl, ad, adu, adu2, ipiv, ierr)
-      if (ierr .ne. 0) then 
+      if (ierr .ne. 0) then
          print *, ' Error with _gttrf in _SDRV4.'
          go to 9000
       end if
@@ -238,12 +238,12 @@ c           %--------------------------------------------%
 c
             call mv (n, workd(ipntr(1)), workd(ipntr(2)))
 c
-            call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, 
-     &                   workd(ipntr(2)), n, ierr) 
-            if (ierr .ne. 0) then 
+            call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv,
+     &                   workd(ipntr(2)), n, ierr)
+            if (ierr .ne. 0) then
                print *, ' '
                print *, ' Error with _gttrs in _SDRV4. '
-               print *, ' ' 
+               print *, ' '
                go to 9000
             end if
 c
@@ -261,16 +261,16 @@ c           | M*x has been saved in workd(ipntr(3)).  |
 c           | the user only needs the linear system   |
 c           | solver here that takes workd(ipntr(3)   |
 c           | as input, and returns the result to     |
-c           | workd(ipntr(2)).                        | 
+c           | workd(ipntr(2)).                        |
 c           %-----------------------------------------%
 c
             call scopy ( n, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-            call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, 
+            call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv,
      &                   workd(ipntr(2)), n, ierr)
-            if (ierr .ne. 0) then 
+            if (ierr .ne. 0) then
                print *, ' '
                print *, ' Error with _gttrs in _SDRV4.'
-               print *, ' ' 
+               print *, ' '
                go to 9000
             end if
 c
@@ -298,7 +298,7 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-        end if 
+        end if
 c
 c     %-----------------------------------------%
 c     | Either we have convergence, or there is |
@@ -315,9 +315,9 @@ c
          print *, ' '
          print *, ' Error with _saupd, info = ',info
          print *, ' Check the documentation of _saupd '
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
@@ -332,7 +332,7 @@ c
          rvec = .true.
 c
          call sseupd ( rvec, 'All', select, d, v, ldv, sigma,
-     &        bmat, n, which, nev, tol, resid, ncv, v, ldv, 
+     &        bmat, n, which, nev, tol, resid, ncv, v, ldv,
      &        iparam, ipntr, workd, workl, lworkl, ierr )
 c
 c        %----------------------------------------------%
@@ -346,7 +346,7 @@ c        | corresponding to the eigenvalues in D is     |
 c        | returned in V.                               |
 c        %----------------------------------------------%
 c
-         if ( ierr .ne. 0 ) then 
+         if ( ierr .ne. 0 ) then
 c
 c           %------------------------------------%
 c           | Error condition:                   |
@@ -358,7 +358,7 @@ c
             print *, ' Check the documentation of _seupd '
             print *, ' '
 c
-         else 
+         else
 c
             nconv =  iparam(5)
             do 30 j=1, nconv
@@ -375,7 +375,7 @@ c              | indicates how many are    |
 c              | accurate to the requested |
 c              | tolerance)                |
 c              %---------------------------%
-c  
+c
                call av(n, v(1,j), workd)
                call mv(n, v(1,j), workd(n+1))
                call saxpy (n, -d(j,1), workd(n+1), 1, workd, 1)
@@ -414,7 +414,7 @@ c
      &               ' (NCV) is ', ncv
         print *, ' What portion of the spectrum: ', which
         print *, ' The number of converged Ritz values is ',
-     &             nconv 
+     &             nconv
         print *, ' The number of Implicit Arnoldi update',
      &           ' iterations taken is ', iparam(3)
         print *, ' The number of OP*x is ', iparam(9)
@@ -440,15 +440,15 @@ c
       integer         n, j
       Real
      &                v(n),w(n), one, four, six, h
-      parameter       (one = 1.0E+0, four = 4.0E+0, 
+      parameter       (one = 1.0E+0, four = 4.0E+0,
      &                 six = 6.0E+0)
 c
       w(1) =  four*v(1) + v(2)
       do 100 j = 2,n-1
-         w(j) = v(j-1) + four*v(j) + v(j+1) 
+         w(j) = v(j-1) + four*v(j) + v(j+1)
   100 continue
       j = n
-      w(j) = v(j-1) + four*v(j) 
+      w(j) = v(j-1) + four*v(j)
 c
 c     Scale the vector w by h.
 c
@@ -458,8 +458,8 @@ c
       end
 c------------------------------------------------------------------------
 c     matrix vector subroutine
-c     where the matrix is the finite element discretization of the 
-c     1 dimensional discrete Laplacian on [0,1] with zero Dirichlet 
+c     where the matrix is the finite element discretization of the
+c     1 dimensional discrete Laplacian on [0,1] with zero Dirichlet
 c     boundary condition using piecewise linear elements.
 c
       subroutine av (n, v, w)
@@ -470,10 +470,10 @@ c
 c
       w(1) =  two*v(1) - v(2)
       do 100 j = 2,n-1
-         w(j) = - v(j-1) + two*v(j) - v(j+1) 
+         w(j) = - v(j-1) + two*v(j) - v(j+1)
   100 continue
       j = n
-      w(j) = - v(j-1) + two*v(j) 
+      w(j) = - v(j-1) + two*v(j)
 c
 c     Scale the vector w by (1/h)
 c

EXAMPLES/SYM/ssdrv5.f

@@ -1,9 +1,9 @@
-      program ssdrv5 
+      program ssdrv5
 c
 c     Program to illustrate the idea of reverse communication
 c     in Buckling mode for a generalized symmetric eigenvalue
-c     problem.  The following program uses the two LAPACK subroutines 
-c     sgttrf.f and sgttrs.f to factor and solve a tridiagonal system of 
+c     problem.  The following program uses the two LAPACK subroutines
+c     sgttrf.f and sgttrs.f to factor and solve a tridiagonal system of
 c     equations.
 c
 c     We implement example five of ex-sym.doc in DOCUMENTS directory
@@ -21,8 +21,8 @@ c
 c\BeginLib
 c
 c\References:
-c  1. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos 
-c     Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", 
+c  1. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos
+c     Algorithm for Solving Sparse Symmetric Generalized Eigenproblems",
 c     SIAM J. Matr. Anal. Apps.,  January (1993).
 c
 c\Routines called:
@@ -34,7 +34,7 @@ c     sgttrs  LAPACK tridiagonal solve routine.
 c     saxpy   Level 1 BLAS that computes y <- alpha*x+y.
 c     scopy   Level 1 BLAS that copies one vector to another.
 c     sscal   Level 1 BLAS that scales a vector by a scalar.
-c     snrm2   Level 1 BLAS that computes the norm of a vector.   
+c     snrm2   Level 1 BLAS that computes the norm of a vector.
 c     av      Matrix vector multiplication routine that computes A*x.
 c     mv      Matrix vector multiplication routine that computes M*x.
 c
@@ -54,7 +54,7 @@ c\Remarks
 c     1. None
 c
 c\EndLib
-c----------------------------------------------------------------------     
+c----------------------------------------------------------------------
 c
 c     %-----------------------------%
 c     | Define leading dimensions   |
@@ -66,7 +66,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer          maxn, maxnev, maxncv, ldv
-      parameter        (maxn=256, maxnev=10, maxncv=25, 
+      parameter        (maxn=256, maxnev=10, maxncv=25,
      &                 ldv=maxn)
 c
 c     %--------------%
@@ -75,7 +75,7 @@ c     %--------------%
 c
       Real
      &                 v(ldv,maxncv), workl(maxncv*(maxncv+8)),
-     &                 workd(3*maxn), d(maxncv,2), resid(maxn), 
+     &                 workd(3*maxn), d(maxncv,2), resid(maxn),
      &                 ad(maxn), adl(maxn), adu(maxn), adu2(maxn),
      &                 ax(maxn), mx(maxn)
       logical          select(maxncv)
@@ -89,7 +89,7 @@ c
       integer          ido, n, nev, ncv, lworkl, info, j, ierr,
      &                 nconv, maxitr, ishfts, mode
       logical          rvec
-      Real    
+      Real
      &                 h, sigma, r1, r2, tol
 c
 c     %------------%
@@ -130,12 +130,12 @@ c     | NCV, SIGMA to solve problems of different sizes, |
 c     | and to get different parts of the spectrum.      |
 c     | However, The following conditions must be        |
 c     | satisfied:                                       |
-c     |                 N <= MAXN,                       | 
+c     |                 N <= MAXN,                       |
 c     |               NEV <= MAXNEV,                     |
 c     |           NEV + 1 <= NCV <= MAXNCV               |
-c     |                                                  | 
+c     |                                                  |
 c     | The  shift SIGMA cannot be zero!!!               |
-c     %--------------------------------------------------% 
+c     %--------------------------------------------------%
 c
       n = 100
       nev = 4
@@ -152,7 +152,7 @@ c
       end if
       bmat = 'G'
       which = 'LM'
-      sigma = one 
+      sigma = one
 c
 c     %-----------------------------------------------------%
 c     | The work array WORKL is used in SSAUPD as           |
@@ -166,7 +166,7 @@ c     | generated in SSAUPD to start the Arnoldi iteration. |
 c     %-----------------------------------------------------%
 c
       lworkl = ncv*(ncv+8)
-      tol = zero 
+      tol = zero
       ido = 0
       info = 0
 c
@@ -185,8 +185,8 @@ c
       mode   = 4
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %------------------------------------------------------%
 c     | Call LAPACK routine to factor the tridiagonal matrix |
@@ -203,10 +203,10 @@ c
       do 20 j=1,n
          ad(j) = two / h - sigma * r1
          adl(j) = -one / h- sigma * r2
- 20   continue 
+ 20   continue
       call scopy (n, adl, 1, adu, 1)
       call sgttrf (n, adl, ad, adu, adu2, ipiv, ierr)
-      if (ierr .ne. 0) then 
+      if (ierr .ne. 0) then
          print *, ' '
          print *, ' Error with _gttrf in _SDRV5.'
          print *, ' '
@@ -226,8 +226,8 @@ c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call ssaupd ( ido, bmat, n, which, nev, tol, resid, 
-     &        ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, 
+         call ssaupd ( ido, bmat, n, which, nev, tol, resid,
+     &        ncv, v, ldv, iparam, ipntr, workd, workl, lworkl,
      &        info )
 c
          if (ido .eq. -1) then
@@ -246,10 +246,10 @@ c           %-------------------------------------------%
 c
             call av (n, workd(ipntr(1)), workd(ipntr(2)))
 c
-            call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, 
+            call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv,
      &                   workd(ipntr(2)), n, ierr)
-            if (ierr .ne. 0) then 
-               print *, ' ' 
+            if (ierr .ne. 0) then
+               print *, ' '
                print *, ' Error with _gttrs in SDRV5.'
                print *, ' '
                go to 9000
@@ -273,9 +273,9 @@ c           | workd(ipntr(2)).                         |
 c           %------------------------------------------%
 c
             call scopy ( n, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-            call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, 
+            call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv,
      &                   workd(ipntr(2)), n, ierr)
-            if (ierr .ne. 0) then 
+            if (ierr .ne. 0) then
                print *, ' '
                print *, ' Error with _gttrs in _SDRV5.'
                print *, ' '
@@ -306,7 +306,7 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-         end if 
+         end if
 c
 c     %-----------------------------------------%
 c     | Either we have convergence, or there is |
@@ -323,9 +323,9 @@ c
          print *, ' '
          print *, ' Error with _saupd, info = ',info
          print *, ' Check the documentation of _saupd '
-         print *, ' ' 
+         print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
@@ -339,11 +339,11 @@ c        %-------------------------------------------%
 c
          rvec = .true.
 c
-         call sseupd ( rvec, 'All', select, d, v, ldv, sigma, 
-     &        bmat, n, which, nev, tol, resid, ncv, v, ldv, 
+         call sseupd ( rvec, 'All', select, d, v, ldv, sigma,
+     &        bmat, n, which, nev, tol, resid, ncv, v, ldv,
      &        iparam, ipntr, workd, workl, lworkl, ierr )
 c
-         if (ierr .ne. 0) then 
+         if (ierr .ne. 0) then
 c
 c           %------------------------------------%
 c           | Error condition:                   |
@@ -357,7 +357,7 @@ c
 c
          else
 c
-            nconv =  iparam(5) 
+            nconv =  iparam(5)
             do 30 j=1, nconv
 c
 c              %---------------------------%
@@ -412,7 +412,7 @@ c
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
          print *, ' The number of converged Ritz values is ',
-     &              nconv 
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &            ' iterations taken is', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -432,7 +432,7 @@ c
 c------------------------------------------------------------------------
 c     Matrix vector subroutine
 c     where the matrix is the 1-dimensional mass matrix
-c     arising from using piecewise linear finite elements on the 
+c     arising from using piecewise linear finite elements on the
 c     interval [0,1].
 c
       subroutine mv (n, v, w)
@@ -444,10 +444,10 @@ c
 c
       w(1) =  four*v(1) + v(2)
       do 100 j = 2,n-1
-         w(j) = v(j-1) + four*v(j) + v(j+1) 
+         w(j) = v(j-1) + four*v(j) + v(j+1)
   100 continue
       j = n
-      w(j) = v(j-1) + four*v(j) 
+      w(j) = v(j-1) + four*v(j)
 c
 c     Scale the vector w by h.
 c
@@ -470,10 +470,10 @@ c
 c
       w(1) =  two*v(1) - v(2)
       do 100 j = 2,n-1
-         w(j) = - v(j-1) + two*v(j) - v(j+1) 
+         w(j) = - v(j-1) + two*v(j) - v(j+1)
   100 continue
       j = n
-      w(j) = - v(j-1) + two*v(j) 
+      w(j) = - v(j-1) + two*v(j)
 c
 c     Scale the vector w by (1/h)
 c

EXAMPLES/SYM/ssdrv6.f

@@ -1,9 +1,9 @@
-      program ssdrv6 
+      program ssdrv6
 c
 c     Program to illustrate the idea of reverse communication
-c     in Cayley mode for a generalized symmetric eigenvalue 
-c     problem.  The following program uses the two LAPACK subroutines 
-c     sgttrf.f and sgttrs.f to factor and solve a tridiagonal system of 
+c     in Cayley mode for a generalized symmetric eigenvalue
+c     problem.  The following program uses the two LAPACK subroutines
+c     sgttrf.f and sgttrs.f to factor and solve a tridiagonal system of
 c     equations.
 c
 c     We implement example six of ex-sym.doc in DOCUMENTS directory
@@ -23,8 +23,8 @@ c
 c\BeginLib
 c
 c\References:
-c  1. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos 
-c     Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", 
+c  1. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos
+c     Algorithm for Solving Sparse Symmetric Generalized Eigenproblems",
 c     SIAM J. Matr. Anal. Apps.,  January (1993).
 c
 c\Routines called:
@@ -36,7 +36,7 @@ c     sgttrs  LAPACK tridiagonal solve routine.
 c     saxpy   Level 1 BLAS that computes y <- alpha*x+y.
 c     scopy   Level 1 BLAS that copies one vector to another.
 c     sscal   Level 1 BLAS that scales a vector by a scalar.
-c     snrm2   Level 1 BLAS that computes the norm of a vector. 
+c     snrm2   Level 1 BLAS that computes the norm of a vector.
 c     av      Matrix vector multiplication routine that computes A*x.
 c     mv      Matrix vector multiplication routine that computes M*x.
 c
@@ -46,9 +46,9 @@ c     Richard Lehoucq
 c     Chao Yang
 c     Dept. of Computational &
 c     Applied Mathematics
-c     Rice University 
-c     Houston, Texas 
-c 
+c     Rice University
+c     Houston, Texas
+c
 c\SCCS Information: @(#)
 c FILE: sdrv6.F   SID: 2.5   DATE OF SID: 10/17/00   RELEASE: 2
 c
@@ -68,7 +68,7 @@ c     | MAXNCV: Maximum NCV allowed |
 c     %-----------------------------%
 c
       integer          maxn, maxnev, maxncv, ldv
-      parameter        (maxn=256, maxnev=10, maxncv=25, 
+      parameter        (maxn=256, maxnev=10, maxncv=25,
      &                 ldv=maxn)
 c
 c     %--------------%
@@ -77,7 +77,7 @@ c     %--------------%
 c
       Real
      &                 v(ldv,maxncv), workl(maxncv*(maxncv+8)),
-     &                 workd(3*maxn), d(maxncv,2), resid(maxn), 
+     &                 workd(3*maxn), d(maxncv,2), resid(maxn),
      &                 ad(maxn), adl(maxn), adu(maxn), adu2(maxn),
      &                 temp(maxn), ax(maxn), mx(maxn)
       logical          select(maxncv)
@@ -100,9 +100,9 @@ c     %------------%
 c
       Real
      &                 zero, one, two, four, six
-      parameter        (zero = 0.0E+0, one = 1.0E+0, 
+      parameter        (zero = 0.0E+0, one = 1.0E+0,
      &                  four = 4.0E+0, six = 6.0E+0,
-     &                  two = 2.0E+0 ) 
+     &                  two = 2.0E+0 )
 c
 c     %-----------------------------%
 c     | BLAS & LAPACK routines used |
@@ -132,9 +132,9 @@ c     | NCV, SIGMA to solve problems of different sizes, |
 c     | and to get different parts of the spectrum.      |
 c     | However, The following conditions must be        |
 c     | satisfied:                                       |
-c     |                 N <= MAXN,                       | 
+c     |                 N <= MAXN,                       |
 c     |               NEV <= MAXNEV,                     |
-c     |           NEV + 1 <= NCV <= MAXNCV               | 
+c     |           NEV + 1 <= NCV <= MAXNCV               |
 c     %--------------------------------------------------%
 c
       n = 100
@@ -186,8 +186,8 @@ c
       mode   = 5
 c
       iparam(1) = ishfts
-      iparam(3) = maxitr 
-      iparam(7) = mode 
+      iparam(3) = maxitr
+      iparam(7) = mode
 c
 c     %------------------------------------------------------%
 c     | Call LAPACK routine to factor (A-sigma*M).  The      |
@@ -203,10 +203,10 @@ c
       do 20 j=1,n
          ad(j) = two / h - sigma * r1
          adl(j) = -one / h - sigma * r2
- 20   continue 
+ 20   continue
       call scopy (n, adl, 1, adu, 1)
       call sgttrf (n, adl, ad, adu, adu2, ipiv, ierr)
-      if (ierr .ne. 0) then 
+      if (ierr .ne. 0) then
          print *, ' '
          print *, ' Error with _gttrf in _SDRV6.'
          print *, ' '
@@ -226,8 +226,8 @@ c        | either convergence is indicated or maxitr   |
 c        | has been exceeded.                          |
 c        %---------------------------------------------%
 c
-         call ssaupd ( ido, bmat, n, which, nev, tol, resid, ncv, 
-     &                 v, ldv, iparam, ipntr, workd, workl, lworkl, 
+         call ssaupd ( ido, bmat, n, which, nev, tol, resid, ncv,
+     &                 v, ldv, iparam, ipntr, workd, workl, lworkl,
      &                 info )
 c
          if (ido .eq. -1) then
@@ -239,19 +239,19 @@ c           | user should provide his/her matrix vector (A*x, M*x)  |
 c           | multiplication routines and a linear system solver    |
 c           | here.  The matrix vector multiplication routine takes |
 c           | workd(ipntr(1)) as the input vector.  The final       |
-c           | result is returned to workd(ipntr(2)).                | 
+c           | result is returned to workd(ipntr(2)).                |
 c           %-------------------------------------------------------%
 c
             call av (n, workd(ipntr(1)), workd(ipntr(2)))
             call mv (n, workd(ipntr(1)), temp)
-            call saxpy(n, sigma, temp, 1, workd(ipntr(2)), 1) 
+            call saxpy(n, sigma, temp, 1, workd(ipntr(2)), 1)
 c
-            call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, 
+            call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv,
      &                workd(ipntr(2)), n, ierr)
-            if (ierr .ne. 0) then 
+            if (ierr .ne. 0) then
                print *, ' '
                print *, ' Error with _gttrs in _SDRV6.'
-               print *, ' ' 
+               print *, ' '
                go to 9000
             end if
 c
@@ -272,15 +272,15 @@ c           | matrix vector multiplication routine takes         |
 c           | workd(ipntr(1)) as the input, and the result is    |
 c           | combined with workd(ipntr(3)) to form the input    |
 c           | for the linear system solver.  The final result is |
-c           | returned to workd(ipntr(2)).                       | 
+c           | returned to workd(ipntr(2)).                       |
 c           %----------------------------------------------------%
 c
             call av (n, workd(ipntr(1)), workd(ipntr(2)))
             call saxpy(n, sigma, workd(ipntr(3)), 1, workd(ipntr(2)), 1)
-            call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, 
+            call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv,
      &                   workd(ipntr(2)), n, ierr)
-            if (ierr .ne. 0) then 
-               print *, ' ' 
+            if (ierr .ne. 0) then
+               print *, ' '
                print *, ' Error with _gttrs in _SDRV6. '
                print *, ' '
                go to 9000
@@ -309,7 +309,7 @@ c           %-----------------------------------------%
 c
             go to 10
 c
-         end if 
+         end if
 c
 c     %-----------------------------------------%
 c     | Either we have convergence, or there is |
@@ -328,7 +328,7 @@ c
            print *, ' Check the documentation of _saupd. '
            print *, ' '
 c
-      else 
+      else
 c
 c        %-------------------------------------------%
 c        | No fatal errors occurred.                 |
@@ -342,8 +342,8 @@ c        %-------------------------------------------%
 c
          rvec = .true.
 c
-         call sseupd ( rvec, 'All', select, d, v, ldv, sigma, 
-     &        bmat, n, which, nev, tol, resid, ncv, v, ldv, 
+         call sseupd ( rvec, 'All', select, d, v, ldv, sigma,
+     &        bmat, n, which, nev, tol, resid, ncv, v, ldv,
      &        iparam, ipntr, workd, workl, lworkl, ierr )
 c
 c        %----------------------------------------------%
@@ -357,7 +357,7 @@ c        | corresponding to the eigenvalues in D is     |
 c        | returned in V.                               |
 c        %----------------------------------------------%
 c
-         if ( ierr .ne. 0 ) then 
+         if ( ierr .ne. 0 ) then
 c
 c           %------------------------------------%
 c           | Error condition:                   |
@@ -383,7 +383,7 @@ c           | indicates how many are    |
 c           | accurate to the requested |
 c           | tolerance)                |
 c           %---------------------------%
-c  
+c
             nconv = iparam(5)
             do 30 j=1, nconv
                call av(n, v(1,j), ax)
@@ -423,7 +423,7 @@ c
      &            ' (NCV) is ', ncv
          print *, ' What portion of the spectrum: ', which
          print *, ' The number of converged Ritz values is ',
-     &              nconv 
+     &              nconv
          print *, ' The number of Implicit Arnoldi update',
      &           ' iterations taken is', iparam(3)
          print *, ' The number of OP*x is ', iparam(9)
@@ -448,17 +448,17 @@ c     on the interval [0,1].
 c
       subroutine mv (n, v, w)
       integer           n, j
-      Real 
+      Real
      &                  v(n), w(n), one, four, six, h
-      parameter         (one = 1.0E+0, four = 4.0E+0, 
-     &                   six = 6.0E+0) 
+      parameter         (one = 1.0E+0, four = 4.0E+0,
+     &                   six = 6.0E+0)
 c
       w(1) =  four*v(1) + v(2)
       do 100 j = 2,n-1
-         w(j) = v(j-1) + four*v(j) + v(j+1) 
+         w(j) = v(j-1) + four*v(j) + v(j+1)
   100 continue
       j = n
-      w(j) = v(j-1) + four*v(j) 
+      w(j) = v(j-1) + four*v(j)
 c
 c     Scale the vector w by h.
 c
@@ -469,7 +469,7 @@ c
 c
 c------------------------------------------------------------------------
 c     Matrix vector subroutine
-c     where the matrix is the stiffness matrix obtained from the 
+c     where the matrix is the stiffness matrix obtained from the
 c     finite element discretization of the 1-dimensional discrete Laplacian
 c     on the interval [0,1] with zero Dirichlet boundary condition
 c     using piecewise linear elements.
@@ -482,14 +482,14 @@ c
 c
       w(1) =  two*v(1) - v(2)
       do 100 j = 2,n-1
-         w(j) = - v(j-1) + two*v(j) - v(j+1) 
+         w(j) = - v(j-1) + two*v(j) - v(j+1)
   100 continue
       j = n
       w(j) = - v(j-1) + two*v(j)
-c     
+c
 c     Scale the vector w by (1/h).
 c
       h = one / real(n+1)
-      call sscal(n, one/h, w, 1) 
+      call sscal(n, one/h, w, 1)
       return
       end