Select different targets for building in CI on Alpine

The Alpine repository for the PowerPC target got more and more unreliable
recently.
Additionally, the PowerPC target is covered with the cross-build rules on
Ubuntu now.

Drop some (expensive) targets to reduce the overlap in coverage with the
workflow that cross-builds on Ubuntu.
Add LoongArch64 target which is not (yet?) available for Ubuntu.
Keep targets that can be build natively (which should be reasonably fast).
Use an Ubuntu on ARM runner for the armv7 target.
Rename workflow because out of the three remaining targets only one is
actually emulated - the others can execute natively.

.github/ISSUE_TEMPLATE.md

@@ -0,0 +1,39 @@
+## Expected behavior
+
+Do this.
+
+## Actual behavior
+
+Do that.
+
+## Where/how to reproduce the problem
+
+- arpack-ng: release or commit (SHA)
+- OS: debian ? ubuntu ? mac ?...
+- compiler: gcc ? intel ? clang ? version ?...
+- environment: export FFLAGS ?...
+- configure: ./configure --enable-stuff ? cmake -DSTUFFS=ON ?
+- input data ?
+
+## Steps to reproduce the problem
+
+-
+-
+-
+
+## Error message
+
+Bad stuff.
+
+## Traces
+
+~/arpack-ng> tail -n 300 test-suite.log
+
+~/arpack-ng/build> tail -n 300 Testing/Temporary/LastTest.log
+
+## Callstack
+
+(gdb) bt
+
+## Notes, remarks
+

.github/PULL_REQUEST_TEMPLATE.md

@@ -0,0 +1,9 @@
+## Pull request purpose
+
+fixing issue #xx ? enhancement ? new feature ?...
+
+## Detailed changes proposed in this pull request
+
+-
+-
+-

.github/dependabot.yml

@@ -0,0 +1,10 @@
+# Set update schedule for GitHub Actions
+
+version: 2
+updates:
+
+  - package-ecosystem: "github-actions"
+    directory: "/"
+    schedule:
+      # Check for updates to GitHub Actions every week
+      interval: "weekly"

.github/workflows/build-alpine.yml

@@ -0,0 +1,128 @@
+name: build-alpine
+on:
+  workflow_dispatch:
+  push:
+  pull_request:
+
+concurrency: ci-arch-emu-${{ github.ref }}
+
+jobs:
+
+  alpine:
+    # Run armv7 on aarch64 runners
+    runs-on: ${{ matrix.arch == 'armv7' && 'ubuntu-24.04-arm' || 'ubuntu-latest' }}
+
+    defaults:
+      run:
+        # Use emulated shell as default
+        shell: alpine.sh {0}
+
+    strategy:
+      # Allow other runners in the matrix to continue if some fail
+      fail-fast: false
+
+      matrix:
+        # For available CPU architectures, see:
+        # https://github.com/marketplace/actions/setup-alpine-linux-environment
+        arch: [x86, armv7, loongarch64]
+
+    name: alpine (${{ matrix.arch }})
+
+    steps:
+      - name: get CPU information (host)
+        shell: bash
+        run: lscpu
+
+      - name: checkout repository
+        uses: actions/checkout@v7
+
+      - name: install dependencies
+        uses: jirutka/setup-alpine@v1
+        with:
+          arch: ${{ matrix.arch }}
+          apk-tools-url: ${{ matrix.arch == 'armv7'
+              && 'https://gitlab.alpinelinux.org/api/v4/projects/5/packages/generic/v2.14.7/aarch64/apk.static#!sha256!27a975638ddc95a411c9f17c63383e335da9edf6bb7de2281d950c291a11f878'
+              || 'https://gitlab.alpinelinux.org/api/v4/projects/5/packages/generic/v2.14.7/x86_64/apk.static#!sha256!bdd044e0fd6cc388c5e571e1093efa5f35f7767cc5aa338b0a2576a429009a62' }}
+          packages: >
+            bash
+            build-base
+            ccache
+            cmake
+            gfortran
+            eigen-dev
+            lapack-dev
+            lscpu
+
+      - name: disable QEMU emulation
+        if: matrix.arch == 'armv7'
+        shell: bash
+        run: sudo update-binfmts --disable qemu-arm
+
+      - name: get CPU information (emulated)
+        run: lscpu
+
+      - name: prepare ccache
+        # create key with human readable timestamp
+        # used in action/cache/restore and action/cache/save steps
+        id: ccache-prepare
+        run: |
+          echo "key=ccache:alpine:${{ matrix.arch }}:${{ github.ref }}:$(date +"%Y-%m-%d_%H-%M-%S"):${{ github.sha }}" >> $GITHUB_OUTPUT
+
+      - name: restore ccache
+        # setup the GitHub cache used to maintain the ccache from one job to the next
+        uses: actions/cache/restore@v6
+        with:
+          # location of the ccache of the chroot in the root file system
+          path: /home/runner/rootfs/alpine-latest-${{ matrix.arch }}/home/runner/.ccache
+          key: ${{ steps.ccache-prepare.outputs.key }}
+          # Prefer caches from the same branch. Fall back to caches from the default branch.
+          restore-keys: |
+            ccache:alpine:${{ matrix.arch }}:${{ github.ref }}
+            ccache:alpine:${{ matrix.arch }}
+
+      - name: configure ccache
+        run: |
+          test -d ~/.ccache || mkdir ~/.ccache
+          echo "max_size = 20M" >> ~/.ccache/ccache.conf
+          echo "compression = true" >> ~/.ccache/ccache.conf
+          ccache -s
+          which ccache
+
+      - name: configure
+        run: |
+          echo "gcc --version"
+          gcc --version
+          echo "gcc -dumpmachine"
+          gcc -dumpmachine
+          echo " "
+          mkdir -p ${GITHUB_WORKSPACE}/build && cd ${GITHUB_WORKSPACE}/build
+          cmake \
+            -DEXAMPLES=ON \
+            -DMPI=OFF \
+            -DICB=ON \
+            -DEIGEN=ON \
+            -DCMAKE_C_COMPILER_LAUNCHER="ccache" \
+            -DCMAKE_CXX_COMPILER_LAUNCHER="ccache" \
+            ..
+
+      - name: build
+        run: |
+          cd ${GITHUB_WORKSPACE}/build
+          cmake --build .
+
+      - name: ccache status
+        continue-on-error: true
+        run: ccache -s
+
+      - name: save ccache
+        # Save the cache after we are done (successfully) building
+        # This helps to retain the ccache even if the subsequent steps are failing.
+        uses: actions/cache/save@v6
+        with:
+          path: /home/runner/rootfs/alpine-latest-${{ matrix.arch }}/home/runner/.ccache
+          key: ${{ steps.ccache-prepare.outputs.key }}
+
+      - name: test
+        run: |
+          cd ${GITHUB_WORKSPACE}/build
+          CTEST_OUTPUT_ON_FAILURE=1 ctest .

.github/workflows/cross-build-ubuntu.yml

@@ -0,0 +1,219 @@
+name: cross-build-ubuntu
+on:
+  workflow_dispatch:
+  push:
+  pull_request:
+
+concurrency: ci-cross-build-ubuntu-${{ github.ref }}
+
+jobs:
+
+  cross-build:
+    runs-on: ${{ matrix.os }}
+
+    strategy:
+      # Allow other runners in the matrix to continue if some fail
+      fail-fast: false
+
+      matrix:
+        # List of architectures that are supported by Ubuntu:
+        # https://canonical-ubuntu-packaging-guide.readthedocs-hosted.com/en/latest/reference/architectures/
+        arch: [armhf, ppc64el, s390x, riscv64]
+        include:
+          - arch: armhf
+            target-triple: arm-linux-gnueabihf
+            os: ubuntu-24.04-arm
+            ccache-max: 1G
+            qemu-user:
+          - arch: ppc64el
+            target-triple: powerpc64le-linux-gnu
+            os: ubuntu-24.04-arm
+            ccache-max: 1G
+            qemu-user: qemu-ppc64le
+          - arch: s390x
+            target-triple: s390x-linux-gnu
+            os: ubuntu-24.04
+            ccache-max: 1G
+            qemu-user: qemu-s390x
+          - arch: riscv64
+            target-triple: riscv64-linux-gnu
+            os: ubuntu-24.04-arm
+            ccache-max: 1.4G
+            qemu-user: qemu-riscv64
+
+    name: cross ${{ matrix.arch }}
+
+    env:
+      CC: ${{ matrix.target-triple }}-gcc
+      CXX: ${{ matrix.target-triple }}-g++
+      FC: ${{ matrix.target-triple }}-gfortran
+
+    steps:
+      - name: get CPU information
+        run: lscpu
+
+      - name: checkout repository
+        uses: actions/checkout@v7
+
+      - name: install toolchain for ${{ matrix.arch }}
+        run: |
+          sudo apt -qq update
+          sudo apt install -y \
+            g++-${{ matrix.target-triple }} \
+            gfortran-${{ matrix.target-triple }} \
+            cmake \
+            ccache \
+            ${{ matrix.arch == 'armhf' && ' ' || 'qemu-user-binfmt' }}
+
+      - name: add repositories for ${{ matrix.arch }} packages
+        # deb822-style format:
+        # https://manpages.ubuntu.com/manpages/noble/man5/sources.list.5.html
+        run: |
+          sudo dpkg --add-architecture ${{ matrix.arch }}
+          case ${{ matrix.os }} in
+            "ubuntu-24.04-arm")
+              sudo bash -c 'cat - >/etc/apt/sources.list.d/ubuntu.sources' <<-EOF
+          Types: deb
+          URIs: http://ports.ubuntu.com/ubuntu-ports/
+          Suites: noble noble-updates noble-backports
+          Components: main restricted universe multiverse
+          Architectures: arm64 ${{ matrix.arch }}
+          Signed-By: /usr/share/keyrings/ubuntu-archive-keyring.gpg
+          
+          Types: deb
+          URIs: http://security.ports.ubuntu.com/ubuntu-ports/
+          Suites: noble-security
+          Components: main restricted universe multiverse
+          Architectures: arm64 ${{ matrix.arch }}
+          Signed-By: /usr/share/keyrings/ubuntu-archive-keyring.gpg
+          
+          EOF
+              ;;
+            "ubuntu-24.04")
+              sudo bash -c 'cat - >/etc/apt/sources.list.d/ubuntu.sources' <<-EOF
+          Types: deb
+          URIs: http://archive.ubuntu.com/ubuntu/
+          Suites: noble noble-updates noble-backports
+          Components: main restricted universe multiverse
+          Architectures: amd64
+          Signed-By: /usr/share/keyrings/ubuntu-archive-keyring.gpg
+          
+          Types: deb
+          URIs: http://security.ubuntu.com/ubuntu/
+          Suites: noble-security
+          Components: main restricted universe multiverse
+          Architectures: amd64
+          Signed-By: /usr/share/keyrings/ubuntu-archive-keyring.gpg
+          
+          Types: deb
+          URIs: http://ports.ubuntu.com/ubuntu-ports/
+          Suites: noble noble-updates noble-backports
+          Components: main restricted universe multiverse
+          Architectures: ${{ matrix.arch }}
+          Signed-By: /usr/share/keyrings/ubuntu-archive-keyring.gpg
+          
+          Types: deb
+          URIs: http://security.ports.ubuntu.com/ubuntu-ports/
+          Suites: noble-security
+          Components: main restricted universe multiverse
+          Architectures: ${{ matrix.arch }}
+          Signed-By: /usr/share/keyrings/ubuntu-archive-keyring.gpg
+          
+          EOF
+              ;;
+          esac
+          sudo apt update
+
+      - name: install dependencies for ${{ matrix.arch }}
+        run: |
+          sudo apt install -y \
+            openmpi-bin:${{ matrix.arch }} \
+            libblas-dev:${{ matrix.arch }} \
+            liblapack-dev:${{ matrix.arch }} \
+            libeigen3-dev:${{ matrix.arch }}
+          # Trying to install libopenmpi-dev for the cross-environment causes
+          # apt to complain about missing .mod file dependencies.  Those .mod
+          # files are already installed with the cross-compiler.  Ignore those
+          # bogus dependency errors and install the package manually.
+          apt-get download libopenmpi-dev:${{ matrix.arch }}
+          sudo dpkg -i --force-depends libopenmpi-dev_*_${{ matrix.arch }}.deb
+
+      - name: prepare ccache
+        # create key with human readable timestamp
+        # used in action/cache/restore and action/cache/save steps
+        id: ccache-prepare
+        run: |
+          echo "key=ccache:cross:${{ matrix.os }}:${{ matrix.arch }}:${{ github.ref }}:$(date +"%Y-%m-%d_%H-%M-%S"):${{ github.sha }}" >> $GITHUB_OUTPUT
+
+      - name: restore ccache
+        # setup the github cache used to maintain the ccache from one job to the next
+        uses: actions/cache/restore@v6
+        with:
+          path: ~/.ccache
+          key: ${{ steps.ccache-prepare.outputs.key }}
+          restore-keys: |
+            ccache:cross:${{ matrix.os }}:${{ matrix.arch }}:${{ github.ref }}
+            ccache:cross:${{ matrix.os }}:${{ matrix.arch }}:refs/heads/default
+
+      - name: configure ccache
+        env:
+          CCACHE_MAX: ${{ matrix.ccache-max }}
+        run: |
+          test -d ~/.ccache || mkdir ~/.ccache
+          echo "max_size = $CCACHE_MAX" >> ~/.ccache/ccache.conf
+          echo "compression = true" >> ~/.ccache/ccache.conf
+          ccache -s
+          echo "/usr/lib/ccache" >> $GITHUB_PATH
+
+      - name: configure
+        run: |
+          echo $PATH
+          echo which ccache
+          which ccache
+          echo which $CC
+          which $CC
+          echo $CC --version
+          $CC --version
+          echo which $CXX
+          which $CXX
+          echo $CXX --version
+          $CXX --version
+          echo which $FC
+          which $FC
+          echo $FC --version
+          $FC --version
+          mkdir -p ${GITHUB_WORKSPACE}/build && cd ${GITHUB_WORKSPACE}/build
+          echo "::group::Configure with CMake"
+          cmake \
+            -DEXAMPLES=ON \
+            -DMPI=OFF \
+            -DICB=ON \
+            -DEIGEN=ON \
+            -DCMAKE_C_COMPILER_LAUNCHER="ccache" \
+            -DCMAKE_CXX_COMPILER_LAUNCHER="ccache" \
+            -DBLA_VENDOR="Generic" \
+            ..
+          echo "::endgroup::"
+
+      - name: build
+        run: |
+          cd ${GITHUB_WORKSPACE}/build
+          cmake --build .
+
+      - name: ccache status
+        continue-on-error: true
+        run: ccache -s
+
+      - name: save ccache
+        # Save the cache after we are done (successfully) building
+        uses: actions/cache/save@v6
+        with:
+          path: ~/.ccache
+          key: ${{ steps.ccache-prepare.outputs.key }}
+
+      - name: test
+        env:
+          driver: ${{ matrix.qemu-user }}
+        run: |
+          cd ${GITHUB_WORKSPACE}/build
+          CTEST_OUTPUT_ON_FAILURE=1 ctest .

.github/workflows/jobs.yml

@@ -0,0 +1,359 @@
+name: arpack-ng
+on: [push, pull_request]
+jobs:
+  ubuntu_latest_cmake:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Clone and check out repository code
+        uses: actions/checkout@v7
+        with:
+          fetch-depth: 0
+          ref: ${{github.event.pull_request.head.ref}} # Branch where changes are implemented.
+          repository: ${{github.event.pull_request.head.repo.full_name}} # Repo where changes are implemented.
+      - name: Check commit
+        run: |
+          git log -1
+      - name: Update OS
+        run: sudo apt-get update
+      - name: Install apt-get dependencies
+        run: sudo apt-get install -y gfortran gcc g++ openmpi-bin libopenmpi-dev libblas-dev liblapack-dev libeigen3-dev cmake
+      - name: Run job
+        run: |
+          mkdir build
+          cd build
+          cmake -DEXAMPLES=ON -DMPI=ON -DICB=ON -DEIGEN=ON ..
+          make all
+          CTEST_OUTPUT_ON_FAILURE=1 make test
+          make package_source
+  ubuntu_latest_cmake_install:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Clone and check out repository code
+        uses: actions/checkout@v7
+        with:
+          fetch-depth: 0
+          ref: ${{github.event.pull_request.head.ref}} # Branch where changes are implemented.
+          repository: ${{github.event.pull_request.head.repo.full_name}} # Repo where changes are implemented.
+      - name: Check commit
+        run: |
+          git log -1
+      - name: Update OS
+        run: sudo apt-get update
+      - name: Install apt-get dependencies
+        run: sudo apt-get install -y gfortran gcc g++ openmpi-bin libopenmpi-dev libblas-dev liblapack-dev libeigen3-dev cmake
+      - name: Run job
+        run: |
+          mkdir build
+          cd build
+          cmake ..
+          bash ./tstCMakeInstall.sh
+          bash ./tstCMakeInstall.sh 64-
+          bash ./tstCMakeInstall.sh   -ILP64
+          bash ./tstCMakeInstall.sh 64-ILP64
+  ubuntu_latest_autotools:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Clone and check out repository code
+        uses: actions/checkout@v7
+        with:
+          fetch-depth: 0
+          ref: ${{github.event.pull_request.head.ref}} # Branch where changes are implemented.
+          repository: ${{github.event.pull_request.head.repo.full_name}} # Repo where changes are implemented.
+      - name: Check commit
+        run: |
+          git log -1
+      - name: Update OS
+        run: sudo apt-get update
+      - name: Install apt-get dependencies
+        run: sudo apt-get install -y gfortran gcc g++ openmpi-bin libopenmpi-dev libblas-dev liblapack-dev libeigen3-dev automake autoconf pkg-config libtool
+      - name: Run job
+        run: |
+          ./bootstrap
+          ./configure --enable-mpi --enable-icb --enable-eigen
+          make all
+          make check
+          make distcheck
+  ubuntu_latest_autotools_install:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Clone and check out repository code
+        uses: actions/checkout@v7
+        with:
+          fetch-depth: 0
+          ref: ${{github.event.pull_request.head.ref}} # Branch where changes are implemented.
+          repository: ${{github.event.pull_request.head.repo.full_name}} # Repo where changes are implemented.
+      - name: Check commit
+        run: |
+          git log -1
+      - name: Update OS
+        run: sudo apt-get update
+      - name: Install apt-get dependencies
+        run: sudo apt-get install -y gfortran gcc g++ openmpi-bin libopenmpi-dev libblas-dev liblapack-dev libeigen3-dev automake autoconf pkg-config libtool
+      - name: Run job
+        run: |
+          ./bootstrap
+          ./configure
+          bash ./tstAutotoolsInstall.sh
+          bash ./tstAutotoolsInstall.sh 64-
+          bash ./tstAutotoolsInstall.sh   -ILP64
+          bash ./tstAutotoolsInstall.sh 64-ILP64
+  ubuntu_latest_cmake_python:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Clone and check out repository code
+        uses: actions/checkout@v7
+        with:
+          fetch-depth: 0
+          ref: ${{github.event.pull_request.head.ref}} # Branch where changes are implemented.
+          repository: ${{github.event.pull_request.head.repo.full_name}} # Repo where changes are implemented.
+      - name: Check commit
+        run: |
+          git log -1
+      - name: Update OS
+        run: sudo apt-get update
+      - name: Install apt-get dependencies
+        run: sudo apt-get install -y gfortran gcc g++ openmpi-bin libopenmpi-dev libblas-dev liblapack-dev cmake libeigen3-dev
+      - name: Install python dependencies
+        run: sudo apt-get -y install python3-minimal python3-pip python3-numpy
+      - name: Build boost-python for python3 (not provided by apt-cache)
+        run : |
+          sudo apt-get -y install wget
+          wget https://sourceforge.net/projects/boost/files/boost/1.79.0/boost_1_79_0.tar.gz
+          tar -xf boost_1_79_0.tar.gz
+          cd boost_1_79_0
+          ./bootstrap.sh --with-libraries=python --with-python=/usr/bin/python3 --with-toolset=gcc
+          sudo ./b2 toolset=gcc install
+          sudo apt-get install locate
+          sudo updatedb
+      - name: Run job
+        run: |
+          mkdir build
+          cd build
+          cmake -DEXAMPLES=ON -DMPI=ON -DICB=ON -DEIGEN=ON -DPYTHON3=ON ..
+          make all
+          CTEST_OUTPUT_ON_FAILURE=1 make test
+  ubuntu_latest_autotools_ilp64:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Clone and check out repository code
+        uses: actions/checkout@v7
+        with:
+          fetch-depth: 0
+          ref: ${{github.event.pull_request.head.ref}} # Branch where changes are implemented.
+          repository: ${{github.event.pull_request.head.repo.full_name}} # Repo where changes are implemented.
+      - name: Check commit
+        run: |
+          git log -1
+      - name: Update OS
+        run: sudo apt-get update
+      - name: Install apt-get dependencies
+        run: sudo apt-get install -y gfortran gcc g++ openmpi-bin libopenmpi-dev libblas-dev liblapack-dev automake autoconf pkg-config libtool libeigen3-dev
+      - name: Install Intel MKL (ILP64 blas/lapack)
+        run: echo yes | sudo apt-get -y install intel-mkl libmkl-dev
+      - name: Run job
+        run: |
+          ./bootstrap
+          ./configure --enable-icb --with-blas=mkl_gf_ilp64 --with-lapack=mkl_gf_ilp64
+          make all
+          make check
+        env:
+          FFLAGS: "-DMKL_ILP64 -I/usr/include/mkl"
+          FCFLAGS: "-DMKL_ILP64 -I/usr/include/mkl"
+          LIBS: "-Wl,--no-as-needed -L/usr/lib/x86_64-linux-gnu -lmkl_sequential -lmkl_core -lpthread -lm -ldl"
+          INTERFACE64: "1"
+  macos_latest_cmake:
+    runs-on: macos-latest
+    steps:
+      - name: Clone and check out repository code
+        uses: actions/checkout@v7
+        with:
+          fetch-depth: 0
+          ref: ${{github.event.pull_request.head.ref}} # Branch where changes are implemented.
+          repository: ${{github.event.pull_request.head.repo.full_name}} # Repo where changes are implemented.
+      - name: Check commit
+        run: |
+          git log -1
+      - name: Install brew dependencies
+        run: |
+          brew reinstall gcc # brings gfortran on path
+          brew install cmake open-mpi eigen veclibfort
+      - name: Run job
+        run: |
+          mkdir -p build
+          cd build
+          export FC=mpif90 # Uses gfortran.
+          export CC=mpicc # Uses clang.
+          export CFLAGS="-Qunused-arguments"
+          export CXX=mpic++ # Uses clang++.
+          export CXXFLAGS="-Qunused-arguments"
+          export VECLIBFORT_PREFIX=$(brew --prefix veclibfort)
+          cmake \
+            -DBLAS_LIBRARIES="${VECLIBFORT_PREFIX}/lib/libvecLibFort.dylib" \
+            -DLAPACK_LIBRARIES="${VECLIBFORT_PREFIX}/lib/libvecLibFort.dylib" \
+            -DEXAMPLES=ON -DICB=ON -DEIGEN=ON -DMPI=ON ..
+          make all
+          CTEST_OUTPUT_ON_FAILURE=1 make test
+  macos_latest_cmake_python:
+    runs-on: macos-latest
+    steps:
+      - name: Clone and check out repository code
+        uses: actions/checkout@v7
+        with:
+          fetch-depth: 0
+          ref: ${{github.event.pull_request.head.ref}} # Branch where changes are implemented.
+          repository: ${{github.event.pull_request.head.repo.full_name}} # Repo where changes are implemented.
+      - name: Check commit
+        run: |
+          git log -1
+      - name: Install brew dependencies
+        run: |
+          # Unlink and re-link to prevent errors when github mac runner images
+          # install python outside of brew, for example:
+          # https://github.com/orgs/Homebrew/discussions/3895
+          # https://github.com/actions/setup-python/issues/577
+          # https://github.com/actions/runner-images/issues/6459
+          # https://github.com/actions/runner-images/issues/6507
+          # https://github.com/actions/runner-images/issues/2322
+          brew list -1 | grep python | while read formula; do brew unlink $formula; brew link --overwrite $formula; done
+          brew reinstall gcc # brings gfortran on path
+          brew install cmake eigen boost-python3 python3 numpy veclibfort
+      - name: Run job
+        run: |
+          mkdir -p build
+          cd build
+          export FC=gfortran
+          export CC=clang
+          export CFLAGS="-Qunused-arguments"
+          export CXX=clang++
+          export CXXFLAGS="-Qunused-arguments"
+          export VECLIBFORT_PREFIX=$(brew --prefix veclibfort)
+          cmake \
+            -DBLAS_LIBRARIES="${VECLIBFORT_PREFIX}/lib/libvecLibFort.dylib" \
+            -DLAPACK_LIBRARIES="${VECLIBFORT_PREFIX}/lib/libvecLibFort.dylib" \
+            -DEXAMPLES=ON -DICB=ON -DEIGEN=ON -DPYTHON3=ON ..
+          make all
+          CTEST_OUTPUT_ON_FAILURE=1 make test
+  macos_latest_autotools:
+    runs-on: macos-latest
+    steps:
+      - name: Clone and check out repository code
+        uses: actions/checkout@v7
+        with:
+          fetch-depth: 0
+          ref: ${{github.event.pull_request.head.ref}} # Branch where changes are implemented.
+          repository: ${{github.event.pull_request.head.repo.full_name}} # Repo where changes are implemented.
+      - name: Check commit
+        run: |
+          git log -1
+      - name: Install brew dependencies
+        run: |
+          brew reinstall gcc # brings gfortran on path
+          brew install autoconf automake libtool pkgconfig open-mpi eigen veclibfort
+      - name: Run job
+        run: |
+          ./bootstrap
+          export VECLIBFORT_PREFIX=$(brew --prefix veclibfort)
+          BLAS_LIBS="-L${VECLIBFORT_PREFIX}/lib -lvecLibFort" \
+          LAPACK_LIBS="-L${VECLIBFORT_PREFIX}/lib -lvecLibFort" \
+            ./configure --enable-icb --enable-eigen --enable-mpi
+          make all
+          make check
+  windows_latest_cmake:
+    runs-on: windows-latest
+    name: MinGW-w64 ${{ matrix.msystem }} INTERFACE64=${{ matrix.int64 }}/MPI=${{ matrix.mpi }}
+    strategy:
+      fail-fast: false
+      matrix:
+        msystem: [UCRT64, CLANG64]
+        int64: [ON, OFF]
+        mpi: [ON, OFF]
+        exclude:
+          - int64: ON
+            mpi: ON
+    defaults:
+      run:
+        # Use MSYS2 as default shell
+        shell: msys2 {0}
+    steps:
+      - name: Install MSYS2 build environment
+        uses: msys2/setup-msys2@v2
+        with:
+          update: true
+          msystem: ${{ matrix.msystem }}
+          install: >-
+            base-devel
+            git
+          pacboy: >-
+            cmake:p
+            ninja:p
+            cc:p
+            fc:p
+            eigen3:p
+      - name: Install OpenBLAS and MS-MPI from MSYS2
+        run: |
+          if [[ ${{ matrix.int64 }} != ON ]]; then
+            pacboy -S openblas:p --noconfirm
+          else
+            pacboy -S openblas64:p --noconfirm
+          fi
+          if [[ ${{ matrix.mpi }} = ON ]]; then
+            # This installs only the link library.
+            # The actual library will be installed in the next step.
+            pacboy -S msmpi:p --noconfirm
+          fi
+      - name: Install MS-MPI (for mpiexec)
+        uses: mpi4py/setup-mpi@v1
+      - name: Clone and check out repository code
+        uses: actions/checkout@v7
+        with:
+          fetch-depth: 0
+          ref: ${{github.event.pull_request.head.ref}} # Branch where changes are implemented.
+          repository: ${{github.event.pull_request.head.repo.full_name}} # Repo where changes are implemented.
+      - name: Check commit
+        run: |
+          git log -1
+      - name: Run job
+        run: |
+          mkdir -p build && cd build
+          echo "::group::Configure"
+          if [[ ${{ matrix.int64 }} == ON ]]; then
+            _blas_lib_flag="-DBLAS_LIBRARIES=openblas_64"
+          fi
+          cmake \
+            -GNinja \
+            -DICB=ON \
+            -DEIGEN=ON \
+            -DEXAMPLES=ON \
+            -DMPI=${{ matrix.mpi }} \
+            -DINTERFACE64=${{ matrix.int64 }} \
+            ${_blas_lib_flag} \
+            ..
+          echo "::endgroup::"
+          echo "::group::Build"
+          cmake --build . -v
+          echo "::endgroup::"
+      - name: Run tests
+        id: run-ctest
+        run: |
+          if [[ ${{ matrix.mpi }} == ON ]]; then
+            export PATH="/c/Program Files/Microsoft MPI/Bin":$PATH # add mpiexec to msys2 path
+          fi
+          cd build
+          ctest
+      - name: Re-run tests
+        if: always() && (steps.run-ctest.outcome == 'failure')
+        timeout-minutes: 60
+        run: |
+          if [[ ${{ matrix.mpi }} == ON ]]; then
+            export PATH="/c/Program Files/Microsoft MPI/Bin":$PATH # add mpiexec to msys2 path
+          fi
+          cd build
+          echo "::group::Re-run ctest"
+          ctest --rerun-failed --output-on-failure || true
+          echo "::endgroup::"
+          echo "::group::Log from these tests"
+          [ ! -f Testing/Temporary/LastTest.log ] || cat Testing/Temporary/LastTest.log
+          echo "::endgroup::"
+          echo "::group::Content of arpackmm.run.log"
+          [ ! -f EXAMPLES/MATRIX_MARKET/arpackmm.run.log ] || cat EXAMPLES/MATRIX_MARKET/arpackmm.run.log
+          echo "::endgroup::"

.gitignore

@@ -15,9 +15,16 @@ config.log
 config.status
 libtool
 .deps/
-arpack.pc
+arpack*.pc
+parpack*.pc
+arpackdef.h
+arpackicb.h
+tstAutotoolsInstall.sh
+cmake/arpackng-config-version.cmake
+cmake/arpackng-config.cmake
 
 # Generated by `make`
+.dirstamp
 *.o
 *.mod
 *.lo
@@ -40,6 +47,8 @@ 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]
@@ -48,6 +57,9 @@ EXAMPLES/SIMPLE/[sd]ssimp
 EXAMPLES/SIMPLE/[sdcz]nsimp
 EXAMPLES/SVD/[sd]svd
 EXAMPLES/SYM/[sd]sdrv[123456]
+EXAMPLES/MATRIX_MARKET/arpackmm
+EXAMPLES/MATRIX_MARKET/arpackSolver.resid.out
+EXAMPLES/MATRIX_MARKET/arpackSolver.v.out
 PARPACK/EXAMPLES/MPI/p[sd]ndrv[13]
 PARPACK/EXAMPLES/MPI/p[sd]sdrv1
 PARPACK/EXAMPLES/MPI/p[cz]ndrv1
@@ -64,3 +76,7 @@ PARPACK/TESTS/MPI/issue46
 *.suo
 VISUAL_STUDIO/Release MKL/
 VISUAL_STUDIO/bin/
+
+# Temporary files
+*~
+\#*#

.mergify.yml

@@ -0,0 +1,8 @@
+pull_request_rules:
+  - name: automatic merge on CI success and review
+    conditions:
+      - status-success=continuous-integration/travis-ci/pr
+      - "#approved-reviews-by>=1"
+    actions:
+      merge:
+        method: merge

.travis.yml

@@ -1,75 +0,0 @@
-sudo: false
-
-language: c
-
-compiler:
-  - gcc
-
-addons:
-  apt:
-    packages:
-      - gfortran
-      - gcc
-      - g++
-      - libblas-dev
-      - liblapack-dev
-      - libopenmpi-dev
-      - openmpi-bin
-
-env:
-  - BUILD=cmake
-  - BUILD=configure
-
-script:
-  # CMAKE
-  - if [ "$BUILD" == "cmake" ]; then mkdir build ; fi
-  - if [ "$BUILD" == "cmake" ]; then cd build ; fi
-  - if [ "$BUILD" == "cmake" ]; then cmake -D EXAMPLES=ON -D MPI=ON  -D ICB=OFF .. ; fi
-  - if [ "$BUILD" == "cmake" ]; then make all ; fi
-  - if [ "$BUILD" == "cmake" ]; then make test ; fi
-  - if [ "$BUILD" == "cmake" ]; then rm -fr * ; fi # Restart cmake from scratch.
-  - if [ "$BUILD" == "cmake" ]; then cmake -D EXAMPLES=ON -D MPI=ON  -D ICB=ON  .. ; fi
-  - if [ "$BUILD" == "cmake" ]; then make all ; fi
-  - if [ "$BUILD" == "cmake" ]; then make test ; fi
-  - if [ "$BUILD" == "cmake" ]; then rm -fr * ; fi # Restart cmake from scratch.
-  - if [ "$BUILD" == "cmake" ]; then cmake -D EXAMPLES=ON -D MPI=OFF -D ICB=OFF .. ; fi
-  - if [ "$BUILD" == "cmake" ]; then make all ; fi
-  - if [ "$BUILD" == "cmake" ]; then make test ; fi
-  - if [ "$BUILD" == "cmake" ]; then rm -fr * ; fi # Restart cmake from scratch.
-  - if [ "$BUILD" == "cmake" ]; then cmake -D EXAMPLES=ON -D MPI=OFF -D ICB=ON  .. ; fi
-  - if [ "$BUILD" == "cmake" ]; then make all ; fi
-  - if [ "$BUILD" == "cmake" ]; then make test ; fi
-  - if [ "$BUILD" == "cmake" ]; then rm -fr * ; fi # Restart cmake from scratch.
-  - if [ "$BUILD" == "cmake" ]; then cmake -D BUILD_SHARED_LIBS=ON -D MPI=ON  -D ICB=OFF .. ; fi
-  - if [ "$BUILD" == "cmake" ]; then make all ; fi
-  - if [ "$BUILD" == "cmake" ]; then make test ; fi
-  - if [ "$BUILD" == "cmake" ]; then rm -fr * ; fi # Restart cmake from scratch.
-  - if [ "$BUILD" == "cmake" ]; then cmake -D BUILD_SHARED_LIBS=ON -D MPI=ON  -D ICB=ON  .. ; fi
-  - if [ "$BUILD" == "cmake" ]; then make all ; fi
-  - if [ "$BUILD" == "cmake" ]; then make test ; fi
-  - if [ "$BUILD" == "cmake" ]; then rm -fr * ; fi # Restart cmake from scratch.
-  - if [ "$BUILD" == "cmake" ]; then cmake -D BUILD_SHARED_LIBS=ON -D MPI=OFF -D ICB=OFF .. ; fi
-  - if [ "$BUILD" == "cmake" ]; then make all ; fi
-  - if [ "$BUILD" == "cmake" ]; then make test ; fi
-  - if [ "$BUILD" == "cmake" ]; then rm -fr * ; fi # Restart cmake from scratch.
-  - if [ "$BUILD" == "cmake" ]; then cmake -D BUILD_SHARED_LIBS=ON -D MPI=OFF -D ICB=ON  .. ; fi
-  - if [ "$BUILD" == "cmake" ]; then make all ; fi
-  - if [ "$BUILD" == "cmake" ]; then make test ; fi
-  - if [ "$BUILD" == "cmake" ]; then rm -fr * ; fi # Restart cmake from scratch for code coverage
-  - if [ "$BUILD" == "cmake" ]; then cmake -D EXAMPLES=ON -DCOVERALLS=ON -D MPI=ON -D ICB=ON ..  ; fi
-  - if [ "$BUILD" == "cmake" ]; then make all test coveralls VERBOSE=1 ; fi
-  # CONFIGURE
-  - if [ "$BUILD" == "configure" ]; then ./bootstrap ; fi
-  - if [ "$BUILD" == "configure" ]; then ./configure --enable-mpi ; fi
-  - if [ "$BUILD" == "configure" ]; then make all ; fi
-  - if [ "$BUILD" == "configure" ]; then make check ; fi
-  - if [ "$BUILD" == "configure" ]; then make distcheck ; fi
-  - if [ "$BUILD" == "configure" ]; then ./configure --enable-mpi --enable-icb ; fi
-  - if [ "$BUILD" == "configure" ]; then make all ; fi
-  - if [ "$BUILD" == "configure" ]; then make check ; fi
-  - if [ "$BUILD" == "configure" ]; then ./configure --enable-icb ; fi
-  - if [ "$BUILD" == "configure" ]; then make all ; fi
-  - if [ "$BUILD" == "configure" ]; then make check ; fi
-  - if [ "$BUILD" == "configure" ]; then ./configure ; fi
-  - if [ "$BUILD" == "configure" ]; then make all ; fi
-  - if [ "$BUILD" == "configure" ]; then make check ; fi

CHANGES

@@ -1,12 +1,225 @@
-arpack-ng - 3.6.1
+arpack-ng - next
 
- * Rename debug.h to debug-arpack.h to avoid collision (Closes #126)
+[ Evan Biederstedt ]
+* Fix warnings for "Warning: Obsolescent feature: Old-style character length at (1)", compiled with `gfortran-16  -fpic  -g -O2 -Wall -pedantic -mtune=native`
+* Changed GitHub CI workflows for Mac OS to use 'brew install open-mpi', as `mpich` fails. 
+
+[ Theodore Chang ]
+ * CMake: Improve dependency linking, bump up minimum C++ standard version.
+
+[ Franck Houssen ]
+ * [BUG FIX] Fix arpack solver to handle real and imag shifts.
+ * [BUG FIX] Make sure the restart file of the arpack solver i written.
+ * [BUG FIX] Change arpack solver API.
+
+[ Henri Menke ]
+ * [BUG FIX] Add missing stdexcept header
+
+[ Kyle Guinn ]
+ * Build PARPACK p[sd]lamch10.f with FFLAGS from ./configure instead of forcing -O0.  Build all of PARPACK with AM_FFLAGS.
+ * [BUG FIX] Don't install pkg-config files for libraries that were not built.
+
+[ Markus Mützel ]
+ * CMake: Fix running CTests on Windows.
+ * Use GNU Fortran ABI in CI tests on macOS.
+ * Initialize machine dependent constants only once in `PDNAITR`.
+
+[ Szabolcs Horvát ]
+ * fix obsolescent character length warnings
+
+ -- TODO <TODO@users.noreply.github.com> DATE
+
+arpack-ng - 3.9.1
+
+[ Fabien Péan ]
+ * pyarpack: Ensure that the matrix properties (symmetric/hermitian) fit the solver (CG/LDL) with which they are used in the tests
+ * [BUG FIX] Tests for PARPACK with C/C++ bindings icb_parpack_c and icb_parpack_cpp are now really parallel and split the problem across MPI processes.
+ * Update arpackmm test suite: enable solving non-symmetric tests with BiCG solver
+ * README: Add details on Windows installation.
+ 
+[ Szabolcs Horvát ]
+ * [BUG FIX] Ensure that LAPACK RNG state is propagated (regression in 3.9.0).
+ * [BUG FIX] Ensure that separate random seeds are used on different parallel thread in D and S versions of functions (issue from original ARPACK).
+
+[ Ruoyu Feng ]
+ * ICB(arpackdef.h): distinct intel llvm compiler (icx with clang-cl) from msvc on windows
+ * ICB(arpackdef.h): Undef macro I if complex.h from msvc version is loaded, which is an usual name and causes issues on arpackSolver.
+
+[ Franck Houssen ]
+ * [BUG FIX] Fix install: headers in /path/to/local/include/arpack for ICB samples
+ * [BUG FIX] Fix install: headers in /path/to/local/include/arpack
+ * arpackmm: allow for using LA/SA magnitudes.
+ * Rename icbexmm option into eigen option.
+ * README: document how to use ICB.
+ * [BUG FIX] arpackmm: fix restart.
+ * README: document where to find arpack user's guide.
+
+ -- Franck Houssen <fghoussen@users.noreply.github.com> Sat, 14 Oct 2023 13:37:37 +0200
+
+[ Franck Houssen ]
+ * Add documentation on ILP64.
+
+arpack-ng - 3.9.0
+
+[ Vikas Sharma ]
+ * Improve README.
+
+[ Fabien Péan ]
+ * CI: Enable job `windows_latest_cmake` to run all tests
+ * CMake: Fix BLAS and LAPACK static library order needed to consume the library on Windows with static linkage
+ * Fix using ARPACK on Windows with MSVC compiler from C++17 onwards
+
+[ Zhentao Wang ]
+ * [BUG FIX] parpack.h and parpack.hpp: type of rwork should be real instead of complex.
+ * Allow ritz_option {"LR", "SR", "LI", "SI"} for complex eigenvalue problems in ICB.
+
+[ Jose E. Roman ]
+ * Avoid using isnan() in tests, since is GNU-specific
+
+[ Tom Payerle ]
+ * Change the continuation line format for stat.h, debug.h
+
+[ John Doe ]
+ * Avoid calling [c|z]dotc for better portability on macOS
+
+[ Dima Pasechnik ]
+ * [BUG FIX] autotools: replace obsolete AC_TRY_COMPILE macros.
+ * Support for NAG's nagfor Fortran compiler
+
+[ Franck Houssen ]
+ * Create one .cmake file per arpack-ng flavor (32-bits, 64-bits, ILP64).
+ * Test autotools pkg-config (*.pc files) with/without LIBSUFFIX/ITF64SUFFIX.
+ * Test CMake find_package (*.cmake files) with/without LIBSUFFIX/ITF64SUFFIX.
+ * [BUG FIX] autotools: ICB must be checked first (MPI changes compilers).
+ * [BUG FIX] BLAS/LAPACK: allow suffixes in case BLAS/LAPACK can not provide ICB.
+ * [BUG FIX] Compile C programs with ICB.
+ * arpackmm: command line bug fix.
+ * arpackmm: restart bug fix.
+ * pyarpack: fix compilation warning, test on macos and latest boost-python (1.79).
+ * arpackSolver: fix error messages.
+ * [BUG FIX] Make sure iseed is always initialized to values allowed by lapack ?larnv.
+ * [BUG FIX] According to lapack doc of ?larnv, iseed(4) must be odd.
+ * [BUG FIX] Use MPI ICB types (mpi_f08) instead of integer(kind=i_int).
+ * parpack: no ILP64 support.
+
+[ Haoyang Liu ]
+ * CMake: minimum required version changed to 3.0
+ * CMake: add C99 standard checking
+ * CI: Support for centos7 added.
+ * CI: Add `scripts/travis_centos.sh` for centos builds
+
+[ Robert Schütz ]
+ * use CMAKE_INSTALL_FULL_<dir> in arpack.pc
+
+[ Markus Mützel ]
+ * CMake: Handle libraries without "lib" prefix.
+ * CMake: Don't override BLAS/LAPACK/MPI flags. Directly use results from the Find* modules instead.
+
+[ Juan José García-Ripoll ]
+ * Adapt the C/C++ interface to accept also MSVC's non-standard complex types.
+ * Propagate dependencies to CMake targets that use arpack-ng:
+   - Create CMake-generated targets and configuration files that keep track of
+     arpack's dependencies (libraries, directories) and expose them to users.
+   - Install those files under ${prefix}/lib/cmake/arpackng* so that arpack can be
+     found using 'find_package(arpackng)' from CMake files.
+   - Add code to the arpackng-config.cmake to find required dependencies when this
+     module is loaded by find_package(arpackng).
+
+ -- Sylvestre Ledru <sylvestre@debian.org> Mon, 07 Dec 2020 11:37:40 +0100
+
+arpack-ng - 3.8.0
+
+[ Myron Oikonomakis ]
+ * [BUG FIX]: bmat return "G" instead of "B" for generalized matrix in arpack.hpp
+ * [BUG FIX]: pass arrays of chars as scalar in fortran calls in order not to crash
+ * when calling subroutines through icb interface
+
+[ Izaak "Zaak" Beekman ]
+ * [BUG FIX]: fix 'Unknown CMake command "check_symbol_exists".' when ICB=ON.
+
+[ Franck Houssen ]
+ * CI: Support for Mac OS X added in automation (GNU + "-ff2c -fno-second-underscore" options).
+ * CI: Support for centos added in automation.
+ * CI: Support for opensuse added in automation.
+ * arpackSolver/arpackmm: switch eigen version to 3.3.
+ * [BUG FIX] fix arpackdef.h (resp. arpackicb.h) must be included only by C/C++ (resp. F77/F90).
+ * [BUG FIX] iparam/ipntr sizes may change depending on cases.
+ * pyarpack: python binding based on Boost.Python.Numpy exposing C++ API.
+ * [CLEAN] arpackSolver API: more convenient, suppress template parameters when possible.
+ * [BUG FIX] ICB using rvec/select: rvec/select turned to integer
+   bool should be, but, is not always supported (depend on compiler, options).
+ * extract arpackSolver.hpp from arpakmm.cpp.
+ * arpackmm: add --slvItrPC option (PC: Jacobi, ILU).
+ * arpackmm: add --slv LLT LDLT (for SPD matrices).
+ * arpackmm: add --simplePrec option (to enable use of s*upd).
+ * arpackmm: add --dense option.
+ * autotools: provide *.cmake files (in addition to *.pc file).
+ * [BUG FIX] ILP64 support: using debug_c and stat_c.
+ * [BUG FIX] fix check precision which may fail with some ATLAS versions.
+
+[ Kyle Guinn ]
+ * [BUG FIX]: fix 'eval: Syntax error: "(" unexpected' error at build time.
+ * Only build shared libraries by default.  To build static libraries, use
+   --enable-static (autotools) or -DBUILD_SHARED_LIBS=OFF (cmake).
+ * Add parpack.pc and arpackSolver.pc.
+
+[ David Schwörer ]
+ * Support of gfortran 10
+
+ -- Sylvestre Ledru <sylvestre@debian.org> Mon, 07 Dec 2020 11:35:57 +0100
+
+arpack-ng - 3.7.0
+
+[ Franck Houssen ]
+ * [BUG FIX] ICB: missing workev for *[ds]neupd (real+not-sym) => API/ABI change for *[ds]neupd_c.
+ * [BUG FIX] autotools - make distcheck: fix circular dependencies.
+ * arpackmm: utility to test arpack with matrix market files.
+ * ICB: add ILP64 support.
+    The idea is:
+    - autoheader/cmake generates arpackdef.h/arpackicb.h from arpackdef.h.in/arpackicb.h.in
+      - in C/C++ files: arpackdef.h defines a_int according to architecture.
+      - in F77/F90 files: arpackicb.h defines i_int to architecture.
+    - MPI does not support ILP64: integer*4 must be imposed in all
+      calls involving MPI (f90 example/test code).
+    To enable ILP64 users to compile/link, arpackdef.h/arpackicb.h is added in
+    the arpack installation (make install).
+
+ [ Kyle Guinn ]
+ * Autoconf/Automake simplifications and fixes.
+ * Simplify the generation of arpackdef.h.
+
+ -- Sylvestre Ledru <sylvestre@debian.org> Sat, 12 Jan 2019 16:24:00 +0100
+
+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 ]
@@ -45,7 +258,7 @@ arpack-ng - 3.5.0
  * 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
+ * Use AC_PROG_FC instead of AC_PROG_F77 for proper initialization
    for the usage of AC_FC_LINE_LENGTH. Noted on Cygwin.
 
  [ Denis Davydov ]
@@ -163,7 +376,7 @@ arpack-ng - 3.1.3
   * Replace arpack.pc with proper autotooled arpack.pc.in
   * Add debug.h to TESTS/Makefile.am sources
 
-  * "make dist" is functionnal
+  * "make dist" is functional
   * Also build the library "libparpacksrcblacs" (PARPACK/UTIL/BLACS/)
 
  -- Sylvestre Ledru <sylvestre.ledru@scilab-enterprises.com>  Tue, 02 Apr 2013 10:53:08 +0200
@@ -176,7 +389,7 @@ arpack-ng - 3.1.2
    * 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
+   * Fixed division by zero in smlnum by using 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

DOCUMENTS/debug.doc

@@ -4,7 +4,7 @@
  The following statements may be used within the calling program to 
  initiate and request this output.
 
-      include 'debug-arpack.h'
+      include 'debug.h'
       ndigit = -3
       logfil = 6
       msgets = 0
@@ -63,13 +63,13 @@
  once some familiarity has been gained with the routines. 
 
  The include statement sets up the storage declarations that are
- solely associated with this trace debugging feature. "debug-arpack.h"
+ solely associated with this trace debugging feature. "debug.h"
  has the following structure:
 
 ---------------------------------------------------------------------
 c
 c\SCCS Information: @(#) 
-c FILE: debug-arpack.h   SID: 2.3   DATE OF SID: 11/16/95   RELEASE: 2 
+c FILE: debug.h   SID: 2.3   DATE OF SID: 11/16/95   RELEASE: 2 
 c
 c     %---------------------------------%
 c     | See debug.doc for documentation |

EXAMPLES/BAND/Makefile.am

@@ -1,4 +1,4 @@
-LDADD = $(top_builddir)/SRC/libarpack$(LIBSUFFIX).la $(LAPACK_LIBS) $(BLAS_LIBS)
+LDADD = $(top_builddir)/SRC/libarpack$(LIBSUFFIX)$(ITF64SUFFIX).la $(LAPACK_LIBS) $(BLAS_LIBS)
 
 SSBDR = ssbdr1 ssbdr2 ssbdr3 ssbdr4 ssbdr5 ssbdr6
 DSBDR = dsbdr1 dsbdr2 dsbdr3 dsbdr4 dsbdr5 dsbdr6

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.
@@ -152,7 +152,7 @@ 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))
@@ -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 +206,14 @@ c
       idiag = kl+ku+1
       do 30 j = 1, n
          a(idiag,j) = (4.0E+0, 0.0E+0)  / h2
-  30  continue 
-c 
+         m(idiag,j) = (1.0E+0, 0.0E+0)
+  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 +221,8 @@ 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 +236,8 @@ 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 +245,11 @@ 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 +298,11 @@ 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 +313,8 @@ 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/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.
@@ -152,7 +152,7 @@ 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))
@@ -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 +206,14 @@ c
       idiag = kl+ku+1
       do 30 j = 1, n
          a(idiag,j) = (4.0D+0, 0.0D+0)  / h2
-  30  continue 
-c 
+         m(idiag,j) = (1.0D+0, 0.0D+0)
+  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 +221,8 @@ 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 +236,8 @@ 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 +245,11 @@ 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 +298,11 @@ 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 +313,8 @@ 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

@@ -1,4 +1,4 @@
-LDADD = $(top_builddir)/SRC/libarpack$(LIBSUFFIX).la $(LAPACK_LIBS) $(BLAS_LIBS)
+LDADD = $(top_builddir)/SRC/libarpack$(LIBSUFFIX)$(ITF64SUFFIX).la $(LAPACK_LIBS) $(BLAS_LIBS)
 
 CNDRV = cndrv1 cndrv2 cndrv3 cndrv4
 ZNDRV = zndrv1 zndrv2 zndrv3 zndrv4

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/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/MATRIX_MARKET/An.mtx

@@ -0,0 +1,79 @@
+%% MatrixMarket matrix coordinate double symmetric
+% This example is 0-based without (optional) nnz
+%
+% This is a 1D diffusive laplacian matrix (fixed at first end <=> invertible)
+%
+%              1                              1          
+%              .                             .--.        
+%             / \                            |  |        
+%            /   \ 0                       0 |  |        
+%  phi_i  --o  o  o--o--  =>  grad(phi_i)  --o  o  o--o--
+%              i  j                            i|  |j    
+%                                               |  |     
+%                                               .--.     
+%                                                -1.     
+%
+%                 1                              1       
+%                 .                             .--.     
+%                / \                            |  |     
+%               /   \ 0                        i|  |j    
+%  phi_j  --o--o  o  o--  =>  grad(phi_j)  --o--o  o  o--
+%              i  j                                |  | 0
+%                                                  |  |  
+%                                                  .--.  
+%                                                   -1.  
+%
+%                  i     j
+%              | l_ii  l_ij | i
+%  laplacian = |            |
+%              | l_ji  l_jj | j
+%
+%  distance(i, j) = d = 1.
+%
+%  l_ii = int_[i,j](grad(phi_i).grad(phi_i)) = d*(-1.)*(-1.) =  1.
+%  l_ij = int_[i,j](grad(phi_i).grad(phi_j)) = d*(-1.)*( 1.) = -1.
+%  l_ji = int_[i,j](grad(phi_j).grad(phi_i)) = d*( 1.)*(-1.) = -1.
+%  l_jj = int_[i,j](grad(phi_j).grad(phi_j)) = d*( 1.)*( 1.) =  1.
+%
+%                i     j
+%              | d_ii  d_ij | i
+%  diffusion = |            |
+%              | d_ji  d_jj | j
+%
+%  d_ii = int_[i,j](phi_i.grad(phi_i)) = int_[i,j]((1-x)*(-1.)) = -d*0.5  = -0.5
+%  d_ij = int_[i,j](phi_i.grad(phi_j)) = int_[i,j]((1-x)*( 1.)) =  d*0.5  =  0.5
+%  d_ji = int_[i,j](phi_j.grad(phi_i)) = int_[i,j](   x *(-1.)) = -d*0.5  = -0.5
+%  d_jj = int_[i,j](phi_j.grad(phi_j)) = int_[i,j](   x *( 1.)) =  d*0.5  =  0.5
+%
+% A <=> assembly of {kappa*laplacian + rho*diffusion}
+%       where kappa = 100 and rho = 2
+%
+% n m [nnz]
+% i j Aij
+
+8 8
+
+0  0    1.
+1  1  200.
+2  2  200.
+3  3  200.
+4  4  200.
+5  5  200.
+6  6  200.
+7  7  101.
+
+1  0     0.
+2  1  -101.
+3  2  -101.
+4  3  -101.
+5  4  -101.
+6  5  -101.
+7  6  -101.
+
+0  1    0.
+1  2  -99.
+2  3  -99.
+3  4  -99.
+4  5  -99.
+5  6  -99.
+6  7  -99.

EXAMPLES/MATRIX_MARKET/As.mtx

@@ -0,0 +1,69 @@
+%% MatrixMarket matrix coordinate double symmetric
+% This example is 0-based without (optional) nnz
+%
+% This is a 1D laplacian matrix (fixed at first end <=> invertible)
+%
+%              1                              1          
+%              .                             .--.        
+%             / \                            |  |        
+%            /   \ 0                       0 |  |        
+%  phi_i  --o  o  o--o--  =>  grad(phi_i)  --o  o  o--o--
+%              i  j                            i|  |j    
+%                                               |  |     
+%                                               .--.     
+%                                                -1.     
+%
+%                 1                              1       
+%                 .                             .--.     
+%                / \                            |  |     
+%               /   \ 0                        i|  |j    
+%  phi_j  --o--o  o  o--  =>  grad(phi_j)  --o--o  o  o--
+%              i  j                                |  | 0
+%                                                  |  |  
+%                                                  .--.  
+%                                                   -1.  
+%
+%                  i     j
+%              | l_ii  l_ij | i
+%  laplacian = |            |
+%              | l_ji  l_jj | j
+%
+%  distance(i, j) = d = 1.
+%
+%  l_ii = int_[i,j](grad(phi_i).grad(phi_i)) = d*(-1.)*(-1.) =  1.
+%  l_ij = int_[i,j](grad(phi_i).grad(phi_j)) = d*(-1.)*( 1.) = -1.
+%  l_ji = int_[i,j](grad(phi_j).grad(phi_i)) = d*( 1.)*(-1.) = -1.
+%  l_jj = int_[i,j](grad(phi_j).grad(phi_j)) = d*( 1.)*( 1.) =  1.
+%
+% A <=> assembly of {kappa*laplacian}
+%       where kappa = 100
+%
+% n m [nnz]
+% i j Aij
+
+8 8
+
+0  0    1.
+1  1  200.
+2  2  200.
+3  3  200.
+4  4  200.
+5  5  200.
+6  6  200.
+7  7  100.
+
+1  0     0.00
+2  1  -100.00
+3  2  -100.00
+4  3  -100.00
+5  4  -100.00
+6  5  -100.00
+7  6  -100.00
+
+0  1     0.00
+1  2  -100.00
+2  3  -100.00
+3  4  -100.00
+4  5  -100.00
+5  6  -100.00
+6  7  -100.00

EXAMPLES/MATRIX_MARKET/Az.mtx

@@ -0,0 +1,79 @@
+%% MatrixMarket matrix coordinate double symmetric
+% This example is 0-based without (optional) nnz
+%
+% This is a 1D diffusive laplacian matrix (fixed at first end <=> invertible)
+%
+%              1                              1          
+%              .                             .--.        
+%             / \                            |  |        
+%            /   \ 0                       0 |  |        
+%  phi_i  --o  o  o--o--  =>  grad(phi_i)  --o  o  o--o--
+%              i  j                            i|  |j    
+%                                               |  |     
+%                                               .--.     
+%                                                -1.     
+%
+%                 1                              1       
+%                 .                             .--.     
+%                / \                            |  |     
+%               /   \ 0                        i|  |j    
+%  phi_j  --o--o  o  o--  =>  grad(phi_j)  --o--o  o  o--
+%              i  j                                |  | 0
+%                                                  |  |  
+%                                                  .--.  
+%                                                   -1.  
+%
+%                  i     j
+%              | l_ii  l_ij | i
+%  laplacian = |            |
+%              | l_ji  l_jj | j
+%
+%  distance(i, j) = d = 1.
+%
+%  l_ii = int_[i,j](grad(phi_i).grad(phi_i)) = d*(-1.)*(-1.) =  1.
+%  l_ij = int_[i,j](grad(phi_i).grad(phi_j)) = d*(-1.)*( 1.) = -1.
+%  l_ji = int_[i,j](grad(phi_j).grad(phi_i)) = d*( 1.)*(-1.) = -1.
+%  l_jj = int_[i,j](grad(phi_j).grad(phi_j)) = d*( 1.)*( 1.) =  1.
+%
+%                i     j
+%              | d_ii  d_ij | i
+%  diffusion = |            |
+%              | d_ji  d_jj | j
+%
+%  d_ii = int_[i,j](phi_i.grad(phi_i)) = int_[i,j]((1-x)*(-1.)) = -d*0.5  = -0.5
+%  d_ij = int_[i,j](phi_i.grad(phi_j)) = int_[i,j]((1-x)*( 1.)) =  d*0.5  =  0.5
+%  d_ji = int_[i,j](phi_j.grad(phi_i)) = int_[i,j](   x *(-1.)) = -d*0.5  = -0.5
+%  d_jj = int_[i,j](phi_j.grad(phi_j)) = int_[i,j](   x *( 1.)) =  d*0.5  =  0.5
+%
+% A <=> assembly of {kappa*laplacian + rho*diffusion}
+%       where kappa = 100 and rho = 2
+%
+% n m [nnz]
+% i j Aij
+
+8 8
+
+0  0  (  1., 0.)
+1  1  (200., 0.)
+2  2  (200., 0.)
+3  3  (200., 0.)
+4  4  (200., 0.)
+5  5  (200., 0.)
+6  6  (200., 0.)
+7  7  (101., 0.)
+
+1  0  (   0., 0.)
+2  1  (-101., 0.)
+3  2  (-101., 0.)
+4  3  (-101., 0.)
+5  4  (-101., 0.)
+6  5  (-101., 0.)
+7  6  (-101., 0.)
+
+0  1  (  0., 0.)
+1  2  (-99., 0.)
+2  3  (-99., 0.)
+3  4  (-99., 0.)
+4  5  (-99., 0.)
+5  6  (-99., 0.)
+6  7  (-99., 0.)

EXAMPLES/MATRIX_MARKET/B.mtx

@@ -0,0 +1,62 @@
+%% MatrixMarket matrix coordinate double general
+% This example is 1-based with (optional) nnz
+%
+% This is a 1D mass matrix
+%
+%              1        
+%              .        
+%             / \       
+%            /   \ 0    
+%  phi_i  --o  o  o--o--
+%              i  j     
+%
+%                 1     
+%                 .     
+%                / \    
+%               /   \ 0 
+%  phi_j  --o--o  o  o--
+%              i  j     
+%
+%                i     j
+%            | i_ii  i_ij | i
+%  inertia = |            |
+%            | i_ji  i_jj | j
+%
+%  distance(i, j) = d = 1.
+%
+%  i_ii = int_[i,j](phi_i.phi_i) = int_[i,j]((1-x)(1-x)) = i_jj (area under the curve)
+%  i_ij = int_[i,j](phi_i.phi_j) = int_[i,j]((1-x)   x ) = i_ji
+%  i_ji = int_[i,j](phi_j.phi_i) = int_[i,j](   x (1-x)) = d*1./6.
+%  i_jj = int_[i,j](phi_j.phi_j) = int_[i,j](   x    x ) = d*1./3.
+%
+% B <=> mass assembly
+%
+% n m [nnz]
+% i j Bij
+
+8 8 22
+
+1  1  0.333
+2  2  0.333
+3  3  0.333
+4  4  0.333
+5  5  0.333
+6  6  0.333
+7  7  0.333
+8  8  0.333
+
+2  1  0.166
+3  2  0.166
+4  3  0.166
+5  4  0.166
+6  5  0.166
+7  6  0.166
+8  7  0.166
+
+1  2  0.166
+2  3  0.166
+3  4  0.166
+4  5  0.166
+5  6  0.166
+6  7  0.166
+7  8  0.166

EXAMPLES/MATRIX_MARKET/Bz.mtx

@@ -0,0 +1,62 @@
+%% MatrixMarket matrix coordinate double general
+% This example is 1-based with (optional) nnz
+%
+% This is a 1D mass matrix
+%
+%              1        
+%              .        
+%             / \       
+%            /   \ 0    
+%  phi_i  --o  o  o--o--
+%              i  j     
+%
+%                 1     
+%                 .     
+%                / \    
+%               /   \ 0 
+%  phi_j  --o--o  o  o--
+%              i  j     
+%
+%                i     j
+%            | i_ii  i_ij | i
+%  inertia = |            |
+%            | i_ji  i_jj | j
+%
+%  distance(i, j) = d = 1.
+%
+%  i_ii = int_[i,j](phi_i.phi_i) = int_[i,j]((1-x)(1-x)) = i_jj (area under the curve)
+%  i_ij = int_[i,j](phi_i.phi_j) = int_[i,j]((1-x)   x ) = i_ji
+%  i_ji = int_[i,j](phi_j.phi_i) = int_[i,j](   x (1-x)) = d*1./6.
+%  i_jj = int_[i,j](phi_j.phi_j) = int_[i,j](   x    x ) = d*1./3.
+%
+% B <=> mass assembly
+%
+% n m [nnz]
+% i j Bij
+
+8 8 22
+
+1  1  (0.333, 0.)
+2  2  (0.333, 0.)
+3  3  (0.333, 0.)
+4  4  (0.333, 0.)
+5  5  (0.333, 0.)
+6  6  (0.333, 0.)
+7  7  (0.333, 0.)
+8  8  (0.333, 0.)
+
+2  1  (0.166, 0.)
+3  2  (0.166, 0.)
+4  3  (0.166, 0.)
+5  4  (0.166, 0.)
+6  5  (0.166, 0.)
+7  6  (0.166, 0.)
+8  7  (0.166, 0.)
+
+1  2  (0.166, 0.)
+2  3  (0.166, 0.)
+3  4  (0.166, 0.)
+4  5  (0.166, 0.)
+5  6  (0.166, 0.)
+6  7  (0.166, 0.)
+7  8  (0.166, 0.)

EXAMPLES/MATRIX_MARKET/Makefile.am

@@ -0,0 +1,23 @@
+LDADD = $(top_builddir)/SRC/libarpack$(LIBSUFFIX)$(ITF64SUFFIX).la
+AM_CPPFLAGS = -I$(top_builddir) -I$(top_srcdir)/ICB $(EIGEN3_CFLAGS)
+
+EXTRA_DIST = README
+
+check_PROGRAMS = arpackmm
+dist_check_SCRIPTS = arpackmm.sh issue401.sh issue215.sh
+dist_check_DATA = An.mtx As.mtx Az.mtx B.mtx Bz.mtx issue401.mtx issue215.mtx
+TESTS = arpackmm.sh issue401.sh issue215.sh
+
+arpackmm_SOURCES = arpackmm.cpp
+
+pkgincludedir = $(includedir)/arpack@ITF64SUFFIX@
+if EIGEN
+pkginclude_HEADERS = arpackSolver.hpp
+endif
+
+CLEANFILES = \
+	arpackmm.run.log \
+	arpackmm.resid.out \
+	arpackmm.v.out \
+	arpackSolver.resid.out \
+	arpackSolver.v.out

EXAMPLES/MATRIX_MARKET/README

@@ -0,0 +1,39 @@
+arpackmm: utility to test arpack with matrix market files.
+
+This is meant to run arpack with different options to find
+what are the ones that are the best for your particular
+problem.
+
+Typically: computing small eigen values may breakdown and/or
+be slow (arpack is good at finding large eigen values only).
+To compute small eigen values, it may be a better choice
+to look for large eigen values with invert or shift+invert.
+
+How to use this utility ?
+Start simple, then, increase complexity if/when needed:
+- defaults to: standard real symmetric eigen problem to be
+  solved accurately (double precision).
+- list all possible options with --help.
+- add --verbose or --debug to get more informations.
+- if solve breaks down, you may:
+  - play with --nbCV (increase workspace size).
+  - play with --shiftReal/Imag and/or --invert.
+  - if arpack mode > 1, change solver with --slv.
+  - if arpack mode > 1, change solver parameters with --slv
+    (typically: pivoting threshold, solver tolerance, ...).
+  - try --restart (restart from previous eigen basis
+    approximation computed by previous run).
+  - etc...
+
+Note: using openblas/mkl/atlas instead of netlib blas/lapack
+may impact results. In some cases, it may also fail checks.
+Use --noCheck to skip checks.
+
+To build this utility, you need:
+- to use a fortran compiler which supports iso_c_binding.
+- to have installed eigen3 (to deal with the RCI).
+- to configure arpack-ng this way:
+  - autotools:
+    ~arpack-ng> ./configure --enable-eigen; make all check
+  - cmake:
+    ~arpack-ng/build> cmake -D EIGEN=ON ..; make all test

EXAMPLES/MATRIX_MARKET/arpackmm.sh

@@ -0,0 +1,102 @@
+#!/bin/bash -eu
+
+trap 'catch' ERR
+catch() {
+  grep OPT arpackmm.run.log
+  grep Error arpackmm.run.log
+  exit 1
+}
+
+# For all these eigen problems, the first eigen value is about 382 or (382, 0.).
+
+for stdPb in "--A As.mtx" "--nonSymPb --A An.mtx" "--nonSymPb --cpxPb --A Az.mtx"
+do
+  # Choose B matrix according to A.
+  export fileB=""
+  if [[ "$stdPb" == *cpxPb* ]]; then
+    export fileB="--B Bz.mtx"
+  else
+    export fileB="--B B.mtx"
+  fi
+
+  for genPb in "" "$fileB"
+  do
+    # SM may not converge so we can not apply checks.
+    # LM + invert is equivalent to SM and does converge.
+    # Note: this is expected as "power-like" methods are designed to find largest eigen values.
+    for magOpt in "--mag LM" "--mag SM --noCheck"
+    do
+      export mrn="--maxResNorm 1.e-1" # Relax residual check to get stable tests.
+
+      # Shift slightly to avoid the zero-vector starting problem.
+      export shiftZV=""
+      if [[ "$stdPb" == *cpxPb* ]]; then
+        export shiftZV="--shiftReal 1.0 --shiftImag 1.0"
+      else
+        export shiftZV="--shiftReal 1.0"
+      fi
+
+      # Shift according to the estimation of the eigen value we may have.
+      export shiftEV=""
+      if [[ "$stdPb" == *cpxPb* ]]; then
+        export shiftEV="--shiftReal 380.0 --shiftImag 1.0"
+      else
+        export shiftEV="--shiftReal 380.0"
+      fi
+
+      for shiftRI in "$shiftZV" "$shiftEV"
+      do
+        for invert in "" "--invert"
+        do
+          # Choose solver according to the sym/non-sym type of the problem.
+          export cgSlv=""
+          if [[ "$stdPb" == *nonSymPb* ]]; then
+            export cgSlv="BiCG"
+          else
+            export cgSlv="CG"
+          fi
+
+          for slv in "--slv $cgSlv" "--slv LU"
+          do
+            for rs in "" "--schur"
+            do
+              for dsPrec in "" "--simplePrec"
+              do
+                for dsMat in "" "--dense true"
+                do
+                  # Skip not supported cases.
+                  if [[ "$dsMat" == *dense* ]]; then
+                    if [[ "$slv" == *CG* ]]; then
+                      continue # Iterative solvers are not allowed when using dense matrices.
+                    fi
+                  fi
+
+                  export easeCV="--nbCV 6 --maxIt 200" # Use --nbCV 6 and --maxIt 200 to ease convergence.
+                  echo "CLI: ./arpackmm $stdPb $genPb $magOpt $mrn $shiftRI $invert $slv $rs $dsPrec $dsMat $easeCV"
+                  echo "----------------------------------------------------------------------------------------"
+
+                  # Run arpackmm.
+                  ./arpackmm "$stdPb" "$genPb" "$magOpt" "$mrn" "$shiftRI" "$invert" "$slv" "$rs" "$dsPrec" "$dsMat" \
+                             "$easeCV" --verbose 3 &> arpackmm.run.log
+                  grep OPT arpackmm.run.log
+                  grep OUT arpackmm.run.log
+                  echo "----------------------------------------------------------------------------------------"
+
+                  # Run arpackmm: re-run with restart always with small shift to avoid the zero-starting vector problem.
+                  ./arpackmm "$stdPb" "$genPb" "$magOpt" "$mrn" "$shiftZV" "$invert" "$slv" "$rs" "$dsPrec" "$dsMat" \
+                             --restart                                                                               \
+                             "$easeCV" --verbose 3 &> arpackmm.run.log
+                  grep OPT arpackmm.run.log
+                  grep OUT arpackmm.run.log
+                  echo "========================================================================================"
+                done
+              done
+            done
+          done
+        done
+      done
+    done
+  done
+done
+
+echo "arpackmm: OK"

EXAMPLES/MATRIX_MARKET/issue215.mtx

@@ -0,0 +1,6 @@
+%% MatrixMarket matrix coordinate double symmetric
+% 4x4 matrix filled with zero
+%
+
+4 4 0
+

EXAMPLES/MATRIX_MARKET/issue215.sh

@@ -0,0 +1,9 @@
+#!/bin/bash -eu
+
+# Note: need to shift slightly as eigen value is zero.
+./arpackmm --A issue215.mtx --mag LM --nbEV 1 --nbCV 4 --shiftReal 0.1
+if [ "$?" -ne "0" ]; then exit 1; fi
+./arpackmm --A issue215.mtx --mag LM --nbEV 1 --nbCV 4 --shiftReal 0.1 --restart
+if [ "$?" -ne "0" ]; then exit 1; fi
+
+echo "OK"

EXAMPLES/MATRIX_MARKET/issue401.mtx

@@ -0,0 +1,8 @@
+%% MatrixMarket matrix coordinate double symmetric
+% 10x10 matrix with 2 non-zero values
+%
+
+10 10 2
+
+0  1  1.
+1  0  1.

EXAMPLES/MATRIX_MARKET/issue401.sh

@@ -0,0 +1,10 @@
+#!/bin/bash -eu
+
+./arpackmm --A issue401.mtx --mag LA --nbEV 1 --nbCV 5
+if [ "$?" -ne "0" ]; then exit 1; fi
+./arpackmm --A issue401.mtx --mag LA --nbEV 1 --nbCV 5 --restart
+if [ "$?" -ne "0" ]; then exit 1; fi
+./arpackmm --A issue401.mtx --mag LA --nbEV 1 --nbCV 5 --restart --shiftReal 0.9
+if [ "$?" -ne "0" ]; then exit 1; fi
+
+echo "OK"

EXAMPLES/Makefile.am

@@ -1,2 +1,6 @@
 SUBDIRS = BAND COMPLEX NONSYM SIMPLE SVD SYM
-EXTRA_DIST = README
+if EIGEN
+SUBDIRS += MATRIX_MARKET
+endif
+
+EXTRA_DIST = README README.CALLING-ARPACK-FROM-C-OR-CPP

EXAMPLES/NONSYM/Makefile.am

@@ -1,4 +1,4 @@
-LDADD = $(top_builddir)/SRC/libarpack$(LIBSUFFIX).la $(LAPACK_LIBS) $(BLAS_LIBS)
+LDADD = $(top_builddir)/SRC/libarpack$(LIBSUFFIX)$(ITF64SUFFIX).la $(LAPACK_LIBS) $(BLAS_LIBS)
 
 SNDRV = sndrv1 sndrv2 sndrv3 sndrv4 sndrv5 sndrv6
 DNDRV = dndrv1 dndrv2 dndrv3 dndrv4 dndrv5 dndrv6

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/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/PYARPACK/README

@@ -0,0 +1,73 @@
+pyarpack: python binding based on Boost.Python.Numpy used to expose arpack C++ API
+
+Installation:
+-------------
+
+Python3: ~/arpack-ng/build> cmake -DCMAKE_INSTALL_PREFIX=/tmp/local -DPYTHON3=ON -DBOOST_PYTHON_LIBSUFFIX="3" ..
+         ~/arpack-ng/build> make all test
+         ~/arpack-ng/build> make install
+Note: Boost must have been compiled for Python3.
+Note: installation will install libpyarpack.so in the install directory.
+Note: python3 minimal packages must be installed (apt-get install python3-minimal python3-pip).
+      numpy must be installed (apt-get install python3-numpy) as the A/B matrices used by arpack
+      solver must be numpy arrays.
+
+Usage:
+------
+
+PYTHONPATH must include the directory where libpyarpack.so has been installed.
+
+>> export PYTHONPATH="/tmp/local/lib/pyarpack:${PYTHONPATH}"
+>> python
+>> import pyarpack
+>> help(pyarpack)
+
+You can use sparse or dense matrices, and, play with iterative or direct mode solvers (CG, LU, ...):
+
+1. choose arpack solver with a given mode solver
+   1.1. if you need to handle sparse matrices
+        >> from pyarpack import sparseBiCG as pyarpackSlv
+   1.2. if you need to handle dense matrices
+        >> from pyarpack import denseBiCG as pyarpackSlv
+2. choose arpack data type (float, double, ...)
+   >> arpackSlv = pyarpackSlv.double()
+3. solve the eigen problem
+   >> arpackSlv.solve(A, B)
+4. get eigen values and vectors
+   >> print(arpackSlv.vec)
+   >> print(arpackSlv.val)
+
+You can also:
+
+1. restart a solve from the workspace of a previous solve: check out pyarpackRestart.py.in.
+2. compute eigen and / or schur vectors.
+
+Note:
+
+1. arpack data type (float, double, ...) must be consistent with A/B numpy dtypes (float32, float64, ...).
+   at python side, the data MUST be casted in the EXACT expected type (int32, int64, float, double, ...).
+   otherwise, C++ may not get the data the way it expects them: C++ will not know how to read python data.
+   if you are not sure how data have been passed from python to C++, set arpackSlv.debug = 1 and check out debug traces.
+   in other words, pyarpack users MUST :
+   1.1. create numpy arrays specifying explicitly the type:
+        >> Aij = np.array([], dtype='complex128')
+   1.2. filling numpy arrays casting value on append:
+        >> Aij = np.append(Aij, np.complex128(complex( 200.,  200.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+   1.3. calling the solver flavor which is consistent with the numpy array data type:
+        >> arpackSlv = pyarpackSlv.complexDouble() # Caution: complexDouble <=> np.array(..., dtype='complex128')
+   note: NO data type check can be done at C++ side, the pyarpack user MUST insure data consistency.
+2. sparse matrices must be provided in coo format (n, i, j, Mij), that is, as a tuple where:
+   2.1. n is an integer.
+   2.2. i, j, Mij are 1 x nnz numpy arrays.
+3. dense  matrices must be provided in raw format (Mij, rowOrdered), that is, as a tuple where:
+   3.1. Mij is an n x n numpy array.
+   3.2. rowOrdered is a boolean (column ordered if False).
+4. arpack mode solver are provided by eigen:
+   4.1. when solver is iterative, A and B can be sparse only.
+   4.2. when solver is direct,    A and B can be sparse or dense.
+
+Examples:
+---------
+
+~/arpack-ng> find . -name *.py.in (template files from which python scripts will result)
+

EXAMPLES/PYARPACK/pyarpack.cpp

@@ -0,0 +1,434 @@
+#include <Python.h>  // PyErr_SetString.
+
+#include <boost/python.hpp>
+#include <boost/python/numpy.hpp>
+#include <boost/python/suite/indexing/vector_indexing_suite.hpp>
+#include <complex>
+#include <pyarpackDrtSolver.hpp>
+#include <pyarpackItrSolver.hpp>
+#include <sstream>  // ostringstream.
+#include <string>
+#include <vector>
+
+namespace bp = boost::python;
+namespace bn = boost::python::numpy;
+
+template <typename RC, typename FD, typename EM, typename SLV>
+void exportArpackSparseItr(bp::scope& pySlv, std::string const& dtype) {
+  // Created nested namespace in module.
+
+  pySlv.attr(dtype.c_str()) =
+      bp::class_<pyarpackSparseItrSolver<RC, FD, EM, SLV>>(
+          dtype.c_str(),
+          "arpack data type (must be consistent with numpy dtype)")
+          .def("solve", &pyarpackSparseItrSolver<RC, FD, EM, SLV>::solve,
+               (bp::arg("A"), bp::arg("B") = bp::tuple()),
+               "solve standard or generalised eigen problem where A and B must "
+               "be sparse and provided in coo format: (dimension, row-indice "
+               "array, column-indice array, matrice-value array) tuple")
+          .def("checkEigVec",
+               &pyarpackSparseItrSolver<RC, FD, EM, SLV>::checkEigVec,
+               (bp::arg("A"), bp::arg("B") = bp::tuple(),
+                bp::arg("maxResNorm") = 1.e-3),
+               "check eigen vectors accuracy (according to max allowed residual norm) "
+               "where A and B must be sparse and "
+               "provided in coo format: (dimension, row-indice array, "
+               "column-indice array, matrice-value array) tuple")
+              ARPACKSOLVERMEMBER(pyarpackSparseItrSolver)
+          .def_readwrite(
+              "slvTol", &pyarpackSparseItrSolver<RC, FD, EM, SLV>::slvTol,
+              "tolerance of the iterative mode solver - default: 1.e-6")
+          .def_readwrite("slvMaxIt",
+                         &pyarpackSparseItrSolver<RC, FD, EM, SLV>::slvMaxIt,
+                         "maximum number of iterations of the iterative mode "
+                         "solver - default: 100")
+          .def_readwrite(
+              "slvILUDropTol",
+              &pyarpackSparseItrSolver<RC, FD, EM, SLV>::slvILUDropTol,
+              "drop tolerance of the ILU preconditioner (if any) of the "
+              "iterative mode solver - default: 1")
+          .def_readwrite(
+              "slvILUFillFactor",
+              &pyarpackSparseItrSolver<RC, FD, EM, SLV>::slvILUFillFactor,
+              "fill factor of the ILU preconditioner (if any) of the iterative "
+              "mode solver - default: 2");
+};
+
+template <typename RC, typename FD, typename EM, typename SLV>
+void exportArpackSparseDrt(bp::scope& pySlv, std::string const& dtype) {
+  // Created nested namespace in module.
+
+  pySlv.attr(dtype.c_str()) =
+      bp::class_<pyarpackSparseDrtSolver<RC, FD, EM, SLV>>(
+          dtype.c_str(),
+          "arpack data type (must be consistent with numpy dtype)")
+          .def("solve", &pyarpackSparseDrtSolver<RC, FD, EM, SLV>::solve,
+               (bp::arg("A"), bp::arg("B") = bp::tuple()),
+               "solve standard or generalised eigen problem where A and B must "
+               "be sparse and provided in coo format: (dimension, row-indice "
+               "array, column-indice array, matrice-value array) tuple")
+          .def("checkEigVec",
+               &pyarpackSparseDrtSolver<RC, FD, EM, SLV>::checkEigVec,
+               (bp::arg("A"), bp::arg("B") = bp::tuple(),
+                bp::arg("maxResNorm") = 1.e-3),
+               "check eigen vectors accuracy (according to max allowed residual norm) "
+               "where A and B must be sparse and "
+               "provided in coo format: (dimension, row-indice array, "
+               "column-indice array, matrice-value array) tuple")
+              ARPACKSOLVERMEMBER(pyarpackSparseDrtSolver)
+          .def_readwrite(
+              "slvPvtThd", &pyarpackSparseDrtSolver<RC, FD, EM, SLV>::slvPvtThd,
+              "pivoting tolerance of the direct mode solver - default: 1.e-6")
+          .def_readwrite("slvOffset",
+                         &pyarpackSparseDrtSolver<RC, FD, EM, SLV>::slvOffset,
+                         "cholesky offset (LLT, LDLT) of the direct mode "
+                         "solver - default: 0.")
+          .def_readwrite("slvScale",
+                         &pyarpackSparseDrtSolver<RC, FD, EM, SLV>::slvScale,
+                         "cholesky scale (LLT, LDLT) of the direct mode solver "
+                         "- default: 1.");
+};
+
+template <typename RC, typename FD, typename EM, typename SLV>
+void exportArpackDenseDrt(bp::scope& pySlv, std::string const& dtype) {
+  // Created nested namespace in module.
+
+  pySlv.attr(dtype.c_str()) =
+      bp::class_<pyarpackDenseDrtSolver<RC, FD, EM, SLV>>(
+          dtype.c_str(),
+          "arpack data type (must be consistent with numpy dtype)")
+          .def("solve", &pyarpackDenseDrtSolver<RC, FD, EM, SLV>::solve,
+               (bp::arg("A"), bp::arg("B") = bp::tuple()),
+               "solve standard or generalised eigen problem where A and B must "
+               "be dense and provided in raw format: (n-squared matrice-value "
+               "array, row or column ordered boolean)")
+          .def("checkEigVec",
+               &pyarpackDenseDrtSolver<RC, FD, EM, SLV>::checkEigVec,
+               (bp::arg("A"), bp::arg("B") = bp::tuple(),
+                bp::arg("maxResNorm") = 1.e-3),
+               "check eigen vectors accuracy (according to max allowed residual norm) "
+               "where A and B must be dense and "
+               "provided in raw format: (n-squared matrice-value array, row or "
+               "column ordered boolean)")
+              ARPACKSOLVERMEMBER(pyarpackDenseDrtSolver)
+          .def_readwrite(
+              "slvPvtThd", &pyarpackDenseDrtSolver<RC, FD, EM, SLV>::slvPvtThd,
+              "pivoting tolerance of the direct mode solver - default: 1.e-6")
+          .def_readwrite("slvOffset",
+                         &pyarpackDenseDrtSolver<RC, FD, EM, SLV>::slvOffset,
+                         "cholesky offset (LLT, LDLT) of the direct mode "
+                         "solver - default: 0.")
+          .def_readwrite("slvScale",
+                         &pyarpackDenseDrtSolver<RC, FD, EM, SLV>::slvScale,
+                         "cholesky scale (LLT, LDLT) of the direct mode solver "
+                         "- default: 1.");
+};
+
+class sparseBiCGDiag {};
+class sparseBiCGILU {};
+class sparseCGDiag {};
+class sparseCGILU {};
+class sparseLLT {};
+class sparseLDLT {};
+class sparseLU {};
+class sparseQR {};
+
+class denseLLT {};
+class denseLDLT {};
+class denseLURR {};
+class denseQRRR {};
+class denseLUPP {};
+class denseQRPP {};
+
+std::complex<double> EigVecZGetItem(
+    Eigen::Matrix<std::complex<double>, Eigen::Dynamic, 1>& M, int idx) {
+  if (idx < 0 || idx >= M.size()) {
+    pyarpackThrowError("index out of range");
+    return std::complex<double>();
+  }
+  return M[idx];
+};
+
+std::string EigVecZToString(EigVecZ const& vec) {
+  std::ostringstream s;
+  s << vec;
+  return s.str();
+};
+
+BOOST_PYTHON_MODULE(pyarpack) {
+  // Initialize.
+
+  bn::initialize();
+
+  bp::class_<std::vector<std::complex<double>>>("StdVecZ").def(
+      bp::vector_indexing_suite<std::vector<std::complex<double>>>());
+
+  bp::class_<Eigen::Matrix<std::complex<double>, Eigen::Dynamic, 1>>("EigVecZ")
+      .def("__getitem__", &EigVecZGetItem)
+      .def("__str__", &EigVecZToString);
+
+  bp::class_<std::vector<EigVecZ>>("StdVecEVZ")
+      .def("__iter__", bp::iterator<std::vector<EigVecZ>>())
+      .def(bp::vector_indexing_suite<std::vector<EigVecZ>>());
+
+  // Documentation of the python module.
+
+  std::ostringstream doc;
+  doc << "You can use sparse or dense matrices, and, play with iterative or direct mode solvers (CG, LU, ...):" << std::endl;
+  doc << "1. choose arpack solver with a given mode solver" << std::endl;
+  doc << "   1.1. if you need to handle sparse matrices" << std::endl;
+  doc << "        >> from pyarpack import sparseBiCG as pyarpackSlv" << std::endl;
+  doc << "   1.2. if you need to handle dense matrices" << std::endl;
+  doc << "        >> from pyarpack import denseBiCG as pyarpackSlv" << std::endl;
+  doc << "2. choose arpack data type (float, double, ...)" << std::endl;
+  doc << "   >> arpackSlv = pyarpackSlv.double()" << std::endl;
+  doc << "3. solve the eigen problem" << std::endl;
+  doc << "   >> arpackSlv.solve(A, B)" << std::endl;
+  doc << "4. get eigen values and vectors" << std::endl;
+  doc << "   >> print(arpackSlv.vec)" << std::endl;
+  doc << "   >> print(arpackSlv.val)" << std::endl;
+  doc << std::endl;
+  doc << "Notes:" << std::endl;
+  doc << "1. arpack data type (float, double, ...) must be consistent with A/B numpy dtypes (float32, float64, ...)." << std::endl;
+  doc << "   at python side, the data MUST be casted in the EXACT expected type (int32, int64, float, double, ...)." << std::endl;
+  doc << "   otherwise, C++ may not get the data the way it expects them: C++ will not know how to read python data." << std::endl;
+  doc << "   if you are not sure how data have been passed from python to C++, set arpackSlv.debug = 1 and check out debug traces." << std::endl;
+  doc << "   in other words, pyarpack users MUST :" << std::endl;
+  doc << "   1.1. create numpy arrays specifying explicitly the type:" << std::endl;
+  doc << "        >> Aij = np.array([], dtype='complex128')" << std::endl;
+  doc << "   1.2. filling numpy arrays casting value on append:" << std::endl;
+  doc << "        >> Aij = np.append(Aij, np.complex128(complex( 200.,  200.))) # Casting value on append is MANDATORY or C++ won't get the expected type." << std::endl;
+  doc << "   1.3. calling the solver flavor which is consistent with the numpy array data type:" << std::endl;
+  doc << "        >> arpackSlv = pyarpackSlv.complexDouble() # Caution: complexDouble <=> np.array(..., dtype='complex128')" << std::endl;
+  doc << "   note: NO data type check can be done at C++ side, the pyarpack user MUST insure data consistency." << std::endl;
+  doc << "2. sparse matrices must be provided in coo format (n, i, j, Mij), that is, as a tuple where:" << std::endl;
+  doc << "   2.1. n is an integer." << std::endl;
+  doc << "   2.2. i, j, Mij are 1 x nnz numpy arrays." << std::endl;
+  doc << "3. dense  matrices must be provided in raw format (Mij, rowOrdered), that is, as a tuple where:" << std::endl;
+  doc << "   3.1. Mij is an n x n numpy array." << std::endl;
+  doc << "   3.2. rowOrdered is a boolean (column ordered if False)." << std::endl;
+  doc << "4. arpack mode solver are provided by eigen:" << std::endl;
+  doc << "   4.1. when solver is iterative, A and B can be sparse only." << std::endl;
+  doc << "   4.2. when solver is direct,    A and B can be sparse or dense." << std::endl;
+  bp::scope().attr("__doc__") = doc.str().c_str();
+
+  // Specify that this module is actually a package.
+
+  bp::object package = bp::scope();
+  package.attr("__path__") = "pyarpack";
+
+  // Create  python module.
+
+  std::string module = "pyarpack";
+  bp::object pyModule(
+      bp::handle<>(bp::borrowed(PyImport_AddModule(module.c_str()))));
+
+  // Create modules.
+
+  {
+    std::string slv = "sparseBiCGDiag";
+    std::string slvHelp =
+        "arpack internal mode solver (mode > 1): BiCG with diagonal (Jacobi) "
+        "preconditioner";
+    bp::scope pySlvBiCGDiag =
+        bp::class_<sparseBiCGDiag>(slv.c_str(), slvHelp.c_str());
+    exportArpackSparseItr<float, float, EigSMxS, EigSBiCGS>(pySlvBiCGDiag,
+                                                            "float");
+    exportArpackSparseItr<double, double, EigSMxD, EigSBiCGD>(pySlvBiCGDiag,
+                                                              "double");
+    exportArpackSparseItr<std::complex<float>, float, EigSMxC, EigSBiCGC>(
+        pySlvBiCGDiag, "complexFloat");
+    exportArpackSparseItr<std::complex<double>, double, EigSMxZ, EigSBiCGZ>(
+        pySlvBiCGDiag, "complexDouble");
+  }
+
+  {
+    std::string slv = "sparseBiCGILU";
+    std::string slvHelp =
+        "arpack internal mode solver (mode > 1): BiCG with ILU preconditioner";
+    bp::scope pySlvBiCGILU =
+        bp::class_<sparseBiCGILU>(slv.c_str(), slvHelp.c_str());
+    exportArpackSparseItr<float, float, EigSMxS, EigSBiCGILUS>(pySlvBiCGILU,
+                                                               "float");
+    exportArpackSparseItr<double, double, EigSMxD, EigSBiCGILUD>(pySlvBiCGILU,
+                                                                 "double");
+    exportArpackSparseItr<std::complex<float>, float, EigSMxC, EigSBiCGILUC>(
+        pySlvBiCGILU, "complexFloat");
+    exportArpackSparseItr<std::complex<double>, double, EigSMxZ, EigSBiCGILUZ>(
+        pySlvBiCGILU, "complexDouble");
+  }
+
+  {
+    std::string slv = "sparseCGDiag";
+    std::string slvHelp =
+        "arpack internal mode solver (mode > 1): CG with diagonal (Jacobi) "
+        "preconditioner";
+    bp::scope pySlvCGDiag =
+        bp::class_<sparseCGDiag>(slv.c_str(), slvHelp.c_str());
+    exportArpackSparseItr<float, float, EigSMxS, EigSCGS>(pySlvCGDiag, "float");
+    exportArpackSparseItr<double, double, EigSMxD, EigSCGD>(pySlvCGDiag,
+                                                            "double");
+    exportArpackSparseItr<std::complex<float>, float, EigSMxC, EigSCGC>(
+        pySlvCGDiag, "complexFloat");
+    exportArpackSparseItr<std::complex<double>, double, EigSMxZ, EigSCGZ>(
+        pySlvCGDiag, "complexDouble");
+  }
+
+  {
+    std::string slv = "sparseCGILU";
+    std::string slvHelp =
+        "arpack internal mode solver (mode > 1): CG with ILU preconditioner";
+    bp::scope pySlvCGILU =
+        bp::class_<sparseCGILU>(slv.c_str(), slvHelp.c_str());
+    exportArpackSparseItr<float, float, EigSMxS, EigSCGILUS>(pySlvCGILU,
+                                                             "float");
+    exportArpackSparseItr<double, double, EigSMxD, EigSCGILUD>(pySlvCGILU,
+                                                               "double");
+    exportArpackSparseItr<std::complex<float>, float, EigSMxC, EigSCGILUC>(
+        pySlvCGILU, "complexFloat");
+    exportArpackSparseItr<std::complex<double>, double, EigSMxZ, EigSCGILUZ>(
+        pySlvCGILU, "complexDouble");
+  }
+
+  {
+    std::string slv = "sparseLLT";
+    std::string slvHelp = "arpack internal mode solver (mode > 1): LLT";
+    bp::scope pySlvLLT = bp::class_<sparseLLT>(slv.c_str(), slvHelp.c_str());
+    exportArpackSparseDrt<float, float, EigSMxS, EigSLLTS>(pySlvLLT, "float");
+    exportArpackSparseDrt<double, double, EigSMxD, EigSLLTD>(pySlvLLT,
+                                                             "double");
+    exportArpackSparseDrt<std::complex<float>, float, EigSMxC, EigSLLTC>(
+        pySlvLLT, "complexFloat");
+    exportArpackSparseDrt<std::complex<double>, double, EigSMxZ, EigSLLTZ>(
+        pySlvLLT, "complexDouble");
+  }
+
+  {
+    std::string slv = "sparseLDLT";
+    std::string slvHelp = "arpack internal mode solver (mode > 1): LDLT";
+    bp::scope pySlvLDLT = bp::class_<sparseLDLT>(slv.c_str(), slvHelp.c_str());
+    exportArpackSparseDrt<float, float, EigSMxS, EigSLDLTS>(pySlvLDLT, "float");
+    exportArpackSparseDrt<double, double, EigSMxD, EigSLDLTD>(pySlvLDLT,
+                                                              "double");
+    exportArpackSparseDrt<std::complex<float>, float, EigSMxC, EigSLDLTC>(
+        pySlvLDLT, "complexFloat");
+    exportArpackSparseDrt<std::complex<double>, double, EigSMxZ, EigSLDLTZ>(
+        pySlvLDLT, "complexDouble");
+  }
+
+  {
+    std::string slv = "sparseLU";
+    std::string slvHelp = "arpack internal mode solver (mode > 1): LU";
+    bp::scope pySlvLU = bp::class_<sparseLU>(slv.c_str(), slvHelp.c_str());
+    exportArpackSparseDrt<float, float, EigSMxS, EigSLUS>(pySlvLU, "float");
+    exportArpackSparseDrt<double, double, EigSMxD, EigSLUD>(pySlvLU, "double");
+    exportArpackSparseDrt<std::complex<float>, float, EigSMxC, EigSLUC>(
+        pySlvLU, "complexFloat");
+    exportArpackSparseDrt<std::complex<double>, double, EigSMxZ, EigSLUZ>(
+        pySlvLU, "complexDouble");
+  }
+
+  {
+    std::string slv = "sparseQR";
+    std::string slvHelp = "arpack internal mode solver (mode > 1): QR";
+    bp::scope pySlvQR = bp::class_<sparseQR>(slv.c_str(), slvHelp.c_str());
+    exportArpackSparseDrt<float, float, EigSMxS, EigSQRS>(pySlvQR, "float");
+    exportArpackSparseDrt<double, double, EigSMxD, EigSQRD>(pySlvQR, "double");
+    exportArpackSparseDrt<std::complex<float>, float, EigSMxC, EigSQRC>(
+        pySlvQR, "complexFloat");
+    exportArpackSparseDrt<std::complex<double>, double, EigSMxZ, EigSQRZ>(
+        pySlvQR, "complexDouble");
+  }
+
+  {
+    std::string slv = "denseLLT";
+    std::string slvHelp = "arpack internal mode solver (mode > 1): LLT";
+    bp::scope pySlvLLT = bp::class_<denseLLT>(slv.c_str(), slvHelp.c_str());
+    exportArpackDenseDrt<float, float, EigDMxS, EigDLLTS>(pySlvLLT, "float");
+    exportArpackDenseDrt<double, double, EigDMxD, EigDLLTD>(pySlvLLT, "double");
+    exportArpackDenseDrt<std::complex<float>, float, EigDMxC, EigDLLTC>(
+        pySlvLLT, "complexFloat");
+    exportArpackDenseDrt<std::complex<double>, double, EigDMxZ, EigDLLTZ>(
+        pySlvLLT, "complexDouble");
+  }
+
+  {
+    std::string slv = "denseLDLT";
+    std::string slvHelp = "arpack internal mode solver (mode > 1): LDLT";
+    bp::scope pySlvLDLT = bp::class_<denseLDLT>(slv.c_str(), slvHelp.c_str());
+    exportArpackDenseDrt<float, float, EigDMxS, EigDLDLTS>(pySlvLDLT, "float");
+    exportArpackDenseDrt<double, double, EigDMxD, EigDLDLTD>(pySlvLDLT,
+                                                             "double");
+    exportArpackDenseDrt<std::complex<float>, float, EigDMxC, EigDLDLTC>(
+        pySlvLDLT, "complexFloat");
+    exportArpackDenseDrt<std::complex<double>, double, EigDMxZ, EigDLDLTZ>(
+        pySlvLDLT, "complexDouble");
+  }
+
+  {
+    std::string slv = "denseLURR";
+    std::string slvHelp =
+        "arpack internal mode solver (mode > 1): LU Rank Revealing (slower, "
+        "more stable)";
+    bp::scope pySlvLURR = bp::class_<denseLURR>(slv.c_str(), slvHelp.c_str());
+    exportArpackDenseDrt<float, float, EigDMxS, EigDFLUS>(pySlvLURR, "float");
+    exportArpackDenseDrt<double, double, EigDMxD, EigDFLUD>(pySlvLURR,
+                                                            "double");
+    exportArpackDenseDrt<std::complex<float>, float, EigDMxC, EigDFLUC>(
+        pySlvLURR, "complexFloat");
+    exportArpackDenseDrt<std::complex<double>, double, EigDMxZ, EigDFLUZ>(
+        pySlvLURR, "complexDouble");
+  }
+
+  {
+    std::string slv = "denseQRRR";
+    std::string slvHelp =
+        "arpack internal mode solver (mode > 1): QR Rank Revealing (slower, "
+        "more stable)";
+    bp::scope pySlvQRRR = bp::class_<denseQRRR>(slv.c_str(), slvHelp.c_str());
+    exportArpackDenseDrt<float, float, EigDMxS, EigDFQRS>(pySlvQRRR, "float");
+    exportArpackDenseDrt<double, double, EigDMxD, EigDFQRD>(pySlvQRRR,
+                                                            "double");
+    exportArpackDenseDrt<std::complex<float>, float, EigDMxC, EigDFQRC>(
+        pySlvQRRR, "complexFloat");
+    exportArpackDenseDrt<std::complex<double>, double, EigDMxZ, EigDFQRZ>(
+        pySlvQRRR, "complexDouble");
+  }
+
+  {
+    std::string slv = "denseLUPP";
+    std::string slvHelp =
+        "arpack internal mode solver (mode > 1): LU Partial Pivoting (faster, "
+        "less stable)";
+    bp::scope pySlvLUPP = bp::class_<denseLUPP>(slv.c_str(), slvHelp.c_str());
+    exportArpackDenseDrt<float, float, EigDMxS, EigDPLUS>(pySlvLUPP, "float");
+    exportArpackDenseDrt<double, double, EigDMxD, EigDPLUD>(pySlvLUPP,
+                                                            "double");
+    exportArpackDenseDrt<std::complex<float>, float, EigDMxC, EigDPLUC>(
+        pySlvLUPP, "complexFloat");
+    exportArpackDenseDrt<std::complex<double>, double, EigDMxZ, EigDPLUZ>(
+        pySlvLUPP, "complexDouble");
+  }
+
+  {
+    std::string slv = "denseQRPP";
+    std::string slvHelp =
+        "arpack internal mode solver (mode > 1): QR Partial Pivoting (faster, "
+        "less stable)";
+    bp::scope pySlvQPPR = bp::class_<denseQRPP>(slv.c_str(), slvHelp.c_str());
+    exportArpackDenseDrt<float, float, EigDMxS, EigDPQRS>(pySlvQPPR, "float");
+    exportArpackDenseDrt<double, double, EigDMxD, EigDPQRD>(pySlvQPPR,
+                                                            "double");
+    exportArpackDenseDrt<std::complex<float>, float, EigDMxC, EigDPQRC>(
+        pySlvQPPR, "complexFloat");
+    exportArpackDenseDrt<std::complex<double>, double, EigDMxZ, EigDPQRZ>(
+        pySlvQPPR, "complexDouble");
+  }
+}
+
+// Local Variables:
+// mode: c++
+// c-file-style:"stroustrup"
+// show-trailing-whitespace: t
+// End:
+/* vim: set sw=2 ts=2 et smartindent :*/

EXAMPLES/PYARPACK/pyarpackDenseLDLT.py.in

@@ -0,0 +1,113 @@
+#!/usr/bin/env python
+
+import numpy as np
+from pyarpack import denseLDLT as pyarpackSlv
+
+# Build laplacian.
+
+n = 4
+Aij = np.array([], dtype='float64')
+for k in range(n):
+    for l in range(n):
+        if l == k:
+            Aij = np.append(Aij, np.float64( 200.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k-1 or l == k+1:
+            Aij = np.append(Aij, np.float64(-100.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        else:
+            Aij = np.append(Aij, np.float64(   0.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+for idx, val in enumerate(Aij):
+    print("A[", idx, "] =", val)
+A = (Aij, False) # raw format: Aij values, row ordered (or not).
+
+# Get and tune arpack solver.
+
+arpackSlv = pyarpackSlv.double() # Caution: double <=> np.array(..., dtype='float64')
+arpackSlv.verbose = 3 # Set to 0 to get a quiet solve.
+arpackSlv.debug = 1 # Set to 0 to get a quiet solve.
+arpackSlv.nbEV = 1
+arpackSlv.nbCV = 2*arpackSlv.nbEV + 1
+arpackSlv.mag = 'LM'
+arpackSlv.maxIt = 200
+arpackSlv.slvOffset = 0.
+arpackSlv.slvScale = 1.
+arpackSlv.symPb = True
+
+# Solve eigen problem.
+
+rc = arpackSlv.solve(A)
+assert rc == 0, "bad solve"
+rc = arpackSlv.checkEigVec(A)
+assert rc == 0, "bad checkEigVec"
+
+# Print out results (mode selected, eigen vectors, eigen values, ...).
+
+assert arpackSlv.nbEV == len(arpackSlv.val), "bad result"
+print("\nresults:\n")
+print("mode selected:", arpackSlv.mode)
+print("nb iterations:", arpackSlv.nbIt)
+print("Reverse Communication Interface time:", arpackSlv.rciTime, "s")
+for val, vec in zip(arpackSlv.val, arpackSlv.vec):
+    print("eigen value:", val)
+    print("eigen vector:")
+    print(vec)
+
+#######################################################################################
+print("\n##########################################################################\n")
+#######################################################################################
+
+# Build laplacian.
+
+n = 8
+Aij = np.array([], dtype='float32')
+Bij = np.array([], dtype='float32')
+for k in range(n):
+    for l in range(n):
+        if l == k:
+            Aij = np.append(Aij, np.float32( 200.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.float32( 33.3)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k-1 or l == k+1:
+            Aij = np.append(Aij, np.float32(-100.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.float32( 16.6)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        else:
+            Aij = np.append(Aij, np.float32(   0.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.float32(   0.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+for idx, val in enumerate(Aij):
+    print("A[", idx, "] =", val)
+for idx, val in enumerate(Bij):
+    print("B[", idx, "] =", val)
+A = (Aij, False) # raw format: Aij values, row ordered (or not).
+B = (Bij,  True) # raw format: Bij values, row ordered (or not).
+
+# Get and tune arpack solver.
+
+arpackSlv = pyarpackSlv.float() # Caution: float <=> np.array(..., dtype='float32')
+arpackSlv.verbose = 3 # Set to 0 to get a quiet solve.
+arpackSlv.debug = 1 # Set to 0 to get a quiet solve.
+arpackSlv.nbEV = 2
+arpackSlv.nbCV = 2*arpackSlv.nbEV + 1
+arpackSlv.mag = 'LM'
+arpackSlv.maxIt = 200
+arpackSlv.slvOffset = 0.
+arpackSlv.slvScale = 1.
+arpackSlv.sigmaReal = 1
+arpackSlv.symPb = True
+
+# Solve eigen problem.
+
+rc = arpackSlv.solve(A, B)
+assert rc == 0, "bad solve"
+rc = arpackSlv.checkEigVec(A, B, 1.e-2)
+assert rc == 0, "bad checkEigVec"
+
+# Print out results (mode selected, eigen vectors, eigen values, ...).
+
+assert arpackSlv.nbEV == len(arpackSlv.val), "bad result"
+print("\nresults:\n")
+print("mode selected:", arpackSlv.mode)
+print("nb iterations:", arpackSlv.nbIt)
+print("Reverse Communication Interface time:", arpackSlv.rciTime, "s")
+for val, vec in zip(arpackSlv.val, arpackSlv.vec):
+    print("eigen value:", val)
+    print("eigen vector:")
+    for v in range(n):
+        print(vec[v])

EXAMPLES/PYARPACK/pyarpackDenseLLT.py.in

@@ -0,0 +1,110 @@
+#!/usr/bin/env python
+
+import numpy as np
+from pyarpack import denseLLT as pyarpackSlv
+
+# Build laplacian.
+
+n = 4
+Aij = np.array([], dtype='float64')
+for k in range(n):
+    for l in range(n):
+        if l == k:
+            Aij = np.append(Aij, np.float64( 200.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k-1 or l == k+1:
+            Aij = np.append(Aij, np.float64(-100.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        else:
+            Aij = np.append(Aij, np.float64(   0.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+for idx, val in enumerate(Aij):
+    print("A[", idx, "] =", val)
+A = (Aij, False) # raw format: Aij values, row ordered (or not).
+
+# Get and tune arpack solver.
+
+arpackSlv = pyarpackSlv.double() # Caution: double <=> np.array(..., dtype='float64')
+arpackSlv.verbose = 3 # Set to 0 to get a quiet solve.
+arpackSlv.debug = 1 # Set to 0 to get a quiet solve.
+arpackSlv.nbEV = 1
+arpackSlv.nbCV = 2*arpackSlv.nbEV + 1
+arpackSlv.mag = 'LM'
+arpackSlv.maxIt = 200
+arpackSlv.slvOffset = 0.
+arpackSlv.slvScale = 1.
+
+# Solve eigen problem.
+
+rc = arpackSlv.solve(A)
+assert rc == 0, "bad solve"
+rc = arpackSlv.checkEigVec(A)
+assert rc == 0, "bad checkEigVec"
+
+# Print out results (mode selected, eigen vectors, eigen values, ...).
+
+assert arpackSlv.nbEV == len(arpackSlv.val), "bad result"
+print("\nresults:\n")
+print("mode selected:", arpackSlv.mode)
+print("nb iterations:", arpackSlv.nbIt)
+print("Reverse Communication Interface time:", arpackSlv.rciTime, "s")
+for val, vec in zip(arpackSlv.val, arpackSlv.vec):
+    print("eigen value:", val)
+    print("eigen vector:")
+    print(vec)
+
+#######################################################################################
+print("\n##########################################################################\n")
+#######################################################################################
+
+# Build laplacian.
+
+n = 8
+Aij = np.array([], dtype='float32')
+Bij = np.array([], dtype='float32')
+for k in range(n):
+    for l in range(n):
+        if l == k:
+            Aij = np.append(Aij, np.float32( 200.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.float32( 33.3)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k-1 or l == k+1:
+            Aij = np.append(Aij, np.float32(-100.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.float32( 16.6)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        else:
+            Aij = np.append(Aij, np.float32(   0.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.float32(   0.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+for idx, val in enumerate(Aij):
+    print("A[", idx, "] =", val)
+for idx, val in enumerate(Bij):
+    print("B[", idx, "] =", val)
+A = (Aij, False) # raw format: Aij values, row ordered (or not).
+B = (Bij,  True) # raw format: Bij values, row ordered (or not).
+
+# Get and tune arpack solver.
+
+arpackSlv = pyarpackSlv.float() # Caution: float <=> np.array(..., dtype='float32')
+arpackSlv.verbose = 3 # Set to 0 to get a quiet solve.
+arpackSlv.debug = 1 # Set to 0 to get a quiet solve.
+arpackSlv.nbEV = 2
+arpackSlv.nbCV = 2*arpackSlv.nbEV + 1
+arpackSlv.mag = 'LM'
+arpackSlv.maxIt = 200
+arpackSlv.slvOffset = 0.
+arpackSlv.slvScale = 1.
+
+# Solve eigen problem.
+
+rc = arpackSlv.solve(A, B)
+assert rc == 0, "bad solve"
+rc = arpackSlv.checkEigVec(A, B, 1.e-2)
+assert rc == 0, "bad checkEigVec"
+
+# Print out results (mode selected, eigen vectors, eigen values, ...).
+
+assert arpackSlv.nbEV == len(arpackSlv.val), "bad result"
+print("\nresults:\n")
+print("mode selected:", arpackSlv.mode)
+print("nb iterations:", arpackSlv.nbIt)
+print("Reverse Communication Interface time:", arpackSlv.rciTime, "s")
+for val, vec in zip(arpackSlv.val, arpackSlv.vec):
+    print("eigen value:", val)
+    print("eigen vector:")
+    for v in range(n):
+        print(vec[v])

EXAMPLES/PYARPACK/pyarpackDenseLUPP.py.in

@@ -0,0 +1,116 @@
+#!/usr/bin/env python
+
+import numpy as np
+from pyarpack import denseLUPP as pyarpackSlv
+
+# Build laplacian.
+
+n = 4
+Aij = np.array([], dtype='complex128')
+for k in range(n):
+    for l in range(n):
+        if l == k:
+            Aij = np.append(Aij, np.complex128(complex( 200.,  200.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k-1:
+            Aij = np.append(Aij, np.complex128(complex(-101., -101.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k+1:
+            Aij = np.append(Aij, np.complex128(complex( -99.,  -99.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        else:
+            Aij = np.append(Aij, np.complex128(complex(   0.,    0.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+for idx, val in enumerate(Aij):
+    print("A[", idx, "] =", val)
+A = (Aij, False) # raw format: Aij values, row ordered (or not).
+
+# Get and tune arpack solver.
+
+arpackSlv = pyarpackSlv.complexDouble() # Caution: complexDouble <=> np.array(..., dtype='complex128')
+arpackSlv.verbose = 3 # Set to 0 to get a quiet solve.
+arpackSlv.debug = 1 # Set to 0 to get a quiet solve.
+arpackSlv.nbEV = 1
+arpackSlv.nbCV = 2*arpackSlv.nbEV + 1
+arpackSlv.mag = 'LM'
+arpackSlv.maxIt = 200
+arpackSlv.slvPvtThd = 1.e-6
+arpackSlv.symPb = False
+
+# Solve eigen problem.
+
+rc = arpackSlv.solve(A)
+assert rc == 0, "bad solve"
+rc = arpackSlv.checkEigVec(A)
+assert rc == 0, "bad checkEigVec"
+
+# Print out results (mode selected, eigen vectors, eigen values, ...).
+
+assert arpackSlv.nbEV == len(arpackSlv.val), "bad result"
+print("\nresults:\n")
+print("mode selected:", arpackSlv.mode)
+print("nb iterations:", arpackSlv.nbIt)
+print("Reverse Communication Interface time:", arpackSlv.rciTime, "s")
+for val, vec in zip(arpackSlv.val, arpackSlv.vec):
+    print("eigen value:", val)
+    print("eigen vector:")
+    print(vec)
+
+#######################################################################################
+print("\n##########################################################################\n")
+#######################################################################################
+
+# Build laplacian.
+
+n = 8
+Aij = np.array([], dtype='complex64')
+Bij = np.array([], dtype='complex64')
+for k in range(n):
+    for l in range(n):
+        if l == k:
+            Aij = np.append(Aij, np.complex64(complex( 200.,  200.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.complex64(complex( 33.3,  33.3))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k-1:
+            Aij = np.append(Aij, np.complex64(complex(-101., -101.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.complex64(complex( 16.6,  16.6))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k+1:
+            Aij = np.append(Aij, np.complex64(complex( -99.,  -99.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.complex64(complex( 16.6,  16.6))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        else:
+            Aij = np.append(Aij, np.complex64(complex(   0.,    0.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.complex64(complex(   0.,    0.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+for idx, val in enumerate(Aij):
+    print("A[", idx, "] =", val)
+for idx, val in enumerate(Bij):
+    print("B[", idx, "] =", val)
+A = (Aij, False) # raw format: Aij values, row ordered (or not).
+B = (Bij,  True) # raw format: Bij values, row ordered (or not).
+
+# Get and tune arpack solver.
+
+arpackSlv = pyarpackSlv.complexFloat() # Caution: complexFloat <=> np.array(..., dtype='complex64')
+arpackSlv.verbose = 3 # Set to 0 to get a quiet solve.
+arpackSlv.debug = 1 # Set to 0 to get a quiet solve.
+arpackSlv.nbEV = 2
+arpackSlv.nbCV = 2*arpackSlv.nbEV + 1
+arpackSlv.mag = 'LM'
+arpackSlv.maxIt = 200
+arpackSlv.slvPvtThd = 1.e-6
+arpackSlv.sigmaReal = 1
+arpackSlv.symPb = False
+
+# Solve eigen problem.
+
+rc = arpackSlv.solve(A, B)
+assert rc == 0, "bad solve"
+rc = arpackSlv.checkEigVec(A, B, 1.e-2)
+assert rc == 0, "bad checkEigVec"
+
+# Print out results (mode selected, eigen vectors, eigen values, ...).
+
+assert arpackSlv.nbEV == len(arpackSlv.val), "bad result"
+print("\nresults:\n")
+print("mode selected:", arpackSlv.mode)
+print("nb iterations:", arpackSlv.nbIt)
+print("Reverse Communication Interface time:", arpackSlv.rciTime, "s")
+for val, vec in zip(arpackSlv.val, arpackSlv.vec):
+    print("eigen value:", val)
+    print("eigen vector:")
+    for v in range(n):
+        print(vec[v])

EXAMPLES/PYARPACK/pyarpackDenseLURR.py.in

@@ -0,0 +1,109 @@
+#!/usr/bin/env python
+
+import numpy as np
+from pyarpack import denseLURR as pyarpackSlv
+
+# Build laplacian.
+
+n = 4
+Aij = np.array([], dtype='float64')
+for k in range(n):
+    for l in range(n):
+        if l == k:
+            Aij = np.append(Aij, np.float64( 200.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k-1 or l == k+1:
+            Aij = np.append(Aij, np.float64(-100.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        else:
+            Aij = np.append(Aij, np.float64(   0.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+for idx, val in enumerate(Aij):
+    print("A[", idx, "] =", val)
+A = (Aij, False) # raw format: Aij values, row ordered (or not).
+
+# Get and tune arpack solver.
+
+arpackSlv = pyarpackSlv.double() # Caution: double <=> np.array(..., dtype='float64')
+arpackSlv.verbose = 3 # Set to 0 to get a quiet solve.
+arpackSlv.debug = 1 # Set to 0 to get a quiet solve.
+arpackSlv.nbEV = 1
+arpackSlv.nbCV = 2*arpackSlv.nbEV + 1
+arpackSlv.mag = 'LM'
+arpackSlv.maxIt = 200
+arpackSlv.slvPvtThd = 1.e-6
+
+# Solve eigen problem.
+
+rc = arpackSlv.solve(A)
+assert rc == 0, "bad solve"
+rc = arpackSlv.checkEigVec(A)
+assert rc == 0, "bad checkEigVec"
+
+# Print out results (mode selected, eigen vectors, eigen values, ...).
+
+assert arpackSlv.nbEV == len(arpackSlv.val), "bad result"
+print("\nresults:\n")
+print("mode selected:", arpackSlv.mode)
+print("nb iterations:", arpackSlv.nbIt)
+print("Reverse Communication Interface time:", arpackSlv.rciTime, "s")
+for val, vec in zip(arpackSlv.val, arpackSlv.vec):
+    print("eigen value:", val)
+    print("eigen vector:")
+    print(vec)
+
+#######################################################################################
+print("\n##########################################################################\n")
+#######################################################################################
+
+# Build laplacian.
+
+n = 8
+Aij = np.array([], dtype='float32')
+Bij = np.array([], dtype='float32')
+for k in range(n):
+    for l in range(n):
+        if l == k:
+            Aij = np.append(Aij, np.float32( 200.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.float32( 33.3)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k-1 or l == k+1:
+            Aij = np.append(Aij, np.float32(-100.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.float32( 16.6)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        else:
+            Aij = np.append(Aij, np.float32(   0.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.float32(   0.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+for idx, val in enumerate(Aij):
+    print("A[", idx, "] =", val)
+for idx, val in enumerate(Bij):
+    print("B[", idx, "] =", val)
+A = (Aij, False) # raw format: Aij values, row ordered (or not).
+B = (Bij,  True) # raw format: Bij values, row ordered (or not).
+
+# Get and tune arpack solver.
+
+arpackSlv = pyarpackSlv.float() # Caution: float <=> np.array(..., dtype='float32')
+arpackSlv.verbose = 3 # Set to 0 to get a quiet solve.
+arpackSlv.debug = 1 # Set to 0 to get a quiet solve.
+arpackSlv.nbEV = 2
+arpackSlv.nbCV = 2*arpackSlv.nbEV + 1
+arpackSlv.mag = 'LM'
+arpackSlv.maxIt = 200
+arpackSlv.slvPvtThd = 1.e-6
+arpackSlv.sigmaReal = 1
+
+# Solve eigen problem.
+
+rc = arpackSlv.solve(A, B)
+assert rc == 0, "bad solve"
+rc = arpackSlv.checkEigVec(A, B, 1.e-2)
+assert rc == 0, "bad checkEigVec"
+
+# Print out results (mode selected, eigen vectors, eigen values, ...).
+
+assert arpackSlv.nbEV == len(arpackSlv.val), "bad result"
+print("\nresults:\n")
+print("mode selected:", arpackSlv.mode)
+print("nb iterations:", arpackSlv.nbIt)
+print("Reverse Communication Interface time:", arpackSlv.rciTime, "s")
+for val, vec in zip(arpackSlv.val, arpackSlv.vec):
+    print("eigen value:", val)
+    print("eigen vector:")
+    for v in range(n):
+        print(vec[v])

EXAMPLES/PYARPACK/pyarpackDenseQRPP.py.in

@@ -0,0 +1,116 @@
+#!/usr/bin/env python
+
+import numpy as np
+from pyarpack import denseQRPP as pyarpackSlv
+
+# Build laplacian.
+
+n = 4
+Aij = np.array([], dtype='complex128')
+for k in range(n):
+    for l in range(n):
+        if l == k:
+            Aij = np.append(Aij, np.complex128(complex( 200.,  200.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k-1:
+            Aij = np.append(Aij, np.complex128(complex(-101., -101.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k+1:
+            Aij = np.append(Aij, np.complex128(complex( -99.,  -99.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        else:
+            Aij = np.append(Aij, np.complex128(complex(   0.,    0.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+for idx, val in enumerate(Aij):
+    print("A[", idx, "] =", val)
+A = (Aij, False) # raw format: Aij values, row ordered (or not).
+
+# Get and tune arpack solver.
+
+arpackSlv = pyarpackSlv.complexDouble() # Caution: complexDouble <=> np.array(..., dtype='complex128')
+arpackSlv.verbose = 3 # Set to 0 to get a quiet solve.
+arpackSlv.debug = 1 # Set to 0 to get a quiet solve.
+arpackSlv.nbEV = 1
+arpackSlv.nbCV = 2*arpackSlv.nbEV + 1
+arpackSlv.mag = 'LM'
+arpackSlv.maxIt = 200
+arpackSlv.slvPvtThd = 1.e-6
+arpackSlv.symPb = False
+
+# Solve eigen problem.
+
+rc = arpackSlv.solve(A)
+assert rc == 0, "bad solve"
+rc = arpackSlv.checkEigVec(A)
+assert rc == 0, "bad checkEigVec"
+
+# Print out results (mode selected, eigen vectors, eigen values, ...).
+
+assert arpackSlv.nbEV == len(arpackSlv.val), "bad result"
+print("\nresults:\n")
+print("mode selected:", arpackSlv.mode)
+print("nb iterations:", arpackSlv.nbIt)
+print("Reverse Communication Interface time:", arpackSlv.rciTime, "s")
+for val, vec in zip(arpackSlv.val, arpackSlv.vec):
+    print("eigen value:", val)
+    print("eigen vector:")
+    print(vec)
+
+#######################################################################################
+print("\n##########################################################################\n")
+#######################################################################################
+
+# Build laplacian.
+
+n = 8
+Aij = np.array([], dtype='complex64')
+Bij = np.array([], dtype='complex64')
+for k in range(n):
+    for l in range(n):
+        if l == k:
+            Aij = np.append(Aij, np.complex64(complex( 200.,  200.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.complex64(complex( 33.3,  33.3))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k-1:
+            Aij = np.append(Aij, np.complex64(complex(-101., -101.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.complex64(complex( 16.6,  16.6))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k+1:
+            Aij = np.append(Aij, np.complex64(complex( -99.,  -99.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.complex64(complex( 16.6,  16.6))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        else:
+            Aij = np.append(Aij, np.complex64(complex(   0.,    0.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.complex64(complex(   0.,    0.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+for idx, val in enumerate(Aij):
+    print("A[", idx, "] =", val)
+for idx, val in enumerate(Bij):
+    print("B[", idx, "] =", val)
+A = (Aij, False) # raw format: Aij values, row ordered (or not).
+B = (Bij,  True) # raw format: Bij values, row ordered (or not).
+
+# Get and tune arpack solver.
+
+arpackSlv = pyarpackSlv.complexFloat() # Caution: complexFloat <=> np.array(..., dtype='complex64')
+arpackSlv.verbose = 3 # Set to 0 to get a quiet solve.
+arpackSlv.debug = 1 # Set to 0 to get a quiet solve.
+arpackSlv.nbEV = 2
+arpackSlv.nbCV = 2*arpackSlv.nbEV + 1
+arpackSlv.mag = 'LM'
+arpackSlv.maxIt = 200
+arpackSlv.slvPvtThd = 1.e-6
+arpackSlv.sigmaReal = 1
+arpackSlv.symPb = False
+
+# Solve eigen problem.
+
+rc = arpackSlv.solve(A, B)
+assert rc == 0, "bad solve"
+rc = arpackSlv.checkEigVec(A, B, 1.e-2)
+assert rc == 0, "bad checkEigVec"
+
+# Print out results (mode selected, eigen vectors, eigen values, ...).
+
+assert arpackSlv.nbEV == len(arpackSlv.val), "bad result"
+print("\nresults:\n")
+print("mode selected:", arpackSlv.mode)
+print("nb iterations:", arpackSlv.nbIt)
+print("Reverse Communication Interface time:", arpackSlv.rciTime, "s")
+for val, vec in zip(arpackSlv.val, arpackSlv.vec):
+    print("eigen value:", val)
+    print("eigen vector:")
+    for v in range(n):
+        print(vec[v])

EXAMPLES/PYARPACK/pyarpackDenseQRRR.py.in

@@ -0,0 +1,116 @@
+#!/usr/bin/env python
+
+import numpy as np
+from pyarpack import denseQRRR as pyarpackSlv
+
+# Build laplacian.
+
+n = 4
+Aij = np.array([], dtype='complex128')
+for k in range(n):
+    for l in range(n):
+        if l == k:
+            Aij = np.append(Aij, np.complex128(complex( 200.,  200.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k-1:
+            Aij = np.append(Aij, np.complex128(complex(-101., -101.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k+1:
+            Aij = np.append(Aij, np.complex128(complex( -99.,  -99.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        else:
+            Aij = np.append(Aij, np.complex128(complex(   0.,    0.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+for idx, val in enumerate(Aij):
+    print("A[", idx, "] =", val)
+A = (Aij, False) # raw format: Aij values, row ordered (or not).
+
+# Get and tune arpack solver.
+
+arpackSlv = pyarpackSlv.complexDouble() # Caution: complexDouble <=> np.array(..., dtype='complex128')
+arpackSlv.verbose = 3 # Set to 0 to get a quiet solve.
+arpackSlv.debug = 1 # Set to 0 to get a quiet solve.
+arpackSlv.nbEV = 1
+arpackSlv.nbCV = 2*arpackSlv.nbEV + 1
+arpackSlv.mag = 'LM'
+arpackSlv.maxIt = 200
+arpackSlv.slvPvtThd = 1.e-6
+arpackSlv.symPb = False
+
+# Solve eigen problem.
+
+rc = arpackSlv.solve(A)
+assert rc == 0, "bad solve"
+rc = arpackSlv.checkEigVec(A)
+assert rc == 0, "bad checkEigVec"
+
+# Print out results (mode selected, eigen vectors, eigen values, ...).
+
+assert arpackSlv.nbEV == len(arpackSlv.val), "bad result"
+print("\nresults:\n")
+print("mode selected:", arpackSlv.mode)
+print("nb iterations:", arpackSlv.nbIt)
+print("Reverse Communication Interface time:", arpackSlv.rciTime, "s")
+for val, vec in zip(arpackSlv.val, arpackSlv.vec):
+    print("eigen value:", val)
+    print("eigen vector:")
+    print(vec)
+
+#######################################################################################
+print("\n##########################################################################\n")
+#######################################################################################
+
+# Build laplacian.
+
+n = 8
+Aij = np.array([], dtype='complex64')
+Bij = np.array([], dtype='complex64')
+for k in range(n):
+    for l in range(n):
+        if l == k:
+            Aij = np.append(Aij, np.complex64(complex( 200.,  200.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.complex64(complex( 33.3,  33.3))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k-1:
+            Aij = np.append(Aij, np.complex64(complex(-101., -101.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.complex64(complex( 16.6,  16.6))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        elif l == k+1:
+            Aij = np.append(Aij, np.complex64(complex( -99.,  -99.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.complex64(complex( 16.6,  16.6))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        else:
+            Aij = np.append(Aij, np.complex64(complex(   0.,    0.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+            Bij = np.append(Bij, np.complex64(complex(   0.,    0.))) # Casting value on append is MANDATORY or C++ won't get the expected type.
+for idx, val in enumerate(Aij):
+    print("A[", idx, "] =", val)
+for idx, val in enumerate(Bij):
+    print("B[", idx, "] =", val)
+A = (Aij, False) # raw format: Aij values, row ordered (or not).
+B = (Bij,  True) # raw format: Bij values, row ordered (or not).
+
+# Get and tune arpack solver.
+
+arpackSlv = pyarpackSlv.complexFloat() # Caution: complexFloat <=> np.array(..., dtype='complex64')
+arpackSlv.verbose = 3 # Set to 0 to get a quiet solve.
+arpackSlv.debug = 1 # Set to 0 to get a quiet solve.
+arpackSlv.nbEV = 2
+arpackSlv.nbCV = 2*arpackSlv.nbEV + 1
+arpackSlv.mag = 'LM'
+arpackSlv.maxIt = 200
+arpackSlv.slvPvtThd = 1.e-6
+arpackSlv.sigmaReal = 1
+arpackSlv.symPb = False
+
+# Solve eigen problem.
+
+rc = arpackSlv.solve(A, B)
+assert rc == 0, "bad solve"
+rc = arpackSlv.checkEigVec(A, B, 1.e-2)
+assert rc == 0, "bad checkEigVec"
+
+# Print out results (mode selected, eigen vectors, eigen values, ...).
+
+assert arpackSlv.nbEV == len(arpackSlv.val), "bad result"
+print("\nresults:\n")
+print("mode selected:", arpackSlv.mode)
+print("nb iterations:", arpackSlv.nbIt)
+print("Reverse Communication Interface time:", arpackSlv.rciTime, "s")
+for val, vec in zip(arpackSlv.val, arpackSlv.vec):
+    print("eigen value:", val)
+    print("eigen vector:")
+    for v in range(n):
+        print(vec[v])

EXAMPLES/PYARPACK/pyarpackDrtSolver.hpp

@@ -0,0 +1,138 @@
+#ifndef __PYARPACKDRTSOLVER_HPP__
+#define __PYARPACKDRTSOLVER_HPP__
+
+#include <string>
+
+#include <arpackSolver.hpp>
+#include <pyarpackServices.hpp>
+#include "debug_c.hpp"
+#include "stat_c.hpp"
+
+#include <boost/python.hpp>
+#include <boost/python/numpy.hpp>
+
+namespace bp = boost::python;
+namespace bn = boost::python::numpy;
+
+template<typename RC, typename FD, typename EM, typename SLV>
+class pyarpackSparseDrtSolver: public arpackDrtSolver<RC, FD, EM, SLV> {
+  // Public methods.
+
+  public:
+
+    pyarpackSparseDrtSolver(): arpackDrtSolver<RC, FD, EM, SLV>() {
+      debug  = 0;
+
+      nopx = 0, nbx = 0, nrorth = 0, nitref = 0, nrstrt = 0;
+      tsaupd = 0., tsaup2 = 0., tsaitr = 0., tseigt = 0., tsgets = 0., tsapps = 0., tsconv = 0.;
+      tnaupd = 0., tnaup2 = 0., tnaitr = 0., tneigt = 0., tngets = 0., tnapps = 0., tnconv = 0.;
+      tcaupd = 0., tcaup2 = 0., tcaitr = 0., tceigt = 0., tcgets = 0., tcapps = 0., tcconv = 0.;
+      tmvopx = 0., tmvbx = 0., tgetv0 = 0., titref = 0., trvec = 0.;
+    };
+
+    int solve(bp::tuple & A, bp::tuple B = bp::tuple()) {
+      ARPACKSOLVERDEBUGSTAT();
+      EM M;
+      int rc = pyarpackServices<RC, EM>::buildSparseMatrice(A, M, debug, "A");
+      if (rc != 0) {pyarpackThrowError("build matrice from A KO"); return rc;}
+      bool stdPb = (bp::len(B) > 0) ? false : true;
+      EM N;
+      if (!stdPb) {
+        rc = pyarpackServices<RC, EM>::buildSparseMatrice(B, N, debug, "B");
+        if (rc != 0) {pyarpackThrowError("build matrice from B KO"); return rc;}
+      }
+      return arpackDrtSolver<RC, FD, EM, SLV>::solve(M, (stdPb ? NULL : &N));
+    };
+
+    int checkEigVec(bp::tuple const & A, bp::tuple const B = bp::tuple(), double const maxResNorm = 1.e-3) {
+      ARPACKSOLVERDEBUGSTAT();
+      EM M;
+      int rc = pyarpackServices<RC, EM>::buildSparseMatrice(A, M, debug, "A");
+      if (rc != 0) {pyarpackThrowError("build matrice from A KO"); return rc;}
+      bool stdPb = (bp::len(B) > 0) ? false : true;
+      EM N;
+      if (!stdPb) {
+        rc = pyarpackServices<RC, EM>::buildSparseMatrice(B, N, debug, "B");
+        if (rc != 0) {pyarpackThrowError("build matrice from B KO"); return rc;}
+      }
+      return arpackDrtSolver<RC, FD, EM, SLV>::checkEigVec(M, (stdPb ? NULL : &N), maxResNorm);
+    };
+
+  // Public members.
+
+  public:
+
+    a_int debug;
+
+    a_int nopx, nbx, nrorth, nitref, nrstrt;
+    float tsaupd, tsaup2, tsaitr, tseigt, tsgets, tsapps, tsconv;
+    float tnaupd, tnaup2, tnaitr, tneigt, tngets, tnapps, tnconv;
+    float tcaupd, tcaup2, tcaitr, tceigt, tcgets, tcapps, tcconv;
+    float tmvopx, tmvbx, tgetv0, titref, trvec;
+};
+
+template<typename RC, typename FD, typename EM, typename SLV>
+class pyarpackDenseDrtSolver: public arpackDrtSolver<RC, FD, EM, SLV> {
+  // Public methods.
+
+  public:
+
+    pyarpackDenseDrtSolver(): arpackDrtSolver<RC, FD, EM, SLV>() {
+      debug  = 0;
+
+      nopx = 0, nbx = 0, nrorth = 0, nitref = 0, nrstrt = 0;
+      tsaupd = 0., tsaup2 = 0., tsaitr = 0., tseigt = 0., tsgets = 0., tsapps = 0., tsconv = 0.;
+      tnaupd = 0., tnaup2 = 0., tnaitr = 0., tneigt = 0., tngets = 0., tnapps = 0., tnconv = 0.;
+      tcaupd = 0., tcaup2 = 0., tcaitr = 0., tceigt = 0., tcgets = 0., tcapps = 0., tcconv = 0.;
+      tmvopx = 0., tmvbx = 0., tgetv0 = 0., titref = 0., trvec = 0.;
+    };
+
+    int solve(bp::tuple & A, bp::tuple B = bp::tuple()) {
+      ARPACKSOLVERDEBUGSTAT();
+      EM M;
+      int rc = pyarpackServices<RC, EM>::buildDenseMatrice(A, M, debug, "A");
+      if (rc != 0) {pyarpackThrowError("build matrice from A KO"); return rc;}
+      bool stdPb = (bp::len(B) > 0) ? false : true;
+      EM N;
+      if (!stdPb) {
+        rc = pyarpackServices<RC, EM>::buildDenseMatrice(B, N, debug, "B");
+        if (rc != 0) {pyarpackThrowError("build matrice from B KO"); return rc;}
+      }
+      return arpackDrtSolver<RC, FD, EM, SLV>::solve(M, (stdPb ? NULL : &N));
+    };
+
+    int checkEigVec(bp::tuple const & A, bp::tuple const B = bp::tuple(), double const maxResNorm = 1.e-3) {
+      ARPACKSOLVERDEBUGSTAT();
+      EM M;
+      int rc = pyarpackServices<RC, EM>::buildDenseMatrice(A, M, debug, "A");
+      if (rc != 0) {pyarpackThrowError("build matrice from A KO"); return rc;}
+      bool stdPb = (bp::len(B) > 0) ? false : true;
+      EM N;
+      if (!stdPb) {
+        rc = pyarpackServices<RC, EM>::buildDenseMatrice(B, N, debug, "B");
+        if (rc != 0) {pyarpackThrowError("build matrice from B KO"); return rc;}
+      }
+      return arpackDrtSolver<RC, FD, EM, SLV>::checkEigVec(M, (stdPb ? NULL : &N), maxResNorm);
+    };
+
+  // Public members.
+
+  public:
+
+    a_int debug;
+
+    a_int nopx, nbx, nrorth, nitref, nrstrt;
+    float tsaupd, tsaup2, tsaitr, tseigt, tsgets, tsapps, tsconv;
+    float tnaupd, tnaup2, tnaitr, tneigt, tngets, tnapps, tnconv;
+    float tcaupd, tcaup2, tcaitr, tceigt, tcgets, tcapps, tcconv;
+    float tmvopx, tmvbx, tgetv0, titref, trvec;
+};
+
+#endif
+
+// Local Variables:
+// mode: c++
+// c-file-style:"stroustrup"
+// show-trailing-whitespace: t
+// End:
+/* vim: set sw=2 ts=2 et smartindent :*/

EXAMPLES/PYARPACK/pyarpackItrSolver.hpp

@@ -0,0 +1,80 @@
+#ifndef __PYARPACKITRSOLVER_HPP__
+#define __PYARPACKITRSOLVER_HPP__
+
+#include <string>
+
+#include <arpackSolver.hpp>
+#include <pyarpackServices.hpp>
+#include "debug_c.hpp"
+#include "stat_c.hpp"
+
+#include <boost/python.hpp>
+#include <boost/python/numpy.hpp>
+
+namespace bp = boost::python;
+
+template<typename RC, typename FD, typename EM, typename SLV>
+class pyarpackSparseItrSolver: public arpackItrSolver<RC, FD, EM, SLV> {
+  // Public methods.
+
+  public:
+
+    pyarpackSparseItrSolver(): arpackItrSolver<RC, FD, EM, SLV>() {
+      debug  = 0;
+
+      nopx = 0, nbx = 0, nrorth = 0, nitref = 0, nrstrt = 0;
+      tsaupd = 0., tsaup2 = 0., tsaitr = 0., tseigt = 0., tsgets = 0., tsapps = 0., tsconv = 0.;
+      tnaupd = 0., tnaup2 = 0., tnaitr = 0., tneigt = 0., tngets = 0., tnapps = 0., tnconv = 0.;
+      tcaupd = 0., tcaup2 = 0., tcaitr = 0., tceigt = 0., tcgets = 0., tcapps = 0., tcconv = 0.;
+      tmvopx = 0., tmvbx = 0., tgetv0 = 0., titref = 0., trvec = 0.;
+    };
+
+    int solve(bp::tuple & A, bp::tuple B = bp::tuple()) {
+      ARPACKSOLVERDEBUGSTAT();
+      EM M;
+      int rc = pyarpackServices<RC, EM>::buildSparseMatrice(A, M, debug, "A");
+      if (rc != 0) {pyarpackThrowError("build matrice from A KO"); return rc;}
+      bool stdPb = (bp::len(B) > 0) ? false : true;
+      EM N;
+      if (!stdPb) {
+        rc = pyarpackServices<RC, EM>::buildSparseMatrice(B, N, debug, "B");
+        if (rc != 0) {pyarpackThrowError("build matrice from B KO"); return rc;}
+      }
+      return arpackItrSolver<RC, FD, EM, SLV>::solve(M, (stdPb ? NULL : &N));
+    };
+
+    int checkEigVec(bp::tuple const & A, bp::tuple const B = bp::tuple(), double const maxResNorm = 1.e-3) {
+      ARPACKSOLVERDEBUGSTAT();
+      EM M;
+      int rc = pyarpackServices<RC, EM>::buildSparseMatrice(A, M, debug, "A");
+      if (rc != 0) {pyarpackThrowError("build matrice from A KO"); return rc;}
+      bool stdPb = (bp::len(B) > 0) ? false : true;
+      EM N;
+      if (!stdPb) {
+        rc = pyarpackServices<RC, EM>::buildSparseMatrice(B, N, debug, "B");
+        if (rc != 0) {pyarpackThrowError("build matrice from B KO"); return rc;}
+      }
+      return arpackItrSolver<RC, FD, EM, SLV>::checkEigVec(M, (stdPb ? NULL : &N), maxResNorm);
+    };
+
+  // Public members.
+
+  public:
+
+    a_int debug;
+
+    a_int nopx, nbx, nrorth, nitref, nrstrt;
+    float tsaupd, tsaup2, tsaitr, tseigt, tsgets, tsapps, tsconv;
+    float tnaupd, tnaup2, tnaitr, tneigt, tngets, tnapps, tnconv;
+    float tcaupd, tcaup2, tcaitr, tceigt, tcgets, tcapps, tcconv;
+    float tmvopx, tmvbx, tgetv0, titref, trvec;
+};
+
+#endif
+
+// Local Variables:
+// mode: c++
+// c-file-style:"stroustrup"
+// show-trailing-whitespace: t
+// End:
+/* vim: set sw=2 ts=2 et smartindent :*/

EXAMPLES/PYARPACK/pyarpackRestart.py.in

@@ -0,0 +1,119 @@
+#!/usr/bin/env python
+
+import numpy as np
+from pyarpack import sparseBiCGDiag as pyarpackSlv
+
+# Build laplacian.
+
+n = 8
+i = np.array([], dtype='@PYINT@')
+j = np.array([], dtype='@PYINT@')
+Aij = np.array([], dtype='float64')
+for k in range(n):
+    for l in [k-1, k, k+1]:
+        if l < 0 or l > n-1:
+            continue
+        i = np.append(i, np.@PYINT@(k)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        j = np.append(j, np.@PYINT@(l)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        if l == k:
+            Aij = np.append(Aij, np.float64( 200.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        if l == k-1 or l == k+1:
+            Aij = np.append(Aij, np.float64(-100.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+for k, l, Akl in zip(i, j, Aij):
+    print("A[", k, ",", l, "] =", Akl)
+A = (n, i, j, Aij) # coo format: dimension, i 0-based indices, j 0-based indices, Aij values.
+
+# Get and tune arpack solver.
+
+arpackSlv = pyarpackSlv.double() # Caution: double <=> np.array(..., dtype='float64')
+arpackSlv.verbose = 3 # Set to 0 to get a quiet solve.
+arpackSlv.debug = 1 # Set to 0 to get a quiet solve.
+arpackSlv.nbEV = 1
+arpackSlv.nbCV = 2*arpackSlv.nbEV + 1
+arpackSlv.mag = 'LM'
+arpackSlv.maxIt = 200
+arpackSlv.slvTol = 1.e-6
+arpackSlv.slvMaxIt = 100
+arpackSlv.dumpToFile = True # Dump eigen vectors to arpackSolver.*.out files.
+arpackSlv.schur = True # Schur vectors and eigenvectors of A are the same if A is a normal matrix.
+
+# Solve eigen problem.
+
+rc = arpackSlv.solve(A)
+assert rc == 0, "bad solve"
+rc = arpackSlv.checkEigVec(A)
+assert rc == 0, "bad checkEigVec"
+
+nbIt1 = arpackSlv.nbIt
+
+# Print out results (mode selected, eigen vectors, eigen values, ...).
+
+assert arpackSlv.nbEV == len(arpackSlv.val), "bad result"
+print("\nresults:\n")
+print("mode selected:", arpackSlv.mode)
+print("nb iterations:", arpackSlv.nbIt)
+print("Reverse Communication Interface time:", arpackSlv.rciTime, "s")
+for val, vec in zip(arpackSlv.val, arpackSlv.vec):
+    print("eigen value:", val)
+    print("eigen vector:")
+    print(vec)
+
+#######################################################################################
+print("\n##########################################################################\n")
+#######################################################################################
+
+# Build laplacian (similar-but-different from the previous one).
+
+n = 8
+i = np.array([], dtype='@PYINT@')
+j = np.array([], dtype='@PYINT@')
+Aij = np.array([], dtype='float64')
+for k in range(n):
+    for l in [k-1, k, k+1]:
+        if l < 0 or l > n-1:
+            continue
+        i = np.append(i, np.@PYINT@(k)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        j = np.append(j, np.@PYINT@(l)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        if l == k:
+            Aij = np.append(Aij, np.float64( 210.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+        if l == k-1 or l == k+1:
+            Aij = np.append(Aij, np.float64( -90.)) # Casting value on append is MANDATORY or C++ won't get the expected type.
+for k, l, Akl in zip(i, j, Aij):
+    print("A[", k, ",", l, "] =", Akl)
+A = (n, i, j, Aij) # coo format: dimension, i 0-based indices, j 0-based indices, Aij values.
+
+# Get and tune arpack solver.
+
+arpackSlv = pyarpackSlv.double() # Caution: double <=> np.array(..., dtype='float64')
+arpackSlv.verbose = 3 # Set to 0 to get a quiet solve.
+arpackSlv.debug = 1 # Set to 0 to get a quiet solve.
+arpackSlv.nbEV = 1
+arpackSlv.nbCV = 2*arpackSlv.nbEV + 1
+arpackSlv.mag = 'LM'
+arpackSlv.maxIt = 200
+arpackSlv.slvTol = 1.e-6
+arpackSlv.slvMaxIt = 100
+arpackSlv.restartFromFile = True # Restart from eigen vectors found in arpackSolver.*.out files.
+arpackSlv.schur = True # Schur vectors and eigenvectors of A are the same if A is a normal matrix.
+
+# Solve eigen problem.
+
+rc = arpackSlv.solve(A)
+assert rc == 0, "bad solve"
+rc = arpackSlv.checkEigVec(A)
+assert rc == 0, "bad checkEigVec"
+
+nbIt2 = arpackSlv.nbIt
+assert nbIt2 < nbIt1, "bad restart" # Restart from the first solve to run the second solve for a similar-but-different A.
+
+# Print out results (mode selected, eigen vectors, eigen values, ...).
+
+assert arpackSlv.nbEV == len(arpackSlv.val), "bad result"
+print("\nresults:\n")
+print("mode selected:", arpackSlv.mode)
+print("nb iterations:", arpackSlv.nbIt)
+print("Reverse Communication Interface time:", arpackSlv.rciTime, "s")
+for val, vec in zip(arpackSlv.val, arpackSlv.vec):
+    print("eigen value:", val)
+    print("eigen vector:")
+    print(vec)

EXAMPLES/PYARPACK/pyarpackServices.hpp

@@ -0,0 +1,194 @@
+#ifndef __PYARPACKSERVICES_HPP__
+#define __PYARPACKSERVICES_HPP__
+
+#include <vector>
+#include <string>
+#include <complex>
+#include <iostream>
+#include <cmath> // sqrt.
+
+#include <Eigen/Sparse>
+
+#include <boost/python.hpp>
+#include <boost/python/numpy.hpp>
+
+namespace bp = boost::python;
+namespace bn = boost::python::numpy;
+
+#define ARPACKSOLVERMEMBER(pyarpackSolver)                                                          \
+    .def_readwrite("symPb",           &pyarpackSolver<RC, FD, EM, SLV>::symPb,                      \
+                   "symmetric problem - default: true")                                             \
+    .def_readwrite("nbEV",            &pyarpackSolver<RC, FD, EM, SLV>::nbEV,                       \
+                   "number of eigen vectors to find - default: 1")                                  \
+    .def_readwrite("nbCV",            &pyarpackSolver<RC, FD, EM, SLV>::nbCV,                       \
+                   "number of dimensions of the workspace - default: 3")                            \
+    .def_readwrite("tol",             &pyarpackSolver<RC, FD, EM, SLV>::tol,                        \
+                   "tolerance - default: 1.e-6")                                                    \
+    .def_readwrite("sigmaReal",       &pyarpackSolver<RC, FD, EM, SLV>::sigmaReal,                  \
+                   "shift over real axis - default: 0.")                                            \
+    .def_readwrite("sigmaImag",       &pyarpackSolver<RC, FD, EM, SLV>::sigmaImag,                  \
+                   "shift over imaginary axis - default: 0.")                                       \
+    .def_readwrite("dumpToFile",      &pyarpackSolver<RC, FD, EM, SLV>::dumpToFile,                 \
+                   "dump eigen vectors to arpackSolver.*.out files - default: false")               \
+    .def_readwrite("restartFromFile", &pyarpackSolver<RC, FD, EM, SLV>::restartFromFile,            \
+                   "restart from eigen vectors found in arpackSolver.*.out files - default: false") \
+    .def_readwrite("mag",             &pyarpackSolver<RC, FD, EM, SLV>::mag,                        \
+                   "magnitude - default: LM")                                                       \
+    .def_readwrite("maxIt",           &pyarpackSolver<RC, FD, EM, SLV>::maxIt,                      \
+                   "maximum number of arpack iterations - default: 100")                            \
+    .def_readwrite("schur",           &pyarpackSolver<RC, FD, EM, SLV>::schur,                      \
+                   "compute schur vectors - default: false")                                        \
+    .def_readwrite("verbose",         &pyarpackSolver<RC, FD, EM, SLV>::verbose,                    \
+                   "verbosity level - default: 0")                                                  \
+    .def_readonly ("stdPb",           &pyarpackSolver<RC, FD, EM, SLV>::stdPb,                      \
+                   "standard or generalised problem - default: true")                               \
+    .def_readonly ("val",             &pyarpackSolver<RC, FD, EM, SLV>::val,                        \
+                   "eigen values found")                                                            \
+    .def_readonly ("vec",             &pyarpackSolver<RC, FD, EM, SLV>::vec,                        \
+                   "eigen vectors found")                                                           \
+    .def_readonly ("mode",            &pyarpackSolver<RC, FD, EM, SLV>::mode,                       \
+                   "selected arpack mode (according to input options: std/gen, shift, ...)")        \
+    .def_readonly ("nbIt",            &pyarpackSolver<RC, FD, EM, SLV>::nbIt,                       \
+                   "number of arpack iterations")                                                   \
+    .def_readonly ("imsTime",         &pyarpackSolver<RC, FD, EM, SLV>::imsTime,                    \
+                   "time spent to initialize the mode solver if needed")                            \
+    .def_readonly ("rciTime",         &pyarpackSolver<RC, FD, EM, SLV>::rciTime,                    \
+                   "time spent in Reverse Communication Interface")                                 \
+    .def_readwrite("debug",           &pyarpackSolver<RC, FD, EM, SLV>::debug,                      \
+                   "debug traces (up to 3) - default: 0")                                           \
+
+#define ARPACKSOLVERDEBUGSTAT()                                                             \
+if (debug > 3) debug = 3;                                                                   \
+debug_c(6, -6, debug, debug, debug, debug, debug, debug, debug, debug, debug, debug, debug, \
+        debug, debug, debug, debug, debug, debug, debug, debug, debug, debug, debug);       \
+stat_c(nopx, nbx, nrorth, nitref, nrstrt, tsaupd, tsaup2,                                   \
+       tsaitr, tseigt, tsgets, tsapps, tsconv, tnaupd, tnaup2,                              \
+       tnaitr, tneigt, tngets, tnapps, tnconv, tcaupd, tcaup2,                              \
+       tcaitr, tceigt, tcgets, tcapps, tcconv, tmvopx, tmvbx,                               \
+       tgetv0, titref, trvec);                                                              \
+
+void pyarpackThrowError(std::string const & msg) {
+  std::string const info = "Error: " + msg;
+  std::cerr << info << std::endl;
+  PyErr_SetString(PyExc_IndexError, info.c_str());
+  bp::throw_error_already_set();
+};
+
+template<typename RC, typename EM>
+class pyarpackServices {
+  // Public methods.
+
+  public:
+
+    static int buildSparseMatrice(bp::tuple const & T, Eigen::SparseMatrix<RC> & M,
+                                  a_int const & debug, std::string const & msg) {
+      // Get boost data as C++ data.
+
+      if (bp::len(T) != 4) {pyarpackThrowError(msg + " must be a 3-tuple"); return 1;}
+      bp::extract<int>           nExt(T[0]);
+      bp::extract<bn::ndarray>   iExt(T[1]);
+      bp::extract<bn::ndarray>   jExt(T[2]);
+      bp::extract<bn::ndarray> mijExt(T[3]);
+      if (!  nExt.check()) {pyarpackThrowError(msg + "[0] must be an integer" ); return 1;}
+      if (!  iExt.check()) {pyarpackThrowError(msg + "[1] must be numpy.array"); return 1;}
+      if (!  jExt.check()) {pyarpackThrowError(msg + "[2] must be numpy.array"); return 1;}
+      if (!mijExt.check()) {pyarpackThrowError(msg + "[3] must be numpy.array"); return 1;}
+      bn::ndarray   iArray =   iExt();
+      bn::ndarray   jArray =   jExt();
+      bn::ndarray mijArray = mijExt();
+      if (iArray.get_dtype()   != bn::dtype::get_builtin<a_int>()) {pyarpackThrowError(msg + "[1] type is not consistent"); return 1;}
+      if (jArray.get_dtype()   != bn::dtype::get_builtin<a_int>()) {pyarpackThrowError(msg + "[2] type is not consistent"); return 1;}
+      if (mijArray.get_dtype() != bn::dtype::get_builtin<RC>()   ) {pyarpackThrowError(msg + "[3] type is not consistent with arpack type"); return 1;}
+
+      a_int iSz = iArray.shape(0);
+      a_int * iPtr = reinterpret_cast<a_int*>(iArray.get_data());
+      a_int jSz = jArray.shape(0);
+      a_int * jPtr = reinterpret_cast<a_int*>(jArray.get_data());
+      a_int mSz = mijArray.shape(0);
+      RC * mPtr = reinterpret_cast<RC*>(mijArray.get_data());
+
+      if (iSz != jSz) {pyarpackThrowError(msg + "[1] and " + msg + "[2] must have same lenght"); return 1;}
+      if (iSz != mSz) {pyarpackThrowError(msg + "[1] and " + msg + "[3] must have same lenght"); return 1;}
+
+      // Debug on demand: casting value on numpy.append is MANDATORY or C++ won't get the expected type..
+
+      for (auto k = 0; debug && k < mSz; k++) {
+        std::cout << "pyarpackServices::buildSparseMatrice - " << msg << "[" << iPtr[k] << ", " << jPtr[k] << "] = " << mPtr[k] << std::endl;
+      };
+
+      // Build sparse matrice.
+
+      a_uint n = nExt();
+      a_uint iMin = n+1, jMin = n+1;
+      for (auto k = 0; k < mSz; k++) {
+        if (iPtr[k] < iMin) iMin = iPtr[k];
+        if (jPtr[k] < jMin) jMin = jPtr[k];
+      };
+      if (iMin != 0 && iMin != 1) {pyarpackThrowError(msg + ": smallest row indice must be 0 or 1"); return 1;}
+      if (jMin != 0 && jMin != 1) {pyarpackThrowError(msg + ": smallest column indice must be 0 or 1"); return 1;}
+      a_int iBased = 0, jBased = 0;
+      if (iMin == 1) iBased = 1;
+      if (jMin == 1) jBased = 1;
+
+      M = Eigen::SparseMatrix<RC>(n, n); // Set matrice dimensions.
+      std::vector<Eigen::Triplet<RC>> triplets;
+      a_uint nnz = mSz;
+      triplets.reserve(nnz);
+      for (auto k = 0; k < nnz; k++) triplets.emplace_back(iPtr[k] - iBased, jPtr[k] - jBased, mPtr[k]);
+      M.setFromTriplets(triplets.begin(), triplets.end()); // Set all (i, j, Mij).
+
+      return 0;
+    };
+
+    static int buildDenseMatrice(bp::tuple const & T, Eigen::Matrix<RC, Eigen::Dynamic, Eigen::Dynamic> & M,
+                                 a_int const & debug, std::string const & msg) {
+      // Get boost data as C++ data.
+
+      if (bp::len(T) != 2) {pyarpackThrowError(msg + " must be a 2-tuple"); return 1;}
+      bp::extract<bn::ndarray> mijExt(T[0]);
+      bp::extract<bool>          oExt(T[1]);
+      if (!mijExt.check()) {pyarpackThrowError(msg + " must be numpy.array"); return 1;}
+      if (  !oExt.check()) {pyarpackThrowError(msg + " must be a boolean"); return 1;}
+      bn::ndarray   mijArray = mijExt();
+      bool        rowOrdered = oExt();
+      if (mijArray.get_dtype() != bn::dtype::get_builtin<RC>()) {pyarpackThrowError(msg + " type is not consistent with arpack type"); return 1;}
+
+      a_int mSz = mijArray.shape(0);
+      RC * mPtr = reinterpret_cast<RC*>(mijArray.get_data());
+
+      a_uint n = std::sqrt(mSz);
+      if (n*n != mSz) {pyarpackThrowError(msg + " must be a squared matrice"); return 1;}
+
+      // Debug on demand: casting value on numpy.append is MANDATORY or C++ won't get the expected type..
+
+      for (auto k = 0; debug && k < mSz; k++) {
+        std::cout << "pyarpackServices::buildDenseMatrice - " << msg << "[" << k << "] = " << mPtr[k] << std::endl;
+      };
+
+      // Build dense matrice.
+
+      M = Eigen::Matrix<RC, Eigen::Dynamic, Eigen::Dynamic>(n, n); // Set matrice dimensions.
+      M.setZero(n, n); // Avoid spurious/random values which may break solves (LU, QR, ...).
+      if (rowOrdered) {
+        for (size_t k = 0; k < n; k++) {
+          for (size_t l = 0; l < n; l++) M(k, l) = mPtr[l+k*n];
+        }
+      }
+      else {
+        for (size_t l = 0; l < n; l++) {
+          for (size_t k = 0; k < n; k++) M(k, l) = mPtr[k+l*n];
+        }
+      }
+
+      return 0;
+    };
+};
+
+#endif
+
+// Local Variables:
+// mode: c++
+// c-file-style:"stroustrup"
+// show-trailing-whitespace: t
+// End:
+/* vim: set sw=2 ts=2 et smartindent :*/