612 lines
20 KiB
FortranFixed
612 lines
20 KiB
FortranFixed
program psndrv3
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c
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c Message Passing Layer: MPI
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c
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c Simple program to illustrate the idea of reverse communication
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c in inverse mode for a generalized nonsymmetric eigenvalue problem.
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c
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c We implement example three of ex-nonsym.doc in DOCUMENTS directory
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c
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c\Example-3
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c ... Suppose we want to solve A*x = lambda*B*x in inverse mode,
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c where A is derived from the 1-dimensional convection-diffusion
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c operator on the interval [0,1] with zero boundary condition,
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c and M is the tridiagonal matrix with 4 on the diagonal and 1
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c on the subdiagonals.
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c ... So OP = inv[M]*A and B = M.
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c ... Use mode 2 of PSNAUPD.
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c
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c\BeginLib
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c
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c\Routines called:
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c psnaupd Parallel ARPACK reverse communication interface routine.
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c psneupd Parallel ARPACK routine that returns Ritz values and (optionally)
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c Ritz vectors.
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c spttrf LAPACK symmetric positive definite tridiagonal factorization
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c routine.
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c spttrs LAPACK symmetric positive definite tridiagonal solve routine.
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c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully.
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c saxpy Level 1 BLAS that computes y <- alpha*x+y.
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c psnorm2 Parallel version of Level 1 BLAS that computes the norm of a vector.
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c av Parallel Matrix vector multiplication routine that computes A*x.
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c mv Matrix vector multiplication routine that computes M*x.
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c
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c\Author
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c Richard Lehoucq
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c Danny Sorensen
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c Chao Yang
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c Dept. of Computational &
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c Applied Mathematics
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c Rice University
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c Houston, Texas
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c
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c\Parallel Modifications
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c Kristi Maschhoff
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c
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c\Revision history:
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c Starting Point: Serial Code FILE: ndrv3.F SID: 2.2
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c
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c\SCCS Information:
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c FILE: ndrv3.F SID: 1.1 DATE OF SID: 8/13/96 RELEASE: 1
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c
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c\Remarks
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c 1. None
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c
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c\EndLib
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c--------------------------------------------------------------------------
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c
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include 'mpif.h'
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include 'debug.h'
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include 'stat.h'
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c %---------------%
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c | MPI INTERFACE |
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c %---------------%
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integer comm, myid, nprocs, rc, nloc
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c
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c %-----------------------------%
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c | Define leading dimensions |
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c | for all arrays. |
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c | MAXN: Maximum dimension |
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c | of the A allowed. |
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c | MAXNEV: Maximum NEV allowed |
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c | MAXNCV: Maximum NCV allowed |
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c %-----------------------------%
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c
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integer maxn, maxnev, maxncv, ldv
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parameter (maxn=256, maxnev=10, maxncv=25,
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& ldv=maxn )
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c
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c %--------------%
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c | Local Arrays |
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c %--------------%
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c
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integer iparam(11), ipntr(14)
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logical select(maxncv)
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Real
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& ax(maxn), mx(maxn), d(maxncv, 3), resid(maxn),
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& v(ldv,maxncv), workd(3*maxn),
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& workev(3*maxncv),
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& workl(3*maxncv*maxncv+6*maxncv),
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& md(maxn), me(maxn-1), temp(maxn), temp_buf(maxn)
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c
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c %---------------%
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c | Local Scalars |
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c %---------------%
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c
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character bmat*1, which*2
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integer ido, n, nev, ncv, lworkl, info, ierr, j,
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& nconv, maxitr, ishfts, mode, blk
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Real
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& tol, sigmar, sigmai
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logical first, rvec
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c
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c %------------%
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c | Parameters |
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c %------------%
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c
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Real
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& zero, one
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parameter (zero = 0.0, one = 1.0)
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c
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c %-----------------------------%
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c | BLAS & LAPACK routines used |
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c %-----------------------------%
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Real
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& psnorm2, slapy2
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external saxpy, psnorm2, spttrf, spttrs, slapy2
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c
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c %-----------------------%
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c | Executable Statements |
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c %-----------------------%
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c
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call MPI_INIT( ierr )
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comm = MPI_COMM_WORLD
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call MPI_COMM_RANK( comm, myid, ierr )
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call MPI_COMM_SIZE( comm, nprocs, ierr )
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c
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ndigit = -3
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logfil = 6
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mnaupd = 1
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c
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c %----------------------------------------------------%
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c | The number N is the dimension of the matrix. A |
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c | generalized eigenvalue problem is solved (BMAT = |
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c | 'G'). NEV is the number of eigenvalues to be |
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c | approximated. The user can modify NEV, NCV, WHICH |
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c | to solve problems of different sizes, and to get |
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c | different parts of the spectrum. However, The |
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c | following conditions must be satisfied: |
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c | N <= MAXN, |
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c | NEV <= MAXNEV, |
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c | NEV + 2 <= NCV <= MAXNCV |
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c %----------------------------------------------------%
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c
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n = 100
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nev = 4
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ncv = 20
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c
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c %--------------------------------------%
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c | Set up distribution of data to nodes |
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c %--------------------------------------%
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c
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nloc = (n / nprocs )
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blk = nloc
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if ( mod(n, nprocs) .gt. 0 ) then
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if ( myid .eq. nprocs-1 ) nloc = nloc + mod(n, nprocs)
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* if ( mod(n, nprocs) .gt. myid ) nloc = nloc + 1
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endif
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c
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if ( nloc .gt. maxn ) then
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print *, ' ERROR with _NDRV3: NLOC is greater than MAXN '
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go to 9000
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else if ( nev .gt. maxnev ) then
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print *, ' ERROR with _NDRV3: NEV is greater than MAXNEV '
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go to 9000
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else if ( ncv .gt. maxncv ) then
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print *, ' ERROR with _NDRV3: NCV is greater than MAXNCV '
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go to 9000
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end if
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bmat = 'G'
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which = 'LM'
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c
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c %-----------------------------------------------------%
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c | The matrix M is chosen to be the symmetric tri- |
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c | diagonal matrix with 4 on the diagonal and 1 on the |
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c | off diagonals. It is factored by LAPACK subroutine |
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c | spttrf. |
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c %-----------------------------------------------------%
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c
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do 20 j = 1, n-1
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md(j) = 4.0
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me(j) = one
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20 continue
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md(n) = 4.0*one
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c
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call spttrf(n, md, me, ierr)
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if ( ierr .ne. 0 ) then
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print*, ' '
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print*, ' ERROR with _pttrf. '
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print*, ' '
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go to 9000
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end if
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c
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c %-----------------------------------------------------%
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c | The work array WORKL is used in SNAUPD as |
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c | workspace. Its dimension LWORKL is set as |
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c | illustrated below. The parameter TOL determines |
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c | the stopping criterion. If TOL<=0, machine |
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c | precision is used. The variable IDO is used for |
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c | reverse communication, and is initially set to 0. |
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c | Setting INFO=0 indicates that a random vector is |
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c | generated in SNAUPD to start the Arnoldi iteration. |
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c %-----------------------------------------------------%
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c
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lworkl = 3*ncv**2+6*ncv
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tol = 0.0
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ido = 0
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info = 0
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c
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c %---------------------------------------------------%
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c | This program uses exact shifts with respect to |
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c | the current Hessenberg matrix (IPARAM(1) = 1). |
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c | IPARAM(3) specifies the maximum number of Arnoldi |
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c | iterations allowed. Mode 2 of SNAUPD is used |
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c | (IPARAM(7) = 2). All these options can be |
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c | changed by the user. For details, see the |
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c | documentation in SNAUPD. |
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c %---------------------------------------------------%
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c
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ishfts = 1
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maxitr = 300
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mode = 2
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c
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iparam(1) = ishfts
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iparam(3) = maxitr
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iparam(7) = mode
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c
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c %-------------------------------------------%
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c | M A I N L O O P (Reverse communication) |
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c %-------------------------------------------%
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c
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10 continue
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c
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c %---------------------------------------------%
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c | Repeatedly call the routine SNAUPD and take |
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c | actions indicated by parameter IDO until |
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c | either convergence is indicated or maxitr |
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c | has been exceeded. |
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c %---------------------------------------------%
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c
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call psnaupd( comm, ido, bmat, nloc, which, nev, tol, resid,
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& ncv, v, ldv, iparam, ipntr, workd,
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& workl, lworkl, info )
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c
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if (ido .eq. -1 .or. ido .eq. 1) then
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c
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c %----------------------------------------%
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c | Perform y <--- OP*x = inv[M]*A*x |
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c | The user should supply his/her own |
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c | matrix vector routine and a linear |
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c | system solver. The matrix-vector |
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c | subroutine should take workd(ipntr(1)) |
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c | as input, and the final result should |
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c | be returned to workd(ipntr(2)). |
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c %----------------------------------------%
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c
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call av (comm, nloc, n, workd(ipntr(1)), workd(ipntr(2)))
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c======== Hack for Linear system ======= ccc
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call sscal(n, zero, temp, 1)
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call sscal(n, zero, temp_buf, 1)
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do 15 j=1,nloc
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temp_buf(myid*blk + j) = workd(ipntr(2) + j - 1)
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15 continue
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call MPI_ALLREDUCE( temp_buf, temp, n,
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& MPI_REAL, MPI_SUM, comm, ierr )
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call spttrs(n, 1, md, me, temp, n,
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& ierr)
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if ( ierr .ne. 0 ) then
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print*, ' '
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print*, ' ERROR with _pttrs. '
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print*, ' '
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go to 9000
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end if
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do 16 j=1,nloc
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workd(ipntr(2) + j - 1 ) = temp(myid*blk + j)
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16 continue
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c
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c %-----------------------------------------%
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c | L O O P B A C K to call SNAUPD again. |
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c %-----------------------------------------%
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c
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go to 10
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c
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else if ( ido .eq. 2) then
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c
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c %-------------------------------------%
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c | Perform y <--- M*x |
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c | The matrix vector multiplication |
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c | routine should take workd(ipntr(1)) |
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c | as input and return the result to |
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c | workd(ipntr(2)). |
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c %-------------------------------------%
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c
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call mv (comm, nloc, workd(ipntr(1)), workd(ipntr(2)))
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c
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c %-----------------------------------------%
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c | L O O P B A C K to call SNAUPD again. |
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c %-----------------------------------------%
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c
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go to 10
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c
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end if
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c
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c
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c %-----------------------------------------%
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c | Either we have convergence, or there is |
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c | an error. |
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c %-----------------------------------------%
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c
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if ( info .lt. 0 ) then
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c
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c %---------------------------%
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c | Error message. Check the |
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c | documentation in PSNAUPD. |
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c %---------------------------%
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c
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if ( myid .eq. 0 ) then
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print *, ' '
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print *, ' Error with _naupd, info = ', info
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print *, ' Check the documentation of _naupd.'
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print *, ' '
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endif
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c
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else
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c
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c %-------------------------------------------%
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c | No fatal errors occurred. |
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c | Post-Process using SNEUPD. |
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c | |
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c | Computed eigenvalues may be extracted. |
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c | |
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c | Eigenvectors may also be computed now if |
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c | desired. (indicated by rvec = .true.) |
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c %-------------------------------------------%
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c
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rvec = .true.
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call psneupd ( comm, rvec, 'A', select, d, d(1,2), v, ldv,
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& sigmar, sigmai, workev, bmat, nloc, which, nev, tol,
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& resid, ncv, v, ldv, iparam, ipntr, workd,
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& workl, lworkl, ierr )
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c
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c %-----------------------------------------------%
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c | The real part of the eigenvalue is returned |
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c | in the first column of the two dimensional |
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c | array D, and the IMAGINARY part is returned |
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c | in the second column of D. The corresponding |
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c | eigenvectors are returned in the first NEV |
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c | columns of the two dimensional array V if |
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c | requested. Otherwise, an orthogonal basis |
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c | for the invariant subspace corresponding to |
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c | the eigenvalues in D is returned in V. |
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c %-----------------------------------------------%
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c
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if ( ierr .ne. 0 ) then
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c
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c %------------------------------------%
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c | Error condition: |
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c | Check the documentation of SNEUPD. |
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c %------------------------------------%
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c
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if ( myid .eq. 0 ) then
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print *, ' '
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print *, ' Error with _neupd, info = ', ierr
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print *, ' Check the documentation of _neupd'
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print *, ' '
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endif
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c
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else
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c
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first = .true.
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nconv = iparam(5)
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do 30 j=1, iparam(5)
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c
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c %---------------------------%
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c | Compute the residual norm |
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c | |
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c | || A*x - lambda*M*x || |
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c | |
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c | for the NCONV accurately |
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c | computed eigenvalues and |
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c | eigenvectors. (iparam(5) |
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c | indicates how many are |
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c | accurate to the requested |
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c | tolerance) |
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c %---------------------------%
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c
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if (d(j,2) .eq. zero) then
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c
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c %--------------------%
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c | Ritz value is real |
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c %--------------------%
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c
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call av(comm, nloc, n, v(1,j), ax)
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call mv(comm, nloc, v(1,j), mx)
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call saxpy(nloc, -d(j,1), mx, 1, ax, 1)
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d(j,3) = psnorm2(comm, nloc, ax, 1)
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c
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else if (first) then
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c
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c %------------------------%
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c | Ritz value is complex |
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c | Residual of one Ritz |
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c | value of the conjugate |
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c | pair is computed. |
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c %------------------------%
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c
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call av(comm, nloc, n, v(1,j), ax)
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call mv(comm, nloc, v(1,j), mx)
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call saxpy(nloc, -d(j,1), mx, 1, ax, 1)
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call mv(comm, nloc, v(1,j+1), mx)
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call saxpy(nloc, d(j,2), mx, 1, ax, 1)
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d(j,3) = psnorm2(comm, nloc, ax, 1)**2
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call av(comm, nloc, n, v(1,j+1), ax)
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call mv(comm, nloc, v(1,j+1), mx)
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call saxpy(nloc, -d(j,1), mx, 1, ax, 1)
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call mv(comm, nloc, v(1,j), mx)
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call saxpy(nloc, -d(j,2), mx, 1, ax, 1)
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d(j,3) = slapy2( d(j,3), psnorm2(comm,nloc,ax,1) )
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d(j+1,3) = d(j,3)
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first = .false.
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else
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first = .true.
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end if
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c
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30 continue
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c
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c %-----------------------------%
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c | Display computed residuals. |
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c %-----------------------------%
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c
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call psmout(comm, 6, nconv, 3, d, maxncv, -6,
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& 'Ritz values (Real,Imag) and direct residuals')
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c
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end if
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c
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c %------------------------------------------%
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c | Print additional convergence information |
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c %------------------------------------------%
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c
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if (myid .eq. 0)then
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if ( info .eq. 1) then
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print *, ' '
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print *, ' Maximum number of iterations reached.'
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print *, ' '
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else if ( info .eq. 3) then
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print *, ' '
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print *, ' No shifts could be applied during implicit
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& Arnoldi update, try increasing NCV.'
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print *, ' '
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end if
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c
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print *, ' '
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print *, '_NDRV3 '
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print *, '====== '
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print *, ' '
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print *, ' Size of the matrix is ', n
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print *, ' The number of processors is ', nprocs
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print *, ' The number of Ritz values requested is ', nev
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print *, ' The number of Arnoldi vectors generated',
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& ' (NCV) is ', ncv
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print *, ' What portion of the spectrum: ', which
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print *, ' The number of converged Ritz values is ',
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& nconv
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print *, ' The number of Implicit Arnoldi update',
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& ' iterations taken is ', iparam(3)
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print *, ' The number of OP*x is ', iparam(9)
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print *, ' The convergence criterion is ', tol
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print *, ' '
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c
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endif
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end if
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c
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c %----------------------------%
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c | Done with program psndrv3. |
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c %----------------------------%
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c
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9000 continue
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c
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c %-------------------------%
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c | Release resources MPI |
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c %-------------------------%
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c
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call MPI_FINALIZE(rc)
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c
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end
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c
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c==========================================================================
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c
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c parallel matrix vector multiplication subroutine
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c
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c Compute the matrix vector multiplication y<---A*x
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c where A is a n by n nonsymmetric tridiagonal matrix derived
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c from the central difference discretization of the 1-dimensional
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c convection diffusion operator on the interval [0,1] with
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c zero Dirichlet boundary condition.
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c
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subroutine av (comm, nloc, n, v, w)
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c
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c .. MPI Declarations ...
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include 'mpif.h'
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integer comm, nprocs, myid, ierr,
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& status(MPI_STATUS_SIZE)
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c
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integer nloc, n, j, next, prev
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Real
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& v(nloc), w(nloc), one, two, dd, dl, du,
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& s, h, rho, mv_buf
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parameter ( rho = 10.0, one = 1.0,
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& two = 2.0)
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c
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call MPI_COMM_RANK( comm, myid, ierr )
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call MPI_COMM_SIZE( comm, nprocs, ierr )
|
|
h = one / real(n+1)
|
|
s = rho*h / two
|
|
dd = two
|
|
dl = -one - s
|
|
du = -one + s
|
|
c
|
|
w(1) = dd*v(1) + du*v(2)
|
|
do 10 j = 2,nloc-1
|
|
w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1)
|
|
10 continue
|
|
w(nloc) = dl*v(nloc-1) + dd*v(nloc)
|
|
c
|
|
next = myid + 1
|
|
prev = myid - 1
|
|
if ( myid .lt. nprocs-1 ) then
|
|
call mpi_send( v(nloc), 1, MPI_REAL,
|
|
& next, myid+1, comm, ierr )
|
|
endif
|
|
if ( myid .gt. 0 ) then
|
|
call mpi_recv( mv_buf, 1, MPI_REAL, prev, myid,
|
|
& comm, status, ierr )
|
|
w(1) = w(1) + dl*mv_buf
|
|
endif
|
|
c
|
|
if ( myid .gt. 0 ) then
|
|
call mpi_send( v(1), 1, MPI_REAL,
|
|
& prev, myid-1, comm, ierr )
|
|
endif
|
|
if ( myid .lt. nprocs-1 ) then
|
|
call mpi_recv( mv_buf, 1, MPI_REAL, next, myid,
|
|
& comm, status, ierr )
|
|
w(nloc) = w(nloc) + du*mv_buf
|
|
endif
|
|
c
|
|
return
|
|
end
|
|
c------------------------------------------------------------------------
|
|
c
|
|
c Compute the matrix vector multiplication y<---M*x
|
|
c where M is a n by n tridiagonal matrix with 4 on the
|
|
c diagonal, 1 on the subdiagonal and the superdiagonal.
|
|
c
|
|
subroutine mv (comm, nloc, v, w)
|
|
c
|
|
c .. MPI Declarations ...
|
|
include 'mpif.h'
|
|
integer comm, nprocs, myid, ierr,
|
|
& status(MPI_STATUS_SIZE)
|
|
c
|
|
integer nloc, j, next, prev
|
|
Real
|
|
& v(nloc), w(nloc), one, four, mv_buf
|
|
parameter ( one = 1.0, four = 4.0)
|
|
c
|
|
call MPI_COMM_RANK( comm, myid, ierr )
|
|
call MPI_COMM_SIZE( comm, nprocs, ierr )
|
|
c
|
|
w(1) = four*v(1) + one*v(2)
|
|
do 10 j = 2,nloc-1
|
|
w(j) = one*v(j-1) + four*v(j) + one*v(j+1)
|
|
10 continue
|
|
w(nloc) = one*v(nloc-1) + four*v(nloc)
|
|
c
|
|
next = myid + 1
|
|
prev = myid - 1
|
|
if ( myid .lt. nprocs-1 ) then
|
|
call mpi_send( v(nloc), 1, MPI_REAL,
|
|
& next, myid+1, comm, ierr )
|
|
endif
|
|
if ( myid .gt. 0 ) then
|
|
call mpi_recv( mv_buf, 1, MPI_REAL, prev, myid,
|
|
& comm, status, ierr )
|
|
w(1) = w(1) + mv_buf
|
|
endif
|
|
c
|
|
if ( myid .gt. 0 ) then
|
|
call mpi_send( v(1), 1, MPI_REAL,
|
|
& prev, myid-1, comm, ierr )
|
|
endif
|
|
if ( myid .lt. nprocs-1 ) then
|
|
call mpi_recv( mv_buf, 1, MPI_REAL, next, myid,
|
|
& comm, status, ierr )
|
|
w(nloc) = w(nloc) + mv_buf
|
|
endif
|
|
c
|
|
return
|
|
end
|
|
c------------------------------------------------------------
|
|
subroutine mv2 (comm, n, v, w)
|
|
integer n, j, comm
|
|
Real
|
|
& v(n), w(n)
|
|
do 10 j=1,n
|
|
w(j) = v(j)
|
|
10 continue
|
|
c
|
|
return
|
|
end
|