460 lines
15 KiB
FortranFixed
460 lines
15 KiB
FortranFixed
program psntest1
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c
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c Message Passing Layer: BLACS
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c
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c Example program to illustrate the idea of reverse communication
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c for a standard nonsymmetric eigenvalue problem.
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c
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c We implement example one of ex-nonsym.doc in DOCUMENTS directory
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c
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c\Test-1
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c ... Suppose we want to solve A*x = lambda*x in regular mode,
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c where A is random diagonal matrix with 4 separated eigenvalues.
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c ... OP = A and B = I.
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c ... Assume "call av ( nloc, diag, x, y)" computes y = A*x.
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c ... Use mode 1 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 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 Distributed matrix vector multiplication routine that computes A*x.
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c
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c\Author
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c Kristi Maschhoff
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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\SCCS Information:
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c FILE: %M% SID: %I% DATE OF SID: %G% RELEASE: %R%
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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 'debug.h'
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include 'stat.h'
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c %-----------------%
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c | BLACS INTERFACE |
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c %-----------------%
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c
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integer comm, iam, nprocs, nloc,
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& nprow, npcol, myprow, mypcol
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c
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external BLACS_PINFO, BLACS_SETUP, BLACS_GET,
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& BLACS_GRIDINIT, BLACS_GRIDINFO
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c
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c %-----------------------------%
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c | Define maximum dimensions |
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c | for all arrays. |
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c | MAXN: Maximum dimension |
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c | of the distributed |
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c | block of 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=12, maxncv=30, 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), iseed(4)
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logical select(maxncv)
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Real
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& ax(maxn), d(maxncv,3), resid(maxn), diag(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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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, nx, nev, ncv, lworkl, info, j,
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& ierr, nconv, maxitr, ishfts, mode, idist
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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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c
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Real
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& slapy2, psnorm2
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external slapy2, saxpy, psnorm2, slarnv
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c
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c %---------------------%
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c | Intrinsic Functions |
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c %---------------------%
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c
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intrinsic abs, sqrt
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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 BLACS_PINFO( iam, nprocs )
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c
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c If in PVM, create virtual machine if it doesn't exist
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c
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if (nprocs .lt. 1) then
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if (iam .eq. 0) then
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write(*,1000)
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read(*, 2000) nprocs
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endif
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call BLACS_SETUP( iam, nprocs )
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endif
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c
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1000 format('How many processes in machine?')
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2000 format(I3)
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c
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c Set up processors in 1D Grid
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c
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nprow = nprocs
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npcol = 1
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c
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c Get default system context, and define grid
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c
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call BLACS_GET( 0, 0, comm )
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call BLACS_GRIDINIT( comm, 'Row', nprow, npcol )
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call BLACS_GRIDINFO( comm, nprow, npcol, myprow, mypcol )
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c
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c If I'm not in grid, go to end of program
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c
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if ( (myprow .ge. nprow) .or. (mypcol .ge. npcol) ) goto 9000
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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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n = 10000*nprocs
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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 = 10000
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c
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if ( nloc .gt. maxn ) then
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print *, ' ERROR with _NDRV1: 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 _NDRV1: 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 _NDRV1: NCV is greater than MAXNCV '
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go to 9000
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end if
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bmat = 'I'
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which = 'SM'
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c
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c %-----------------------------------%
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c | Generate random diagonal matrix |
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c | Isolate 4 extreamal eigenvalues |
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c %-----------------------------------%
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c
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idist = 1
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iseed(1) = 15
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iseed(2) = 35
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iseed(3) = 52
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iseed(4) = 7
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call slarnv ( idist, iseed, nloc, diag )
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diag(1) = diag(1) + 1.01
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diag(2) = diag(2) + 1.01
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diag(3) = diag(3) + 1.01
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diag(4) = diag(4) + 1.01
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c
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c %-----------------------------------------------------%
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c | The work array WORKL is used in PSNAUPD 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 PSNAUPD 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 = zero
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ido = 0
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info = 1
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do 50 j=1,nloc
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resid(j) = one
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50 continue
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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 1 of PSNAUPD is used |
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c | (IPARAM(7) = 1). All these options can be changed |
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c | by the user. For details see the documentation in |
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c | PSNAUPD. |
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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 = 1
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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 PSNAUPD 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, 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 matrix vector multiplication |
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c | y <--- OP*x |
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c | The user should supply his/her own |
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c | matrix vector multiplication routine here |
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c | that takes workd(ipntr(1)) as the input |
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c | vector, and return the matrix vector |
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c | product to workd(ipntr(2)). |
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c %-------------------------------------------%
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c
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call av ( nloc, diag, 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 PSNAUPD 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 | 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 ( myprow .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 PSNEUPD. |
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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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c
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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, workl,
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& 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 PSNEUPD.|
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c %------------------------------------%
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c
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if ( myprow .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 20 j=1, nconv
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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*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( nloc, diag, v(1,j), ax)
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call saxpy(nloc, -d(j,1), v(1,j), 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( nloc, diag, v(1,j), ax)
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call saxpy(nloc, -d(j,1), v(1,j), 1, ax, 1)
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call saxpy(nloc, d(j,2), v(1,j+1), 1, ax, 1)
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d(j,3) = psnorm2( comm, nloc, ax, 1)
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call av( nloc, diag, v(1,j+1), ax)
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call saxpy(nloc, -d(j,2), v(1,j), 1, ax, 1)
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call saxpy(nloc, -d(j,1), v(1,j+1), 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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20 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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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 (myprow .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 *, '_NDRV1 '
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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 pdndrv1.|
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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 BLACS |
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c %-------------------------%
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c
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call BLACS_GRIDEXIT ( comm )
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call BLACS_EXIT(0)
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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 subroutine
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c
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subroutine av (n, diag, v, w)
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integer n, j
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Real
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& v(n), w(n), diag(n)
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c
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do 10 j = 1, n
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w(j) = diag(j)*v(j)
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10 continue
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c
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return
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end
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