Date: 2021-02-01T14:42:09+00:00

Actual source code: ex15f.F
slepc-3.14.2 2021-02-01
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      1: !
      2: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3: !  SLEPc - Scalable Library for Eigenvalue Problem Computations
      4: !  Copyright (c) 2002-2020, Universitat Politecnica de Valencia, Spain
      5: !
      6: !  This file is part of SLEPc.
      7: !  SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: !
     10: !  Program usage: mpiexec -n <np> ./ex15f [-help] [-n <n>] [-mu <mu>] [all SLEPc options]
     11: !
     12: !  Description: Singular value decomposition of the Lauchli matrix.
     13: !
     14: !  The command line options are:
     15: !    -n <n>, where <n> = matrix dimension.
     16: !    -mu <mu>, where <mu> = subdiagonal value.
     17: !
     18: ! ----------------------------------------------------------------------
     19: !
     20:       program main
     21: #include <slepc/finclude/slepcsvd.h>
     22:       use slepcsvd
     23:       implicit none

     25: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     26: !     Declarations
     27: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     28: !
     29: !  Variables:
     30: !     A     operator matrix
     31: !     svd   singular value solver context

     33:       Mat            A
     34:       SVD            svd
     35:       SVDType        tname
     36:       PetscReal      tol, error, sigma, mu
     37:       PetscInt       n, i, j, Istart, Iend
     38:       PetscInt       nsv, maxit, its, nconv
     39:       PetscMPIInt    rank
     40:       PetscErrorCode ierr
     41:       PetscBool      flg
     42:       PetscScalar    one, alpha

     44: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     45: !     Beginning of program
     46: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

     48:       call SlepcInitialize(PETSC_NULL_CHARACTER,ierr)
     49:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
     50:       n = 100
     51:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,  &
     52:      &                        '-n',n,flg,ierr)
     53:       mu = PETSC_SQRT_MACHINE_EPSILON
     54:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER, &
     55:      &                        '-mu',mu,flg,ierr)

     57:       if (rank .eq. 0) then
     58:         write(*,100) n, mu
     59:       endif
     60:  100  format (/'Lauchli SVD, n =',I3,', mu=',E12.4,' (Fortran)')

     62: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     63: !     Build the Lauchli matrix
     64: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

     66:       call MatCreate(PETSC_COMM_WORLD,A,ierr)
     67:       call MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n+1,n,ierr)
     68:       call MatSetFromOptions(A,ierr)
     69:       call MatSetUp(A,ierr)

     71:       call MatGetOwnershipRange(A,Istart,Iend,ierr)
     72:       one = 1.0
     73:       do i=Istart,Iend-1
     74:         if (i .eq. 0) then
     75:           do j=0,n-1
     76:             call MatSetValue(A,i,j,one,INSERT_VALUES,ierr)
     77:           end do
     78:         else
     79:           alpha = mu
     80:           call MatSetValue(A,i,i-1,alpha,INSERT_VALUES,ierr)
     81:         end if
     82:       enddo

     84:       call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
     85:       call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)

     87: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     88: !     Create the singular value solver and display info
     89: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

     91: !     ** Create singular value solver context
     92:       call SVDCreate(PETSC_COMM_WORLD,svd,ierr)

     94: !     ** Set operator
     95:       call SVDSetOperator(svd,A,ierr)

     97: !     ** Use thick-restart Lanczos as default solver
     98:       call SVDSetType(svd,SVDTRLANCZOS,ierr)

    100: !     ** Set solver parameters at runtime
    101:       call SVDSetFromOptions(svd,ierr)

    103: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    104: !     Solve the singular value system
    105: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    107:       call SVDSolve(svd,ierr)
    108:       call SVDGetIterationNumber(svd,its,ierr)
    109:       if (rank .eq. 0) then
    110:         write(*,110) its
    111:       endif
    112:  110  format (/' Number of iterations of the method:',I4)

    114: !     ** Optional: Get some information from the solver and display it
    115:       call SVDGetType(svd,tname,ierr)
    116:       if (rank .eq. 0) then
    117:         write(*,120) tname
    118:       endif
    119:  120  format (' Solution method: ',A)
    120:       call SVDGetDimensions(svd,nsv,PETSC_NULL_INTEGER,                 &
    121:      &                      PETSC_NULL_INTEGER,ierr)
    122:       if (rank .eq. 0) then
    123:         write(*,130) nsv
    124:       endif
    125:  130  format (' Number of requested singular values:',I2)
    126:       call SVDGetTolerances(svd,tol,maxit,ierr)
    127:       if (rank .eq. 0) then
    128:         write(*,140) tol, maxit
    129:       endif
    130:  140  format (' Stopping condition: tol=',1P,E11.4,', maxit=',I4)

    132: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    133: !     Display solution and clean up
    134: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    136: !     ** Get number of converged singular triplets
    137:       call SVDGetConverged(svd,nconv,ierr)
    138:       if (rank .eq. 0) then
    139:         write(*,150) nconv
    140:       endif
    141:  150  format (' Number of converged approximate singular triplets:',I2/)

    143: !     ** Display singular values and relative errors
    144:       if (nconv.gt.0) then
    145:         if (rank .eq. 0) then
    146:           write(*,*) '       sigma          relative error'
    147:           write(*,*) ' ----------------- ------------------'
    148:         endif
    149:         do i=0,nconv-1
    150: !         ** Get i-th singular value
    151:           call SVDGetSingularTriplet(svd,i,sigma,PETSC_NULL_VEC,        &
    152:      &         PETSC_NULL_VEC,ierr)

    154: !         ** Compute the relative error for each singular triplet
    155:           call SVDComputeError(svd,i,SVD_ERROR_RELATIVE,error,ierr)
    156:           if (rank .eq. 0) then
    157:             write(*,160) sigma, error
    158:           endif
    159:  160      format (1P,'   ',E12.4,'       ',E12.4)

    161:         enddo
    162:         if (rank .eq. 0) then
    163:           write(*,*)
    164:         endif
    165:       endif

    167: !     ** Free work space
    168:       call SVDDestroy(svd,ierr)
    169:       call MatDestroy(A,ierr)

    171:       call SlepcFinalize(ierr)
    172:       end

    174: !/*TEST
    175: !
    176: !   test:
    177: !      suffix: 1
    178: !      filter: sed -e "s/[0-9]\.[0-9]*E[+-]\([0-9]*\)/removed/g"
    179: !
    180: !TEST*/