Actual source code: ex15f.F90

slepc-main 2024-11-22
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  1: !
  2: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3: !  SLEPc - Scalable Library for Eigenvalue Problem Computations
  4: !  Copyright (c) 2002-, 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:       PetscCallA(SlepcInitialize(PETSC_NULL_CHARACTER,ierr))
 49:       PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr))
 50:       n = 100
 51:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-n',n,flg,ierr))
 52:       mu = PETSC_SQRT_MACHINE_EPSILON
 53:       PetscCallA(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-mu',mu,flg,ierr))

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

 60: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 61: !     Build the Lauchli matrix
 62: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 64:       PetscCallA(MatCreate(PETSC_COMM_WORLD,A,ierr))
 65:       PetscCallA(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n+1,n,ierr))
 66:       PetscCallA(MatSetFromOptions(A,ierr))

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

 81:       PetscCallA(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr))
 82:       PetscCallA(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr))

 84: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 85: !     Create the singular value solver and display info
 86: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 88: !     ** Create singular value solver context
 89:       PetscCallA(SVDCreate(PETSC_COMM_WORLD,svd,ierr))

 91: !     ** Set operators and problem type
 92:       PetscCallA(SVDSetOperators(svd,A,PETSC_NULL_MAT,ierr))
 93:       PetscCallA(SVDSetProblemType(svd,SVD_STANDARD,ierr))

 95: !     ** Use thick-restart Lanczos as default solver
 96:       PetscCallA(SVDSetType(svd,SVDTRLANCZOS,ierr))

 98: !     ** Set solver parameters at runtime
 99:       PetscCallA(SVDSetFromOptions(svd,ierr))

101: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102: !     Solve the singular value system
103: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

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

129: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130: !     Display solution and clean up
131: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

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

150: !         ** Compute the relative error for each singular triplet
151:           PetscCallA(SVDComputeError(svd,i,SVD_ERROR_RELATIVE,error,ierr))
152:           if (rank .eq. 0) then
153:             write(*,160) sigma, error
154:           endif
155:  160      format (1P,'   ',E12.4,'       ',E12.4)

157:         enddo
158:         if (rank .eq. 0) then
159:           write(*,*)
160:         endif
161:       endif

163: !     ** Free work space
164:       PetscCallA(SVDDestroy(svd,ierr))
165:       PetscCallA(MatDestroy(A,ierr))

167:       PetscCallA(SlepcFinalize(ierr))
168:       end

170: !/*TEST
171: !
172: !   test:
173: !      suffix: 1
174: !      filter: sed -e "s/[0-9]\.[0-9]*E[+-]\([0-9]*\)/removed/g"
175: !
176: !TEST*/