Date: 2026-03-09T09:12:03+00:00

Actual source code: ex23f.F90

      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> ./ex23f [-help] [-t <t>] [-m <m>] [SLEPc opts]
     11: !
     12: !  Description: Computes exp(t*A)*v for a matrix from a Markov model.
     13: !  This is the Fortran90 equivalent to ex23.c
     14: !
     15: !  The command line options are:
     16: !    -t <t>, where <t> = time parameter (multiplies the matrix)
     17: !    -m <m>, where <m> = number of grid subdivisions in each dimension
     18: !
     19: ! ----------------------------------------------------------------------
     20: !
     21:       program main
     22: #include <slepc/finclude/slepcmfn.h>
     23:       use slepcmfn
     24:       implicit none

     26: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     27: !     Declarations
     28: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     29: !
     30: !  Variables:
     31: !     A      problem matrix
     32: !     mfn    matrix function solver context

     34:       Mat            A
     35:       MFN            mfn
     36:       FN             f
     37:       PetscReal      tol, norm, cst, pd, pu
     38:       PetscScalar    t, z
     39:       Vec            v, y
     40:       PetscInt       N, m, ncv, maxit, its, ii, jj
     41:       PetscInt       i, j, jmax, ix, Istart, Iend
     42:       PetscMPIInt    rank
     43:       PetscErrorCode ierr
     44:       PetscBool      flg
     45:       MFNConvergedReason reason

     47: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     48: !     Beginning of program
     49: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

     51:       PetscCallA(SlepcInitialize(PETSC_NULL_CHARACTER,ierr))
     52:       PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr))
     53:       m = 15
     54:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-m',m,flg,ierr))
     55:       t = 2.0
     56:       PetscCallA(PetscOptionsGetScalar(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-t',t,flg,ierr))
     57:       N = m*(m+1)/2
     58:       if (rank .eq. 0) then
     59:         write(*,100) N, m
     60:       endif
     61:  100  format (/'Markov y=exp(t*A)*e_1, N=',I6,' (m=',I4,')')

     63: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     64: !     Compute the transition probability matrix, A
     65: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

     67:       PetscCallA(MatCreate(PETSC_COMM_WORLD,A,ierr))
     68:       PetscCallA(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N,ierr))
     69:       PetscCallA(MatSetFromOptions(A,ierr))
     70:       PetscCallA(MatGetOwnershipRange(A,Istart,Iend,ierr))
     71:       ix = 0
     72:       cst = 0.5/real(m-1)
     73:       do i=1,m
     74:         jmax = m-i+1
     75:         do j=1,jmax
     76:           ix = ix + 1
     77:           ii = ix - 1
     78:           if (ix-1.ge.Istart .and. ix.le.Iend) then
     79:             if (j.ne.jmax) then
     80:               pd = cst*(i+j-1)
     81:               !** north
     82:               if (i.eq.1) then
     83:                 z = 2.0*pd
     84:               else
     85:                 z = pd
     86:               end if
     87:               PetscCallA(MatSetValue(A,ii,ix,z,INSERT_VALUES,ierr))
     88:               !** east
     89:               if (j.eq.1) then
     90:                 z = 2.0*pd
     91:               else
     92:                 z = pd
     93:               end if
     94:               jj = ix+jmax-1
     95:               PetscCallA(MatSetValue(A,ii,jj,z,INSERT_VALUES,ierr))
     96:             end if

     98:             !** south
     99:             pu = 0.5 - cst*(i+j-3)
    100:             z = pu
    101:             if (j.gt.1) then
    102:               jj = ix-2
    103:               PetscCallA(MatSetValue(A,ii,jj,z,INSERT_VALUES,ierr))
    104:             end if
    105:             !** west
    106:             if (i.gt.1) then
    107:               jj = ix-jmax-2
    108:               PetscCallA(MatSetValue(A,ii,jj,z,INSERT_VALUES,ierr))
    109:             end if
    110:           end if
    111:         end do
    112:       end do
    113:       PetscCallA(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr))
    114:       PetscCallA(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr))

    116: !     ** Set v = e_1
    117:       PetscCallA(MatCreateVecs(A,y,v,ierr))
    118:       ii = 0
    119:       z = 1.0
    120:       PetscCallA(VecSetValue(v,ii,z,INSERT_VALUES,ierr))
    121:       PetscCallA(VecAssemblyBegin(v,ierr))
    122:       PetscCallA(VecAssemblyEnd(v,ierr))

    124: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    125: !     Create the solver and set various options
    126: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    128: !     ** Create matrix function solver context
    129:       PetscCallA(MFNCreate(PETSC_COMM_WORLD,mfn,ierr))

    131: !     ** Set operator matrix, the function to compute, and other options
    132:       PetscCallA(MFNSetOperator(mfn,A,ierr))
    133:       PetscCallA(MFNGetFN(mfn,f,ierr))
    134:       PetscCallA(FNSetType(f,FNEXP,ierr))
    135:       z = 1.0
    136:       PetscCallA(FNSetScale(f,t,z,ierr))
    137:       tol = 0.0000001
    138:       PetscCallA(MFNSetTolerances(mfn,tol,PETSC_CURRENT_INTEGER,ierr))

    140: !     ** Set solver parameters at runtime
    141:       PetscCallA(MFNSetFromOptions(mfn,ierr))

    143: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    144: !     Solve the problem, y=exp(t*A)*v
    145: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    147:       PetscCallA(MFNSolve(mfn,v,y,ierr))
    148:       PetscCallA(MFNGetConvergedReason(mfn,reason,ierr))
    149:       if (reason%v.lt.0) then; SETERRA(PETSC_COMM_WORLD,1,'Solver did not converge'); endif
    150:       PetscCallA(VecNorm(y,NORM_2,norm,ierr))

    152: !     ** Optional: Get some information from the solver and display it
    153:       PetscCallA(MFNGetIterationNumber(mfn,its,ierr))
    154:       if (rank .eq. 0) then
    155:         write(*,120) its
    156:       endif
    157:  120  format (' Number of iterations of the method: ',I4)
    158:       PetscCallA(MFNGetDimensions(mfn,ncv,ierr))
    159:       if (rank .eq. 0) then
    160:         write(*,130) ncv
    161:       endif
    162:  130  format (' Subspace dimension:',I4)
    163:       PetscCallA(MFNGetTolerances(mfn,tol,maxit,ierr))
    164:       if (rank .eq. 0) then
    165:         write(*,140) tol,maxit
    166:       endif
    167:  140  format (' Stopping condition: tol=',f10.7,' maxit=',I4)

    169: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    170: !     Display solution and clean up
    171: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    173:       if (rank .eq. 0) then
    174:         write(*,150) PetscRealPart(t),norm
    175:       endif
    176:  150  format (' Computed vector at time t=',f4.1,' has norm ',f8.5)

    178:       PetscCallA(MFNDestroy(mfn,ierr))
    179:       PetscCallA(MatDestroy(A,ierr))
    180:       PetscCallA(VecDestroy(v,ierr))
    181:       PetscCallA(VecDestroy(y,ierr))
    182:       PetscCallA(SlepcFinalize(ierr))
    183:       end

    185: !/*TEST
    186: !
    187: !   test:
    188: !      suffix: 1
    189: !      args: -mfn_ncv 6
    190: !
    191: !TEST*/