Actual source code: ex23f.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> ./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.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*/