Date: 2026-01-20T11:35:15+00:00

Actual source code: ex23.c

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */

     11: static char help[] = "Computes exp(t*A)*v for a matrix associated with a Markov model.\n\n"
     12:   "The command line options are:\n"
     13:   "  -t <t>, where <t> = time parameter (multiplies the matrix).\n"
     14:   "  -m <m>, where <m> = number of grid subdivisions in each dimension.\n\n"
     15:   "To draw the solution run with -mfn_view_solution draw -draw_pause -1\n\n";

     17: #include <slepcmfn.h>

     19: /*
     20:    User-defined routines
     21: */
     22: PetscErrorCode MatMarkovModel(PetscInt m,Mat A);

     24: int main(int argc,char **argv)
     25: {
     26:   Mat                A;           /* problem matrix */
     27:   MFN                mfn;
     28:   FN                 f;
     29:   PetscReal          tol,norm;
     30:   PetscScalar        t=2.0;
     31:   Vec                v,y;
     32:   PetscInt           N,m=15,ncv,maxit,its;
     33:   MFNConvergedReason reason;

     35:   PetscFunctionBeginUser;
     36:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     38:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL));
     39:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-t",&t,NULL));
     40:   N = m*(m+1)/2;
     41:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMarkov y=exp(t*A)*e_1, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n\n",N,m));

     43:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     44:             Compute the transition probability matrix, A
     45:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     47:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
     48:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
     49:   PetscCall(MatSetFromOptions(A));
     50:   PetscCall(MatMarkovModel(m,A));

     52:   /* set v = e_1 */
     53:   PetscCall(MatCreateVecs(A,NULL,&y));
     54:   PetscCall(MatCreateVecs(A,NULL,&v));
     55:   PetscCall(VecSetValue(v,0,1.0,INSERT_VALUES));
     56:   PetscCall(VecAssemblyBegin(v));
     57:   PetscCall(VecAssemblyEnd(v));

     59:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     60:                 Create the solver and set various options
     61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     62:   /*
     63:      Create matrix function solver context
     64:   */
     65:   PetscCall(MFNCreate(PETSC_COMM_WORLD,&mfn));

     67:   /*
     68:      Set operator matrix, the function to compute, and other options
     69:   */
     70:   PetscCall(MFNSetOperator(mfn,A));
     71:   PetscCall(MFNGetFN(mfn,&f));
     72:   PetscCall(FNSetType(f,FNEXP));
     73:   PetscCall(FNSetScale(f,t,1.0));
     74:   PetscCall(MFNSetTolerances(mfn,1e-07,PETSC_CURRENT));

     76:   /*
     77:      Set solver parameters at runtime
     78:   */
     79:   PetscCall(MFNSetFromOptions(mfn));

     81:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     82:                       Solve the problem, y=exp(t*A)*v
     83:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     85:   PetscCall(MFNSolve(mfn,v,y));
     86:   PetscCall(MFNGetConvergedReason(mfn,&reason));
     87:   PetscCheck(reason>=0,PETSC_COMM_WORLD,PETSC_ERR_CONV_FAILED,"Solver did not converge");
     88:   PetscCall(VecNorm(y,NORM_2,&norm));

     90:   /*
     91:      Optional: Get some information from the solver and display it
     92:   */
     93:   PetscCall(MFNGetIterationNumber(mfn,&its));
     94:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",its));
     95:   PetscCall(MFNGetDimensions(mfn,&ncv));
     96:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Subspace dimension: %" PetscInt_FMT "\n",ncv));
     97:   PetscCall(MFNGetTolerances(mfn,&tol,&maxit));
     98:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit));

    100:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    101:                     Display solution and clean up
    102:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    103:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computed vector at time t=%.4g has norm %g\n\n",(double)PetscRealPart(t),(double)norm));

    105:   /*
    106:      Free work space
    107:   */
    108:   PetscCall(MFNDestroy(&mfn));
    109:   PetscCall(MatDestroy(&A));
    110:   PetscCall(VecDestroy(&v));
    111:   PetscCall(VecDestroy(&y));
    112:   PetscCall(SlepcFinalize());
    113:   return 0;
    114: }

    116: /*
    117:     Matrix generator for a Markov model of a random walk on a triangular grid.
    118:     See ex5.c for additional details.
    119: */
    120: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
    121: {
    122:   const PetscReal cst = 0.5/(PetscReal)(m-1);
    123:   PetscReal       pd,pu;
    124:   PetscInt        Istart,Iend,i,j,jmax,ix=0;

    126:   PetscFunctionBeginUser;
    127:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
    128:   for (i=1;i<=m;i++) {
    129:     jmax = m-i+1;
    130:     for (j=1;j<=jmax;j++) {
    131:       ix = ix + 1;
    132:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
    133:       if (j!=jmax) {
    134:         pd = cst*(PetscReal)(i+j-1);
    135:         /* north */
    136:         if (i==1) PetscCall(MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES));
    137:         else PetscCall(MatSetValue(A,ix-1,ix,pd,INSERT_VALUES));
    138:         /* east */
    139:         if (j==1) PetscCall(MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES));
    140:         else PetscCall(MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES));
    141:       }
    142:       /* south */
    143:       pu = 0.5 - cst*(PetscReal)(i+j-3);
    144:       if (j>1) PetscCall(MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES));
    145:       /* west */
    146:       if (i>1) PetscCall(MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES));
    147:     }
    148:   }
    149:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
    150:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
    151:   PetscFunctionReturn(PETSC_SUCCESS);
    152: }

    154: /*TEST

    156:    test:
    157:       suffix: 1
    158:       args: -mfn_ncv 6

    160: TEST*/