Actual source code: test2.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[] = "Tests the case when both arguments of MFNSolve() are the same Vec.\n\n"
     12:   "The command line options are:\n"
     13:   "  -t <sval>, where <sval> = scalar value that multiplies the argument.\n"
     14:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
     15:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

     17: #include <slepcmfn.h>

     19: int main(int argc,char **argv)
     20: {
     21:   Mat            A;           /* problem matrix */
     22:   MFN            mfn;
     23:   FN             f;
     24:   PetscReal      norm;
     25:   PetscScalar    t=0.3;
     26:   PetscInt       N,n=25,m,Istart,Iend,II,i,j;
     27:   PetscBool      flag;
     28:   Vec            v,y;

     30:   PetscFunctionBeginUser;
     31:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     33:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     34:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag));
     35:   if (!flag) m=n;
     36:   N = n*m;
     37:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-t",&t,NULL));
     38:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMatrix exponential y=exp(t*A)*e, of the 2-D Laplacian, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m));

     40:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     41:                          Build the 2-D Laplacian
     42:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     44:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
     45:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
     46:   PetscCall(MatSetFromOptions(A));

     48:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
     49:   for (II=Istart;II<Iend;II++) {
     50:     i = II/n; j = II-i*n;
     51:     if (i>0) PetscCall(MatSetValue(A,II,II-n,-1.0,INSERT_VALUES));
     52:     if (i<m-1) PetscCall(MatSetValue(A,II,II+n,-1.0,INSERT_VALUES));
     53:     if (j>0) PetscCall(MatSetValue(A,II,II-1,-1.0,INSERT_VALUES));
     54:     if (j<n-1) PetscCall(MatSetValue(A,II,II+1,-1.0,INSERT_VALUES));
     55:     PetscCall(MatSetValue(A,II,II,4.0,INSERT_VALUES));
     56:   }

     58:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
     59:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));

     61:   /* set v = ones(n,1) */
     62:   PetscCall(MatCreateVecs(A,&v,&y));
     63:   PetscCall(VecSet(v,1.0));

     65:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     66:                 Create the solver and set various options
     67:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     69:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f));
     70:   PetscCall(FNSetType(f,FNEXP));

     72:   PetscCall(MFNCreate(PETSC_COMM_WORLD,&mfn));
     73:   PetscCall(MFNSetOperator(mfn,A));
     74:   PetscCall(MFNSetFN(mfn,f));
     75:   PetscCall(MFNSetErrorIfNotConverged(mfn,PETSC_TRUE));
     76:   PetscCall(MFNSetFromOptions(mfn));

     78:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     79:                       Solve the problem, y=exp(t*A)*v
     80:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     82:   PetscCall(FNSetScale(f,t,1.0));
     83:   PetscCall(MFNSolve(mfn,v,y));
     84:   PetscCall(VecNorm(y,NORM_2,&norm));
     85:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computed vector at time t=%.4g has norm %g\n\n",(double)PetscRealPart(t),(double)norm));

     87:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     88:            Repeat the computation in two steps, overwriting v:
     89:               v=exp(0.5*t*A)*v,  v=exp(0.5*t*A)*v
     90:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     92:   PetscCall(FNSetScale(f,0.5*t,1.0));
     93:   PetscCall(MFNSolve(mfn,v,v));
     94:   PetscCall(MFNSolve(mfn,v,v));
     95:   /* compute norm of difference */
     96:   PetscCall(VecAXPY(y,-1.0,v));
     97:   PetscCall(VecNorm(y,NORM_2,&norm));
     98:   if (norm<100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD," The norm of the difference is <100*eps\n\n"));
     99:   else PetscCall(PetscPrintf(PETSC_COMM_WORLD," The norm of the difference is %g\n\n",(double)norm));

    101:   /*
    102:      Free work space
    103:   */
    104:   PetscCall(MFNDestroy(&mfn));
    105:   PetscCall(FNDestroy(&f));
    106:   PetscCall(MatDestroy(&A));
    107:   PetscCall(VecDestroy(&v));
    108:   PetscCall(VecDestroy(&y));
    109:   PetscCall(SlepcFinalize());
    110:   return 0;
    111: }

    113: /*TEST

    115:    testset:
    116:       args: -mfn_type {{krylov expokit}}
    117:       output_file: output/test2_1.out
    118:       test:
    119:          suffix: 1
    120:       test:
    121:          suffix: 1_cuda
    122:          args: -mat_type aijcusparse
    123:          requires: cuda
    124:       test:
    125:          suffix: 1_hip
    126:          args: -mat_type aijhipsparse
    127:          requires: hip

    129:    test:
    130:       suffix: 3
    131:       args: -mfn_type expokit -t 0.6 -mfn_ncv 24
    132:       requires: !__float128

    134: TEST*/