Date: 2021-02-01T14:42:20+00:00

Actual source code: test2.c
slepc-3.14.2 2021-02-01
Report Typos and Errors

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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;

     31:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

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

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

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

     49:   MatGetOwnershipRange(A,&Istart,&Iend);
     50:   for (II=Istart;II<Iend;II++) {
     51:     i = II/n; j = II-i*n;
     52:     if (i>0) { MatSetValue(A,II,II-n,-1.0,INSERT_VALUES); }
     53:     if (i<m-1) { MatSetValue(A,II,II+n,-1.0,INSERT_VALUES); }
     54:     if (j>0) { MatSetValue(A,II,II-1,-1.0,INSERT_VALUES); }
     55:     if (j<n-1) { MatSetValue(A,II,II+1,-1.0,INSERT_VALUES); }
     56:     MatSetValue(A,II,II,4.0,INSERT_VALUES);
     57:   }

     59:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     60:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

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

     67:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     68:                 Create the solver and set various options
     69:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     71:   FNCreate(PETSC_COMM_WORLD,&f);
     72:   FNSetType(f,FNEXP);

     74:   MFNCreate(PETSC_COMM_WORLD,&mfn);
     75:   MFNSetOperator(mfn,A);
     76:   MFNSetFN(mfn,f);
     77:   MFNSetErrorIfNotConverged(mfn,PETSC_TRUE);
     78:   MFNSetFromOptions(mfn);

     80:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     81:                       Solve the problem, y=exp(t*A)*v
     82:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     89:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     90:            Repeat the computation in two steps, overwriting v:
     91:               v=exp(0.5*t*A)*v,  v=exp(0.5*t*A)*v
     92:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     94:   FNSetScale(f,0.5*t,1.0);
     95:   MFNSolve(mfn,v,v);
     96:   MFNSolve(mfn,v,v);
     97:   /* compute norm of difference */
     98:   VecAXPY(y,-1.0,v);
     99:   VecNorm(y,NORM_2,&norm);
    100:   if (norm<100*PETSC_MACHINE_EPSILON) {
    101:     PetscPrintf(PETSC_COMM_WORLD," The norm of the difference is <100*eps\n\n");
    102:   } else {
    103:     PetscPrintf(PETSC_COMM_WORLD," The norm of the difference is %g\n\n",(double)norm);
    104:   }

    106:   /*
    107:      Free work space
    108:   */
    109:   MFNDestroy(&mfn);
    110:   FNDestroy(&f);
    111:   MatDestroy(&A);
    112:   VecDestroy(&v);
    113:   VecDestroy(&y);
    114:   SlepcFinalize();
    115:   return ierr;
    116: }

    118: /*TEST

    120:    testset:
    121:       args: -mfn_type {{krylov expokit}}
    122:       output_file: output/test2_1.out
    123:       test:
    124:          suffix: 1
    125:       test:
    126:          suffix: 1_cuda
    127:          args: -mat_type aijcusparse
    128:          requires: cuda

    130:    test:
    131:       suffix: 3
    132:       args: -mfn_type expokit -t 0.6 -mfn_ncv 35
    133:       requires: !__float128

    135: TEST*/