Date: 2021-02-01T14:41:41+00:00

Actual source code: test12.c
slepc-3.14.2 2021-02-01
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      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[] = "Test matrix function evaluation via diagonalization.\n\n";

     13: #include <slepcfn.h>

     15: int main(int argc,char **argv)
     16: {
     18:   FN             fn;
     19:   Mat            A,F,G;
     20:   PetscInt       i,j,n=10;
     21:   PetscReal      nrm;
     22:   PetscScalar    *As,alpha,beta;
     23:   PetscViewer    viewer;
     24:   PetscBool      verbose;

     26:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     27:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     28:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
     29:   PetscPrintf(PETSC_COMM_WORLD,"Matrix function of symmetric/Hermitian matrix, n=%D.\n",n);

     31:   /* Create function object */
     32:   FNCreate(PETSC_COMM_WORLD,&fn);
     33:   FNSetType(fn,FNEXP);   /* default to exponential */
     34: #if defined(PETSC_USE_COMPLEX)
     35:   alpha = PetscCMPLX(0.3,0.8);
     36:   beta  = PetscCMPLX(1.1,-0.1);
     37: #else
     38:   alpha = 0.3;
     39:   beta  = 1.1;
     40: #endif
     41:   FNSetScale(fn,alpha,beta);
     42:   FNSetFromOptions(fn);

     44:   /* Set up viewer */
     45:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
     46:   if (verbose) {
     47:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
     48:   }

     50:   /* Create a symmetric/Hermitian Toeplitz matrix */
     51:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
     52:   PetscObjectSetName((PetscObject)A,"A");
     53:   MatDenseGetArray(A,&As);
     54:   for (i=0;i<n;i++) As[i+i*n]=2.0;
     55:   for (j=1;j<3;j++) {
     56:     for (i=0;i<n-j;i++) {
     57: #if defined(PETSC_USE_COMPLEX)
     58:       As[i+(i+j)*n]=PetscCMPLX(1.0,0.1); As[(i+j)+i*n]=PetscCMPLX(1.0,-0.1);
     59: #else
     60:       As[i+(i+j)*n]=0.5; As[(i+j)+i*n]=0.5;
     61: #endif
     62:     }
     63:   }
     64:   MatDenseRestoreArray(A,&As);
     65:   if (verbose) {
     66:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
     67:     MatView(A,viewer);
     68:   }

     70:   /* compute matrix function */
     71:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&F);
     72:   PetscObjectSetName((PetscObject)F,"F");
     73:   FNEvaluateFunctionMat(fn,A,F);
     74:   if (verbose) {
     75:     PetscPrintf(PETSC_COMM_WORLD,"Computed f(A) - - - - - - -\n");
     76:     MatView(F,viewer);
     77:   }

     79:   /* Repeat with MAT_HERMITIAN flag set */
     80:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
     81:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&G);
     82:   PetscObjectSetName((PetscObject)G,"G");
     83:   FNEvaluateFunctionMat(fn,A,G);
     84:   if (verbose) {
     85:     PetscPrintf(PETSC_COMM_WORLD,"Computed f(A) symm - - - - - - -\n");
     86:     MatView(G,viewer);
     87:   }

     89:   /* compare the two results */
     90:   MatAXPY(F,-1.0,G,SAME_NONZERO_PATTERN);
     91:   MatNorm(F,NORM_FROBENIUS,&nrm);
     92:   if (nrm>100*PETSC_MACHINE_EPSILON) {
     93:     PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of F-G is %g\n",(double)nrm);
     94:   } else {
     95:     PetscPrintf(PETSC_COMM_WORLD,"Computed results match.\n");
     96:   }

     98:   MatDestroy(&A);
     99:   MatDestroy(&F);
    100:   MatDestroy(&G);
    101:   FNDestroy(&fn);
    102:   SlepcFinalize();
    103:   return ierr;
    104: }

    106: /*TEST

    108:    test:
    109:       suffix: 1
    110:       nsize: 1
    111:       args: -fn_type {{exp sqrt}shared output}
    112:       output_file: output/test12_1.out

    114:    test:
    115:       suffix: 1_rational
    116:       nsize: 1
    117:       args: -fn_type rational -fn_rational_numerator 2,-1.5 -fn_rational_denominator 1,0.8
    118:       output_file: output/test12_1.out

    120: TEST*/