Actual source code: test12.c

slepc-3.11.2 2019-07-30
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2019, 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 = 0.3+0.8*PETSC_i;
 36:   beta  = 1.1-0.1*PETSC_i;
 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]=1.0+0.1*PETSC_i; As[(i+j)+i*n]=1.0-0.1*PETSC_i;
 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*/