Actual source code: test12.c

slepc-3.17.0 2022-03-31
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  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[] = "Test matrix function evaluation via diagonalization.\n\n";

 13: #include <slepcfn.h>

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

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

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

 43:   /* Set up viewer */
 44:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
 45:   if (verbose) PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);

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

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

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

 86:   /* compare the two results */
 87:   MatAXPY(F,-1.0,G,SAME_NONZERO_PATTERN);
 88:   MatNorm(F,NORM_FROBENIUS,&nrm);
 89:   if (nrm>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of F-G is %g\n",(double)nrm);
 90:   else PetscPrintf(PETSC_COMM_WORLD,"Computed results match.\n");

 92:   MatDestroy(&A);
 93:   MatDestroy(&F);
 94:   MatDestroy(&G);
 95:   FNDestroy(&fn);
 96:   SlepcFinalize();
 97:   return 0;
 98: }

100: /*TEST

102:    test:
103:       suffix: 1
104:       nsize: 1
105:       args: -fn_type {{exp sqrt}shared output}
106:       output_file: output/test12_1.out

108:    test:
109:       suffix: 1_rational
110:       nsize: 1
111:       args: -fn_type rational -fn_rational_numerator 2,-1.5 -fn_rational_denominator 1,0.8
112:       output_file: output/test12_1.out

114: TEST*/