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

 31:   /* Create function object */
 32:   PetscCall(FNCreate(PETSC_COMM_WORLD,&fn));
 33:   PetscCall(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:   PetscCall(FNSetScale(fn,alpha,beta));
 42:   PetscCall(FNSetFromOptions(fn));

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

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

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

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

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

 93:   PetscCall(MatDestroy(&A));
 94:   PetscCall(MatDestroy(&F));
 95:   PetscCall(MatDestroy(&G));
 96:   PetscCall(FNDestroy(&fn));
 97:   PetscCall(SlepcFinalize());
 98:   return 0;
 99: }

101: /*TEST

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

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

115: TEST*/