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

Actual source code: test5.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 rational function.\n\n";

     13: #include <slepcfn.h>

     15: /*
     16:    Compute matrix rational function B = q(A)\p(A)
     17:  */
     18: PetscErrorCode TestMatRational(FN fn,Mat A,PetscViewer viewer,PetscBool verbose,PetscBool inplace)
     19: {
     21:   PetscBool      set,flg;
     22:   PetscInt       n;
     23:   Mat            F;
     24:   Vec            v,f0;
     25:   PetscReal      nrm;

     28:   MatGetSize(A,&n,NULL);
     29:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&F);
     30:   PetscObjectSetName((PetscObject)F,"F");
     31:   /* compute matrix function */
     32:   if (inplace) {
     33:     MatCopy(A,F,SAME_NONZERO_PATTERN);
     34:     MatIsHermitianKnown(A,&set,&flg);
     35:     if (set && flg) { MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE); }
     36:     FNEvaluateFunctionMat(fn,F,NULL);
     37:   } else {
     38:     FNEvaluateFunctionMat(fn,A,F);
     39:   }
     40:   if (verbose) {
     41:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
     42:     MatView(A,viewer);
     43:     PetscPrintf(PETSC_COMM_WORLD,"Computed f(A) - - - - - - -\n");
     44:     MatView(F,viewer);
     45:   }
     46:   /* print matrix norm for checking */
     47:   MatNorm(F,NORM_1,&nrm);
     48:   PetscPrintf(PETSC_COMM_WORLD,"The 1-norm of f(A) is %g\n",(double)nrm);
     49:   /* check FNEvaluateFunctionMatVec() */
     50:   MatCreateVecs(A,&v,&f0);
     51:   MatGetColumnVector(F,f0,0);
     52:   FNEvaluateFunctionMatVec(fn,A,v);
     53:   VecAXPY(v,-1.0,f0);
     54:   VecNorm(v,NORM_2,&nrm);
     55:   if (nrm>100*PETSC_MACHINE_EPSILON) {
     56:     PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
     57:   }
     58:   MatDestroy(&F);
     59:   VecDestroy(&v);
     60:   VecDestroy(&f0);
     61:   return(0);
     62: }

     64: int main(int argc,char **argv)
     65: {
     67:   FN             fn;
     68:   Mat            A;
     69:   PetscInt       i,j,n=10,np,nq;
     70:   PetscScalar    *As,p[10],q[10];
     71:   PetscViewer    viewer;
     72:   PetscBool      verbose,inplace;

     74:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     75:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     76:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
     77:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
     78:   PetscPrintf(PETSC_COMM_WORLD,"Matrix rational function, n=%D.\n",n);

     80:   /* Create rational function r(x)=p(x)/q(x) */
     81:   FNCreate(PETSC_COMM_WORLD,&fn);
     82:   FNSetType(fn,FNRATIONAL);
     83:   np = 2; nq = 3;
     84:   p[0] = -3.1; p[1] = 1.1;
     85:   q[0] = 1.0; q[1] = -2.0; q[2] = 3.5;
     86:   FNRationalSetNumerator(fn,np,p);
     87:   FNRationalSetDenominator(fn,nq,q);
     88:   FNSetFromOptions(fn);

     90:   /* Set up viewer */
     91:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
     92:   FNView(fn,viewer);
     93:   if (verbose) {
     94:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
     95:   }

     97:   /* Create matrices */
     98:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
     99:   PetscObjectSetName((PetscObject)A,"A");

    101:   /* Fill A with a symmetric Toeplitz matrix */
    102:   MatDenseGetArray(A,&As);
    103:   for (i=0;i<n;i++) As[i+i*n]=2.0;
    104:   for (j=1;j<3;j++) {
    105:     for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
    106:   }
    107:   MatDenseRestoreArray(A,&As);
    108:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
    109:   TestMatRational(fn,A,viewer,verbose,inplace);

    111:   /* Repeat with same matrix as non-symmetric */
    112:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
    113:   TestMatRational(fn,A,viewer,verbose,inplace);

    115:   MatDestroy(&A);
    116:   FNDestroy(&fn);
    117:   SlepcFinalize();
    118:   return ierr;
    119: }

    121: /*TEST

    123:    testset:
    124:       output_file: output/test5_1.out
    125:       requires: !single
    126:       test:
    127:          suffix: 1
    128:       test:
    129:          suffix: 2
    130:          args: -inplace

    132: TEST*/