Date: 2022-03-31T15:28:48+00:00

Actual source code: test5.c
slepc-3.17.0 2022-03-31
Report Typos and Errors

      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 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: {
     20:   PetscBool      set,flg;
     21:   PetscInt       n;
     22:   Mat            F;
     23:   Vec            v,f0;
     24:   PetscReal      nrm;

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

     59: int main(int argc,char **argv)
     60: {
     61:   FN             fn;
     62:   Mat            A;
     63:   PetscInt       i,j,n=10,np,nq;
     64:   PetscScalar    *As,p[10],q[10];
     65:   PetscViewer    viewer;
     66:   PetscBool      verbose,inplace;

     68:   SlepcInitialize(&argc,&argv,(char*)0,help);
     69:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     70:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
     71:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
     72:   PetscPrintf(PETSC_COMM_WORLD,"Matrix rational function, n=%" PetscInt_FMT ".\n",n);

     74:   /* Create rational function r(x)=p(x)/q(x) */
     75:   FNCreate(PETSC_COMM_WORLD,&fn);
     76:   FNSetType(fn,FNRATIONAL);
     77:   np = 2; nq = 3;
     78:   p[0] = -3.1; p[1] = 1.1;
     79:   q[0] = 1.0; q[1] = -2.0; q[2] = 3.5;
     80:   FNRationalSetNumerator(fn,np,p);
     81:   FNRationalSetDenominator(fn,nq,q);
     82:   FNSetFromOptions(fn);

     84:   /* Set up viewer */
     85:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
     86:   FNView(fn,viewer);
     87:   if (verbose) PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);

     89:   /* Create matrices */
     90:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
     91:   PetscObjectSetName((PetscObject)A,"A");

     93:   /* Fill A with a symmetric Toeplitz matrix */
     94:   MatDenseGetArray(A,&As);
     95:   for (i=0;i<n;i++) As[i+i*n]=2.0;
     96:   for (j=1;j<3;j++) {
     97:     for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
     98:   }
     99:   MatDenseRestoreArray(A,&As);
    100:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
    101:   TestMatRational(fn,A,viewer,verbose,inplace);

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

    107:   MatDestroy(&A);
    108:   FNDestroy(&fn);
    109:   SlepcFinalize();
    110:   return 0;
    111: }

    113: /*TEST

    115:    testset:
    116:       output_file: output/test5_1.out
    117:       requires: !single
    118:       test:
    119:          suffix: 1
    120:       test:
    121:          suffix: 2
    122:          args: -inplace

    124: TEST*/