Actual source code: test5.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 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*/