Actual source code: test5.c

      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,Acopy;
     23:   Vec            v,f0;
     24:   PetscReal      nrm;

     26:   PetscFunctionBeginUser;
     27:   PetscCall(MatGetSize(A,&n,NULL));
     28:   PetscCall(MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&F));
     29:   PetscCall(PetscObjectSetName((PetscObject)F,"F"));
     30:   /* compute matrix function */
     31:   if (inplace) {
     32:     PetscCall(MatCopy(A,F,SAME_NONZERO_PATTERN));
     33:     PetscCall(MatIsHermitianKnown(A,&set,&flg));
     34:     if (set && flg) PetscCall(MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE));
     35:     PetscCall(FNEvaluateFunctionMat(fn,F,NULL));
     36:   } else {
     37:     PetscCall(MatDuplicate(A,MAT_COPY_VALUES,&Acopy));
     38:     PetscCall(FNEvaluateFunctionMat(fn,A,F));
     39:     /* check that A has not been modified */
     40:     PetscCall(MatAXPY(Acopy,-1.0,A,SAME_NONZERO_PATTERN));
     41:     PetscCall(MatNorm(Acopy,NORM_1,&nrm));
     42:     if (nrm>100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: the input matrix has changed by %g\n",(double)nrm));
     43:     PetscCall(MatDestroy(&Acopy));
     44:   }
     45:   if (verbose) {
     46:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n"));
     47:     PetscCall(MatView(A,viewer));
     48:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Computed f(A) - - - - - - -\n"));
     49:     PetscCall(MatView(F,viewer));
     50:   }
     51:   /* print matrix norm for checking */
     52:   PetscCall(MatNorm(F,NORM_1,&nrm));
     53:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"The 1-norm of f(A) is %g\n",(double)nrm));
     54:   /* check FNEvaluateFunctionMatVec() */
     55:   PetscCall(MatCreateVecs(A,&v,&f0));
     56:   PetscCall(MatGetColumnVector(F,f0,0));
     57:   PetscCall(FNEvaluateFunctionMatVec(fn,A,v));
     58:   PetscCall(VecAXPY(v,-1.0,f0));
     59:   PetscCall(VecNorm(v,NORM_2,&nrm));
     60:   if (nrm>100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm));
     61:   PetscCall(MatDestroy(&F));
     62:   PetscCall(VecDestroy(&v));
     63:   PetscCall(VecDestroy(&f0));
     64:   PetscFunctionReturn(PETSC_SUCCESS);
     65: }

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

     76:   PetscFunctionBeginUser;
     77:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     78:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     79:   PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));
     80:   PetscCall(PetscOptionsHasName(NULL,NULL,"-inplace",&inplace));
     81:   PetscCall(PetscOptionsHasName(NULL,NULL,"-matcuda",&matcuda));
     82:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix rational function, n=%" PetscInt_FMT ".\n",n));

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

     94:   /* Set up viewer */
     95:   PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
     96:   PetscCall(FNView(fn,viewer));
     97:   if (verbose) PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB));

     99:   /* Create matrices */
    100:   if (matcuda) {
    101: #if defined(PETSC_HAVE_CUDA)
    102:     PetscCall(MatCreateSeqDenseCUDA(PETSC_COMM_SELF,n,n,NULL,&A));
    103: #endif
    104:   } else PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A));
    105:   PetscCall(PetscObjectSetName((PetscObject)A,"A"));

    107:   /* Fill A with a symmetric Toeplitz matrix */
    108:   PetscCall(MatDenseGetArray(A,&As));
    109:   for (i=0;i<n;i++) As[i+i*n]=2.0;
    110:   for (j=1;j<3;j++) {
    111:     for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
    112:   }
    113:   PetscCall(MatDenseRestoreArray(A,&As));
    114:   PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE));
    115:   PetscCall(TestMatRational(fn,A,viewer,verbose,inplace));

    117:   /* Repeat with same matrix as non-symmetric */
    118:   PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE));
    119:   PetscCall(TestMatRational(fn,A,viewer,verbose,inplace));

    121:   PetscCall(MatDestroy(&A));
    122:   PetscCall(FNDestroy(&fn));
    123:   PetscCall(SlepcFinalize());
    124:   return 0;
    125: }

    127: /*TEST

    129:    testset:
    130:       output_file: output/test5_1.out
    131:       requires: !single
    132:       test:
    133:          suffix: 1
    134:       test:
    135:          suffix: 1_cuda
    136:          args: -matcuda
    137:          requires: cuda
    138:       test:
    139:          suffix: 2
    140:          args: -inplace
    141:       test:
    142:          suffix: 2_cuda
    143:          args: -inplace -matcuda
    144:          requires: cuda

    146: TEST*/