Actual source code: test13.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 logarithm.\n\n";

     13: #include <slepcfn.h>

     15: /*
     16:    Compute matrix logarithm B = logm(A)
     17:  */
     18: PetscErrorCode TestMatLog(FN fn,Mat A,PetscViewer viewer,PetscBool verbose,PetscBool inplace)
     19: {
     20:   PetscBool      set,flg;
     21:   PetscScalar    tau,eta;
     22:   PetscInt       n;
     23:   Mat            F,R;
     24:   Vec            v,f0;
     25:   FN             fnexp;
     26:   PetscReal      nrm;

     28:   PetscFunctionBeginUser;
     29:   PetscCall(MatGetSize(A,&n,NULL));
     30:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&F));
     31:   PetscCall(PetscObjectSetName((PetscObject)F,"F"));
     32:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&R));
     33:   PetscCall(PetscObjectSetName((PetscObject)R,"R"));
     34:   PetscCall(FNGetScale(fn,&tau,&eta));
     35:   /* compute matrix logarithm */
     36:   if (inplace) {
     37:     PetscCall(MatCopy(A,F,SAME_NONZERO_PATTERN));
     38:     PetscCall(MatIsHermitianKnown(A,&set,&flg));
     39:     if (set && flg) PetscCall(MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE));
     40:     PetscCall(FNEvaluateFunctionMat(fn,F,NULL));
     41:   } else PetscCall(FNEvaluateFunctionMat(fn,A,F));
     42:   if (verbose) {
     43:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n"));
     44:     PetscCall(MatView(A,viewer));
     45:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Computed logm(A) - - - - - - -\n"));
     46:     PetscCall(MatView(F,viewer));
     47:   }
     48:   /* check error ||expm(F)-A||_F */
     49:   PetscCall(FNCreate(PETSC_COMM_WORLD,&fnexp));
     50:   PetscCall(FNSetType(fnexp,FNEXP));
     51:   PetscCall(MatCopy(F,R,SAME_NONZERO_PATTERN));
     52:   if (eta!=1.0) PetscCall(MatScale(R,1.0/eta));
     53:   PetscCall(FNEvaluateFunctionMat(fnexp,R,NULL));
     54:   PetscCall(FNDestroy(&fnexp));
     55:   PetscCall(MatAXPY(R,-tau,A,SAME_NONZERO_PATTERN));
     56:   PetscCall(MatNorm(R,NORM_FROBENIUS,&nrm));
     57:   if (nrm<100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"||expm(F)-A||_F < 100*eps\n"));
     58:   else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"||expm(F)-A||_F = %g\n",(double)nrm));
     59:   /* check FNEvaluateFunctionMatVec() */
     60:   PetscCall(MatCreateVecs(A,&v,&f0));
     61:   PetscCall(MatGetColumnVector(F,f0,0));
     62:   PetscCall(FNEvaluateFunctionMatVec(fn,A,v));
     63:   PetscCall(VecAXPY(v,-1.0,f0));
     64:   PetscCall(VecNorm(v,NORM_2,&nrm));
     65:   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));
     66:   PetscCall(MatDestroy(&F));
     67:   PetscCall(MatDestroy(&R));
     68:   PetscCall(VecDestroy(&v));
     69:   PetscCall(VecDestroy(&f0));
     70:   PetscFunctionReturn(PETSC_SUCCESS);
     71: }

     73: int main(int argc,char **argv)
     74: {
     75:   FN             fn;
     76:   Mat            A;
     77:   PetscInt       i,j,n=10;
     78:   PetscScalar    *As;
     79:   PetscViewer    viewer;
     80:   PetscBool      verbose,inplace,random,triang;

     82:   PetscFunctionBeginUser;
     83:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     84:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     85:   PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));
     86:   PetscCall(PetscOptionsHasName(NULL,NULL,"-inplace",&inplace));
     87:   PetscCall(PetscOptionsHasName(NULL,NULL,"-random",&random));
     88:   PetscCall(PetscOptionsHasName(NULL,NULL,"-triang",&triang));
     89:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix logarithm, n=%" PetscInt_FMT ".\n",n));

     91:   /* Create logarithm function object */
     92:   PetscCall(FNCreate(PETSC_COMM_WORLD,&fn));
     93:   PetscCall(FNSetType(fn,FNLOG));
     94:   PetscCall(FNSetFromOptions(fn));

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

    101:   /* Create matrices */
    102:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A));
    103:   PetscCall(PetscObjectSetName((PetscObject)A,"A"));

    105:   if (random) PetscCall(MatSetRandom(A,NULL));
    106:   else {
    107:     /* Fill A with a non-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++) {
    112:         As[i+(i+j)*n]=1.0;
    113:         if (!triang) As[(i+j)+i*n]=-1.0;
    114:       }
    115:     }
    116:     As[(n-1)*n] = -5.0;
    117:     As[0] = 2.01;
    118:     PetscCall(MatDenseRestoreArray(A,&As));
    119:   }
    120:   PetscCall(TestMatLog(fn,A,viewer,verbose,inplace));

    122:   PetscCall(MatDestroy(&A));
    123:   PetscCall(FNDestroy(&fn));
    124:   PetscCall(SlepcFinalize());
    125:   return 0;
    126: }

    128: /*TEST

    130:    testset:
    131:       filter: grep -v "computing matrix functions"
    132:       output_file: output/test13_1.out
    133:       test:
    134:          suffix: 1
    135:          args: -fn_scale .04,2 -n 75 -inplace {{0 1}}
    136:          requires: c99_complex !__float128
    137:       test:
    138:          suffix: 1_triang
    139:          args: -fn_scale .04,2 -n 75 -triang
    140:          requires: c99_complex !__float128
    141:       test:
    142:          suffix: 1_random
    143:          args: -fn_scale .02,2 -n 75 -random
    144:          requires: complex !__float128
    145:          filter_output: sed -e 's/04/02/'

    147: TEST*/