Date: 2022-08-09T09:05:19+00:00

Actual source code: test13.c
slepc-3.17.2 2022-08-09
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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 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;

     29:   MatGetSize(A,&n,NULL);
     30:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&F);
     31:   PetscObjectSetName((PetscObject)F,"F");
     32:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&R);
     33:   PetscObjectSetName((PetscObject)R,"R");
     34:   FNGetScale(fn,&tau,&eta);
     35:   /* compute matrix logarithm */
     36:   if (inplace) {
     37:     MatCopy(A,F,SAME_NONZERO_PATTERN);
     38:     MatIsHermitianKnown(A,&set,&flg);
     39:     if (set && flg) MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE);
     40:     FNEvaluateFunctionMat(fn,F,NULL);
     41:   } else FNEvaluateFunctionMat(fn,A,F);
     42:   if (verbose) {
     43:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
     44:     MatView(A,viewer);
     45:     PetscPrintf(PETSC_COMM_WORLD,"Computed logm(A) - - - - - - -\n");
     46:     MatView(F,viewer);
     47:   }
     48:   /* check error ||expm(F)-A||_F */
     49:   FNCreate(PETSC_COMM_WORLD,&fnexp);
     50:   FNSetType(fnexp,FNEXP);
     51:   MatCopy(F,R,SAME_NONZERO_PATTERN);
     52:   if (eta!=1.0) MatScale(R,1.0/eta);
     53:   FNEvaluateFunctionMat(fnexp,R,NULL);
     54:   FNDestroy(&fnexp);
     55:   MatAXPY(R,-tau,A,SAME_NONZERO_PATTERN);
     56:   MatNorm(R,NORM_FROBENIUS,&nrm);
     57:   if (nrm<100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"||expm(F)-A||_F < 100*eps\n");
     58:   else PetscPrintf(PETSC_COMM_WORLD,"||expm(F)-A||_F = %g\n",(double)nrm);
     59:   /* check FNEvaluateFunctionMatVec() */
     60:   MatCreateVecs(A,&v,&f0);
     61:   MatGetColumnVector(F,f0,0);
     62:   FNEvaluateFunctionMatVec(fn,A,v);
     63:   VecAXPY(v,-1.0,f0);
     64:   VecNorm(v,NORM_2,&nrm);
     65:   if (nrm>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
     66:   MatDestroy(&F);
     67:   MatDestroy(&R);
     68:   VecDestroy(&v);
     69:   VecDestroy(&f0);
     70:   PetscFunctionReturn(0);
     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:   SlepcInitialize(&argc,&argv,(char*)0,help);
     83:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     84:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
     85:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
     86:   PetscOptionsHasName(NULL,NULL,"-random",&random);
     87:   PetscOptionsHasName(NULL,NULL,"-triang",&triang);
     88:   PetscPrintf(PETSC_COMM_WORLD,"Matrix logarithm, n=%" PetscInt_FMT ".\n",n);

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

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

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

    104:   if (random) MatSetRandom(A,NULL);
    105:   else {
    106:     /* Fill A with a non-symmetric Toeplitz matrix */
    107:     MatDenseGetArray(A,&As);
    108:     for (i=0;i<n;i++) As[i+i*n]=2.0;
    109:     for (j=1;j<3;j++) {
    110:       for (i=0;i<n-j;i++) {
    111:         As[i+(i+j)*n]=1.0;
    112:         if (!triang) As[(i+j)+i*n]=-1.0;
    113:       }
    114:     }
    115:     As[(n-1)*n] = -5.0;
    116:     As[0] = 2.01;
    117:     MatDenseRestoreArray(A,&As);
    118:   }
    119:   TestMatLog(fn,A,viewer,verbose,inplace);

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

    127: /*TEST

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

    146: TEST*/