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

Actual source code: test3.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 exponential.\n\n";

     13: #include <slepcfn.h>

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

     29:   MatGetSize(A,&n,NULL);
     30:   MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&F);
     31:   PetscObjectSetName((PetscObject)F,"F");
     32:   /* compute matrix exponential */
     33:   if (inplace) {
     34:     MatCopy(A,F,SAME_NONZERO_PATTERN);
     35:     MatIsHermitianKnown(A,&set,&flg);
     36:     if (set && flg) MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE);
     37:     FNEvaluateFunctionMat(fn,F,NULL);
     38:   } else {
     39:     MatDuplicate(A,MAT_COPY_VALUES,&Acopy);
     40:     FNEvaluateFunctionMat(fn,A,F);
     41:     /* check that A has not been modified */
     42:     MatAXPY(Acopy,-1.0,A,SAME_NONZERO_PATTERN);
     43:     MatNorm(Acopy,NORM_1,&nrm);
     44:     if (nrm>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the input matrix has changed by %g\n",(double)nrm);
     45:     MatDestroy(&Acopy);
     46:   }
     47:   if (verbose) {
     48:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
     49:     MatView(A,viewer);
     50:     PetscPrintf(PETSC_COMM_WORLD,"Computed expm(A) - - - - - - -\n");
     51:     MatView(F,viewer);
     52:   }
     53:   /* print matrix norm for checking */
     54:   MatNorm(F,NORM_1,&nrmf);
     55:   PetscPrintf(PETSC_COMM_WORLD,"The 1-norm of f(A) is %g\n",(double)nrmf);
     56:   if (checkerror) {
     57:     MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&Finv);
     58:     PetscObjectSetName((PetscObject)Finv,"Finv");
     59:     FNGetScale(fn,&tau,&eta);
     60:     /* compute inverse exp(-tau*A)/eta */
     61:     FNCreate(PETSC_COMM_WORLD,&finv);
     62:     FNSetType(finv,FNEXP);
     63:     FNSetFromOptions(finv);
     64:     FNSetScale(finv,-tau,1.0/eta);
     65:     if (inplace) {
     66:       MatCopy(A,Finv,SAME_NONZERO_PATTERN);
     67:       MatIsHermitianKnown(A,&set,&flg);
     68:       if (set && flg) MatSetOption(Finv,MAT_HERMITIAN,PETSC_TRUE);
     69:       FNEvaluateFunctionMat(finv,Finv,NULL);
     70:     } else FNEvaluateFunctionMat(finv,A,Finv);
     71:     FNDestroy(&finv);
     72:     /* check error ||F*Finv-I||_F */
     73:     MatMatMult(F,Finv,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&R);
     74:     MatShift(R,-1.0);
     75:     MatNorm(R,NORM_FROBENIUS,&nrm);
     76:     if (nrm<100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"||exp(A)*exp(-A)-I||_F < 100*eps\n");
     77:     else PetscPrintf(PETSC_COMM_WORLD,"||exp(A)*exp(-A)-I||_F = %g\n",(double)nrm);
     78:     MatDestroy(&R);
     79:     MatDestroy(&Finv);
     80:   }
     81:   /* check FNEvaluateFunctionMatVec() */
     82:   MatCreateVecs(A,&v,&f0);
     83:   MatGetColumnVector(F,f0,0);
     84:   FNEvaluateFunctionMatVec(fn,A,v);
     85:   VecAXPY(v,-1.0,f0);
     86:   VecNorm(v,NORM_2,&nrm);
     87:   if (nrm/nrmf>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
     88:   MatDestroy(&F);
     89:   VecDestroy(&v);
     90:   VecDestroy(&f0);
     91:   PetscFunctionReturn(0);
     92: }

     94: int main(int argc,char **argv)
     95: {
     96:   FN             fn;
     97:   Mat            A;
     98:   PetscInt       i,j,n=10;
     99:   PetscScalar    *As;
    100:   PetscViewer    viewer;
    101:   PetscBool      verbose,inplace,checkerror;

    103:   SlepcInitialize(&argc,&argv,(char*)0,help);
    104:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
    105:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
    106:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
    107:   PetscOptionsHasName(NULL,NULL,"-checkerror",&checkerror);
    108:   PetscPrintf(PETSC_COMM_WORLD,"Matrix exponential, n=%" PetscInt_FMT ".\n",n);

    110:   /* Create exponential function object */
    111:   FNCreate(PETSC_COMM_WORLD,&fn);
    112:   FNSetType(fn,FNEXP);
    113:   FNSetFromOptions(fn);

    115:   /* Set up viewer */
    116:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
    117:   FNView(fn,viewer);
    118:   if (verbose) PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);

    120:   /* Create matrices */
    121:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
    122:   PetscObjectSetName((PetscObject)A,"A");

    124:   /* Fill A with a symmetric Toeplitz matrix */
    125:   MatDenseGetArray(A,&As);
    126:   for (i=0;i<n;i++) As[i+i*n]=2.0;
    127:   for (j=1;j<3;j++) {
    128:     for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
    129:   }
    130:   MatDenseRestoreArray(A,&As);
    131:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
    132:   TestMatExp(fn,A,viewer,verbose,inplace,checkerror);

    134:   /* Repeat with non-symmetric A */
    135:   MatDenseGetArray(A,&As);
    136:   for (j=1;j<3;j++) {
    137:     for (i=0;i<n-j;i++) { As[(i+j)+i*n]=-1.0; }
    138:   }
    139:   MatDenseRestoreArray(A,&As);
    140:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
    141:   TestMatExp(fn,A,viewer,verbose,inplace,checkerror);

    143:   MatDestroy(&A);
    144:   FNDestroy(&fn);
    145:   SlepcFinalize();
    146:   return 0;
    147: }

    149: /*TEST

    151:    testset:
    152:       filter: grep -v "computing matrix functions"
    153:       output_file: output/test3_1.out
    154:       test:
    155:          suffix: 1
    156:          args: -fn_method {{0 1}}
    157:       test:
    158:          suffix: 1_subdiagonalpade
    159:          args: -fn_method {{2 3}}
    160:          requires: c99_complex !single
    161:       test:
    162:          suffix: 1_cuda
    163:          args: -fn_method 4
    164:          requires: cuda
    165:       test:
    166:          suffix: 1_magma
    167:          args: -fn_method {{5 6 7 8}}
    168:          requires: cuda magma
    169:       test:
    170:          suffix: 2
    171:          args: -inplace -fn_method{{0 1}}
    172:       test:
    173:          suffix: 2_subdiagonalpade
    174:          args: -inplace -fn_method{{2 3}}
    175:          requires: c99_complex !single
    176:       test:
    177:          suffix: 2_cuda
    178:          args: -inplace -fn_method 4
    179:          requires: cuda
    180:       test:
    181:          suffix: 2_magma
    182:          args: -inplace -fn_method {{5 6 7 8}}
    183:          requires: cuda magma

    185:    testset:
    186:       args: -fn_scale 0.1
    187:       filter: grep -v "computing matrix functions"
    188:       output_file: output/test3_3.out
    189:       test:
    190:          suffix: 3
    191:          args: -fn_method {{0 1}}
    192:       test:
    193:         suffix: 3_subdiagonalpade
    194:         args: -fn_method {{2 3}}
    195:         requires: c99_complex !single

    197:    testset:
    198:       args: -n 120 -fn_scale 0.6,1.5
    199:       filter: grep -v "computing matrix functions"
    200:       output_file: output/test3_4.out
    201:       test:
    202:          suffix: 4
    203:          args: -fn_method {{0 1}}
    204:          requires: !single
    205:       test:
    206:         suffix: 4_subdiagonalpade
    207:         args: -fn_method {{2 3}}
    208:         requires: c99_complex !single

    210:    test:
    211:       suffix: 5
    212:       args: -fn_scale 30 -fn_method {{2 3}}
    213:       filter: grep -v "computing matrix functions"
    214:       requires: c99_complex !single
    215:       output_file: output/test3_5.out

    217:    test:
    218:       suffix: 6
    219:       args: -fn_scale 1e-9 -fn_method {{2 3}}
    220:       filter: grep -v "computing matrix functions"
    221:       requires: c99_complex !single
    222:       output_file: output/test3_6.out

    224: TEST*/