Date: 2021-02-01T14:41:41+00:00

Actual source code: test7.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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 square root.\n\n";

     13: #include <slepcfn.h>

     15: /*
     16:    Compute matrix square root B = sqrtm(A)
     17:    Check result as norm(B*B-A)
     18:  */
     19: PetscErrorCode TestMatSqrt(FN fn,Mat A,PetscViewer viewer,PetscBool verbose,PetscBool inplace)
     20: {
     22:   PetscScalar    tau,eta;
     23:   PetscReal      nrm;
     24:   PetscBool      set,flg;
     25:   PetscInt       n;
     26:   Mat            S,R;
     27:   Vec            v,f0;

     30:   MatGetSize(A,&n,NULL);
     31:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&S);
     32:   PetscObjectSetName((PetscObject)S,"S");
     33:   FNGetScale(fn,&tau,&eta);
     34:   /* compute square root */
     35:   if (inplace) {
     36:     MatCopy(A,S,SAME_NONZERO_PATTERN);
     37:     MatIsHermitianKnown(A,&set,&flg);
     38:     if (set && flg) { MatSetOption(S,MAT_HERMITIAN,PETSC_TRUE); }
     39:     FNEvaluateFunctionMat(fn,S,NULL);
     40:   } else {
     41:     FNEvaluateFunctionMat(fn,A,S);
     42:   }
     43:   if (verbose) {
     44:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
     45:     MatView(A,viewer);
     46:     PetscPrintf(PETSC_COMM_WORLD,"Computed sqrtm(A) - - - - - - -\n");
     47:     MatView(S,viewer);
     48:   }
     49:   /* check error ||S*S-A||_F */
     50:   MatMatMult(S,S,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&R);
     51:   if (eta!=1.0) {
     52:     MatScale(R,1.0/(eta*eta));
     53:   }
     54:   MatAXPY(R,-tau,A,SAME_NONZERO_PATTERN);
     55:   MatNorm(R,NORM_FROBENIUS,&nrm);
     56:   if (nrm<100*PETSC_MACHINE_EPSILON) {
     57:     PetscPrintf(PETSC_COMM_WORLD,"||S*S-A||_F < 100*eps\n");
     58:   } else {
     59:     PetscPrintf(PETSC_COMM_WORLD,"||S*S-A||_F = %g\n",(double)nrm);
     60:   }
     61:   /* check FNEvaluateFunctionMatVec() */
     62:   MatCreateVecs(A,&v,&f0);
     63:   MatGetColumnVector(S,f0,0);
     64:   FNEvaluateFunctionMatVec(fn,A,v);
     65:   VecAXPY(v,-1.0,f0);
     66:   VecNorm(v,NORM_2,&nrm);
     67:   if (nrm>100*PETSC_MACHINE_EPSILON) {
     68:     PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
     69:   }
     70:   MatDestroy(&S);
     71:   MatDestroy(&R);
     72:   VecDestroy(&v);
     73:   VecDestroy(&f0);
     74:   return(0);
     75: }

     77: int main(int argc,char **argv)
     78: {
     80:   FN             fn;
     81:   Mat            A;
     82:   PetscInt       i,j,n=10;
     83:   PetscScalar    *As;
     84:   PetscViewer    viewer;
     85:   PetscBool      verbose,inplace;
     86:   PetscRandom    myrand;
     87:   PetscReal      v;

     89:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     90:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     91:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
     92:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
     93:   PetscPrintf(PETSC_COMM_WORLD,"Matrix square root, n=%D.\n",n);

     95:   /* Create function object */
     96:   FNCreate(PETSC_COMM_WORLD,&fn);
     97:   FNSetType(fn,FNSQRT);
     98:   FNSetFromOptions(fn);

    100:   /* Set up viewer */
    101:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
    102:   FNView(fn,viewer);
    103:   if (verbose) {
    104:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
    105:   }

    107:   /* Create matrix */
    108:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
    109:   PetscObjectSetName((PetscObject)A,"A");

    111:   /* Compute square root of a symmetric matrix A */
    112:   MatDenseGetArray(A,&As);
    113:   for (i=0;i<n;i++) As[i+i*n]=2.5;
    114:   for (j=1;j<3;j++) {
    115:     for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
    116:   }
    117:   MatDenseRestoreArray(A,&As);
    118:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
    119:   TestMatSqrt(fn,A,viewer,verbose,inplace);

    121:   /* Repeat with upper triangular A */
    122:   MatDenseGetArray(A,&As);
    123:   for (j=1;j<3;j++) {
    124:     for (i=0;i<n-j;i++) As[(i+j)+i*n]=0.0;
    125:   }
    126:   MatDenseRestoreArray(A,&As);
    127:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
    128:   TestMatSqrt(fn,A,viewer,verbose,inplace);

    130:   /* Repeat with non-symmetic A */
    131:   PetscRandomCreate(PETSC_COMM_WORLD,&myrand);
    132:   PetscRandomSetFromOptions(myrand);
    133:   PetscRandomSetInterval(myrand,0.0,1.0);
    134:   MatDenseGetArray(A,&As);
    135:   for (j=1;j<3;j++) {
    136:     for (i=0;i<n-j;i++) {
    137:       PetscRandomGetValueReal(myrand,&v);
    138:       As[(i+j)+i*n]=v;
    139:     }
    140:   }
    141:   MatDenseRestoreArray(A,&As);
    142:   PetscRandomDestroy(&myrand);
    143:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
    144:   TestMatSqrt(fn,A,viewer,verbose,inplace);

    146:   MatDestroy(&A);
    147:   FNDestroy(&fn);
    148:   SlepcFinalize();
    149:   return ierr;
    150: }

    152: /*TEST

    154:    test:
    155:       suffix: 1
    156:       nsize: 1
    157:       args: -fn_scale .05,2 -n 100 -fn_method {{0 1 2}shared output}
    158:       filter: grep -v "computing matrix functions"
    159:       output_file: output/test7_1.out
    160:       timeoutfactor: 2

    162:    test:
    163:       suffix: 1_sadeghi
    164:       nsize: 1
    165:       args: -fn_scale .05,2 -n 100 -fn_method 3
    166:       requires: !single
    167:       filter: grep -v "computing matrix functions"
    168:       output_file: output/test7_1.out

    170:    test:
    171:       suffix: 2
    172:       nsize: 1
    173:       args: -fn_scale .05,2 -n 100 -inplace -fn_method {{0 1 2}shared output}
    174:       filter: grep -v "computing matrix functions"
    175:       output_file: output/test7_1.out
    176:       timeoutfactor: 2

    178:    test:
    179:       suffix: 2_sadeghi
    180:       nsize: 1
    181:       args: -fn_scale .05,2 -n 100 -inplace -fn_method 3
    182:       requires: !single
    183:       filter: grep -v "computing matrix functions"
    184:       output_file: output/test7_1.out

    186:    test:
    187:       suffix: 3
    188:       nsize: 3
    189:       args: -fn_scale .05,2 -n 100 -fn_parallel synchronized
    190:       filter: grep -v "computing matrix functions" | grep -v "SYNCHRONIZED" | sed -e "s/3 MPI/1 MPI/g"
    191:       output_file: output/test7_1.out

    193:    test:
    194:       suffix: 4
    195:       nsize: 3
    196:       args: -fn_scale .05,2 -n 100 -inplace -fn_parallel synchronized
    197:       filter: grep -v "computing matrix functions" | grep -v "SYNCHRONIZED" | sed -e "s/3 MPI/1 MPI/g"
    198:       output_file: output/test7_1.out

    200: TEST*/