Actual source code: test7.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 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: {
     21:   PetscScalar    tau,eta;
     22:   PetscReal      nrm;
     23:   PetscBool      set,flg;
     24:   PetscInt       n;
     25:   Mat            S,R,Acopy;
     26:   Vec            v,f0;

     28:   PetscFunctionBeginUser;
     29:   PetscCall(MatGetSize(A,&n,NULL));
     30:   PetscCall(MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&S));
     31:   PetscCall(PetscObjectSetName((PetscObject)S,"S"));
     32:   PetscCall(FNGetScale(fn,&tau,&eta));
     33:   /* compute square root */
     34:   if (inplace) {
     35:     PetscCall(MatCopy(A,S,SAME_NONZERO_PATTERN));
     36:     PetscCall(MatIsHermitianKnown(A,&set,&flg));
     37:     if (set && flg) PetscCall(MatSetOption(S,MAT_HERMITIAN,PETSC_TRUE));
     38:     PetscCall(FNEvaluateFunctionMat(fn,S,NULL));
     39:   } else {
     40:     PetscCall(MatDuplicate(A,MAT_COPY_VALUES,&Acopy));
     41:     PetscCall(FNEvaluateFunctionMat(fn,A,S));
     42:     /* check that A has not been modified */
     43:     PetscCall(MatAXPY(Acopy,-1.0,A,SAME_NONZERO_PATTERN));
     44:     PetscCall(MatNorm(Acopy,NORM_1,&nrm));
     45:     if (nrm>100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: the input matrix has changed by %g\n",(double)nrm));
     46:     PetscCall(MatDestroy(&Acopy));
     47:   }
     48:   if (verbose) {
     49:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n"));
     50:     PetscCall(MatView(A,viewer));
     51:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Computed sqrtm(A) - - - - - - -\n"));
     52:     PetscCall(MatView(S,viewer));
     53:   }
     54:   /* check error ||S*S-A||_F */
     55:   PetscCall(MatMatMult(S,S,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&R));
     56:   if (eta!=1.0) PetscCall(MatScale(R,1.0/(eta*eta)));
     57:   PetscCall(MatAXPY(R,-tau,A,SAME_NONZERO_PATTERN));
     58:   PetscCall(MatNorm(R,NORM_FROBENIUS,&nrm));
     59:   if (nrm<100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"||S*S-A||_F < 100*eps\n"));
     60:   else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"||S*S-A||_F = %g\n",(double)nrm));
     61:   /* check FNEvaluateFunctionMatVec() */
     62:   PetscCall(MatCreateVecs(A,&v,&f0));
     63:   PetscCall(MatGetColumnVector(S,f0,0));
     64:   PetscCall(FNEvaluateFunctionMatVec(fn,A,v));
     65:   PetscCall(VecAXPY(v,-1.0,f0));
     66:   PetscCall(VecNorm(v,NORM_2,&nrm));
     67:   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));
     68:   PetscCall(MatDestroy(&S));
     69:   PetscCall(MatDestroy(&R));
     70:   PetscCall(VecDestroy(&v));
     71:   PetscCall(VecDestroy(&f0));
     72:   PetscFunctionReturn(PETSC_SUCCESS);
     73: }

     75: int main(int argc,char **argv)
     76: {
     77:   FN             fn;
     78:   Mat            A=NULL;
     79:   PetscInt       i,j,n=10;
     80:   PetscScalar    *As;
     81:   PetscViewer    viewer;
     82:   PetscBool      verbose,inplace,matcuda;
     83:   PetscRandom    myrand;
     84:   PetscReal      v;

     86:   PetscFunctionBeginUser;
     87:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     88:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     89:   PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));
     90:   PetscCall(PetscOptionsHasName(NULL,NULL,"-inplace",&inplace));
     91:   PetscCall(PetscOptionsHasName(NULL,NULL,"-matcuda",&matcuda));
     92:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix square root, n=%" PetscInt_FMT ".\n",n));

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

     99:   /* Set up viewer */
    100:   PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
    101:   PetscCall(FNView(fn,viewer));
    102:   if (verbose) PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB));

    104:   /* Create matrix */
    105:   if (matcuda) {
    106: #if defined(PETSC_HAVE_CUDA)
    107:     PetscCall(MatCreateSeqDenseCUDA(PETSC_COMM_SELF,n,n,NULL,&A));
    108: #endif
    109:   } else PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A));
    110:   PetscCall(PetscObjectSetName((PetscObject)A,"A"));

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

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

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

    147:   PetscCall(MatDestroy(&A));
    148:   PetscCall(FNDestroy(&fn));
    149:   PetscCall(SlepcFinalize());
    150:   return 0;
    151: }

    153: /*TEST

    155:    testset:
    156:       args: -fn_scale .05,2 -n 100
    157:       filter: grep -v "computing matrix functions"
    158:       output_file: output/test7_1.out
    159:       requires: !__float128
    160:       timeoutfactor: 2
    161:       test:
    162:          suffix: 1
    163:          args: -fn_method {{0 1 2}}
    164:       test:
    165:          suffix: 1_sadeghi
    166:          args: -fn_method 3
    167:          requires: !single
    168:       test:
    169:          suffix: 1_cuda
    170:          args: -fn_method 2 -matcuda
    171:          requires: cuda !single
    172:       test:
    173:          suffix: 1_magma
    174:          args: -fn_method {{1 3}} -matcuda
    175:          requires: cuda magma !single
    176:       test:
    177:          suffix: 2
    178:          args: -inplace -fn_method {{0 1 2}}
    179:       test:
    180:          suffix: 2_sadeghi
    181:          args: -inplace -fn_method 3
    182:          requires: !single
    183:       test:
    184:          suffix: 2_cuda
    185:          args: -inplace -fn_method 2 -matcuda
    186:          requires: cuda !single
    187:       test:
    188:          suffix: 2_magma
    189:          args: -inplace -fn_method {{1 3}} -matcuda
    190:          requires: cuda magma !single

    192:    testset:
    193:       nsize: 3
    194:       args: -fn_scale .05,2 -n 100 -fn_parallel synchronized
    195:       filter: grep -v "computing matrix functions" | grep -v "SYNCHRONIZED" | sed -e "s/3 MPI processes/1 MPI process/g"
    196:       requires: !__float128
    197:       output_file: output/test7_1.out
    198:       test:
    199:          suffix: 3
    200:       test:
    201:          suffix: 3_inplace
    202:          args: -inplace

    204: TEST*/