Date: 2026-03-31T13:23:21+00:00

Actual source code: test8.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 inverse square root.\n\n";

     13: #include <slepcfn.h>

     15: /*
     16:    Compute matrix inverse square root B = inv(sqrtm(A))
     17:    Check result as norm(B*B*A-I)
     18:  */
     19: PetscErrorCode TestMatInvSqrt(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 inverse 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 inv(sqrtm(A)) - - - - - - -\n"));
     52:     PetscCall(MatView(S,viewer));
     53:   }
     54:   /* check error ||S*S*A-I||_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(MatCreateVecs(A,&v,&f0));
     58:   PetscCall(MatGetColumnVector(S,f0,0));
     59:   PetscCall(MatCopy(R,S,SAME_NONZERO_PATTERN));
     60:   PetscCall(MatDestroy(&R));
     61:   if (tau!=1.0) PetscCall(MatScale(S,tau));
     62:   PetscCall(MatMatMult(S,A,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&R));
     63:   PetscCall(MatShift(R,-1.0));
     64:   PetscCall(MatNorm(R,NORM_FROBENIUS,&nrm));
     65:   PetscCall(MatDestroy(&R));
     66:   if (nrm<100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"||S*S*A-I||_F < 100*eps\n"));
     67:   else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"||S*S*A-I||_F = %g\n",(double)nrm));
     68:   /* check FNEvaluateFunctionMatVec() */
     69:   PetscCall(FNEvaluateFunctionMatVec(fn,A,v));
     70:   PetscCall(VecAXPY(v,-1.0,f0));
     71:   PetscCall(VecNorm(v,NORM_2,&nrm));
     72:   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));
     73:   PetscCall(MatDestroy(&S));
     74:   PetscCall(VecDestroy(&v));
     75:   PetscCall(VecDestroy(&f0));
     76:   PetscFunctionReturn(PETSC_SUCCESS);
     77: }

     79: int main(int argc,char **argv)
     80: {
     81:   FN             fn;
     82:   Mat            A=NULL;
     83:   PetscInt       i,j,n=10;
     84:   PetscScalar    x,y,yp,*As;
     85:   PetscViewer    viewer;
     86:   PetscBool      verbose,inplace,matcuda;
     87:   PetscRandom    myrand;
     88:   PetscReal      v;
     89:   char           strx[50],str[50];

     91:   PetscFunctionBeginUser;
     92:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     93:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     94:   PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));
     95:   PetscCall(PetscOptionsHasName(NULL,NULL,"-inplace",&inplace));
     96:   PetscCall(PetscOptionsHasName(NULL,NULL,"-matcuda",&matcuda));
     97:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix inverse square root, n=%" PetscInt_FMT ".\n",n));

     99:   /* Create function object */
    100:   PetscCall(FNCreate(PETSC_COMM_WORLD,&fn));
    101:   PetscCall(FNSetType(fn,FNINVSQRT));
    102:   PetscCall(FNSetFromOptions(fn));

    104:   /* Set up viewer */
    105:   PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
    106:   PetscCall(FNView(fn,viewer));
    107:   if (verbose) PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB));

    109:   /* Scalar evaluation */
    110:   x = 2.2;
    111:   PetscCall(SlepcSNPrintfScalar(strx,sizeof(strx),x,PETSC_FALSE));
    112:   PetscCall(FNEvaluateFunction(fn,x,&y));
    113:   PetscCall(FNEvaluateDerivative(fn,x,&yp));
    114:   PetscCall(SlepcSNPrintfScalar(str,sizeof(str),y,PETSC_FALSE));
    115:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"  f(%s)=%s\n",strx,str));
    116:   PetscCall(SlepcSNPrintfScalar(str,sizeof(str),yp,PETSC_FALSE));
    117:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"  f'(%s)=%s\n",strx,str));

    119:   /* Create matrix */
    120:   if (matcuda) {
    121: #if defined(PETSC_HAVE_CUDA)
    122:     PetscCall(MatCreateSeqDenseCUDA(PETSC_COMM_SELF,n,n,NULL,&A));
    123: #endif
    124:   } else PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A));
    125:   PetscCall(PetscObjectSetName((PetscObject)A,"A"));

    127:   /* Compute square root of a symmetric matrix A */
    128:   PetscCall(MatDenseGetArray(A,&As));
    129:   for (i=0;i<n;i++) As[i+i*n]=2.5;
    130:   for (j=1;j<3;j++) {
    131:     for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
    132:   }
    133:   PetscCall(MatDenseRestoreArray(A,&As));
    134:   PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE));
    135:   PetscCall(TestMatInvSqrt(fn,A,viewer,verbose,inplace));

    137:   /* Repeat with upper triangular A */
    138:   PetscCall(MatDenseGetArray(A,&As));
    139:   for (j=1;j<3;j++) {
    140:     for (i=0;i<n-j;i++) As[(i+j)+i*n]=0.0;
    141:   }
    142:   PetscCall(MatDenseRestoreArray(A,&As));
    143:   PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE));
    144:   PetscCall(TestMatInvSqrt(fn,A,viewer,verbose,inplace));

    146:   /* Repeat with non-symmetic A */
    147:   PetscCall(PetscRandomCreate(PETSC_COMM_WORLD,&myrand));
    148:   PetscCall(PetscRandomSetFromOptions(myrand));
    149:   PetscCall(PetscRandomSetInterval(myrand,0.0,1.0));
    150:   PetscCall(MatDenseGetArray(A,&As));
    151:   for (j=1;j<3;j++) {
    152:     for (i=0;i<n-j;i++) {
    153:       PetscCall(PetscRandomGetValueReal(myrand,&v));
    154:       As[(i+j)+i*n]=v;
    155:     }
    156:   }
    157:   PetscCall(MatDenseRestoreArray(A,&As));
    158:   PetscCall(PetscRandomDestroy(&myrand));
    159:   PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE));
    160:   PetscCall(TestMatInvSqrt(fn,A,viewer,verbose,inplace));

    162:   PetscCall(MatDestroy(&A));
    163:   PetscCall(FNDestroy(&fn));
    164:   PetscCall(SlepcFinalize());
    165:   return 0;
    166: }

    168: /*TEST

    170:    testset:
    171:       args: -fn_scale 0.9,0.5 -n 10
    172:       filter: grep -v "computing matrix functions"
    173:       requires: !__float128
    174:       output_file: output/test8_1.out
    175:       test:
    176:          suffix: 1
    177:          args: -fn_method {{0 1 2 3}}
    178:       test:
    179:          suffix: 1_cuda
    180:          args: -fn_method 2 -matcuda
    181:          requires: cuda
    182:       test:
    183:          suffix: 1_magma
    184:          args: -fn_method {{1 3}} -matcuda
    185:          requires: cuda magma
    186:       test:
    187:          suffix: 2
    188:          args: -inplace -fn_method {{0 1 2 3}}
    189:       test:
    190:          suffix: 2_cuda
    191:          args: -inplace -fn_method 2 -matcuda
    192:          requires: cuda
    193:       test:
    194:          suffix: 2_magma
    195:          args: -inplace -fn_method {{1 3}} -matcuda
    196:          requires: cuda magma

    198: TEST*/