Date: 2022-03-31T15:28:48+00:00

Actual source code: test8.c
slepc-3.17.0 2022-03-31
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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 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;
     26:   Vec            v,f0;

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

     71: int main(int argc,char **argv)
     72: {
     73:   FN             fn;
     74:   Mat            A;
     75:   PetscInt       i,j,n=10;
     76:   PetscScalar    x,y,yp,*As;
     77:   PetscViewer    viewer;
     78:   PetscBool      verbose,inplace;
     79:   PetscRandom    myrand;
     80:   PetscReal      v;
     81:   char           strx[50],str[50];

     83:   SlepcInitialize(&argc,&argv,(char*)0,help);
     84:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     85:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
     86:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
     87:   PetscPrintf(PETSC_COMM_WORLD,"Matrix inverse square root, n=%" PetscInt_FMT ".\n",n);

     89:   /* Create function object */
     90:   FNCreate(PETSC_COMM_WORLD,&fn);
     91:   FNSetType(fn,FNINVSQRT);
     92:   FNSetFromOptions(fn);

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

     99:   /* Scalar evaluation */
    100:   x = 2.2;
    101:   SlepcSNPrintfScalar(strx,sizeof(strx),x,PETSC_FALSE);
    102:   FNEvaluateFunction(fn,x,&y);
    103:   FNEvaluateDerivative(fn,x,&yp);
    104:   SlepcSNPrintfScalar(str,sizeof(str),y,PETSC_FALSE);
    105:   PetscPrintf(PETSC_COMM_WORLD,"  f(%s)=%s\n",strx,str);
    106:   SlepcSNPrintfScalar(str,sizeof(str),yp,PETSC_FALSE);
    107:   PetscPrintf(PETSC_COMM_WORLD,"  f'(%s)=%s\n",strx,str);

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

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

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

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

    148:   MatDestroy(&A);
    149:   FNDestroy(&fn);
    150:   SlepcFinalize();
    151:   return 0;
    152: }

    154: /*TEST

    156:    testset:
    157:       args: -fn_scale 0.9,0.5 -n 10
    158:       filter: grep -v "computing matrix functions"
    159:       output_file: output/test8_1.out
    160:       test:
    161:          suffix: 1
    162:          args: -fn_method {{0 1 2 3}}
    163:       test:
    164:          suffix: 1_cuda
    165:          args: -fn_method 4
    166:          requires: cuda
    167:       test:
    168:          suffix: 1_magma
    169:          args: -fn_method {{5 6}}
    170:          requires: cuda magma
    171:       test:
    172:          suffix: 2
    173:          args: -inplace -fn_method {{0 1 2 3}}
    174:       test:
    175:          suffix: 2_cuda
    176:          args: -inplace -fn_method 4
    177:          requires: cuda
    178:       test:
    179:          suffix: 2_magma
    180:          args: -inplace -fn_method {{5 6}}
    181:          requires: cuda magma

    183: TEST*/