Date: 2022-11-02T11:46:08+00:00

Actual source code: test6.c
slepc-3.18.1 2022-11-02
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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: */
     10: /*
     11:    Define the function

     13:         f(x) = (1-x^2) exp(-x/(1+x^2))

     15:    with the following tree:

     17:             f(x)                  f(x)              (combined by product)
     18:            /    \                 g(x) = 1-x^2      (polynomial)
     19:         g(x)    h(x)              h(x)              (combined by composition)
     20:                /    \             r(x) = -x/(1+x^2) (rational)
     21:              r(x)   e(x)          e(x) = exp(x)     (exponential)
     22: */

     24: static char help[] = "Test combined function.\n\n";

     26: #include <slepcfn.h>

     28: /*
     29:    Compute matrix function B = (I-A^2) exp(-(I+A^2)\A)
     30:  */
     31: PetscErrorCode TestMatCombine(FN fn,Mat A,PetscViewer viewer,PetscBool verbose,PetscBool inplace)
     32: {
     33:   PetscBool      set,flg;
     34:   PetscInt       n;
     35:   Mat            F,Acopy;
     36:   Vec            v,f0;
     37:   PetscReal      nrm;

     40:   MatGetSize(A,&n,NULL);
     41:   MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&F);
     42:   PetscObjectSetName((PetscObject)F,"F");
     43:   /* compute matrix function */
     44:   if (inplace) {
     45:     MatCopy(A,F,SAME_NONZERO_PATTERN);
     46:     MatIsHermitianKnown(A,&set,&flg);
     47:     if (set && flg) MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE);
     48:     FNEvaluateFunctionMat(fn,F,NULL);
     49:   } else {
     50:     MatDuplicate(A,MAT_COPY_VALUES,&Acopy);
     51:     FNEvaluateFunctionMat(fn,A,F);
     52:     /* check that A has not been modified */
     53:     MatAXPY(Acopy,-1.0,A,SAME_NONZERO_PATTERN);
     54:     MatNorm(Acopy,NORM_1,&nrm);
     55:     if (nrm>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the input matrix has changed by %g\n",(double)nrm);
     56:     MatDestroy(&Acopy);
     57:   }
     58:   if (verbose) {
     59:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
     60:     MatView(A,viewer);
     61:     PetscPrintf(PETSC_COMM_WORLD,"Computed f(A) - - - - - - -\n");
     62:     MatView(F,viewer);
     63:   }
     64:   /* print matrix norm for checking */
     65:   MatNorm(F,NORM_1,&nrm);
     66:   PetscPrintf(PETSC_COMM_WORLD,"The 1-norm of f(A) is %6.3f\n",(double)nrm);
     67:   /* check FNEvaluateFunctionMatVec() */
     68:   MatCreateVecs(A,&v,&f0);
     69:   MatGetColumnVector(F,f0,0);
     70:   FNEvaluateFunctionMatVec(fn,A,v);
     71:   VecAXPY(v,-1.0,f0);
     72:   VecNorm(v,NORM_2,&nrm);
     73:   if (nrm>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
     74:   MatDestroy(&F);
     75:   VecDestroy(&v);
     76:   VecDestroy(&f0);
     77:   return 0;
     78: }

     80: int main(int argc,char **argv)
     81: {
     82:   FN             f,g,h,e,r,fcopy;
     83:   Mat            A=NULL;
     84:   PetscInt       i,j,n=10,np,nq;
     85:   PetscScalar    x,y,yp,*As,p[10],q[10];
     86:   char           strx[50],str[50];
     87:   PetscViewer    viewer;
     88:   PetscBool      verbose,inplace,matcuda;

     91:   SlepcInitialize(&argc,&argv,(char*)0,help);
     92:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     93:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
     94:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
     95:   PetscOptionsHasName(NULL,NULL,"-matcuda",&matcuda);
     96:   PetscPrintf(PETSC_COMM_WORLD,"Combined function, n=%" PetscInt_FMT ".\n",n);

     98:   /* Create function */

    100:   /* e(x) = exp(x) */
    101:   FNCreate(PETSC_COMM_WORLD,&e);
    102:   FNSetType(e,FNEXP);
    103:   FNSetFromOptions(e);
    104:   /* r(x) = x/(1+x^2) */
    105:   FNCreate(PETSC_COMM_WORLD,&r);
    106:   FNSetType(r,FNRATIONAL);
    107:   FNSetFromOptions(r);
    108:   np = 2; nq = 3;
    109:   p[0] = -1.0; p[1] = 0.0;
    110:   q[0] = 1.0; q[1] = 0.0; q[2] = 1.0;
    111:   FNRationalSetNumerator(r,np,p);
    112:   FNRationalSetDenominator(r,nq,q);
    113:   /* h(x) */
    114:   FNCreate(PETSC_COMM_WORLD,&h);
    115:   FNSetType(h,FNCOMBINE);
    116:   FNSetFromOptions(h);
    117:   FNCombineSetChildren(h,FN_COMBINE_COMPOSE,r,e);
    118:   /* g(x) = 1-x^2 */
    119:   FNCreate(PETSC_COMM_WORLD,&g);
    120:   FNSetType(g,FNRATIONAL);
    121:   FNSetFromOptions(g);
    122:   np = 3;
    123:   p[0] = -1.0; p[1] = 0.0; p[2] = 1.0;
    124:   FNRationalSetNumerator(g,np,p);
    125:   /* f(x) */
    126:   FNCreate(PETSC_COMM_WORLD,&f);
    127:   FNSetType(f,FNCOMBINE);
    128:   FNSetFromOptions(f);
    129:   FNCombineSetChildren(f,FN_COMBINE_MULTIPLY,g,h);

    131:   /* Set up viewer */
    132:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
    133:   FNView(f,viewer);
    134:   if (verbose) PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);

    136:   /* Scalar evaluation */
    137:   x = 2.2;
    138:   SlepcSNPrintfScalar(strx,sizeof(strx),x,PETSC_FALSE);
    139:   FNEvaluateFunction(f,x,&y);
    140:   FNEvaluateDerivative(f,x,&yp);
    141:   SlepcSNPrintfScalar(str,sizeof(str),y,PETSC_FALSE);
    142:   PetscPrintf(PETSC_COMM_WORLD,"  f(%s)=%s\n",strx,str);
    143:   SlepcSNPrintfScalar(str,sizeof(str),yp,PETSC_FALSE);
    144:   PetscPrintf(PETSC_COMM_WORLD,"  f'(%s)=%s\n",strx,str);

    146:   /* Test duplication */
    147:   FNDuplicate(f,PetscObjectComm((PetscObject)f),&fcopy);

    149:   /* Create matrices */
    150:   if (matcuda) {
    151: #if defined(PETSC_HAVE_CUDA)
    152:     MatCreateSeqDenseCUDA(PETSC_COMM_SELF,n,n,NULL,&A);
    153: #endif
    154:   } else MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
    155:   PetscObjectSetName((PetscObject)A,"A");

    157:   /* Fill A with a symmetric Toeplitz matrix */
    158:   MatDenseGetArray(A,&As);
    159:   for (i=0;i<n;i++) As[i+i*n]=2.0;
    160:   for (j=1;j<3;j++) {
    161:     for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
    162:   }
    163:   MatDenseRestoreArray(A,&As);
    164:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
    165:   TestMatCombine(fcopy,A,viewer,verbose,inplace);

    167:   /* Repeat with same matrix as non-symmetric */
    168:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
    169:   TestMatCombine(fcopy,A,viewer,verbose,inplace);

    171:   MatDestroy(&A);
    172:   FNDestroy(&f);
    173:   FNDestroy(&fcopy);
    174:   FNDestroy(&g);
    175:   FNDestroy(&h);
    176:   FNDestroy(&e);
    177:   FNDestroy(&r);
    178:   SlepcFinalize();
    179:   return 0;
    180: }

    182: /*TEST

    184:    testset:
    185:       output_file: output/test6_1.out
    186:       test:
    187:          suffix: 1
    188:       test:
    189:          suffix: 1_cuda
    190:          args: -matcuda
    191:          requires: cuda
    192:       test:
    193:          suffix: 2
    194:          args: -inplace
    195:       test:
    196:          suffix: 2_cuda
    197:          args: -inplace -matcuda
    198:          requires: cuda

    200: TEST*/