Date: 2022-08-09T09:05:19+00:00

Actual source code: test6.c
slepc-3.17.2 2022-08-09
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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;
     36:   Vec            v,f0;
     37:   PetscReal      nrm;

     40:   MatGetSize(A,&n,NULL);
     41:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&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 FNEvaluateFunctionMat(fn,A,F);
     50:   if (verbose) {
     51:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
     52:     MatView(A,viewer);
     53:     PetscPrintf(PETSC_COMM_WORLD,"Computed f(A) - - - - - - -\n");
     54:     MatView(F,viewer);
     55:   }
     56:   /* print matrix norm for checking */
     57:   MatNorm(F,NORM_1,&nrm);
     58:   PetscPrintf(PETSC_COMM_WORLD,"The 1-norm of f(A) is %6.3f\n",(double)nrm);
     59:   /* check FNEvaluateFunctionMatVec() */
     60:   MatCreateVecs(A,&v,&f0);
     61:   MatGetColumnVector(F,f0,0);
     62:   FNEvaluateFunctionMatVec(fn,A,v);
     63:   VecAXPY(v,-1.0,f0);
     64:   VecNorm(v,NORM_2,&nrm);
     65:   if (nrm>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
     66:   MatDestroy(&F);
     67:   VecDestroy(&v);
     68:   VecDestroy(&f0);
     69:   PetscFunctionReturn(0);
     70: }

     72: int main(int argc,char **argv)
     73: {
     74:   FN             f,g,h,e,r,fcopy;
     75:   Mat            A;
     76:   PetscInt       i,j,n=10,np,nq;
     77:   PetscScalar    x,y,yp,*As,p[10],q[10];
     78:   char           strx[50],str[50];
     79:   PetscViewer    viewer;
     80:   PetscBool      verbose,inplace;

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

     88:   /* Create function */

     90:   /* e(x) = exp(x) */
     91:   FNCreate(PETSC_COMM_WORLD,&e);
     92:   FNSetType(e,FNEXP);
     93:   FNSetFromOptions(e);
     94:   /* r(x) = x/(1+x^2) */
     95:   FNCreate(PETSC_COMM_WORLD,&r);
     96:   FNSetType(r,FNRATIONAL);
     97:   FNSetFromOptions(r);
     98:   np = 2; nq = 3;
     99:   p[0] = -1.0; p[1] = 0.0;
    100:   q[0] = 1.0; q[1] = 0.0; q[2] = 1.0;
    101:   FNRationalSetNumerator(r,np,p);
    102:   FNRationalSetDenominator(r,nq,q);
    103:   /* h(x) */
    104:   FNCreate(PETSC_COMM_WORLD,&h);
    105:   FNSetType(h,FNCOMBINE);
    106:   FNSetFromOptions(h);
    107:   FNCombineSetChildren(h,FN_COMBINE_COMPOSE,r,e);
    108:   /* g(x) = 1-x^2 */
    109:   FNCreate(PETSC_COMM_WORLD,&g);
    110:   FNSetType(g,FNRATIONAL);
    111:   FNSetFromOptions(g);
    112:   np = 3;
    113:   p[0] = -1.0; p[1] = 0.0; p[2] = 1.0;
    114:   FNRationalSetNumerator(g,np,p);
    115:   /* f(x) */
    116:   FNCreate(PETSC_COMM_WORLD,&f);
    117:   FNSetType(f,FNCOMBINE);
    118:   FNSetFromOptions(f);
    119:   FNCombineSetChildren(f,FN_COMBINE_MULTIPLY,g,h);

    121:   /* Set up viewer */
    122:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
    123:   FNView(f,viewer);
    124:   if (verbose) PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);

    126:   /* Scalar evaluation */
    127:   x = 2.2;
    128:   SlepcSNPrintfScalar(strx,sizeof(strx),x,PETSC_FALSE);
    129:   FNEvaluateFunction(f,x,&y);
    130:   FNEvaluateDerivative(f,x,&yp);
    131:   SlepcSNPrintfScalar(str,sizeof(str),y,PETSC_FALSE);
    132:   PetscPrintf(PETSC_COMM_WORLD,"  f(%s)=%s\n",strx,str);
    133:   SlepcSNPrintfScalar(str,sizeof(str),yp,PETSC_FALSE);
    134:   PetscPrintf(PETSC_COMM_WORLD,"  f'(%s)=%s\n",strx,str);

    136:   /* Test duplication */
    137:   FNDuplicate(f,PetscObjectComm((PetscObject)f),&fcopy);

    139:   /* Create matrices */
    140:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
    141:   PetscObjectSetName((PetscObject)A,"A");

    143:   /* Fill A with a symmetric Toeplitz matrix */
    144:   MatDenseGetArray(A,&As);
    145:   for (i=0;i<n;i++) As[i+i*n]=2.0;
    146:   for (j=1;j<3;j++) {
    147:     for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
    148:   }
    149:   MatDenseRestoreArray(A,&As);
    150:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
    151:   TestMatCombine(fcopy,A,viewer,verbose,inplace);

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

    157:   MatDestroy(&A);
    158:   FNDestroy(&f);
    159:   FNDestroy(&fcopy);
    160:   FNDestroy(&g);
    161:   FNDestroy(&h);
    162:   FNDestroy(&e);
    163:   FNDestroy(&r);
    164:   SlepcFinalize();
    165:   return 0;
    166: }

    168: /*TEST

    170:    test:
    171:       suffix: 1
    172:       nsize: 1

    174:    test:
    175:       suffix: 2
    176:       nsize: 1
    177:       args: -inplace
    178:       output_file: output/test6_1.out

    180: TEST*/