Date: 2021-02-01T14:41:41+00:00

Actual source code: test11.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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) = (exp(x)-1)/x    (the phi_1 function)

     15:    with the following tree:

     17:             f(x)                  f(x)              (combined by division)
     18:            /    \                 p(x) = x          (polynomial)
     19:         a(x)    p(x)              a(x)              (combined by addition)
     20:        /    \                     e(x) = exp(x)     (exponential)
     21:      e(x)   c(x)                  c(x) = -1         (constant)
     22: */

     24: static char help[] = "Another test of a combined function.\n\n";

     26: #include <slepcfn.h>

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

     41:   MatGetSize(A,&n,NULL);
     42:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&F);
     43:   PetscObjectSetName((PetscObject)F,"F");
     44:   /* compute matrix function */
     45:   if (inplace) {
     46:     MatCopy(A,F,SAME_NONZERO_PATTERN);
     47:     MatIsHermitianKnown(A,&set,&flg);
     48:     if (set && flg) { MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE); }
     49:     FNEvaluateFunctionMat(fn,F,NULL);
     50:   } else {
     51:     FNEvaluateFunctionMat(fn,A,F);
     52:   }
     53:   if (verbose) {
     54:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
     55:     MatView(A,viewer);
     56:     PetscPrintf(PETSC_COMM_WORLD,"Computed f(A) - - - - - - -\n");
     57:     MatView(F,viewer);
     58:   }
     59:   /* print matrix norm for checking */
     60:   MatNorm(F,NORM_1,&nrm);
     61:   PetscPrintf(PETSC_COMM_WORLD,"The 1-norm of f(A) is %6.3f\n",(double)nrm);
     62:   /* check FNEvaluateFunctionMatVec() */
     63:   MatCreateVecs(A,&v,&f0);
     64:   MatGetColumnVector(F,f0,0);
     65:   FNEvaluateFunctionMatVec(fn,A,v);
     66:   VecAXPY(v,-1.0,f0);
     67:   VecNorm(v,NORM_2,&nrm);
     68:   if (nrm>100*PETSC_MACHINE_EPSILON) {
     69:     PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
     70:   }
     71:   MatDestroy(&F);
     72:   VecDestroy(&v);
     73:   VecDestroy(&f0);
     74:   return(0);
     75: }

     77: int main(int argc,char **argv)
     78: {
     80:   FN             f,p,a,e,c,f1,f2;
     81:   FNCombineType  ctype;
     82:   Mat            A;
     83:   PetscInt       i,j,n=10,np;
     84:   PetscScalar    x,y,yp,*As,coeffs[10];
     85:   char           strx[50],str[50];
     86:   PetscViewer    viewer;
     87:   PetscBool      verbose,inplace;

     89:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     90:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     91:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
     92:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
     93:   PetscPrintf(PETSC_COMM_WORLD,"Phi1 via a combined function, n=%D.\n",n);

     95:   /* Create function */

     97:   /* e(x) = exp(x) */
     98:   FNCreate(PETSC_COMM_WORLD,&e);
     99:   PetscObjectSetName((PetscObject)e,"e");
    100:   FNSetType(e,FNEXP);
    101:   FNSetFromOptions(e);
    102:   /* c(x) = -1 */
    103:   FNCreate(PETSC_COMM_WORLD,&c);
    104:   PetscObjectSetName((PetscObject)c,"c");
    105:   FNSetType(c,FNRATIONAL);
    106:   FNSetFromOptions(c);
    107:   np = 1;
    108:   coeffs[0] = -1.0;
    109:   FNRationalSetNumerator(c,np,coeffs);
    110:   /* a(x) */
    111:   FNCreate(PETSC_COMM_WORLD,&a);
    112:   PetscObjectSetName((PetscObject)a,"a");
    113:   FNSetType(a,FNCOMBINE);
    114:   FNSetFromOptions(a);
    115:   FNCombineSetChildren(a,FN_COMBINE_ADD,e,c);
    116:   /* p(x) = x */
    117:   FNCreate(PETSC_COMM_WORLD,&p);
    118:   PetscObjectSetName((PetscObject)p,"p");
    119:   FNSetType(p,FNRATIONAL);
    120:   FNSetFromOptions(p);
    121:   np = 2;
    122:   coeffs[0] = 1.0; coeffs[1] = 0.0;
    123:   FNRationalSetNumerator(p,np,coeffs);
    124:   /* f(x) */
    125:   FNCreate(PETSC_COMM_WORLD,&f);
    126:   PetscObjectSetName((PetscObject)f,"f");
    127:   FNSetType(f,FNCOMBINE);
    128:   FNSetFromOptions(f);
    129:   FNCombineSetChildren(f,FN_COMBINE_DIVIDE,a,p);

    131:   /* Set up viewer */
    132:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
    133:   FNCombineGetChildren(f,&ctype,&f1,&f2);
    134:   PetscPrintf(PETSC_COMM_WORLD,"Two functions combined with division:\n");
    135:   FNView(f1,viewer);
    136:   FNView(f2,viewer);
    137:   if (verbose) {
    138:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
    139:   }

    141:   /* Scalar evaluation */
    142:   x = 2.2;
    143:   SlepcSNPrintfScalar(strx,sizeof(strx),x,PETSC_FALSE);
    144:   FNEvaluateFunction(f,x,&y);
    145:   FNEvaluateDerivative(f,x,&yp);
    146:   SlepcSNPrintfScalar(str,sizeof(str),y,PETSC_FALSE);
    147:   PetscPrintf(PETSC_COMM_WORLD,"  f(%s)=%s\n",strx,str);
    148:   SlepcSNPrintfScalar(str,sizeof(str),yp,PETSC_FALSE);
    149:   PetscPrintf(PETSC_COMM_WORLD,"  f'(%s)=%s\n",strx,str);

    151:   /* Create matrices */
    152:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
    153:   PetscObjectSetName((PetscObject)A,"A");

    155:   /* Fill A with 1-D Laplacian matrix */
    156:   MatDenseGetArray(A,&As);
    157:   for (i=0;i<n;i++) As[i+i*n]=2.0;
    158:   j=1;
    159:   for (i=0;i<n-j;i++) { As[i+(i+j)*n]=-1.0; As[(i+j)+i*n]=-1.0; }
    160:   MatDenseRestoreArray(A,&As);
    161:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
    162:   TestMatCombine(f,A,viewer,verbose,inplace);

    164:   /* Repeat with same matrix as non-symmetric */
    165:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
    166:   TestMatCombine(f,A,viewer,verbose,inplace);

    168:   MatDestroy(&A);
    169:   FNDestroy(&f);
    170:   FNDestroy(&p);
    171:   FNDestroy(&a);
    172:   FNDestroy(&e);
    173:   FNDestroy(&c);
    174:   SlepcFinalize();
    175:   return ierr;
    176: }

    178: /*TEST

    180:    test:
    181:       suffix: 1
    182:       nsize: 1

    184:    test:
    185:       suffix: 2
    186:       nsize: 1
    187:       args: -inplace
    188:       output_file: output/test11_1.out

    190: TEST*/