Date: 2017-05-17T08:25:01+00:00

Actual source code: test6.c
slepc-3.7.4 2017-05-17
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.

      8:    SLEPc is free software: you can redistribute it and/or modify it under  the
      9:    terms of version 3 of the GNU Lesser General Public License as published by
     10:    the Free Software Foundation.

     12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     15:    more details.

     17:    You  should have received a copy of the GNU Lesser General  Public  License
     18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     20: */
     21: /*
     22:    Define the function

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

     26:    with the following tree:

     28:             f(x)                  f(x)              (combined by product)
     29:            /    \                 g(x) = 1-x^2      (polynomial)
     30:         g(x)    h(x)              h(x)              (combined by composition)
     31:                /    \             r(x) = -x/(1+x^2) (rational)
     32:              r(x)   e(x)          e(x) = exp(x)     (exponential)
     33: */

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

     37: #include <slepcfn.h>

     41: /*
     42:    Compute matrix function B = (I-A^2) exp( -(I+A^2)\A )
     43:  */
     44: PetscErrorCode TestMatCombine(FN fn,Mat A,PetscViewer viewer,PetscBool verbose,PetscBool inplace)
     45: {
     47:   PetscBool      set,flg;
     48:   PetscInt       n;
     49:   Mat            F;
     50:   Vec            v,f0;
     51:   PetscReal      nrm;

     54:   MatGetSize(A,&n,NULL);
     55:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&F);
     56:   PetscObjectSetName((PetscObject)F,"F");
     57:   /* compute square root */
     58:   if (inplace) {
     59:     MatCopy(A,F,SAME_NONZERO_PATTERN);
     60:     MatIsHermitianKnown(A,&set,&flg);
     61:     if (set && flg) { MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE); }
     62:     FNEvaluateFunctionMat(fn,F,NULL);
     63:   } else {
     64:     FNEvaluateFunctionMat(fn,A,F);
     65:   }
     66:   if (verbose) {
     67:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
     68:     MatView(A,viewer);
     69:     PetscPrintf(PETSC_COMM_WORLD,"Computed expm(A) - - - - - - -\n");
     70:     MatView(F,viewer);
     71:   }
     72:   /* print matrix norm for checking */
     73:   MatNorm(F,NORM_1,&nrm);
     74:   PetscPrintf(PETSC_COMM_WORLD,"The 1-norm of f(A) is %g\n",(double)nrm);
     75:   /* check FNEvaluateFunctionMatVec() */
     76:   MatCreateVecs(A,&v,&f0);
     77:   MatGetColumnVector(F,f0,0);
     78:   FNEvaluateFunctionMatVec(fn,A,v);
     79:   VecAXPY(v,-1.0,f0);
     80:   VecNorm(v,NORM_2,&nrm);
     81:   if (nrm>100*PETSC_MACHINE_EPSILON) {
     82:     PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
     83:   }
     84:   MatDestroy(&F);
     85:   VecDestroy(&v);
     86:   VecDestroy(&f0);
     87:   return(0);
     88: }

     92: int main(int argc,char **argv)
     93: {
     95:   FN             f,g,h,e,r;
     96:   Mat            A;
     97:   PetscInt       i,j,n=10,np,nq;
     98:   PetscScalar    x,y,yp,*As,p[10],q[10];
     99:   char           strx[50],str[50];
    100:   PetscViewer    viewer;
    101:   PetscBool      verbose,inplace;

    103:   SlepcInitialize(&argc,&argv,(char*)0,help);
    104:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
    105:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
    106:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
    107:   PetscPrintf(PETSC_COMM_WORLD,"Combined function, n=%D.\n",n);

    109:   /* Create function */

    111:   /* e(x) = exp(x) */
    112:   FNCreate(PETSC_COMM_WORLD,&e);
    113:   FNSetType(e,FNEXP);
    114:   /* r(x) = x/(1+x^2) */
    115:   FNCreate(PETSC_COMM_WORLD,&r);
    116:   FNSetType(r,FNRATIONAL);
    117:   np = 2; nq = 3;
    118:   p[0] = -1.0; p[1] = 0.0;
    119:   q[0] = 1.0; q[1] = 0.0; q[2] = 1.0;
    120:   FNRationalSetNumerator(r,np,p);
    121:   FNRationalSetDenominator(r,nq,q);
    122:   /* h(x) */
    123:   FNCreate(PETSC_COMM_WORLD,&h);
    124:   FNSetType(h,FNCOMBINE);
    125:   FNCombineSetChildren(h,FN_COMBINE_COMPOSE,r,e);
    126:   /* g(x) = 1-x^2 */
    127:   FNCreate(PETSC_COMM_WORLD,&g);
    128:   FNSetType(g,FNRATIONAL);
    129:   np = 3;
    130:   p[0] = -1.0; p[1] = 0.0; p[2] = 1.0;
    131:   FNRationalSetNumerator(g,np,p);
    132:   /* f(x) */
    133:   FNCreate(PETSC_COMM_WORLD,&f);
    134:   FNSetType(f,FNCOMBINE);
    135:   FNCombineSetChildren(f,FN_COMBINE_MULTIPLY,g,h);

    137:   /* Set up viewer */
    138:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
    139:   FNView(f,viewer);
    140:   if (verbose) {
    141:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
    142:   }

    144:   /* Scalar evaluation */
    145:   x = 2.2;
    146:   SlepcSNPrintfScalar(strx,50,x,PETSC_FALSE);
    147:   FNEvaluateFunction(f,x,&y);
    148:   FNEvaluateDerivative(f,x,&yp);
    149:   SlepcSNPrintfScalar(str,50,y,PETSC_FALSE);
    150:   PetscPrintf(PETSC_COMM_WORLD,"  f(%s)=%s\n",strx,str);
    151:   SlepcSNPrintfScalar(str,50,yp,PETSC_FALSE);
    152:   PetscPrintf(PETSC_COMM_WORLD,"  f'(%s)=%s\n",strx,str);

    154:   /* Create matrices */
    155:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
    156:   PetscObjectSetName((PetscObject)A,"A");

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

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

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