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

Actual source code: test3.c
slepc-3.7.4 2017-05-17
Report Typos and Errors

      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: */

     22: static char help[] = "Test matrix exponential.\n\n";

     24: #include <slepcfn.h>

     28: /*
     29:    Compute matrix exponential B = expm(A)
     30:  */
     31: PetscErrorCode TestMatExp(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 square root */
     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 expm(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 %g\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: }

     79: int main(int argc,char **argv)
     80: {
     82:   FN             fn;
     83:   Mat            A;
     84:   PetscInt       i,j,n=10;
     85:   PetscScalar    *As,tau=1.0,eta=1.0;
     86:   PetscViewer    viewer;
     87:   PetscBool      verbose,inplace;

     89:   SlepcInitialize(&argc,&argv,(char*)0,help);
     90:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     91:   PetscOptionsGetScalar(NULL,NULL,"-tau",&tau,NULL);
     92:   PetscOptionsGetScalar(NULL,NULL,"-eta",&eta,NULL);
     93:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
     94:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
     95:   PetscPrintf(PETSC_COMM_WORLD,"Matrix exponential, n=%D.\n",n);

     97:   /* Create exponential function eta*exp(tau*x) */
     98:   FNCreate(PETSC_COMM_WORLD,&fn);
     99:   FNSetType(fn,FNEXP);
    100:   FNSetScale(fn,tau,eta);

    102:   /* Set up viewer */
    103:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
    104:   FNView(fn,viewer);
    105:   if (verbose) {
    106:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
    107:   }

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

    113:   /* Fill A with a symmetric Toeplitz matrix */
    114:   MatDenseGetArray(A,&As);
    115:   for (i=0;i<n;i++) As[i+i*n]=2.0;
    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:   TestMatExp(fn,A,viewer,verbose,inplace);

    123:   /* Repeat with non-symmetric 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]=-1.0; }
    127:   }
    128:   MatDenseRestoreArray(A,&As);
    129:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
    130:   TestMatExp(fn,A,viewer,verbose,inplace);

    132:   MatDestroy(&A);
    133:   FNDestroy(&fn);
    134:   SlepcFinalize();
    135:   return ierr;
    136: }