Date: 2016-03-29T14:58:27+00:00

Actual source code: ex1.c
slepc-3.6.3 2016-03-29
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2015, 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[] = "Standard symmetric eigenproblem corresponding to the Laplacian operator in 1 dimension.\n\n"
     23:   "The command line options are:\n"
     24:   "  -n <n>, where <n> = number of grid subdivisions = matrix dimension.\n\n";

     26: #include <slepceps.h>

     30: int main(int argc,char **argv)
     31: {
     32:   Mat            A;           /* problem matrix */
     33:   EPS            eps;         /* eigenproblem solver context */
     34:   EPSType        type;
     35:   PetscReal      error,tol,re,im;
     36:   PetscScalar    kr,ki;
     37:   Vec            xr,xi;
     38:   PetscInt       n=30,i,Istart,Iend,nev,maxit,its,nconv;

     41:   SlepcInitialize(&argc,&argv,(char*)0,help);

     43:   PetscOptionsGetInt(NULL,"-n",&n,NULL);
     44:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Laplacian Eigenproblem, n=%D\n\n",n);

     46:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     47:      Compute the operator matrix that defines the eigensystem, Ax=kx
     48:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     50:   MatCreate(PETSC_COMM_WORLD,&A);
     51:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
     52:   MatSetFromOptions(A);
     53:   MatSetUp(A);

     55:   MatGetOwnershipRange(A,&Istart,&Iend);
     56:   for (i=Istart;i<Iend;i++) {
     57:     if (i>0) { MatSetValue(A,i,i-1,-1.0,INSERT_VALUES); }
     58:     if (i<n-1) { MatSetValue(A,i,i+1,-1.0,INSERT_VALUES); }
     59:     MatSetValue(A,i,i,2.0,INSERT_VALUES);
     60:   }
     61:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     62:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     64:   MatCreateVecs(A,NULL,&xr);
     65:   MatCreateVecs(A,NULL,&xi);

     67:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     68:                 Create the eigensolver and set various options
     69:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     70:   /*
     71:      Create eigensolver context
     72:   */
     73:   EPSCreate(PETSC_COMM_WORLD,&eps);

     75:   /*
     76:      Set operators. In this case, it is a standard eigenvalue problem
     77:   */
     78:   EPSSetOperators(eps,A,NULL);
     79:   EPSSetProblemType(eps,EPS_HEP);

     81:   /*
     82:      Set solver parameters at runtime
     83:   */
     84:   EPSSetFromOptions(eps);

     86:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     87:                       Solve the eigensystem
     88:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     90:   EPSSolve(eps);
     91:   /*
     92:      Optional: Get some information from the solver and display it
     93:   */
     94:   EPSGetIterationNumber(eps,&its);
     95:   PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %D\n",its);
     96:   EPSGetType(eps,&type);
     97:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
     98:   EPSGetDimensions(eps,&nev,NULL,NULL);
     99:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
    100:   EPSGetTolerances(eps,&tol,&maxit);
    101:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%D\n",(double)tol,maxit);

    103:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    104:                     Display solution and clean up
    105:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    106:   /*
    107:      Get number of converged approximate eigenpairs
    108:   */
    109:   EPSGetConverged(eps,&nconv);
    110:   PetscPrintf(PETSC_COMM_WORLD," Number of converged eigenpairs: %D\n\n",nconv);

    112:   if (nconv>0) {
    113:     /*
    114:        Display eigenvalues and relative errors
    115:     */
    116:     PetscPrintf(PETSC_COMM_WORLD,
    117:          "           k          ||Ax-kx||/||kx||\n"
    118:          "   ----------------- ------------------\n");

    120:     for (i=0;i<nconv;i++) {
    121:       /*
    122:         Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
    123:         ki (imaginary part)
    124:       */
    125:       EPSGetEigenpair(eps,i,&kr,&ki,xr,xi);
    126:       /*
    127:          Compute the relative error associated to each eigenpair
    128:       */
    129:       EPSComputeError(eps,i,EPS_ERROR_RELATIVE,&error);

    131: #if defined(PETSC_USE_COMPLEX)
    132:       re = PetscRealPart(kr);
    133:       im = PetscImaginaryPart(kr);
    134: #else
    135:       re = kr;
    136:       im = ki;
    137: #endif
    138:       if (im!=0.0) {
    139:         PetscPrintf(PETSC_COMM_WORLD," %9f%+9f j %12g\n",(double)re,(double)im,(double)error);
    140:       } else {
    141:         PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12g\n",(double)re,(double)error);
    142:       }
    143:     }
    144:     PetscPrintf(PETSC_COMM_WORLD,"\n");
    145:   }

    147:   /*
    148:      Free work space
    149:   */
    150:   EPSDestroy(&eps);
    151:   MatDestroy(&A);
    152:   VecDestroy(&xr);
    153:   VecDestroy(&xi);
    154:   SlepcFinalize();
    155:   return 0;
    156: }