Date: 2013-09-02T10:05:35+00:00

Actual source code: ex1.c

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2013, 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,value[3];
     37:   Vec            xr,xi;
     38:   PetscInt       n=30,i,Istart,Iend,col[3],nev,maxit,its,nconv;
     39:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

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

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

     47:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     48:      Compute the operator matrix that defines the eigensystem, Ax=kx
     49:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     56:   MatGetOwnershipRange(A,&Istart,&Iend);
     57:   if (Istart==0) FirstBlock=PETSC_TRUE;
     58:   if (Iend==n) LastBlock=PETSC_TRUE;
     59:   value[0]=-1.0; value[1]=2.0; value[2]=-1.0;
     60:   for (i=(FirstBlock? Istart+1: Istart); i<(LastBlock? Iend-1: Iend); i++) {
     61:     col[0]=i-1; col[1]=i; col[2]=i+1;
     62:     MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
     63:   }
     64:   if (LastBlock) {
     65:     i=n-1; col[0]=n-2; col[1]=n-1;
     66:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
     67:   }
     68:   if (FirstBlock) {
     69:     i=0; col[0]=0; col[1]=1; value[0]=2.0; value[1]=-1.0;
     70:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
     71:   }

     73:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     74:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     76:   MatGetVecs(A,NULL,&xr);
     77:   MatGetVecs(A,NULL,&xi);

     79:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     80:                 Create the eigensolver and set various options
     81:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     82:   /*
     83:      Create eigensolver context
     84:   */
     85:   EPSCreate(PETSC_COMM_WORLD,&eps);

     87:   /*
     88:      Set operators. In this case, it is a standard eigenvalue problem
     89:   */
     90:   EPSSetOperators(eps,A,NULL);
     91:   EPSSetProblemType(eps,EPS_HEP);

     93:   /*
     94:      Set solver parameters at runtime
     95:   */
     96:   EPSSetFromOptions(eps);

     98:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     99:                       Solve the eigensystem
    100:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    102:   EPSSolve(eps);
    103:   /*
    104:      Optional: Get some information from the solver and display it
    105:   */
    106:   EPSGetIterationNumber(eps,&its);
    107:   PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %D\n",its);
    108:   EPSGetType(eps,&type);
    109:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
    110:   EPSGetDimensions(eps,&nev,NULL,NULL);
    111:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
    112:   EPSGetTolerances(eps,&tol,&maxit);
    113:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4G, maxit=%D\n",tol,maxit);

    115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    116:                     Display solution and clean up
    117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    118:   /*
    119:      Get number of converged approximate eigenpairs
    120:   */
    121:   EPSGetConverged(eps,&nconv);
    122:   PetscPrintf(PETSC_COMM_WORLD," Number of converged eigenpairs: %D\n\n",nconv);

    124:   if (nconv>0) {
    125:     /*
    126:        Display eigenvalues and relative errors
    127:     */
    128:     PetscPrintf(PETSC_COMM_WORLD,
    129:          "           k          ||Ax-kx||/||kx||\n"
    130:          "   ----------------- ------------------\n");

    132:     for (i=0;i<nconv;i++) {
    133:       /*
    134:         Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
    135:         ki (imaginary part)
    136:       */
    137:       EPSGetEigenpair(eps,i,&kr,&ki,xr,xi);
    138:       /*
    139:          Compute the relative error associated to each eigenpair
    140:       */
    141:       EPSComputeRelativeError(eps,i,&error);

    143: #if defined(PETSC_USE_COMPLEX)
    144:       re = PetscRealPart(kr);
    145:       im = PetscImaginaryPart(kr);
    146: #else
    147:       re = kr;
    148:       im = ki;
    149: #endif
    150:       if (im!=0.0) {
    151:         PetscPrintf(PETSC_COMM_WORLD," %9F%+9F j %12G\n",re,im,error);
    152:       } else {
    153:         PetscPrintf(PETSC_COMM_WORLD,"   %12F       %12G\n",re,error);
    154:       }
    155:     }
    156:     PetscPrintf(PETSC_COMM_WORLD,"\n");
    157:   }

    159:   /*
    160:      Free work space
    161:   */
    162:   EPSDestroy(&eps);
    163:   MatDestroy(&A);
    164:   VecDestroy(&xr);
    165:   VecDestroy(&xi);
    166:   SlepcFinalize();
    167:   return 0;
    168: }