Date: 2017-05-17T08:26:22+00:00

Actual source code: ex13.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: */

     22: static char help[] = "Generalized Symmetric eigenproblem.\n\n"
     23:   "The problem is Ax = lambda Bx, with:\n"
     24:   "   A = Laplacian operator in 2-D\n"
     25:   "   B = diagonal matrix with all values equal to 4 except nulldim zeros\n\n"
     26:   "The command line options are:\n"
     27:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
     28:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n"
     29:   "  -nulldim <k>, where <k> = dimension of the nullspace of B.\n\n";

     31: #include <slepceps.h>

     35: int main(int argc,char **argv)
     36: {
     37:   Mat            A,B;         /* matrices */
     38:   EPS            eps;         /* eigenproblem solver context */
     39:   ST             st;          /* spectral transformation context */
     40:   EPSType        type;
     41:   PetscInt       N,n=10,m,Istart,Iend,II,nev,i,j,nulldim=0;
     42:   PetscBool      flag,terse;

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

     47:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     48:   PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
     49:   if (!flag) m=n;
     50:   N = n*m;
     51:   PetscOptionsGetInt(NULL,NULL,"-nulldim",&nulldim,NULL);
     52:   PetscPrintf(PETSC_COMM_WORLD,"\nGeneralized Symmetric Eigenproblem, N=%D (%Dx%D grid), null(B)=%D\n\n",N,n,m,nulldim);

     54:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     55:      Compute the matrices that define the eigensystem, Ax=kBx
     56:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     58:   MatCreate(PETSC_COMM_WORLD,&A);
     59:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     60:   MatSetFromOptions(A);
     61:   MatSetUp(A);

     63:   MatCreate(PETSC_COMM_WORLD,&B);
     64:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,N,N);
     65:   MatSetFromOptions(B);
     66:   MatSetUp(B);

     68:   MatGetOwnershipRange(A,&Istart,&Iend);
     69:   for (II=Istart;II<Iend;II++) {
     70:     i = II/n; j = II-i*n;
     71:     if (i>0) { MatSetValue(A,II,II-n,-1.0,INSERT_VALUES); }
     72:     if (i<m-1) { MatSetValue(A,II,II+n,-1.0,INSERT_VALUES); }
     73:     if (j>0) { MatSetValue(A,II,II-1,-1.0,INSERT_VALUES); }
     74:     if (j<n-1) { MatSetValue(A,II,II+1,-1.0,INSERT_VALUES); }
     75:     MatSetValue(A,II,II,4.0,INSERT_VALUES);
     76:     if (II>=nulldim) { MatSetValue(B,II,II,4.0,INSERT_VALUES); }
     77:   }

     79:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     80:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     81:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
     82:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);

     84:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     85:                 Create the eigensolver and set various options
     86:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     88:   /*
     89:      Create eigensolver context
     90:   */
     91:   EPSCreate(PETSC_COMM_WORLD,&eps);

     93:   /*
     94:      Set operators. In this case, it is a generalized eigenvalue problem
     95:   */
     96:   EPSSetOperators(eps,A,B);
     97:   EPSSetProblemType(eps,EPS_GHEP);

     99:   /*
    100:      Set solver parameters at runtime
    101:   */
    102:   EPSSetFromOptions(eps);

    104:   PetscObjectTypeCompareAny((PetscObject)eps,&flag,EPSBLOPEX,EPSRQCG,"");
    105:   if (flag) {
    106:     EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);
    107:   } else {
    108:     /*
    109:        Select portion of spectrum
    110:     */
    111:     EPSSetTarget(eps,0.0);
    112:     EPSSetWhichEigenpairs(eps,EPS_TARGET_MAGNITUDE);
    113:     /*
    114:        Use shift-and-invert to avoid solving linear systems with a singular B
    115:        in case nulldim>0
    116:     */
    117:     PetscObjectTypeCompareAny((PetscObject)eps,&flag,EPSGD,EPSJD,"");
    118:     if (!flag) {
    119:       EPSGetST(eps,&st);
    120:       STSetType(st,STSINVERT);
    121:     }
    122:   }

    124:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    125:                       Solve the eigensystem
    126:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    128:   EPSSolve(eps);

    130:   /*
    131:      Optional: Get some information from the solver and display it
    132:   */
    133:   EPSGetType(eps,&type);
    134:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
    135:   EPSGetDimensions(eps,&nev,NULL,NULL);
    136:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

    138:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    139:                     Display solution and clean up
    140:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    142:   /* show detailed info unless -terse option is given by user */
    143:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    144:   if (terse) {
    145:     EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
    146:   } else {
    147:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    148:     EPSReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
    149:     EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    150:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    151:   }
    152:   EPSDestroy(&eps);
    153:   MatDestroy(&A);
    154:   MatDestroy(&B);
    155:   SlepcFinalize();
    156:   return ierr;
    157: }