Date: 2016-03-29T14:58:30+00:00

Actual source code: ex12.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[] = "Compute all eigenvalues in an interval of a symmetric-definite problem.\n\n"
     23:   "The command line options are:\n"
     24:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
     25:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

     27: #include <slepceps.h>

     31: int main(int argc,char **argv)
     32: {
     33:   Mat            A,B;         /* matrices */
     34:   EPS            eps;         /* eigenproblem solver context */
     35:   ST             st;          /* spectral transformation context */
     36:   KSP            ksp;
     37:   PC             pc;
     38:   PetscInt       N,n=35,m,Istart,Iend,II,nev,i,j,k,*inertias;
     39:   PetscBool      flag;
     40:   PetscReal      int0,int1,*shifts;

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

     45:   PetscOptionsGetInt(NULL,"-n",&n,NULL);
     46:   PetscOptionsGetInt(NULL,"-m",&m,&flag);
     47:   if (!flag) m=n;
     48:   N = n*m;
     49:   PetscPrintf(PETSC_COMM_WORLD,"\nSymmetric-definite problem with two intervals, N=%D (%Dx%D grid)\n\n",N,n,m);

     51:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     52:      Compute the matrices that define the eigensystem, Ax=kBx
     53:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     55:   MatCreate(PETSC_COMM_WORLD,&A);
     56:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     57:   MatSetFromOptions(A);
     58:   MatSetUp(A);

     60:   MatCreate(PETSC_COMM_WORLD,&B);
     61:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,N,N);
     62:   MatSetFromOptions(B);
     63:   MatSetUp(B);

     65:   MatGetOwnershipRange(A,&Istart,&Iend);
     66:   for (II=Istart;II<Iend;II++) {
     67:     i = II/n; j = II-i*n;
     68:     if (i>0) { MatSetValue(A,II,II-n,-1.0,INSERT_VALUES); }
     69:     if (i<m-1) { MatSetValue(A,II,II+n,-1.0,INSERT_VALUES); }
     70:     if (j>0) { MatSetValue(A,II,II-1,-1.0,INSERT_VALUES); }
     71:     if (j<n-1) { MatSetValue(A,II,II+1,-1.0,INSERT_VALUES); }
     72:     MatSetValue(A,II,II,4.0,INSERT_VALUES);
     73:     MatSetValue(B,II,II,2.0,INSERT_VALUES);
     74:   }
     75:   if (Istart==0) {
     76:     MatSetValue(B,0,0,6.0,INSERT_VALUES);
     77:     MatSetValue(B,0,1,-1.0,INSERT_VALUES);
     78:     MatSetValue(B,1,0,-1.0,INSERT_VALUES);
     79:     MatSetValue(B,1,1,1.0,INSERT_VALUES);
     80:   }

     82:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     83:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     84:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
     85:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);

     87:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     88:                 Create the eigensolver and set various options
     89:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     91:   EPSCreate(PETSC_COMM_WORLD,&eps);
     92:   EPSSetOperators(eps,A,B);
     93:   EPSSetProblemType(eps,EPS_GHEP);

     95:   /*
     96:      Set first interval and other settings for spectrum slicing
     97:   */
     98:   EPSSetWhichEigenpairs(eps,EPS_ALL);
     99:   EPSSetInterval(eps,1.0,1.3);
    100:   EPSGetST(eps,&st);
    101:   STSetType(st,STSINVERT);
    102:   STGetKSP(st,&ksp);
    103:   KSPGetPC(ksp,&pc);
    104:   KSPSetType(ksp,KSPPREONLY);
    105:   PCSetType(pc,PCCHOLESKY);
    106:   EPSSetFromOptions(eps);

    108:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    109:                  Solve for first interval and display info
    110:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    112:   EPSSolve(eps);
    113:   EPSGetDimensions(eps,&nev,NULL,NULL);
    114:   EPSGetInterval(eps,&int0,&int1);
    115:   PetscPrintf(PETSC_COMM_WORLD," Found %D eigenvalues in interval [%g,%g]\n",nev,(double)int0,(double)int1);
    116:   EPSKrylovSchurGetInertias(eps,&k,&shifts,&inertias);
    117:   PetscPrintf(PETSC_COMM_WORLD," Used %D shifts (inertia):\n",k);
    118:   for (i=0;i<k;i++) {
    119:     PetscPrintf(PETSC_COMM_WORLD," .. %g (%D)\n",(double)shifts[i],inertias[i]);
    120:   }
    121:   PetscFree(shifts);
    122:   PetscFree(inertias);

    124:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    125:                  Solve for second interval and display info
    126:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    127:   EPSSetInterval(eps,1.5,1.6);
    128:   EPSSolve(eps);
    129:   EPSGetDimensions(eps,&nev,NULL,NULL);
    130:   EPSGetInterval(eps,&int0,&int1);
    131:   PetscPrintf(PETSC_COMM_WORLD," Found %D eigenvalues in interval [%g,%g]\n",nev,(double)int0,(double)int1);
    132:   EPSKrylovSchurGetInertias(eps,&k,&shifts,&inertias);
    133:   PetscPrintf(PETSC_COMM_WORLD," Used %D shifts (inertia):\n",k);
    134:   for (i=0;i<k;i++) {
    135:     PetscPrintf(PETSC_COMM_WORLD," .. %g (%D)\n",(double)shifts[i],inertias[i]);
    136:   }
    137:   PetscFree(shifts);
    138:   PetscFree(inertias);

    140:   EPSDestroy(&eps);
    141:   MatDestroy(&A);
    142:   MatDestroy(&B);
    143:   SlepcFinalize();
    144:   return 0;
    145: }