Actual source code: ex13.c
slepc-3.10.1 2018-10-23
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2018, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */

     11: static char help[] = "Generalized Symmetric eigenproblem.\n\n"
     12:   "The problem is Ax = lambda Bx, with:\n"
     13:   "   A = Laplacian operator in 2-D\n"
     14:   "   B = diagonal matrix with all values equal to 4 except nulldim zeros\n\n"
     15:   "The command line options are:\n"
     16:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
     17:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n"
     18:   "  -nulldim <k>, where <k> = dimension of the nullspace of B.\n\n";

     20: #include <slepceps.h>

     22: int main(int argc,char **argv)
     23: {
     24:   Mat            A,B;         /* matrices */
     25:   EPS            eps;         /* eigenproblem solver context */
     26:   ST             st;          /* spectral transformation context */
     27:   EPSType        type;
     28:   PetscInt       N,n=10,m,Istart,Iend,II,nev,i,j,nulldim=0;
     29:   PetscBool      flag,terse;

     32:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

     34:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     35:   PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
     36:   if (!flag) m=n;
     37:   N = n*m;
     38:   PetscOptionsGetInt(NULL,NULL,"-nulldim",&nulldim,NULL);
     39:   PetscPrintf(PETSC_COMM_WORLD,"\nGeneralized Symmetric Eigenproblem, N=%D (%Dx%D grid), null(B)=%D\n\n",N,n,m,nulldim);

     41:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     42:      Compute the matrices that define the eigensystem, Ax=kBx
     43:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     45:   MatCreate(PETSC_COMM_WORLD,&A);
     46:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     47:   MatSetFromOptions(A);
     48:   MatSetUp(A);

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

     55:   MatGetOwnershipRange(A,&Istart,&Iend);
     56:   for (II=Istart;II<Iend;II++) {
     57:     i = II/n; j = II-i*n;
     58:     if (i>0) { MatSetValue(A,II,II-n,-1.0,INSERT_VALUES); }
     59:     if (i<m-1) { MatSetValue(A,II,II+n,-1.0,INSERT_VALUES); }
     60:     if (j>0) { MatSetValue(A,II,II-1,-1.0,INSERT_VALUES); }
     61:     if (j<n-1) { MatSetValue(A,II,II+1,-1.0,INSERT_VALUES); }
     62:     MatSetValue(A,II,II,4.0,INSERT_VALUES);
     63:     if (II>=nulldim) { MatSetValue(B,II,II,4.0,INSERT_VALUES); }
     64:   }

     66:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     67:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     68:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
     69:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);

     71:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     72:                 Create the eigensolver and set various options
     73:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     75:   /*
     76:      Create eigensolver context
     77:   */
     78:   EPSCreate(PETSC_COMM_WORLD,&eps);

     80:   /*
     81:      Set operators. In this case, it is a generalized eigenvalue problem
     82:   */
     83:   EPSSetOperators(eps,A,B);
     84:   EPSSetProblemType(eps,EPS_GHEP);

     86:   /*
     87:      Set solver parameters at runtime
     88:   */
     89:   EPSSetFromOptions(eps);

     91:   PetscObjectTypeCompareAny((PetscObject)eps,&flag,EPSBLOPEX,EPSLOBPCG,EPSRQCG,"");
     92:   if (flag) {
     93:     EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);
     94:   } else {
     95:     /*
     96:        Select portion of spectrum
     97:     */
     98:     EPSSetTarget(eps,0.0);
     99:     EPSSetWhichEigenpairs(eps,EPS_TARGET_MAGNITUDE);
    100:     /*
    101:        Use shift-and-invert to avoid solving linear systems with a singular B
    102:        in case nulldim>0
    103:     */
    104:     PetscObjectTypeCompareAny((PetscObject)eps,&flag,EPSGD,EPSJD,"");
    105:     if (!flag) {
    106:       EPSGetST(eps,&st);
    107:       STSetType(st,STSINVERT);
    108:     }
    109:   }

    111:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    112:                       Solve the eigensystem
    113:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    115:   EPSSolve(eps);

    117:   /*
    118:      Optional: Get some information from the solver and display it
    119:   */
    120:   EPSGetType(eps,&type);
    121:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
    122:   EPSGetDimensions(eps,&nev,NULL,NULL);
    123:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

    125:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    126:                     Display solution and clean up
    127:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    129:   /* show detailed info unless -terse option is given by user */
    130:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    131:   if (terse) {
    132:     EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
    133:   } else {
    134:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    135:     EPSReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
    136:     EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    137:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    138:   }
    139:   EPSDestroy(&eps);
    140:   MatDestroy(&A);
    141:   MatDestroy(&B);
    142:   SlepcFinalize();
    143:   return ierr;
    144: }

    146: /*TEST

    148:    test:
    149:       suffix: 1
    150:       args: -eps_nev 4 -eps_ncv 22 -eps_tol 1e-5 -terse

    152:    test:
    153:       suffix: 2
    154:       args: -n 110 -nulldim 6 -eps_nev 4 -eps_ncv 18 -eps_tol 1e-5 -eps_purify 1 -st_type sinvert -terse
    155:       requires: !single

    157: TEST*/