Actual source code: test4.c

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, 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[] = "Solve a quadratic problem with PEPLINEAR with a user-provided EPS.\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
     14:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

     16: #include <slepcpep.h>

     18: int main(int argc,char **argv)
     19: {
     20:   Mat            M,C,K,A[3];
     21:   PEP            pep;
     22:   PetscInt       N,n=10,m,Istart,Iend,II,i,j;
     23:   PetscBool      flag,expmat;
     24:   PetscReal      alpha,beta;
     25:   EPS            eps;
     26:   ST             st;
     27:   KSP            ksp;
     28:   PC             pc;

     30:   PetscFunctionBeginUser;
     31:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     32:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     33:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag));
     34:   if (!flag) m=n;
     35:   N = n*m;
     36:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nQuadratic Eigenproblem, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m));

     38:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     39:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
     40:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     42:   /* K is the 2-D Laplacian */
     43:   PetscCall(MatCreate(PETSC_COMM_WORLD,&K));
     44:   PetscCall(MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,N,N));
     45:   PetscCall(MatSetFromOptions(K));
     46:   PetscCall(MatGetOwnershipRange(K,&Istart,&Iend));
     47:   for (II=Istart;II<Iend;II++) {
     48:     i = II/n; j = II-i*n;
     49:     if (i>0) PetscCall(MatSetValue(K,II,II-n,-1.0,INSERT_VALUES));
     50:     if (i<m-1) PetscCall(MatSetValue(K,II,II+n,-1.0,INSERT_VALUES));
     51:     if (j>0) PetscCall(MatSetValue(K,II,II-1,-1.0,INSERT_VALUES));
     52:     if (j<n-1) PetscCall(MatSetValue(K,II,II+1,-1.0,INSERT_VALUES));
     53:     PetscCall(MatSetValue(K,II,II,4.0,INSERT_VALUES));
     54:   }
     55:   PetscCall(MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY));
     56:   PetscCall(MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY));

     58:   /* C is the 1-D Laplacian on horizontal lines */
     59:   PetscCall(MatCreate(PETSC_COMM_WORLD,&C));
     60:   PetscCall(MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N));
     61:   PetscCall(MatSetFromOptions(C));
     62:   PetscCall(MatGetOwnershipRange(C,&Istart,&Iend));
     63:   for (II=Istart;II<Iend;II++) {
     64:     i = II/n; j = II-i*n;
     65:     if (j>0) PetscCall(MatSetValue(C,II,II-1,-1.0,INSERT_VALUES));
     66:     if (j<n-1) PetscCall(MatSetValue(C,II,II+1,-1.0,INSERT_VALUES));
     67:     PetscCall(MatSetValue(C,II,II,2.0,INSERT_VALUES));
     68:   }
     69:   PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
     70:   PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));

     72:   /* M is a diagonal matrix */
     73:   PetscCall(MatCreate(PETSC_COMM_WORLD,&M));
     74:   PetscCall(MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,N,N));
     75:   PetscCall(MatSetFromOptions(M));
     76:   PetscCall(MatGetOwnershipRange(M,&Istart,&Iend));
     77:   for (II=Istart;II<Iend;II++) PetscCall(MatSetValue(M,II,II,(PetscReal)(II+1),INSERT_VALUES));
     78:   PetscCall(MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY));
     79:   PetscCall(MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY));

     81:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     82:              Create a standalone EPS with appropriate settings
     83:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     85:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
     86:   PetscCall(EPSSetWhichEigenpairs(eps,EPS_TARGET_MAGNITUDE));
     87: #if defined(PETSC_USE_COMPLEX)
     88:   PetscCall(EPSSetTarget(eps,0.01*PETSC_i));
     89: #endif
     90:   PetscCall(EPSGetST(eps,&st));
     91:   PetscCall(STSetType(st,STSINVERT));
     92:   PetscCall(STGetKSP(st,&ksp));
     93:   PetscCall(KSPSetType(ksp,KSPBCGS));
     94:   PetscCall(KSPGetPC(ksp,&pc));
     95:   PetscCall(PCSetType(pc,PCJACOBI));
     96:   PetscCall(EPSSetFromOptions(eps));

     98:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     99:              Create the eigensolver and solve the eigensystem
    100:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    102:   PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
    103:   PetscCall(PetscObjectSetName((PetscObject)pep,"PEP_solver"));
    104:   A[0] = K; A[1] = C; A[2] = M;
    105:   PetscCall(PEPSetOperators(pep,3,A));
    106:   PetscCall(PEPSetType(pep,PEPLINEAR));
    107:   PetscCall(PEPSetProblemType(pep,PEP_GENERAL));
    108:   PetscCall(PEPLinearSetEPS(pep,eps));
    109:   PetscCall(PEPSetFromOptions(pep));
    110:   PetscCall(PEPSolve(pep));
    111:   PetscCall(PEPLinearGetLinearization(pep,&alpha,&beta));
    112:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Linearization with alpha=%g, beta=%g",(double)alpha,(double)beta));
    113:   PetscCall(PEPLinearGetExplicitMatrix(pep,&expmat));
    114:   if (expmat) PetscCall(PetscPrintf(PETSC_COMM_WORLD," with explicit matrix"));
    115:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));

    117:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    118:                     Display solution and clean up
    119:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    121:   PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
    122:   PetscCall(PEPDestroy(&pep));
    123:   PetscCall(EPSDestroy(&eps));
    124:   PetscCall(MatDestroy(&M));
    125:   PetscCall(MatDestroy(&C));
    126:   PetscCall(MatDestroy(&K));
    127:   PetscCall(SlepcFinalize());
    128:   return 0;
    129: }

    131: /*TEST

    133:    testset:
    134:       args: -pep_linear_explicitmatrix -pep_view_vectors ::ascii_info
    135:       test:
    136:          suffix: 1_real
    137:          requires: !single !complex
    138:       test:
    139:          suffix: 1
    140:          requires: !single complex

    142: TEST*/