Date: 2021-09-20T09:44:06+00:00

Actual source code: test4.c
slepc-3.15.2 2021-09-20
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2021, 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;

     31:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     32:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     33:   PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
     34:   if (!flag) m=n;
     35:   N = n*m;
     36:   PetscPrintf(PETSC_COMM_WORLD,"\nQuadratic Eigenproblem, N=%D (%Dx%D 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:   MatCreate(PETSC_COMM_WORLD,&K);
     44:   MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,N,N);
     45:   MatSetFromOptions(K);
     46:   MatSetUp(K);
     47:   MatGetOwnershipRange(K,&Istart,&Iend);
     48:   for (II=Istart;II<Iend;II++) {
     49:     i = II/n; j = II-i*n;
     50:     if (i>0) { MatSetValue(K,II,II-n,-1.0,INSERT_VALUES); }
     51:     if (i<m-1) { MatSetValue(K,II,II+n,-1.0,INSERT_VALUES); }
     52:     if (j>0) { MatSetValue(K,II,II-1,-1.0,INSERT_VALUES); }
     53:     if (j<n-1) { MatSetValue(K,II,II+1,-1.0,INSERT_VALUES); }
     54:     MatSetValue(K,II,II,4.0,INSERT_VALUES);
     55:   }
     56:   MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY);
     57:   MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY);

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

     74:   /* M is a diagonal matrix */
     75:   MatCreate(PETSC_COMM_WORLD,&M);
     76:   MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,N,N);
     77:   MatSetFromOptions(M);
     78:   MatSetUp(M);
     79:   MatGetOwnershipRange(M,&Istart,&Iend);
     80:   for (II=Istart;II<Iend;II++) {
     81:     MatSetValue(M,II,II,(PetscReal)(II+1),INSERT_VALUES);
     82:   }
     83:   MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
     84:   MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);

     86:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     87:              Create a standalone EPS with appropriate settings
     88:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     90:   EPSCreate(PETSC_COMM_WORLD,&eps);
     91:   EPSSetWhichEigenpairs(eps,EPS_TARGET_MAGNITUDE);
     92: #if defined(PETSC_USE_COMPLEX)
     93:   EPSSetTarget(eps,0.01*PETSC_i);
     94: #endif
     95:   EPSGetST(eps,&st);
     96:   STSetType(st,STSINVERT);
     97:   STGetKSP(st,&ksp);
     98:   KSPSetType(ksp,KSPBCGS);
     99:   KSPGetPC(ksp,&pc);
    100:   PCSetType(pc,PCJACOBI);
    101:   EPSSetFromOptions(eps);

    103:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    104:              Create the eigensolver and solve the eigensystem
    105:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    107:   PEPCreate(PETSC_COMM_WORLD,&pep);
    108:   PetscObjectSetName((PetscObject)pep,"PEP_solver");
    109:   A[0] = K; A[1] = C; A[2] = M;
    110:   PEPSetOperators(pep,3,A);
    111:   PEPSetType(pep,PEPLINEAR);
    112:   PEPSetProblemType(pep,PEP_GENERAL);
    113:   PEPLinearSetEPS(pep,eps);
    114:   PEPSetFromOptions(pep);
    115:   PEPSolve(pep);
    116:   PEPLinearGetLinearization(pep,&alpha,&beta);
    117:   PetscPrintf(PETSC_COMM_WORLD," Linearization with alpha=%g, beta=%g",(double)alpha,(double)beta);
    118:   PEPLinearGetExplicitMatrix(pep,&expmat);
    119:   if (expmat) {
    120:     PetscPrintf(PETSC_COMM_WORLD," with explicit matrix");
    121:   }
    122:   PetscPrintf(PETSC_COMM_WORLD,"\n");

    124:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    125:                     Display solution and clean up
    126:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    128:   PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);
    129:   PEPDestroy(&pep);
    130:   EPSDestroy(&eps);
    131:   MatDestroy(&M);
    132:   MatDestroy(&C);
    133:   MatDestroy(&K);
    134:   SlepcFinalize();
    135:   return ierr;
    136: }

    138: /*TEST

    140:    test:
    141:       suffix: 1
    142:       args: -pep_linear_explicitmatrix -pep_view_vectors ::ascii_info
    143:       requires: !single

    145: TEST*/