Date: 2026-01-20T11:35:40+00:00

Actual source code: test37.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[] = "Tests solving an eigenproblem defined with MatNest.\n\n"
     12:   "Based on ex9.\n"
     13:   "The command line options are:\n"
     14:   "  -n <n>, where <n> = block dimension of the 2x2 block matrix.\n"
     15:   "  -L <L>, where <L> = bifurcation parameter.\n"
     16:   "  -alpha <alpha>, -beta <beta>, -delta1 <delta1>,  -delta2 <delta2>,\n"
     17:   "       where <alpha> <beta> <delta1> <delta2> = model parameters.\n\n";

     19: #include <slepceps.h>

     21: /*
     22:    This example computes the eigenvalues with largest real part of the
     23:    following matrix

     25:         A = [ tau1*T+(beta-1)*I     alpha^2*I
     26:                   -beta*I        tau2*T-alpha^2*I ],

     28:    where

     30:         T = tridiag{1,-2,1}
     31:         h = 1/(n+1)
     32:         tau1 = delta1/(h*L)^2
     33:         tau2 = delta2/(h*L)^2
     34:  */

     36: int main(int argc,char **argv)
     37: {
     38:   EPS            eps;
     39:   Mat            A,T1,T2,D1,D2,mats[4];
     40:   PetscScalar    alpha,beta,tau1,tau2,delta1,delta2,L,h;
     41:   PetscInt       N=30,i,Istart,Iend;

     43:   PetscFunctionBeginUser;
     44:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     45:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL));
     46:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nBrusselator wave model, n=%" PetscInt_FMT "\n\n",N));

     48:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     49:         Generate the matrix
     50:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     52:   alpha  = 2.0;
     53:   beta   = 5.45;
     54:   delta1 = 0.008;
     55:   delta2 = 0.004;
     56:   L      = 0.51302;

     58:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL));
     59:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-alpha",&alpha,NULL));
     60:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-beta",&beta,NULL));
     61:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL));
     62:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-delta2",&delta2,NULL));

     64:   h    = 1.0 / (PetscReal)(N+1);
     65:   tau1 = delta1 / ((h*L)*(h*L));
     66:   tau2 = delta2 / ((h*L)*(h*L));

     68:   /* Create matrices T1, T2 */
     69:   PetscCall(MatCreate(PETSC_COMM_WORLD,&T1));
     70:   PetscCall(MatSetSizes(T1,PETSC_DECIDE,PETSC_DECIDE,N,N));
     71:   PetscCall(MatSetFromOptions(T1));
     72:   PetscCall(MatGetOwnershipRange(T1,&Istart,&Iend));
     73:   for (i=Istart;i<Iend;i++) {
     74:     if (i>0) PetscCall(MatSetValue(T1,i,i-1,1.0,INSERT_VALUES));
     75:     if (i<N-1) PetscCall(MatSetValue(T1,i,i+1,1.0,INSERT_VALUES));
     76:     PetscCall(MatSetValue(T1,i,i,-2.0,INSERT_VALUES));
     77:   }
     78:   PetscCall(MatAssemblyBegin(T1,MAT_FINAL_ASSEMBLY));
     79:   PetscCall(MatAssemblyEnd(T1,MAT_FINAL_ASSEMBLY));

     81:   PetscCall(MatDuplicate(T1,MAT_COPY_VALUES,&T2));
     82:   PetscCall(MatScale(T1,tau1));
     83:   PetscCall(MatShift(T1,beta-1.0));
     84:   PetscCall(MatScale(T2,tau2));
     85:   PetscCall(MatShift(T2,-alpha*alpha));

     87:   /* Create matrices D1, D2 */
     88:   PetscCall(MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,N,N,alpha*alpha,&D1));
     89:   PetscCall(MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,N,N,-beta,&D2));

     91:   /* Create the nest matrix */
     92:   mats[0] = T1;
     93:   mats[1] = D1;
     94:   mats[2] = D2;
     95:   mats[3] = T2;
     96:   PetscCall(MatCreateNest(PETSC_COMM_WORLD,2,NULL,2,NULL,mats,&A));

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

    102:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
    103:   PetscCall(EPSSetOperators(eps,A,NULL));
    104:   PetscCall(EPSSetProblemType(eps,EPS_NHEP));
    105:   PetscCall(EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL));
    106:   PetscCall(EPSSetTrueResidual(eps,PETSC_FALSE));
    107:   PetscCall(EPSSetFromOptions(eps));
    108:   PetscCall(EPSSolve(eps));

    110:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    111:                     Display solution and clean up
    112:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    114:   PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
    115:   PetscCall(EPSDestroy(&eps));
    116:   PetscCall(MatDestroy(&A));
    117:   PetscCall(MatDestroy(&T1));
    118:   PetscCall(MatDestroy(&T2));
    119:   PetscCall(MatDestroy(&D1));
    120:   PetscCall(MatDestroy(&D2));
    121:   PetscCall(SlepcFinalize());
    122:   return 0;
    123: }

    125: /*TEST

    127:    test:
    128:       suffix: 1
    129:       args: -eps_nev 4
    130:       requires: !single
    131:       filter: sed -e "s/0.00019-2.13938i, 0.00019+2.13938i/0.00019+2.13938i, 0.00019-2.13938i/" | sed -e "s/-0.67192-2.52712i, -0.67192+2.52712i/-0.67192+2.52712i, -0.67192-2.52712i/"

    133: TEST*/