Date: 2026-01-20T11:35:37+00:00

Actual source code: test22.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[] = "Illustrates how to obtain invariant subspaces.\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: /* Matrix operations */
     37: PetscErrorCode MatMult_Brussel(Mat,Vec,Vec);

     39: typedef struct {
     40:   Mat         T;
     41:   Vec         x1,x2,y1,y2;
     42:   PetscScalar alpha,beta,tau1,tau2,sigma;
     43: } CTX_BRUSSEL;

     45: int main(int argc,char **argv)
     46: {
     47:   EPS            eps;
     48:   Mat            A;
     49:   Vec            *Q,v;
     50:   PetscScalar    delta1,delta2,L,h,kr,ki;
     51:   PetscReal      errest,tol,re,im,lev;
     52:   PetscInt       N=30,n,i,j,Istart,Iend,nev,nconv;
     53:   CTX_BRUSSEL    *ctx;
     54:   PetscBool      errok,trueres;

     56:   PetscFunctionBeginUser;
     57:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     58:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL));
     59:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nBrusselator wave model, n=%" PetscInt_FMT "\n\n",N));

     61:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     62:         Generate the matrix
     63:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     65:   PetscCall(PetscNew(&ctx));
     66:   ctx->alpha = 2.0;
     67:   ctx->beta  = 5.45;
     68:   delta1     = 0.008;
     69:   delta2     = 0.004;
     70:   L          = 0.51302;

     72:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL));
     73:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-alpha",&ctx->alpha,NULL));
     74:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-beta",&ctx->beta,NULL));
     75:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL));
     76:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-delta2",&delta2,NULL));

     78:   /* Create matrix T */
     79:   PetscCall(MatCreate(PETSC_COMM_WORLD,&ctx->T));
     80:   PetscCall(MatSetSizes(ctx->T,PETSC_DECIDE,PETSC_DECIDE,N,N));
     81:   PetscCall(MatSetFromOptions(ctx->T));
     82:   PetscCall(MatGetOwnershipRange(ctx->T,&Istart,&Iend));
     83:   for (i=Istart;i<Iend;i++) {
     84:     if (i>0) PetscCall(MatSetValue(ctx->T,i,i-1,1.0,INSERT_VALUES));
     85:     if (i<N-1) PetscCall(MatSetValue(ctx->T,i,i+1,1.0,INSERT_VALUES));
     86:     PetscCall(MatSetValue(ctx->T,i,i,-2.0,INSERT_VALUES));
     87:   }
     88:   PetscCall(MatAssemblyBegin(ctx->T,MAT_FINAL_ASSEMBLY));
     89:   PetscCall(MatAssemblyEnd(ctx->T,MAT_FINAL_ASSEMBLY));
     90:   PetscCall(MatGetLocalSize(ctx->T,&n,NULL));

     92:   /* Fill the remaining information in the shell matrix context
     93:      and create auxiliary vectors */
     94:   h = 1.0 / (PetscReal)(N+1);
     95:   ctx->tau1 = delta1 / ((h*L)*(h*L));
     96:   ctx->tau2 = delta2 / ((h*L)*(h*L));
     97:   ctx->sigma = 0.0;
     98:   PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x1));
     99:   PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x2));
    100:   PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y1));
    101:   PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y2));

    103:   /* Create the shell matrix */
    104:   PetscCall(MatCreateShell(PETSC_COMM_WORLD,2*n,2*n,2*N,2*N,(void*)ctx,&A));
    105:   PetscCall(MatShellSetOperation(A,MATOP_MULT,(PetscErrorCodeFn*)MatMult_Brussel));

    107:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    108:                 Create the eigensolver and solve the problem
    109:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    111:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
    112:   PetscCall(EPSSetOperators(eps,A,NULL));
    113:   PetscCall(EPSSetProblemType(eps,EPS_NHEP));
    114:   PetscCall(EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL));
    115:   PetscCall(EPSSetTrueResidual(eps,PETSC_FALSE));
    116:   PetscCall(EPSSetFromOptions(eps));
    117:   PetscCall(EPSSolve(eps));

    119:   PetscCall(EPSGetTrueResidual(eps,&trueres));
    120:   /*if (trueres) PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computing true residuals explicitly\n\n"));*/

    122:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    123:                     Display solution and clean up
    124:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    126:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
    127:   PetscCall(EPSGetTolerances(eps,&tol,NULL));
    128:   PetscCall(EPSGetConverged(eps,&nconv));
    129:   if (nconv<nev) PetscCall(PetscPrintf(PETSC_COMM_WORLD," Problem: less than %" PetscInt_FMT " eigenvalues converged\n\n",nev));
    130:   else {
    131:     /* Check that all converged eigenpairs satisfy the requested tolerance
    132:        (in this example we use the solver's error estimate instead of computing
    133:        the residual norm explicitly) */
    134:     errok = PETSC_TRUE;
    135:     for (i=0;i<nev;i++) {
    136:       PetscCall(EPSGetErrorEstimate(eps,i,&errest));
    137:       PetscCall(EPSGetEigenpair(eps,i,&kr,&ki,NULL,NULL));
    138:       errok = (errok && errest<5.0*SlepcAbsEigenvalue(kr,ki)*tol)? PETSC_TRUE: PETSC_FALSE;
    139:     }
    140:     if (!errok) PetscCall(PetscPrintf(PETSC_COMM_WORLD," Problem: some of the first %" PetscInt_FMT " relative errors are higher than the tolerance\n\n",nev));
    141:     else {
    142:       PetscCall(PetscPrintf(PETSC_COMM_WORLD," All requested eigenvalues computed up to the required tolerance:"));
    143:       for (i=0;i<=(nev-1)/8;i++) {
    144:         PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n     "));
    145:         for (j=0;j<PetscMin(8,nev-8*i);j++) {
    146:           PetscCall(EPSGetEigenpair(eps,8*i+j,&kr,&ki,NULL,NULL));
    147: #if defined(PETSC_USE_COMPLEX)
    148:           re = PetscRealPart(kr);
    149:           im = PetscImaginaryPart(kr);
    150: #else
    151:           re = kr;
    152:           im = ki;
    153: #endif
    154:           if (im!=0.0 && PetscAbs(re)/PetscAbs(im)<PETSC_SMALL) re = 0.0;
    155:           if (re!=0.0 && PetscAbs(im)/PetscAbs(re)<PETSC_SMALL) im = 0.0;
    156:           if (im!=0.0) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%.5f%+.5fi",(double)re,(double)im));
    157:           else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%.5f",(double)re));
    158:           if (8*i+j+1<nev) PetscCall(PetscPrintf(PETSC_COMM_WORLD,", "));
    159:         }
    160:       }
    161:       PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n\n"));
    162:     }
    163:   }

    165:   /* Get an orthogonal basis of the invariant subspace and check it is indeed
    166:      orthogonal (note that eigenvectors are not orthogonal in this case) */
    167:   if (nconv>1) {
    168:     PetscCall(MatCreateVecs(A,&v,NULL));
    169:     PetscCall(VecDuplicateVecs(v,nconv,&Q));
    170:     PetscCall(EPSGetInvariantSubspace(eps,Q));
    171:     PetscCall(VecCheckOrthonormality(Q,nconv,NULL,nconv,NULL,NULL,&lev));
    172:     if (lev<10*tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality below the tolerance\n"));
    173:     else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality: %g\n",(double)lev));
    174:     PetscCall(VecDestroyVecs(nconv,&Q));
    175:     PetscCall(VecDestroy(&v));
    176:   }

    178:   PetscCall(EPSDestroy(&eps));
    179:   PetscCall(MatDestroy(&A));
    180:   PetscCall(MatDestroy(&ctx->T));
    181:   PetscCall(VecDestroy(&ctx->x1));
    182:   PetscCall(VecDestroy(&ctx->x2));
    183:   PetscCall(VecDestroy(&ctx->y1));
    184:   PetscCall(VecDestroy(&ctx->y2));
    185:   PetscCall(PetscFree(ctx));
    186:   PetscCall(SlepcFinalize());
    187:   return 0;
    188: }

    190: PetscErrorCode MatMult_Brussel(Mat A,Vec x,Vec y)
    191: {
    192:   PetscInt          n;
    193:   const PetscScalar *px;
    194:   PetscScalar       *py;
    195:   CTX_BRUSSEL       *ctx;

    197:   PetscFunctionBeginUser;
    198:   PetscCall(MatShellGetContext(A,&ctx));
    199:   PetscCall(MatGetLocalSize(ctx->T,&n,NULL));
    200:   PetscCall(VecGetArrayRead(x,&px));
    201:   PetscCall(VecGetArray(y,&py));
    202:   PetscCall(VecPlaceArray(ctx->x1,px));
    203:   PetscCall(VecPlaceArray(ctx->x2,px+n));
    204:   PetscCall(VecPlaceArray(ctx->y1,py));
    205:   PetscCall(VecPlaceArray(ctx->y2,py+n));

    207:   PetscCall(MatMult(ctx->T,ctx->x1,ctx->y1));
    208:   PetscCall(VecScale(ctx->y1,ctx->tau1));
    209:   PetscCall(VecAXPY(ctx->y1,ctx->beta - 1.0 + ctx->sigma,ctx->x1));
    210:   PetscCall(VecAXPY(ctx->y1,ctx->alpha * ctx->alpha,ctx->x2));

    212:   PetscCall(MatMult(ctx->T,ctx->x2,ctx->y2));
    213:   PetscCall(VecScale(ctx->y2,ctx->tau2));
    214:   PetscCall(VecAXPY(ctx->y2,-ctx->beta,ctx->x1));
    215:   PetscCall(VecAXPY(ctx->y2,-ctx->alpha * ctx->alpha + ctx->sigma,ctx->x2));

    217:   PetscCall(VecRestoreArrayRead(x,&px));
    218:   PetscCall(VecRestoreArray(y,&py));
    219:   PetscCall(VecResetArray(ctx->x1));
    220:   PetscCall(VecResetArray(ctx->x2));
    221:   PetscCall(VecResetArray(ctx->y1));
    222:   PetscCall(VecResetArray(ctx->y2));
    223:   PetscFunctionReturn(PETSC_SUCCESS);
    224: }

    226: /*TEST

    228:    test:
    229:       suffix: 1
    230:       args: -eps_nev 4 -eps_true_residual {{0 1}}
    231:       requires: !single

    233:    test:
    234:       suffix: 2
    235:       args: -eps_nev 4 -eps_true_residual -eps_balance oneside -eps_tol 1e-7
    236:       requires: !single

    238:    test:
    239:       suffix: 3
    240:       args: -n 50 -eps_nev 4 -eps_ncv 16 -eps_type subspace -eps_largest_magnitude -bv_orthog_block {{gs tsqr chol tsqrchol svqb}}
    241:       requires: !single

    243: TEST*/