Date: 2026-05-01T10:02:37+00:00

Actual source code: ex30.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 the use of a region for filtering; the number of wanted eigenvalues is not known a priori.\n\n"
     12:   "The problem is the Brusselator wave model as in ex9.c.\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 tries to compute all eigenvalues lying outside the real axis.
     23:    This could be achieved by computing LARGEST_IMAGINARY eigenvalues, but
     24:    here we take a different route: define a region of the complex plane where
     25:    eigenvalues must be emphasized (eigenvalues outside the region are filtered
     26:    out). In this case, we select the region as the complement of a thin stripe
     27:    around the real axis.
     28:  */

     30: PetscErrorCode MatMult_Brussel(Mat,Vec,Vec);
     31: PetscErrorCode MyStoppingTest(EPS,PetscInt,PetscInt,PetscInt,PetscInt,EPSConvergedReason*,void*);

     33: typedef struct {
     34:   Mat         T;
     35:   Vec         x1,x2,y1,y2;
     36:   PetscScalar alpha,beta,tau1,tau2,sigma;
     37:   PetscInt    lastnconv;      /* last value of nconv; used in stopping test */
     38:   PetscInt    nreps;          /* number of repetitions of nconv; used in stopping test */
     39: } CTX_BRUSSEL;

     41: int main(int argc,char **argv)
     42: {
     43:   Mat            A;               /* eigenvalue problem matrix */
     44:   EPS            eps;             /* eigenproblem solver context */
     45:   RG             rg;              /* region object */
     46:   PetscScalar    delta1,delta2,L,h;
     47:   PetscInt       N=30,n,i,Istart,Iend,mpd;
     48:   CTX_BRUSSEL    *ctx;
     49:   PetscBool      terse;
     50:   PetscViewer    viewer;

     52:   PetscFunctionBeginUser;
     53:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     55:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL));
     56:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nBrusselator wave model, n=%" PetscInt_FMT "\n\n",N));

     58:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     59:         Generate the matrix
     60:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     62:   /*
     63:      Create shell matrix context and set default parameters
     64:   */
     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:   /*
     73:      Look the command line for user-provided parameters
     74:   */
     75:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL));
     76:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-alpha",&ctx->alpha,NULL));
     77:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-beta",&ctx->beta,NULL));
     78:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL));
     79:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-delta2",&delta2,NULL));

     81:   /*
     82:      Create matrix T
     83:   */
     84:   PetscCall(MatCreate(PETSC_COMM_WORLD,&ctx->T));
     85:   PetscCall(MatSetSizes(ctx->T,PETSC_DECIDE,PETSC_DECIDE,N,N));
     86:   PetscCall(MatSetFromOptions(ctx->T));

     88:   PetscCall(MatGetOwnershipRange(ctx->T,&Istart,&Iend));
     89:   for (i=Istart;i<Iend;i++) {
     90:     if (i>0) PetscCall(MatSetValue(ctx->T,i,i-1,1.0,INSERT_VALUES));
     91:     if (i<N-1) PetscCall(MatSetValue(ctx->T,i,i+1,1.0,INSERT_VALUES));
     92:     PetscCall(MatSetValue(ctx->T,i,i,-2.0,INSERT_VALUES));
     93:   }
     94:   PetscCall(MatAssemblyBegin(ctx->T,MAT_FINAL_ASSEMBLY));
     95:   PetscCall(MatAssemblyEnd(ctx->T,MAT_FINAL_ASSEMBLY));
     96:   PetscCall(MatGetLocalSize(ctx->T,&n,NULL));

     98:   /*
     99:      Fill the remaining information in the shell matrix context
    100:      and create auxiliary vectors
    101:   */
    102:   h = 1.0 / (PetscReal)(N+1);
    103:   ctx->tau1 = delta1 / ((h*L)*(h*L));
    104:   ctx->tau2 = delta2 / ((h*L)*(h*L));
    105:   ctx->sigma = 0.0;
    106:   PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x1));
    107:   PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x2));
    108:   PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y1));
    109:   PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y2));

    111:   /*
    112:      Create the shell matrix
    113:   */
    114:   PetscCall(MatCreateShell(PETSC_COMM_WORLD,2*n,2*n,2*N,2*N,(void*)ctx,&A));
    115:   PetscCall(MatShellSetOperation(A,MATOP_MULT,(PetscErrorCodeFn*)MatMult_Brussel));

    117:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    118:                 Create the eigensolver and configure the region
    119:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    121:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
    122:   PetscCall(EPSSetOperators(eps,A,NULL));
    123:   PetscCall(EPSSetProblemType(eps,EPS_NHEP));

    125:   /*
    126:      Define the region containing the eigenvalues of interest
    127:   */
    128:   PetscCall(EPSGetRG(eps,&rg));
    129:   PetscCall(RGSetType(rg,RGINTERVAL));
    130:   PetscCall(RGIntervalSetEndpoints(rg,-PETSC_INFINITY,PETSC_INFINITY,-0.01,0.01));
    131:   PetscCall(RGSetComplement(rg,PETSC_TRUE));
    132:   /* sort eigenvalue approximations wrt a target, otherwise convergence will be erratic */
    133:   PetscCall(EPSSetTarget(eps,0.0));
    134:   PetscCall(EPSSetWhichEigenpairs(eps,EPS_TARGET_MAGNITUDE));

    136:   /*
    137:      Set solver options. In particular, we must allocate sufficient
    138:      storage for all eigenpairs that may converge (ncv). This is
    139:      application-dependent.
    140:   */
    141:   mpd = 40;
    142:   PetscCall(EPSSetDimensions(eps,2*mpd,3*mpd,mpd));
    143:   PetscCall(EPSSetTolerances(eps,1e-7,2000));
    144:   ctx->lastnconv = 0;
    145:   ctx->nreps     = 0;
    146:   PetscCall(EPSSetStoppingTestFunction(eps,MyStoppingTest,(void*)ctx,NULL));
    147:   PetscCall(EPSSetFromOptions(eps));

    149:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    150:                 Solve the eigensystem and display solution
    151:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    153:   PetscCall(EPSSolve(eps));

    155:   /* show detailed info unless -terse option is given by user */
    156:   PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
    157:   PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL));
    158:   PetscCall(EPSConvergedReasonView(eps,viewer));
    159:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    160:   if (!terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer));
    161:   PetscCall(PetscViewerPopFormat(viewer));

    163:   PetscCall(EPSDestroy(&eps));
    164:   PetscCall(MatDestroy(&A));
    165:   PetscCall(MatDestroy(&ctx->T));
    166:   PetscCall(VecDestroy(&ctx->x1));
    167:   PetscCall(VecDestroy(&ctx->x2));
    168:   PetscCall(VecDestroy(&ctx->y1));
    169:   PetscCall(VecDestroy(&ctx->y2));
    170:   PetscCall(PetscFree(ctx));
    171:   PetscCall(SlepcFinalize());
    172:   return 0;
    173: }

    175: PetscErrorCode MatMult_Brussel(Mat A,Vec x,Vec y)
    176: {
    177:   PetscInt          n;
    178:   const PetscScalar *px;
    179:   PetscScalar       *py;
    180:   CTX_BRUSSEL       *ctx;

    182:   PetscFunctionBeginUser;
    183:   PetscCall(MatShellGetContext(A,&ctx));
    184:   PetscCall(MatGetLocalSize(ctx->T,&n,NULL));
    185:   PetscCall(VecGetArrayRead(x,&px));
    186:   PetscCall(VecGetArray(y,&py));
    187:   PetscCall(VecPlaceArray(ctx->x1,px));
    188:   PetscCall(VecPlaceArray(ctx->x2,px+n));
    189:   PetscCall(VecPlaceArray(ctx->y1,py));
    190:   PetscCall(VecPlaceArray(ctx->y2,py+n));

    192:   PetscCall(MatMult(ctx->T,ctx->x1,ctx->y1));
    193:   PetscCall(VecScale(ctx->y1,ctx->tau1));
    194:   PetscCall(VecAXPY(ctx->y1,ctx->beta - 1.0 + ctx->sigma,ctx->x1));
    195:   PetscCall(VecAXPY(ctx->y1,ctx->alpha * ctx->alpha,ctx->x2));

    197:   PetscCall(MatMult(ctx->T,ctx->x2,ctx->y2));
    198:   PetscCall(VecScale(ctx->y2,ctx->tau2));
    199:   PetscCall(VecAXPY(ctx->y2,-ctx->beta,ctx->x1));
    200:   PetscCall(VecAXPY(ctx->y2,-ctx->alpha * ctx->alpha + ctx->sigma,ctx->x2));

    202:   PetscCall(VecRestoreArrayRead(x,&px));
    203:   PetscCall(VecRestoreArray(y,&py));
    204:   PetscCall(VecResetArray(ctx->x1));
    205:   PetscCall(VecResetArray(ctx->x2));
    206:   PetscCall(VecResetArray(ctx->y1));
    207:   PetscCall(VecResetArray(ctx->y2));
    208:   PetscFunctionReturn(PETSC_SUCCESS);
    209: }

    211: /*
    212:     Function for user-defined stopping test.

    214:     Ignores the value of nev. It only takes into account the number of
    215:     eigenpairs that have converged in recent outer iterations (restarts);
    216:     if no new eigenvalues have converged in the last few restarts,
    217:     we stop the iteration, assuming that no more eigenvalues are present
    218:     inside the region.
    219: */
    220: PetscErrorCode MyStoppingTest(EPS eps,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,EPSConvergedReason *reason,void *ptr)
    221: {
    222:   CTX_BRUSSEL    *ctx = (CTX_BRUSSEL*)ptr;

    224:   PetscFunctionBeginUser;
    225:   /* check usual termination conditions, but ignoring the case nconv>=nev */
    226:   PetscCall(EPSStoppingBasic(eps,its,max_it,nconv,PETSC_INT_MAX,reason,NULL));
    227:   if (*reason==EPS_CONVERGED_ITERATING) {
    228:     /* check if nconv is the same as before */
    229:     if (nconv==ctx->lastnconv) ctx->nreps++;
    230:     else {
    231:       ctx->lastnconv = nconv;
    232:       ctx->nreps     = 0;
    233:     }
    234:     /* check if no eigenvalues converged in last 10 restarts */
    235:     if (nconv && ctx->nreps>10) *reason = EPS_CONVERGED_USER;
    236:   }
    237:   PetscFunctionReturn(PETSC_SUCCESS);
    238: }

    240: /*TEST

    242:    test:
    243:       suffix: 1
    244:       args: -n 100 -terse
    245:       requires: !single

    247: TEST*/