Date: 2020-01-13T12:00:48+00:00

Actual source code: ex30.c
slepc-3.12.2 2020-01-13
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2019, 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 in 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 MatGetDiagonal_Brussel(Mat,Vec);
     32: PetscErrorCode MyStoppingTest(EPS,PetscInt,PetscInt,PetscInt,PetscInt,EPSConvergedReason*,void*);

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

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

     54:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

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

     59:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     60:         Generate the matrix
     61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     63:   /*
     64:      Create shell matrix context and set default parameters
     65:   */
     66:   PetscNew(&ctx);
     67:   ctx->alpha = 2.0;
     68:   ctx->beta  = 5.45;
     69:   delta1     = 0.008;
     70:   delta2     = 0.004;
     71:   L          = 0.51302;

     73:   /*
     74:      Look the command line for user-provided parameters
     75:   */
     76:   PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL);
     77:   PetscOptionsGetScalar(NULL,NULL,"-alpha",&ctx->alpha,NULL);
     78:   PetscOptionsGetScalar(NULL,NULL,"-beta",&ctx->beta,NULL);
     79:   PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL);
     80:   PetscOptionsGetScalar(NULL,NULL,"-delta2",&delta2,NULL);

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

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

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

    113:   /*
    114:      Create the shell matrix
    115:   */
    116:   MatCreateShell(PETSC_COMM_WORLD,2*n,2*n,2*N,2*N,(void*)ctx,&A);
    117:   MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_Brussel);
    118:   MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Brussel);

    120:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    121:                 Create the eigensolver and configure the region
    122:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    124:   EPSCreate(PETSC_COMM_WORLD,&eps);
    125:   EPSSetOperators(eps,A,NULL);
    126:   EPSSetProblemType(eps,EPS_NHEP);

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

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

    152:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    153:                 Solve the eigensystem and display solution
    154:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    156:   EPSSolve(eps);

    158:   /* show detailed info unless -terse option is given by user */
    159:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
    160:   PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
    161:   EPSReasonView(eps,viewer);
    162:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    163:   if (!terse) {
    164:     EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer);
    165:   }
    166:   PetscViewerPopFormat(viewer);

    168:   EPSDestroy(&eps);
    169:   MatDestroy(&A);
    170:   MatDestroy(&ctx->T);
    171:   VecDestroy(&ctx->x1);
    172:   VecDestroy(&ctx->x2);
    173:   VecDestroy(&ctx->y1);
    174:   VecDestroy(&ctx->y2);
    175:   PetscFree(ctx);
    176:   SlepcFinalize();
    177:   return ierr;
    178: }

    180: PetscErrorCode MatMult_Brussel(Mat A,Vec x,Vec y)
    181: {
    182:   PetscInt          n;
    183:   const PetscScalar *px;
    184:   PetscScalar       *py;
    185:   CTX_BRUSSEL       *ctx;
    186:   PetscErrorCode    ierr;

    189:   MatShellGetContext(A,(void**)&ctx);
    190:   MatGetLocalSize(ctx->T,&n,NULL);
    191:   VecGetArrayRead(x,&px);
    192:   VecGetArray(y,&py);
    193:   VecPlaceArray(ctx->x1,px);
    194:   VecPlaceArray(ctx->x2,px+n);
    195:   VecPlaceArray(ctx->y1,py);
    196:   VecPlaceArray(ctx->y2,py+n);

    198:   MatMult(ctx->T,ctx->x1,ctx->y1);
    199:   VecScale(ctx->y1,ctx->tau1);
    200:   VecAXPY(ctx->y1,ctx->beta - 1.0 + ctx->sigma,ctx->x1);
    201:   VecAXPY(ctx->y1,ctx->alpha * ctx->alpha,ctx->x2);

    203:   MatMult(ctx->T,ctx->x2,ctx->y2);
    204:   VecScale(ctx->y2,ctx->tau2);
    205:   VecAXPY(ctx->y2,-ctx->beta,ctx->x1);
    206:   VecAXPY(ctx->y2,-ctx->alpha * ctx->alpha + ctx->sigma,ctx->x2);

    208:   VecRestoreArrayRead(x,&px);
    209:   VecRestoreArray(y,&py);
    210:   VecResetArray(ctx->x1);
    211:   VecResetArray(ctx->x2);
    212:   VecResetArray(ctx->y1);
    213:   VecResetArray(ctx->y2);
    214:   return(0);
    215: }

    217: PetscErrorCode MatGetDiagonal_Brussel(Mat A,Vec diag)
    218: {
    219:   Vec            d1,d2;
    220:   PetscInt       n;
    221:   PetscScalar    *pd;
    222:   MPI_Comm       comm;
    223:   CTX_BRUSSEL    *ctx;

    227:   MatShellGetContext(A,(void**)&ctx);
    228:   PetscObjectGetComm((PetscObject)A,&comm);
    229:   MatGetLocalSize(ctx->T,&n,NULL);
    230:   VecGetArray(diag,&pd);
    231:   VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd,&d1);
    232:   VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd+n,&d2);

    234:   VecSet(d1,-2.0*ctx->tau1 + ctx->beta - 1.0 + ctx->sigma);
    235:   VecSet(d2,-2.0*ctx->tau2 - ctx->alpha*ctx->alpha + ctx->sigma);

    237:   VecDestroy(&d1);
    238:   VecDestroy(&d2);
    239:   VecRestoreArray(diag,&pd);
    240:   return(0);
    241: }

    243: /*
    244:     Function for user-defined stopping test.

    246:     Ignores the value of nev. It only takes into account the number of
    247:     eigenpairs that have converged in recent outer iterations (restarts);
    248:     if no new eigenvalus have converged in the last few restarts,
    249:     we stop the iteration, assuming that no more eigenvalues are present
    250:     inside the region.
    251: */
    252: PetscErrorCode MyStoppingTest(EPS eps,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,EPSConvergedReason *reason,void *ptr)
    253: {
    255:   CTX_BRUSSEL    *ctx = (CTX_BRUSSEL*)ptr;

    258:   /* check usual termination conditions, but ignoring the case nconv>=nev */
    259:   EPSStoppingBasic(eps,its,max_it,nconv,PETSC_MAX_INT,reason,NULL);
    260:   if (*reason==EPS_CONVERGED_ITERATING) {
    261:     /* check if nconv is the same as before */
    262:     if (nconv==ctx->lastnconv) ctx->nreps++;
    263:     else {
    264:       ctx->lastnconv = nconv;
    265:       ctx->nreps     = 0;
    266:     }
    267:     /* check if no eigenvalues converged in last 10 restarts */
    268:     if (nconv && ctx->nreps>10) *reason = EPS_CONVERGED_USER;
    269:   }
    270:   return(0);
    271: }

    273: /*TEST

    275:    test:
    276:       suffix: 1
    277:       args: -n 100 -terse
    278:       requires: !single

    280: TEST*/