Date: 2016-09-29T11:12:00+00:00

Actual source code: ex30.c
slepc-3.7.3 2016-09-29
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.

      8:    SLEPc is free software: you can redistribute it and/or modify it under  the
      9:    terms of version 3 of the GNU Lesser General Public License as published by
     10:    the Free Software Foundation.

     12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     15:    more details.

     17:    You  should have received a copy of the GNU Lesser General  Public  License
     18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     20: */

     22: static char help[] = "Illustrates the use of a region for filtering; the number of wanted eigenvalues in not known a priori.\n\n"
     23:   "The problem is the Brusselator wave model as in ex9.c.\n"
     24:   "The command line options are:\n"
     25:   "  -n <n>, where <n> = block dimension of the 2x2 block matrix.\n"
     26:   "  -L <L>, where <L> = bifurcation parameter.\n"
     27:   "  -alpha <alpha>, -beta <beta>, -delta1 <delta1>,  -delta2 <delta2>,\n"
     28:   "       where <alpha> <beta> <delta1> <delta2> = model parameters.\n\n";

     30: #include <slepceps.h>

     32: /*
     33:    This example tries to compute all eigenvalues lying outside the real axis.
     34:    This could be achieved by computing LARGEST_IMAGINARY eigenvalues, but
     35:    here we take a different route: define a region of the complex plane where
     36:    eigenvalues must be emphasized (eigenvalues outside the region are filtered
     37:    out). In this case, we select the region as the complement of a thin stripe
     38:    around the real axis.
     39:  */

     41: PetscErrorCode MatMult_Brussel(Mat,Vec,Vec);
     42: PetscErrorCode MatShift_Brussel(PetscScalar*,Mat);
     43: PetscErrorCode MatGetDiagonal_Brussel(Mat,Vec);
     44: PetscErrorCode MyStoppingTest(EPS,PetscInt,PetscInt,PetscInt,PetscInt,EPSConvergedReason*,void*);

     46: typedef struct {
     47:   Mat         T;
     48:   Vec         x1,x2,y1,y2;
     49:   PetscScalar alpha,beta,tau1,tau2,sigma;
     50:   PetscInt    lastnconv;      /* last value of nconv; used in stopping test */
     51:   PetscInt    nreps;          /* number of repetitions of nconv; used in stopping test */
     52: } CTX_BRUSSEL;

     56: int main(int argc,char **argv)
     57: {
     58:   Mat            A;               /* eigenvalue problem matrix */
     59:   EPS            eps;             /* eigenproblem solver context */
     60:   RG             rg;              /* region object */
     61:   PetscScalar    delta1,delta2,L,h;
     62:   PetscInt       N=30,n,i,Istart,Iend,mpd;
     63:   CTX_BRUSSEL    *ctx;
     64:   PetscBool      terse;
     65:   PetscViewer    viewer;

     68:   SlepcInitialize(&argc,&argv,(char*)0,help);

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

     73:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     74:         Generate the matrix
     75:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     77:   /*
     78:      Create shell matrix context and set default parameters
     79:   */
     80:   PetscNew(&ctx);
     81:   ctx->alpha = 2.0;
     82:   ctx->beta  = 5.45;
     83:   delta1     = 0.008;
     84:   delta2     = 0.004;
     85:   L          = 0.51302;

     87:   /*
     88:      Look the command line for user-provided parameters
     89:   */
     90:   PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL);
     91:   PetscOptionsGetScalar(NULL,NULL,"-alpha",&ctx->alpha,NULL);
     92:   PetscOptionsGetScalar(NULL,NULL,"-beta",&ctx->beta,NULL);
     93:   PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL);
     94:   PetscOptionsGetScalar(NULL,NULL,"-delta2",&delta2,NULL);

     96:   /*
     97:      Create matrix T
     98:   */
     99:   MatCreate(PETSC_COMM_WORLD,&ctx->T);
    100:   MatSetSizes(ctx->T,PETSC_DECIDE,PETSC_DECIDE,N,N);
    101:   MatSetFromOptions(ctx->T);
    102:   MatSetUp(ctx->T);

    104:   MatGetOwnershipRange(ctx->T,&Istart,&Iend);
    105:   for (i=Istart;i<Iend;i++) {
    106:     if (i>0) { MatSetValue(ctx->T,i,i-1,1.0,INSERT_VALUES); }
    107:     if (i<N-1) { MatSetValue(ctx->T,i,i+1,1.0,INSERT_VALUES); }
    108:     MatSetValue(ctx->T,i,i,-2.0,INSERT_VALUES);
    109:   }
    110:   MatAssemblyBegin(ctx->T,MAT_FINAL_ASSEMBLY);
    111:   MatAssemblyEnd(ctx->T,MAT_FINAL_ASSEMBLY);
    112:   MatGetLocalSize(ctx->T,&n,NULL);

    114:   /*
    115:      Fill the remaining information in the shell matrix context
    116:      and create auxiliary vectors
    117:   */
    118:   h = 1.0 / (PetscReal)(N+1);
    119:   ctx->tau1 = delta1 / ((h*L)*(h*L));
    120:   ctx->tau2 = delta2 / ((h*L)*(h*L));
    121:   ctx->sigma = 0.0;
    122:   VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x1);
    123:   VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x2);
    124:   VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y1);
    125:   VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y2);

    127:   /*
    128:      Create the shell matrix
    129:   */
    130:   MatCreateShell(PETSC_COMM_WORLD,2*n,2*n,2*N,2*N,(void*)ctx,&A);
    131:   MatShellSetOperation(A,MATOP_MULT,(void(*)())MatMult_Brussel);
    132:   MatShellSetOperation(A,MATOP_SHIFT,(void(*)())MatShift_Brussel);
    133:   MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)())MatGetDiagonal_Brussel);

    135:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    136:                 Create the eigensolver and configure the region
    137:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    139:   EPSCreate(PETSC_COMM_WORLD,&eps);
    140:   EPSSetOperators(eps,A,NULL);
    141:   EPSSetProblemType(eps,EPS_NHEP);

    143:   /*
    144:      Define the region containing the eigenvalues of interest
    145:   */
    146:   EPSGetRG(eps,&rg);
    147:   RGSetType(rg,RGINTERVAL);
    148:   RGIntervalSetEndpoints(rg,-PETSC_INFINITY,PETSC_INFINITY,-0.01,0.01);
    149:   RGSetComplement(rg,PETSC_TRUE);
    150:   /* sort eigenvalue approximations wrt a target, otherwise convergence will be erratic */
    151:   EPSSetTarget(eps,0.0);
    152:   EPSSetWhichEigenpairs(eps,EPS_TARGET_MAGNITUDE);

    154:   /*
    155:      Set solver options. In particular, we must allocate sufficient
    156:      storage for all eigenpairs that may converge (ncv). This is
    157:      application-dependent.
    158:   */
    159:   mpd = 40;
    160:   EPSSetDimensions(eps,2*mpd,3*mpd,mpd);
    161:   EPSSetTolerances(eps,1e-7,2000);
    162:   ctx->lastnconv = 0;
    163:   ctx->nreps     = 0;
    164:   EPSSetStoppingTestFunction(eps,MyStoppingTest,(void*)ctx,NULL);
    165:   EPSSetFromOptions(eps);

    167:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    168:                 Solve the eigensystem and display solution
    169:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    171:   EPSSolve(eps);

    173:   /* show detailed info unless -terse option is given by user */
    174:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
    175:   PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
    176:   EPSReasonView(eps,viewer);
    177:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    178:   if (!terse) {
    179:     EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer);
    180:   }
    181:   PetscViewerPopFormat(viewer);

    183:   EPSDestroy(&eps);
    184:   MatDestroy(&A);
    185:   MatDestroy(&ctx->T);
    186:   VecDestroy(&ctx->x1);
    187:   VecDestroy(&ctx->x2);
    188:   VecDestroy(&ctx->y1);
    189:   VecDestroy(&ctx->y2);
    190:   PetscFree(ctx);
    191:   SlepcFinalize();
    192:   return ierr;
    193: }

    197: PetscErrorCode MatMult_Brussel(Mat A,Vec x,Vec y)
    198: {
    199:   PetscInt          n;
    200:   const PetscScalar *px;
    201:   PetscScalar       *py;
    202:   CTX_BRUSSEL       *ctx;
    203:   PetscErrorCode    ierr;

    206:   MatShellGetContext(A,(void**)&ctx);
    207:   MatGetLocalSize(ctx->T,&n,NULL);
    208:   VecGetArrayRead(x,&px);
    209:   VecGetArray(y,&py);
    210:   VecPlaceArray(ctx->x1,px);
    211:   VecPlaceArray(ctx->x2,px+n);
    212:   VecPlaceArray(ctx->y1,py);
    213:   VecPlaceArray(ctx->y2,py+n);

    215:   MatMult(ctx->T,ctx->x1,ctx->y1);
    216:   VecScale(ctx->y1,ctx->tau1);
    217:   VecAXPY(ctx->y1,ctx->beta - 1.0 + ctx->sigma,ctx->x1);
    218:   VecAXPY(ctx->y1,ctx->alpha * ctx->alpha,ctx->x2);

    220:   MatMult(ctx->T,ctx->x2,ctx->y2);
    221:   VecScale(ctx->y2,ctx->tau2);
    222:   VecAXPY(ctx->y2,-ctx->beta,ctx->x1);
    223:   VecAXPY(ctx->y2,-ctx->alpha * ctx->alpha + ctx->sigma,ctx->x2);

    225:   VecRestoreArrayRead(x,&px);
    226:   VecRestoreArray(y,&py);
    227:   VecResetArray(ctx->x1);
    228:   VecResetArray(ctx->x2);
    229:   VecResetArray(ctx->y1);
    230:   VecResetArray(ctx->y2);
    231:   return(0);
    232: }

    236: PetscErrorCode MatShift_Brussel(PetscScalar* a,Mat Y)
    237: {
    238:   CTX_BRUSSEL    *ctx;

    242:   MatShellGetContext(Y,(void**)&ctx);
    243:   ctx->sigma += *a;
    244:   return(0);
    245: }

    249: PetscErrorCode MatGetDiagonal_Brussel(Mat A,Vec diag)
    250: {
    251:   Vec            d1,d2;
    252:   PetscInt       n;
    253:   PetscScalar    *pd;
    254:   MPI_Comm       comm;
    255:   CTX_BRUSSEL    *ctx;

    259:   MatShellGetContext(A,(void**)&ctx);
    260:   PetscObjectGetComm((PetscObject)A,&comm);
    261:   MatGetLocalSize(ctx->T,&n,NULL);
    262:   VecGetArray(diag,&pd);
    263:   VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd,&d1);
    264:   VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd+n,&d2);

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

    269:   VecDestroy(&d1);
    270:   VecDestroy(&d2);
    271:   VecRestoreArray(diag,&pd);
    272:   return(0);
    273: }

    277: /*
    278:     Function for user-defined stopping test.

    280:     Ignores the value of nev. It only takes into account the number of
    281:     eigenpairs that have converged in recent outer iterations (restarts);
    282:     if no new eigenvalus have converged in the last few restarts,
    283:     we stop the iteration, assuming that no more eigenvalues are present
    284:     inside the region.
    285: */
    286: PetscErrorCode MyStoppingTest(EPS eps,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,EPSConvergedReason *reason,void *ptr)
    287: {
    289:   CTX_BRUSSEL    *ctx = (CTX_BRUSSEL*)ptr;

    292:   /* check usual termination conditions, but ignoring the case nconv>=nev */
    293:   EPSStoppingBasic(eps,its,max_it,nconv,PETSC_MAX_INT,reason,NULL);
    294:   if (*reason==EPS_CONVERGED_ITERATING) {
    295:     /* check if nconv is the same as before */
    296:     if (nconv==ctx->lastnconv) ctx->nreps++;
    297:     else {
    298:       ctx->lastnconv = nconv;
    299:       ctx->nreps     = 0;
    300:     }
    301:     /* check if no eigenvalues converged in last 10 restarts */
    302:     if (nconv && ctx->nreps>10) *reason = EPS_CONVERGED_USER;
    303:   }
    304:   return(0);
    305: }