Actual source code: ex30.c

slepc-3.7.0 2016-05-16
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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: }