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*/