Actual source code: ex9.c

slepc-3.10.2 2019-02-11
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2018, 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[] = "Solves a problem associated to the Brusselator wave model in chemical reactions, illustrating the use of shell matrices.\n\n"
 12:   "The command line options are:\n"
 13:   "  -n <n>, where <n> = block dimension of the 2x2 block matrix.\n"
 14:   "  -L <L>, where <L> = bifurcation parameter.\n"
 15:   "  -alpha <alpha>, -beta <beta>, -delta1 <delta1>,  -delta2 <delta2>,\n"
 16:   "       where <alpha> <beta> <delta1> <delta2> = model parameters.\n\n";

 18: #include <slepceps.h>

 20: /*
 21:    This example computes the eigenvalues with largest real part of the
 22:    following matrix

 24:         A = [ tau1*T+(beta-1)*I     alpha^2*I
 25:                   -beta*I        tau2*T-alpha^2*I ],

 27:    where

 29:         T = tridiag{1,-2,1}
 30:         h = 1/(n+1)
 31:         tau1 = delta1/(h*L)^2
 32:         tau2 = delta2/(h*L)^2
 33:  */


 36: /*
 37:    Matrix operations
 38: */
 39: PetscErrorCode MatMult_Brussel(Mat,Vec,Vec);
 40: PetscErrorCode MatGetDiagonal_Brussel(Mat,Vec);

 42: typedef struct {
 43:   Mat         T;
 44:   Vec         x1,x2,y1,y2;
 45:   PetscScalar alpha,beta,tau1,tau2,sigma;
 46: } CTX_BRUSSEL;

 48: int main(int argc,char **argv)
 49: {
 50:   Mat            A;               /* eigenvalue problem matrix */
 51:   EPS            eps;             /* eigenproblem solver context */
 52:   EPSType        type;
 53:   PetscScalar    delta1,delta2,L,h;
 54:   PetscInt       N=30,n,i,Istart,Iend,nev;
 55:   CTX_BRUSSEL    *ctx;
 56:   PetscBool      terse;
 57:   PetscViewer    viewer;

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

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

 65:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 66:         Generate the matrix
 67:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 69:   /*
 70:      Create shell matrix context and set default parameters
 71:   */
 72:   PetscNew(&ctx);
 73:   ctx->alpha = 2.0;
 74:   ctx->beta  = 5.45;
 75:   delta1     = 0.008;
 76:   delta2     = 0.004;
 77:   L          = 0.51302;

 79:   /*
 80:      Look the command line for user-provided parameters
 81:   */
 82:   PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL);
 83:   PetscOptionsGetScalar(NULL,NULL,"-alpha",&ctx->alpha,NULL);
 84:   PetscOptionsGetScalar(NULL,NULL,"-beta",&ctx->beta,NULL);
 85:   PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL);
 86:   PetscOptionsGetScalar(NULL,NULL,"-delta2",&delta2,NULL);

 88:   /*
 89:      Create matrix T
 90:   */
 91:   MatCreate(PETSC_COMM_WORLD,&ctx->T);
 92:   MatSetSizes(ctx->T,PETSC_DECIDE,PETSC_DECIDE,N,N);
 93:   MatSetFromOptions(ctx->T);
 94:   MatSetUp(ctx->T);

 96:   MatGetOwnershipRange(ctx->T,&Istart,&Iend);
 97:   for (i=Istart;i<Iend;i++) {
 98:     if (i>0) { MatSetValue(ctx->T,i,i-1,1.0,INSERT_VALUES); }
 99:     if (i<N-1) { MatSetValue(ctx->T,i,i+1,1.0,INSERT_VALUES); }
100:     MatSetValue(ctx->T,i,i,-2.0,INSERT_VALUES);
101:   }
102:   MatAssemblyBegin(ctx->T,MAT_FINAL_ASSEMBLY);
103:   MatAssemblyEnd(ctx->T,MAT_FINAL_ASSEMBLY);
104:   MatGetLocalSize(ctx->T,&n,NULL);

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

119:   /*
120:      Create the shell matrix
121:   */
122:   MatCreateShell(PETSC_COMM_WORLD,2*n,2*n,2*N,2*N,(void*)ctx,&A);
123:   MatShellSetOperation(A,MATOP_MULT,(void(*)())MatMult_Brussel);
124:   MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)())MatGetDiagonal_Brussel);

126:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
127:                 Create the eigensolver and set various options
128:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

130:   /*
131:      Create eigensolver context
132:   */
133:   EPSCreate(PETSC_COMM_WORLD,&eps);

135:   /*
136:      Set operators. In this case, it is a standard eigenvalue problem
137:   */
138:   EPSSetOperators(eps,A,NULL);
139:   EPSSetProblemType(eps,EPS_NHEP);

141:   /*
142:      Ask for the rightmost eigenvalues
143:   */
144:   EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL);

146:   /*
147:      Set other solver options at runtime
148:   */
149:   EPSSetFromOptions(eps);

151:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
152:                       Solve the eigensystem
153:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

155:   EPSSolve(eps);

157:   /*
158:      Optional: Get some information from the solver and display it
159:   */
160:   EPSGetType(eps,&type);
161:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
162:   EPSGetDimensions(eps,&nev,NULL,NULL);
163:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

165:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
166:                     Display solution and clean up
167:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

169:   /* show detailed info unless -terse option is given by user */
170:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
171:   if (terse) {
172:     EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
173:   } else {
174:     PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
175:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
176:     EPSReasonView(eps,viewer);
177:     EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer);
178:     PetscViewerPopFormat(viewer);
179:   }
180:   EPSDestroy(&eps);
181:   MatDestroy(&A);
182:   MatDestroy(&ctx->T);
183:   VecDestroy(&ctx->x1);
184:   VecDestroy(&ctx->x2);
185:   VecDestroy(&ctx->y1);
186:   VecDestroy(&ctx->y2);
187:   PetscFree(ctx);
188:   SlepcFinalize();
189:   return ierr;
190: }

192: PetscErrorCode MatMult_Brussel(Mat A,Vec x,Vec y)
193: {
194:   PetscInt          n;
195:   const PetscScalar *px;
196:   PetscScalar       *py;
197:   CTX_BRUSSEL       *ctx;
198:   PetscErrorCode    ierr;

201:   MatShellGetContext(A,(void**)&ctx);
202:   MatGetLocalSize(ctx->T,&n,NULL);
203:   VecGetArrayRead(x,&px);
204:   VecGetArray(y,&py);
205:   VecPlaceArray(ctx->x1,px);
206:   VecPlaceArray(ctx->x2,px+n);
207:   VecPlaceArray(ctx->y1,py);
208:   VecPlaceArray(ctx->y2,py+n);

210:   MatMult(ctx->T,ctx->x1,ctx->y1);
211:   VecScale(ctx->y1,ctx->tau1);
212:   VecAXPY(ctx->y1,ctx->beta - 1.0 + ctx->sigma,ctx->x1);
213:   VecAXPY(ctx->y1,ctx->alpha * ctx->alpha,ctx->x2);

215:   MatMult(ctx->T,ctx->x2,ctx->y2);
216:   VecScale(ctx->y2,ctx->tau2);
217:   VecAXPY(ctx->y2,-ctx->beta,ctx->x1);
218:   VecAXPY(ctx->y2,-ctx->alpha * ctx->alpha + ctx->sigma,ctx->x2);

220:   VecRestoreArrayRead(x,&px);
221:   VecRestoreArray(y,&py);
222:   VecResetArray(ctx->x1);
223:   VecResetArray(ctx->x2);
224:   VecResetArray(ctx->y1);
225:   VecResetArray(ctx->y2);
226:   return(0);
227: }

229: PetscErrorCode MatGetDiagonal_Brussel(Mat A,Vec diag)
230: {
231:   Vec            d1,d2;
232:   PetscInt       n;
233:   PetscScalar    *pd;
234:   MPI_Comm       comm;
235:   CTX_BRUSSEL    *ctx;

239:   MatShellGetContext(A,(void**)&ctx);
240:   PetscObjectGetComm((PetscObject)A,&comm);
241:   MatGetLocalSize(ctx->T,&n,NULL);
242:   VecGetArray(diag,&pd);
243:   VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd,&d1);
244:   VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd+n,&d2);

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

249:   VecDestroy(&d1);
250:   VecDestroy(&d2);
251:   VecRestoreArray(diag,&pd);
252:   return(0);
253: }

255: /*TEST

257:    test:
258:       suffix: 1
259:       args: -eps_nev 4 -terse
260:       requires: !complex !single

262:    test:
263:       suffix: 2
264:       args: -eps_nev 8 -eps_max_it 300 -eps_target -28 -rg_type interval -rg_interval_endpoints -40,-20,-.1,.1 -terse
265:       requires: !complex !single

267:    test:
268:       suffix: 3
269:       args: -eps_nev 4 -eps_balance oneside -terse
270:       requires: double !complex !define(PETSC_USE_64BIT_INDICES)
271:       output_file: output/ex9_1.out

273:    test:
274:       suffix: 4
275:       args: -eps_smallest_imaginary -eps_ncv 24 -terse
276:       requires: !complex !single

278:    test:
279:       suffix: 5
280:       args: -eps_nev 4 -eps_target_real -eps_target -3 -terse
281:       requires: !complex !single

283:    test:
284:       suffix: 6
285:       args: -eps_nev 2 -eps_target_imaginary -eps_target 3i -terse
286:       requires: complex !single

288:    test:
289:       suffix: 7
290:       args: -n 40 -eps_nev 1 -eps_type arnoldi -eps_smallest_real -eps_refined -eps_max_it 200 -terse
291:       requires: double !complex !define(PETSC_USE_64BIT_INDICES)

293:    test:
294:       suffix: 8
295:       args: -eps_nev 2 -eps_target -30 -eps_type jd -st_matmode shell -eps_jd_fix 0.0001 -eps_jd_const_correction_tol 0 -terse
296:       requires: !complex !single

298: TEST*/