Actual source code: ex9.c

slepc-3.17.2 2022-08-09
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  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[] = "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: */

 35: /*
 36:    Matrix operations
 37: */
 38: PetscErrorCode MatMult_Brussel(Mat,Vec,Vec);
 39: PetscErrorCode MatMultTranspose_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;

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

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

 64:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 65:         Generate the matrix
 66:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 68:   /*
 69:      Create shell matrix context and set default parameters
 70:   */
 71:   PetscNew(&ctx);
 72:   ctx->alpha = 2.0;
 73:   ctx->beta  = 5.45;
 74:   delta1     = 0.008;
 75:   delta2     = 0.004;
 76:   L          = 0.51302;

 78:   /*
 79:      Look the command line for user-provided parameters
 80:   */
 81:   PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL);
 82:   PetscOptionsGetScalar(NULL,NULL,"-alpha",&ctx->alpha,NULL);
 83:   PetscOptionsGetScalar(NULL,NULL,"-beta",&ctx->beta,NULL);
 84:   PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL);
 85:   PetscOptionsGetScalar(NULL,NULL,"-delta2",&delta2,NULL);

 87:   /*
 88:      Create matrix T
 89:   */
 90:   MatCreate(PETSC_COMM_WORLD,&ctx->T);
 91:   MatSetSizes(ctx->T,PETSC_DECIDE,PETSC_DECIDE,N,N);
 92:   MatSetFromOptions(ctx->T);
 93:   MatSetUp(ctx->T);

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

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

118:   /*
119:      Create the shell matrix
120:   */
121:   MatCreateShell(PETSC_COMM_WORLD,2*n,2*n,2*N,2*N,(void*)ctx,&A);
122:   MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_Brussel);
123:   MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMultTranspose_Brussel);
124:   MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)(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: %" PetscInt_FMT "\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) EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
172:   else {
173:     PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
174:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
175:     EPSConvergedReasonView(eps,viewer);
176:     EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer);
177:     PetscViewerPopFormat(viewer);
178:   }
179:   EPSDestroy(&eps);
180:   MatDestroy(&A);
181:   MatDestroy(&ctx->T);
182:   VecDestroy(&ctx->x1);
183:   VecDestroy(&ctx->x2);
184:   VecDestroy(&ctx->y1);
185:   VecDestroy(&ctx->y2);
186:   PetscFree(ctx);
187:   SlepcFinalize();
188:   return 0;
189: }

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

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

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

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

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

227: PetscErrorCode MatMultTranspose_Brussel(Mat A,Vec x,Vec y)
228: {
229:   PetscInt          n;
230:   const PetscScalar *px;
231:   PetscScalar       *py;
232:   CTX_BRUSSEL       *ctx;

235:   MatShellGetContext(A,&ctx);
236:   MatGetLocalSize(ctx->T,&n,NULL);
237:   VecGetArrayRead(x,&px);
238:   VecGetArray(y,&py);
239:   VecPlaceArray(ctx->x1,px);
240:   VecPlaceArray(ctx->x2,px+n);
241:   VecPlaceArray(ctx->y1,py);
242:   VecPlaceArray(ctx->y2,py+n);

244:   MatMultTranspose(ctx->T,ctx->x1,ctx->y1);
245:   VecScale(ctx->y1,ctx->tau1);
246:   VecAXPY(ctx->y1,ctx->beta-1.0+ctx->sigma,ctx->x1);
247:   VecAXPY(ctx->y1,-ctx->beta,ctx->x2);

249:   MatMultTranspose(ctx->T,ctx->x2,ctx->y2);
250:   VecScale(ctx->y2,ctx->tau2);
251:   VecAXPY(ctx->y2,ctx->alpha*ctx->alpha,ctx->x1);
252:   VecAXPY(ctx->y2,-ctx->alpha*ctx->alpha+ctx->sigma,ctx->x2);

254:   VecRestoreArrayRead(x,&px);
255:   VecRestoreArray(y,&py);
256:   VecResetArray(ctx->x1);
257:   VecResetArray(ctx->x2);
258:   VecResetArray(ctx->y1);
259:   VecResetArray(ctx->y2);
260:   PetscFunctionReturn(0);
261: }

263: PetscErrorCode MatGetDiagonal_Brussel(Mat A,Vec diag)
264: {
265:   Vec            d1,d2;
266:   PetscInt       n;
267:   PetscScalar    *pd;
268:   MPI_Comm       comm;
269:   CTX_BRUSSEL    *ctx;

272:   MatShellGetContext(A,&ctx);
273:   PetscObjectGetComm((PetscObject)A,&comm);
274:   MatGetLocalSize(ctx->T,&n,NULL);
275:   VecGetArray(diag,&pd);
276:   VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd,&d1);
277:   VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd+n,&d2);

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

282:   VecDestroy(&d1);
283:   VecDestroy(&d2);
284:   VecRestoreArray(diag,&pd);
285:   PetscFunctionReturn(0);
286: }

288: /*TEST

290:    test:
291:       suffix: 1
292:       args: -n 50 -eps_nev 4 -eps_two_sided {{0 1}} -eps_type {{krylovschur lapack}} -terse
293:       requires: !single
294:       filter: grep -v method

296:    test:
297:       suffix: 2
298:       args: -eps_nev 8 -eps_max_it 300 -eps_target -28 -rg_type interval -rg_interval_endpoints -40,-20,-.1,.1 -terse
299:       requires: !single

301:    test:
302:       suffix: 3
303:       args: -n 50 -eps_nev 4 -eps_balance twoside -terse
304:       requires: double
305:       filter: grep -v method
306:       output_file: output/ex9_1.out

308:    test:
309:       suffix: 4
310:       args: -eps_smallest_imaginary -eps_ncv 24 -terse
311:       requires: !complex !single

313:    test:
314:       suffix: 4_complex
315:       args: -eps_smallest_imaginary -eps_ncv 24 -terse
316:       requires: complex !single

318:    test:
319:       suffix: 5
320:       args: -eps_nev 4 -eps_target_real -eps_target -3 -terse
321:       requires: !single

323:    test:
324:       suffix: 6
325:       args: -eps_nev 2 -eps_target_imaginary -eps_target 3i -terse
326:       requires: complex !single

328:    test:
329:       suffix: 7
330:       args: -n 40 -eps_nev 1 -eps_type arnoldi -eps_smallest_real -eps_refined -eps_ncv 40 -eps_max_it 300 -terse
331:       requires: double

333:    test:
334:       suffix: 8
335:       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
336:       requires: !single
337:       filter: sed -e "s/[+-]0\.0*i//g"
338:       timeoutfactor: 2

340:    test:
341:       suffix: 9
342:       args: -eps_largest_imaginary -eps_ncv 24 -terse
343:       requires: !single

345: TEST*/