Actual source code: ex20.c

  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2013, 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[] = "Simple 1-D nonlinear eigenproblem.\n\n"
 23:   "The command line options are:\n"
 24:   "  -n <n>, where <n> = number of grid subdivisions.\n"
 25:   "  -draw_sol, to draw the computed solution.\n\n";

 27: /*
 28:    Solve 1-D PDE
 29:             -u'' = lambda*u
 30:    on [0,1] subject to
 31:             u(0)=0, u'(1)=u(1)*lambda*kappa/(kappa-lambda)
 32: */

 34: #include <slepcnep.h>

 36: /*
 37:    User-defined routines
 38: */
 39: PetscErrorCode FormInitialGuess(Vec);
 40: PetscErrorCode FormFunction(NEP,PetscScalar,Mat*,Mat*,MatStructure*,void*);
 41: PetscErrorCode FormJacobian(NEP,PetscScalar,Mat*,MatStructure*,void*);
 42: PetscErrorCode CheckSolution(PetscScalar,Vec,PetscReal*,void*);
 43: PetscErrorCode FixSign(Vec);

 45: /*
 46:    User-defined application context
 47: */
 48: typedef struct {
 49:   PetscScalar kappa;   /* ratio between stiffness of spring and attached mass */
 50:   PetscReal   h;       /* mesh spacing */
 51: } ApplicationCtx;

 55: int main(int argc,char **argv)
 56: {
 57:   NEP            nep;             /* nonlinear eigensolver context */
 58:   Vec            x;               /* eigenvector */
 59:   PetscScalar    lambda;          /* eigenvalue */
 60:   Mat            F,J;             /* Function and Jacobian matrices */
 61:   ApplicationCtx ctx;             /* user-defined context */
 62:   NEPType        type;
 63:   PetscInt       n=128,nev,i,its,maxit,maxf,nconv;
 64:   PetscReal      re,im,abstol,rtol,stol,norm,error;
 65:   PetscBool      draw_sol;

 68:   SlepcInitialize(&argc,&argv,(char*)0,help);
 69:   PetscOptionsGetInt(NULL,"-n",&n,NULL);
 70:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Nonlinear Eigenproblem, n=%D\n\n",n);
 71:   ctx.h = 1.0/(PetscReal)n;
 72:   ctx.kappa = 1.0;
 73:   PetscOptionsHasName(NULL,"-draw_sol",&draw_sol);

 75:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 76:      Create nonlinear eigensolver context
 77:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 79:   NEPCreate(PETSC_COMM_WORLD,&nep);

 81:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 82:      Create matrix data structure; set Function evaluation routine
 83:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 85:   MatCreate(PETSC_COMM_WORLD,&F);
 86:   MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n);
 87:   MatSetFromOptions(F);
 88:   MatSeqAIJSetPreallocation(F,3,NULL);
 89:   MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
 90:   MatSetUp(F);

 92:   /*
 93:      Set Function matrix data structure and default Function evaluation
 94:      routine
 95:   */
 96:   NEPSetFunction(nep,F,F,FormFunction,&ctx);

 98:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 99:      Create matrix data structure; set Jacobian evaluation routine
100:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

102:   MatCreate(PETSC_COMM_WORLD,&J);
103:   MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n);
104:   MatSetFromOptions(J);
105:   MatSeqAIJSetPreallocation(J,3,NULL);
106:   MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
107:   MatSetUp(J);

109:   /*
110:      Set Jacobian matrix data structure and default Jacobian evaluation
111:      routine
112:   */
113:   NEPSetJacobian(nep,J,FormJacobian,&ctx);

115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116:      Customize nonlinear solver; set runtime options
117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

119:   NEPSetTolerances(nep,0,1e-9,0,0,0);
120:   NEPSetDimensions(nep,1,0,0);
121:   NEPSetLagPreconditioner(nep,0);

123:   /*
124:      Set solver parameters at runtime
125:   */
126:   NEPSetFromOptions(nep);

128:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
129:                       Initialize application
130:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

132:   /*
133:      Evaluate initial guess
134:   */
135:   MatGetVecs(F,&x,NULL);
136:   FormInitialGuess(x);
137:   NEPSetInitialSpace(nep,1,&x);

139:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
140:                       Solve the eigensystem
141:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

143:   NEPSolve(nep);
144:   NEPGetIterationNumber(nep,&its);
145:   PetscPrintf(PETSC_COMM_WORLD," Number of NEP iterations = %D\n\n",its);

147:   /*
148:      Optional: Get some information from the solver and display it
149:   */
150:   NEPGetType(nep,&type);
151:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n",type);
152:   NEPGetDimensions(nep,&nev,NULL,NULL);
153:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
154:   NEPGetTolerances(nep,&abstol,&rtol,&stol,&maxit,&maxf);
155:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: atol=%G, rtol=%G, stol=%G, maxit=%D, maxf=%D\n",abstol,rtol,stol,maxit,maxf);

157:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
158:                     Display solution and clean up
159:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

161:   /*
162:      Get number of converged approximate eigenpairs
163:   */
164:   NEPGetConverged(nep,&nconv);
165:   PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate eigenpairs: %D\n\n",nconv);

167:   if (nconv>0) {
168:     /*
169:        Display eigenvalues and relative errors
170:     */
171:     PetscPrintf(PETSC_COMM_WORLD,
172:          "           k              ||T(k)x||           error\n"
173:          "   ----------------- ------------------ ------------------\n");
174:     for (i=0;i<nconv;i++) {
175:       /*
176:         Get converged eigenpairs (in this example they are always real)
177:       */
178:       NEPGetEigenpair(nep,i,&lambda,x);
179:       FixSign(x);
180:       /*
181:          Compute residual norm and error
182:       */
183:       NEPComputeRelativeError(nep,i,&norm);
184:       CheckSolution(lambda,x,&error,&ctx);

186: #if defined(PETSC_USE_COMPLEX)
187:       re = PetscRealPart(lambda);
188:       im = PetscImaginaryPart(lambda);
189: #else
190:       re = lambda;
191:       im = 0.0;
192: #endif
193:       if (im!=0.0) {
194:         PetscPrintf(PETSC_COMM_WORLD," %9F%+9F j %12G     %12G\n",re,im,norm,error);
195:       } else {
196:         PetscPrintf(PETSC_COMM_WORLD,"   %12F         %12G     %12G\n",re,norm,error);
197:       }
198:       if (draw_sol) {
199:         PetscViewerDrawSetPause(PETSC_VIEWER_DRAW_WORLD,-1);
200:         VecView(x,PETSC_VIEWER_DRAW_WORLD);
201:       }
202:     }
203:     PetscPrintf(PETSC_COMM_WORLD,"\n");
204:   }

206:   NEPDestroy(&nep);
207:   MatDestroy(&F);
208:   MatDestroy(&J);
209:   VecDestroy(&x);
210:   SlepcFinalize();
211:   return 0;
212: }

214: /* ------------------------------------------------------------------- */
217: /*
218:    FormInitialGuess - Computes initial guess.

220:    Input/Output Parameter:
221: .  x - the solution vector
222: */
223: PetscErrorCode FormInitialGuess(Vec x)
224: {

228:   VecSet(x,1.0);
229:   return(0);
230: }

232: /* ------------------------------------------------------------------- */
235: /*
236:    FormFunction - Computes Function matrix  T(lambda)

238:    Input Parameters:
239: .  nep    - the NEP context
240: .  lambda - the scalar argument
241: .  ctx    - optional user-defined context, as set by NEPSetJacobian()

243:    Output Parameters:
244: .  fun - Function matrix
245: .  B   - optionally different preconditioning matrix
246: .  flg - flag indicating matrix structure
247: */
248: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat *fun,Mat *B,MatStructure *flg,void *ctx)
249: {
251:   ApplicationCtx *user = (ApplicationCtx*)ctx;
252:   PetscScalar    A[3],c,d;
253:   PetscReal      h;
254:   PetscInt       i,n,j[3],Istart,Iend;
255:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

258:   /*
259:      Compute Function entries and insert into matrix
260:   */
261:   MatGetSize(*fun,&n,NULL);
262:   MatGetOwnershipRange(*fun,&Istart,&Iend);
263:   if (Istart==0) FirstBlock=PETSC_TRUE;
264:   if (Iend==n) LastBlock=PETSC_TRUE;
265:   h = user->h;
266:   c = user->kappa/(lambda-user->kappa);
267:   d = n;

269:   /*
270:      Interior grid points
271:   */
272:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
273:     j[0] = i-1; j[1] = i; j[2] = i+1;
274:     A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
275:     MatSetValues(*fun,1,&i,3,j,A,INSERT_VALUES);
276:   }

278:   /*
279:      Boundary points
280:   */
281:   if (FirstBlock) {
282:     i = 0;
283:     j[0] = 0; j[1] = 1;
284:     A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
285:     MatSetValues(*fun,1,&i,2,j,A,INSERT_VALUES);
286:   }

288:   if (LastBlock) {
289:     i = n-1;
290:     j[0] = n-2; j[1] = n-1;
291:     A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
292:     MatSetValues(*fun,1,&i,2,j,A,INSERT_VALUES);
293:   }

295:   /*
296:      Assemble matrix
297:   */
298:   MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);
299:   MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);
300:   if (*fun != *B) {
301:     MatAssemblyBegin(*fun,MAT_FINAL_ASSEMBLY);
302:     MatAssemblyEnd(*fun,MAT_FINAL_ASSEMBLY);
303:   }
304:   return(0);
305: }

307: /* ------------------------------------------------------------------- */
310: /*
311:    FormJacobian - Computes Jacobian matrix  T'(lambda)

313:    Input Parameters:
314: .  nep    - the NEP context
315: .  lambda - the scalar argument
316: .  ctx    - optional user-defined context, as set by NEPSetJacobian()

318:    Output Parameters:
319: .  jac - Jacobian matrix
320: .  B   - optionally different preconditioning matrix
321: .  flg - flag indicating matrix structure
322: */
323: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat *jac,MatStructure *flg,void *ctx)
324: {
326:   ApplicationCtx *user = (ApplicationCtx*)ctx;
327:   PetscScalar    A[3],c;
328:   PetscReal      h;
329:   PetscInt       i,n,j[3],Istart,Iend;
330:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

333:   /*
334:      Compute Jacobian entries and insert into matrix
335:   */
336:   MatGetSize(*jac,&n,NULL);
337:   MatGetOwnershipRange(*jac,&Istart,&Iend);
338:   if (Istart==0) FirstBlock=PETSC_TRUE;
339:   if (Iend==n) LastBlock=PETSC_TRUE;
340:   h = user->h;
341:   c = user->kappa/(lambda-user->kappa);

343:   /*
344:      Interior grid points
345:   */
346:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
347:     j[0] = i-1; j[1] = i; j[2] = i+1;
348:     A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
349:     MatSetValues(*jac,1,&i,3,j,A,INSERT_VALUES);
350:   }

352:   /*
353:      Boundary points
354:   */
355:   if (FirstBlock) {
356:     i = 0;
357:     j[0] = 0; j[1] = 1;
358:     A[0] = -2.0*h/3.0; A[1] = -h/6.0;
359:     MatSetValues(*jac,1,&i,2,j,A,INSERT_VALUES);
360:   }

362:   if (LastBlock) {
363:     i = n-1;
364:     j[0] = n-2; j[1] = n-1;
365:     A[0] = -h/6.0; A[1] = -h/3.0-c*c;
366:     MatSetValues(*jac,1,&i,2,j,A,INSERT_VALUES);
367:   }

369:   /*
370:      Assemble matrix
371:   */
372:   MatAssemblyBegin(*jac,MAT_FINAL_ASSEMBLY);
373:   MatAssemblyEnd(*jac,MAT_FINAL_ASSEMBLY);
374:   return(0);
375: }

377: /* ------------------------------------------------------------------- */
380: /*
381:    CheckSolution - Given a computed solution (lambda,x) check if it
382:    satisfies the analytic solution.

384:    Input Parameters:
385: +  lambda - the computed eigenvalue
386: -  y      - the computed eigenvector

388:    Output Parameter:
389: .  error - norm of difference between the computed and exact eigenvector
390: */
391: PetscErrorCode CheckSolution(PetscScalar lambda,Vec y,PetscReal *error,void *ctx)
392: {
394:   PetscScalar    nu,*uu;
395:   PetscInt       i,n,Istart,Iend;
396:   PetscReal      x;
397:   Vec            u;
398:   ApplicationCtx *user = (ApplicationCtx*)ctx;

401:   nu = PetscSqrtScalar(lambda);
402:   VecDuplicate(y,&u);
403:   VecGetSize(u,&n);
404:   VecGetOwnershipRange(y,&Istart,&Iend);
405:   VecGetArray(u,&uu);
406:   for (i=Istart;i<Iend;i++) {
407:     x = (i+1)*user->h;
408:     uu[i-Istart] = sin(nu*x);
409:   }
410:   VecRestoreArray(u,&uu);
411:   VecNormalize(u,NULL);
412:   VecAXPY(u,-1.0,y);
413:   VecNorm(u,NORM_2,error);
414:   VecDestroy(&u);
415:   return(0);
416: }

418: /* ------------------------------------------------------------------- */
421: /*
422:    FixSign - Force the eigenfunction to be real and positive, since
423:    some eigensolvers may return the eigenvector multiplied by a
424:    complex number of modulus one.

426:    Input/Output Parameter:
427: .  x - the computed vector
428: */
429: PetscErrorCode FixSign(Vec x)
430: {
432:   PetscMPIInt    rank;
433:   PetscScalar    sign,*xx;

436:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
437:   if (!rank) {
438:     VecGetArray(x,&xx);
439:     sign = *xx/PetscAbsScalar(*xx);
440:     VecRestoreArray(x,&xx);
441:   }
442:   MPI_Bcast(&sign,1,MPIU_SCALAR,0,PETSC_COMM_WORLD);
443:   VecScale(x,1.0/sign);
444:   return(0);
445: }