Actual source code: cayley.c

  1: /*
  2:       Implements the Cayley spectral transform.

  4:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  5:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  6:    Copyright (c) 2002-2010, Universidad Politecnica de Valencia, Spain

  8:    This file is part of SLEPc.
  9:       
 10:    SLEPc is free software: you can redistribute it and/or modify it under  the
 11:    terms of version 3 of the GNU Lesser General Public License as published by
 12:    the Free Software Foundation.

 14:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY 
 15:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS 
 16:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for 
 17:    more details.

 19:    You  should have received a copy of the GNU Lesser General  Public  License
 20:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 21:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 22: */

 24:  #include private/stimpl.h

 26: typedef struct {
 27:   PetscScalar nu;
 28:   PetscTruth  nu_set;
 29:   Vec         w2;
 30: } ST_CAYLEY;

 34: PetscErrorCode STApply_Cayley(ST st,Vec x,Vec y)
 35: {
 37:   ST_CAYLEY      *ctx = (ST_CAYLEY *) st->data;
 38:   PetscScalar    nu = ctx->nu;
 39: 
 41:   if (st->shift_matrix == ST_MATMODE_INPLACE) { nu = nu + st->sigma; };

 43:   if (st->B) {
 44:     /* generalized eigenproblem: y = (A - sB)^-1 (A + tB)x */
 45:     MatMult(st->A,x,st->w);
 46:     MatMult(st->B,x,ctx->w2);
 47:     VecAXPY(st->w,nu,ctx->w2);
 48:     STAssociatedKSPSolve(st,st->w,y);
 49:   }
 50:   else {
 51:     /* standard eigenproblem: y = (A - sI)^-1 (A + tI)x */
 52:     MatMult(st->A,x,st->w);
 53:     VecAXPY(st->w,nu,x);
 54:     STAssociatedKSPSolve(st,st->w,y);
 55:   }
 56:   return(0);
 57: }

 61: PetscErrorCode STApplyTranspose_Cayley(ST st,Vec x,Vec y)
 62: {
 64:   ST_CAYLEY      *ctx = (ST_CAYLEY *) st->data;
 65:   PetscScalar    nu = ctx->nu;
 66: 
 68:   if (st->shift_matrix == ST_MATMODE_INPLACE) { nu = nu + st->sigma; };

 70:   if (st->B) {
 71:     /* generalized eigenproblem: y = (A + tB)^T (A - sB)^-T x */
 72:     STAssociatedKSPSolveTranspose(st,x,st->w);
 73:     MatMultTranspose(st->A,st->w,y);
 74:     MatMultTranspose(st->B,st->w,ctx->w2);
 75:     VecAXPY(y,nu,ctx->w2);
 76:   }
 77:   else {
 78:     /* standard eigenproblem: y =  (A + tI)^T (A - sI)^-T x */
 79:     STAssociatedKSPSolveTranspose(st,x,st->w);
 80:     MatMultTranspose(st->A,st->w,y);
 81:     VecAXPY(y,nu,st->w);
 82:   }
 83:   return(0);
 84: }

 88: PetscErrorCode STBilinearMatMult_Cayley(Mat B,Vec x,Vec y)
 89: {
 91:   ST             st;
 92:   ST_CAYLEY      *ctx;
 93:   PetscScalar    nu;
 94: 
 96:   MatShellGetContext(B,(void**)&st);
 97:   ctx = (ST_CAYLEY *) st->data;
 98:   nu = ctx->nu;
 99: 
100:   if (st->shift_matrix == ST_MATMODE_INPLACE) { nu = nu + st->sigma; };

102:   if (st->B) {
103:     /* generalized eigenproblem: y = (A + tB)x */
104:     MatMult(st->A,x,y);
105:     MatMult(st->B,x,ctx->w2);
106:     VecAXPY(y,nu,ctx->w2);
107:   }
108:   else {
109:     /* standard eigenproblem: y = (A + tI)x */
110:     MatMult(st->A,x,y);
111:     VecAXPY(y,nu,x);
112:   }
113:   return(0);
114: }

118: PetscErrorCode STGetBilinearForm_Cayley(ST st,Mat *B)
119: {
121:   PetscInt       n,m;

124:   MatGetLocalSize(st->B,&n,&m);
125:   MatCreateShell(((PetscObject)st)->comm,n,m,PETSC_DETERMINE,PETSC_DETERMINE,st,B);
126:   MatShellSetOperation(*B,MATOP_MULT,(void(*)(void))STBilinearMatMult_Cayley);
127:   return(0);
128: }

132: PetscErrorCode STBackTransform_Cayley(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
133: {
134:   ST_CAYLEY   *ctx = (ST_CAYLEY *) st->data;
135:   PetscInt    j;
136: #ifndef PETSC_USE_COMPLEX
137:   PetscScalar t,i,r;
141:   for (j=0;j<n;j++) {
142:     if (eigi[j] == 0.0) eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);
143:     else {
144:       r = eigr[j];
145:       i = eigi[j];
146:       r = st->sigma * (r * r + i * i - r) + ctx->nu * (r - 1);
147:       i = - st->sigma * i - ctx->nu * i;
148:       t = i * i + r * (r - 2.0) + 1.0;
149:       eigr[j] = r / t;
150:       eigi[j] = i / t;
151:     }
152:   }
153: #else
156:   for (j=0;j<n;j++) {
157:     eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);
158:   }
159: #endif
160:   return(0);
161: }

165: PetscErrorCode STPostSolve_Cayley(ST st)
166: {

170:   if (st->shift_matrix == ST_MATMODE_INPLACE) {
171:     if (st->B) {
172:       MatAXPY(st->A,st->sigma,st->B,st->str);
173:     } else {
174:       MatShift(st->A,st->sigma);
175:     }
176:     st->setupcalled = 0;
177:   }
178:   return(0);
179: }

183: PetscErrorCode STSetUp_Cayley(ST st)
184: {
186:   ST_CAYLEY      *ctx = (ST_CAYLEY *) st->data;


190:   if (st->mat) { MatDestroy(st->mat); }

192:   /* if the user did not set the shift, use the target value */
193:   if (!st->sigma_set) st->sigma = st->defsigma;

195:   if (!ctx->nu_set) { ctx->nu = st->sigma; }
196:   if (ctx->nu == 0.0 &&  st->sigma == 0.0) {
197:     SETERRQ(1,"Values of shift and antishift cannot be zero simultaneously");
198:   }

200:   switch (st->shift_matrix) {
201:   case ST_MATMODE_INPLACE:
202:     st->mat = PETSC_NULL;
203:     if (st->sigma != 0.0) {
204:       if (st->B) {
205:         MatAXPY(st->A,-st->sigma,st->B,st->str);
206:       } else {
207:         MatShift(st->A,-st->sigma);
208:       }
209:     }
210:     KSPSetOperators(st->ksp,st->A,st->A,DIFFERENT_NONZERO_PATTERN);
211:     break;
212:   case ST_MATMODE_SHELL:
213:     STMatShellCreate(st,&st->mat);
214:     KSPSetOperators(st->ksp,st->mat,st->mat,DIFFERENT_NONZERO_PATTERN);
215:     break;
216:   default:
217:     MatDuplicate(st->A,MAT_COPY_VALUES,&st->mat);
218:     if (st->sigma != 0.0) {
219:       if (st->B) {
220:         MatAXPY(st->mat,-st->sigma,st->B,st->str);
221:       } else {
222:         MatShift(st->mat,-st->sigma);
223:       }
224:     }
225:     KSPSetOperators(st->ksp,st->mat,st->mat,DIFFERENT_NONZERO_PATTERN);
226:   }
227:   if (st->B) {
228:    if (ctx->w2) { VecDestroy(ctx->w2); }
229:    MatGetVecs(st->B,&ctx->w2,PETSC_NULL);
230:   }
231:   KSPSetUp(st->ksp);
232:   return(0);
233: }

237: PetscErrorCode STSetShift_Cayley(ST st,PetscScalar newshift)
238: {
240:   ST_CAYLEY      *ctx = (ST_CAYLEY *) st->data;
241:   MatStructure   flg;

244:   if (!ctx->nu_set) { ctx->nu = newshift; }
245:   if (ctx->nu == 0.0 &&  newshift == 0.0) {
246:     SETERRQ(1,"Values of shift and antishift cannot be zero simultaneously");
247:   }

249:   /* Nothing to be done if STSetUp has not been called yet */
250:   if (!st->setupcalled) return(0);

252:   /* Check if the new KSP matrix has the same zero structure */
253:   if (st->B && st->str == DIFFERENT_NONZERO_PATTERN && (st->sigma == 0.0 || newshift == 0.0)) {
254:     flg = DIFFERENT_NONZERO_PATTERN;
255:   } else {
256:     flg = SAME_NONZERO_PATTERN;
257:   }

259:   switch (st->shift_matrix) {
260:   case ST_MATMODE_INPLACE:
261:     /* Undo previous operations */
262:     if (st->sigma != 0.0) {
263:       if (st->B) {
264:         MatAXPY(st->A,st->sigma,st->B,st->str);
265:       } else {
266:         MatShift(st->A,st->sigma);
267:       }
268:     }
269:     /* Apply new shift */
270:     if (newshift != 0.0) {
271:       if (st->B) {
272:         MatAXPY(st->A,-newshift,st->B,st->str);
273:       } else {
274:         MatShift(st->A,-newshift);
275:       }
276:     }
277:     KSPSetOperators(st->ksp,st->A,st->A,flg);
278:     break;
279:   case ST_MATMODE_SHELL:
280:     KSPSetOperators(st->ksp,st->mat,st->mat,DIFFERENT_NONZERO_PATTERN);
281:     break;
282:   default:
283:     MatCopy(st->A, st->mat,SUBSET_NONZERO_PATTERN);
284:     if (newshift != 0.0) {
285:       if (st->B) { MatAXPY(st->mat,-newshift,st->B,st->str); }
286:       else { MatShift(st->mat,-newshift); }
287:     }
288:     KSPSetOperators(st->ksp,st->mat,st->mat,flg);
289:   }
290:   st->sigma = newshift;
291:   KSPSetUp(st->ksp);
292:   return(0);
293: }

297: PetscErrorCode STSetFromOptions_Cayley(ST st)
298: {
300:   PetscScalar    nu;
301:   PetscTruth     flg;
302:   ST_CAYLEY      *ctx = (ST_CAYLEY *) st->data;
303:   PC             pc;
304:   const PCType   pctype;
305:   const KSPType  ksptype;


309:   KSPGetPC(st->ksp,&pc);
310:   KSPGetType(st->ksp,&ksptype);
311:   PCGetType(pc,&pctype);
312:   if (!pctype && !ksptype) {
313:     if (st->shift_matrix == ST_MATMODE_SHELL) {
314:       /* in shell mode use GMRES with Jacobi as the default */
315:       KSPSetType(st->ksp,KSPGMRES);
316:       PCSetType(pc,PCJACOBI);
317:     } else {
318:       /* use direct solver as default */
319:       KSPSetType(st->ksp,KSPPREONLY);
320:       PCSetType(pc,PCREDUNDANT);
321:     }
322:   }

324:   PetscOptionsBegin(((PetscObject)st)->comm,((PetscObject)st)->prefix,"ST Cayley Options","ST");
325:   PetscOptionsScalar("-st_cayley_antishift","Value of the antishift","STCayleySetAntishift",ctx->nu,&nu,&flg);
326:   if (flg) {
327:     STCayleySetAntishift(st,nu);
328:   }
329:   PetscOptionsEnd();
330:   return(0);
331: }

336: PetscErrorCode STCayleySetAntishift_Cayley(ST st,PetscScalar newshift)
337: {
338:   ST_CAYLEY *ctx = (ST_CAYLEY *) st->data;

341:   ctx->nu = newshift;
342:   ctx->nu_set = PETSC_TRUE;
343:   return(0);
344: }

349: /*@
350:    STCayleySetAntishift - Sets the value of the anti-shift for the Cayley
351:    spectral transformation.

353:    Collective on ST

355:    Input Parameters:
356: +  st  - the spectral transformation context
357: -  nu  - the anti-shift

359:    Options Database Key:
360: .  -st_cayley_antishift - Sets the value of the anti-shift

362:    Level: intermediate

364:    Note:
365:    In the generalized Cayley transform, the operator can be expressed as
366:    OP = inv(A - sigma B)*(A + nu B). This function sets the value of nu.
367:    Use STSetShift() for setting sigma.

369: .seealso: STSetShift()
370: @*/
371: PetscErrorCode STCayleySetAntishift(ST st,PetscScalar nu)
372: {
373:   PetscErrorCode ierr, (*f)(ST,PetscScalar);

377:   PetscObjectQueryFunction((PetscObject)st,"STCayleySetAntishift_C",(void (**)(void))&f);
378:   if (f) {
379:     (*f)(st,nu);
380:   }
381:   return(0);
382: }

386: PetscErrorCode STView_Cayley(ST st,PetscViewer viewer)
387: {
389:   ST_CAYLEY      *ctx = (ST_CAYLEY *) st->data;

392: #if !defined(PETSC_USE_COMPLEX)
393:   PetscViewerASCIIPrintf(viewer,"  antishift: %g\n",ctx->nu);
394: #else
395:   PetscViewerASCIIPrintf(viewer,"  antishift: %g+%g i\n",PetscRealPart(ctx->nu),PetscImaginaryPart(ctx->nu));
396: #endif
397:   STView_Default(st,viewer);
398:   return(0);
399: }

403: PetscErrorCode STDestroy_Cayley(ST st)
404: {
406:   ST_CAYLEY      *ctx = (ST_CAYLEY *) st->data;

409:   if (ctx->w2) { VecDestroy(ctx->w2); }
410:   PetscFree(ctx);
411:   PetscObjectComposeFunctionDynamic((PetscObject)st,"STCayleySetAntishift_C","",PETSC_NULL);
412:   return(0);
413: }

418: PetscErrorCode STCreate_Cayley(ST st)
419: {
421:   ST_CAYLEY      *ctx;

424:   PetscNew(ST_CAYLEY,&ctx);
425:   PetscLogObjectMemory(st,sizeof(ST_CAYLEY));
426:   st->data                 = (void *) ctx;

428:   st->ops->apply           = STApply_Cayley;
429:   st->ops->getbilinearform = STGetBilinearForm_Cayley;
430:   st->ops->applytrans      = STApplyTranspose_Cayley;
431:   st->ops->postsolve       = STPostSolve_Cayley;
432:   st->ops->backtr          = STBackTransform_Cayley;
433:   st->ops->setfromoptions  = STSetFromOptions_Cayley;
434:   st->ops->setup           = STSetUp_Cayley;
435:   st->ops->setshift        = STSetShift_Cayley;
436:   st->ops->destroy         = STDestroy_Cayley;
437:   st->ops->view            = STView_Cayley;
438: 
439:   st->checknullspace       = STCheckNullSpace_Default;

441:   ctx->nu                  = 0.0;
442:   ctx->nu_set              = PETSC_FALSE;

444:   PetscObjectComposeFunctionDynamic((PetscObject)st,"STCayleySetAntishift_C","STCayleySetAntishift_Cayley",STCayleySetAntishift_Cayley);

446:   return(0);
447: }