Actual source code: cayley.c

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

  4:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  5:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  6:    Copyright (c) 2002-2011, Universitat 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>          /*I "slepcst.h" I*/

 26: typedef struct {
 27:   PetscScalar nu;
 28:   PetscBool   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: #if !defined(PETSC_USE_COMPLEX)
137:   PetscScalar t,i,r;
138: #endif

141: #if !defined(PETSC_USE_COMPLEX)
142:   for (j=0;j<n;j++) {
143:     if (eigi[j] == 0.0) eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);
144:     else {
145:       r = eigr[j];
146:       i = eigi[j];
147:       r = st->sigma * (r * r + i * i - r) + ctx->nu * (r - 1);
148:       i = - st->sigma * i - ctx->nu * i;
149:       t = i * i + r * (r - 2.0) + 1.0;
150:       eigr[j] = r / t;
151:       eigi[j] = i / t;
152:     }
153:   }
154: #else
155:   for (j=0;j<n;j++) {
156:     eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);
157:   }
158: #endif
159:   return(0);
160: }

164: PetscErrorCode STPostSolve_Cayley(ST st)
165: {

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

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

188:   MatDestroy(&st->mat);

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

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

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

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

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

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

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

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

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

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

323:   PetscOptionsHead("ST Cayley Options");
324:   PetscOptionsScalar("-st_cayley_antishift","Value of the antishift","STCayleySetAntishift",ctx->nu,&nu,&flg);
325:   if (flg) {
326:     STCayleySetAntishift(st,nu);
327:   }
328:   PetscOptionsTail();
329:   return(0);
330: }

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

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

348: /*@
349:    STCayleySetAntishift - Sets the value of the anti-shift for the Cayley
350:    spectral transformation.

352:    Logically Collective on ST

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

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

361:    Level: intermediate

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

368: .seealso: STSetShift(), STCayleyGetAntishift()
369: @*/
370: PetscErrorCode STCayleySetAntishift(ST st,PetscScalar nu)
371: {

377:   PetscTryMethod(st,"STCayleySetAntishift_C",(ST,PetscScalar),(st,nu));
378:   return(0);
379: }
380: EXTERN_C_BEGIN
383: PetscErrorCode STCayleyGetAntishift_Cayley(ST st,PetscScalar *nu)
384: {
385:   ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;

388:   *nu = ctx->nu;
389:   return(0);
390: }
391: EXTERN_C_END

395: /*@
396:    STCayleyGetAntishift - Gets the value of the anti-shift used in the Cayley
397:    spectral transformation.

399:    Not Collective

401:    Input Parameter:
402: .  st  - the spectral transformation context

404:    Output Parameter:
405: .  nu  - the anti-shift

407:    Level: intermediate

409: .seealso: STGetShift(), STCayleySetAntishift()
410: @*/
411: PetscErrorCode STCayleyGetAntishift(ST st,PetscScalar *nu)
412: {

418:   PetscTryMethod(st,"STCayleyGetAntishift_C",(ST,PetscScalar*),(st,nu));
419:   return(0);
420: }

424: PetscErrorCode STView_Cayley(ST st,PetscViewer viewer)
425: {
427:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;

430: #if !defined(PETSC_USE_COMPLEX)
431:   PetscViewerASCIIPrintf(viewer,"  Cayley: antishift: %G\n",ctx->nu);
432: #else
433:   PetscViewerASCIIPrintf(viewer,"  Cayley: antishift: %G+%G i\n",PetscRealPart(ctx->nu),PetscImaginaryPart(ctx->nu));
434: #endif
435:   return(0);
436: }

440: PetscErrorCode STReset_Cayley(ST st)
441: {
443:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;

446:   VecDestroy(&ctx->w2);
447:   return(0);
448: }

452: PetscErrorCode STDestroy_Cayley(ST st)
453: {

457:   PetscFree(st->data);
458:   PetscObjectComposeFunctionDynamic((PetscObject)st,"STCayleySetAntishift_C","",PETSC_NULL);
459:   return(0);
460: }

462: EXTERN_C_BEGIN
465: PetscErrorCode STCreate_Cayley(ST st)
466: {

470:   PetscNewLog(st,ST_CAYLEY,&st->data);
471:   st->ops->apply           = STApply_Cayley;
472:   st->ops->getbilinearform = STGetBilinearForm_Cayley;
473:   st->ops->applytrans      = STApplyTranspose_Cayley;
474:   st->ops->postsolve       = STPostSolve_Cayley;
475:   st->ops->backtr          = STBackTransform_Cayley;
476:   st->ops->setfromoptions  = STSetFromOptions_Cayley;
477:   st->ops->setup           = STSetUp_Cayley;
478:   st->ops->setshift        = STSetShift_Cayley;
479:   st->ops->destroy         = STDestroy_Cayley;
480:   st->ops->reset           = STReset_Cayley;
481:   st->ops->view            = STView_Cayley;
482:   st->ops->checknullspace  = STCheckNullSpace_Default;
483:   PetscObjectComposeFunctionDynamic((PetscObject)st,"STCayleySetAntishift_C","STCayleySetAntishift_Cayley",STCayleySetAntishift_Cayley);
484:   return(0);
485: }
486: EXTERN_C_END