Actual source code: lgmres.c
1: #define PETSCKSP_DLL
3: #include ../src/ksp/ksp/impls/gmres/lgmres/lgmresp.h
5: #define LGMRES_DELTA_DIRECTIONS 10
6: #define LGMRES_DEFAULT_MAXK 30
7: #define LGMRES_DEFAULT_AUGDIM 2 /*default number of augmentation vectors */
8: static PetscErrorCode LGMRESGetNewVectors(KSP,PetscInt);
9: static PetscErrorCode LGMRESUpdateHessenberg(KSP,PetscInt,PetscTruth,PetscReal *);
10: static PetscErrorCode BuildLgmresSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);
14: PetscErrorCode KSPLGMRESSetAugDim(KSP ksp, PetscInt dim)
15: {
19: PetscTryMethod((ksp),"KSPLGMRESSetAugDim_C",(KSP,PetscInt),(ksp,dim));
20: return(0);
21: }
25: PetscErrorCode KSPLGMRESSetConstant(KSP ksp)
26: {
30: PetscTryMethod((ksp),"KSPLGMRESSetConstant_C",(KSP),(ksp));
31: return(0);
32: }
34: /*
35: KSPSetUp_LGMRES - Sets up the workspace needed by lgmres.
37: This is called once, usually automatically by KSPSolve() or KSPSetUp(),
38: but can be called directly by KSPSetUp().
40: */
43: PetscErrorCode KSPSetUp_LGMRES(KSP ksp)
44: {
45: PetscInt size,hh,hes,rs,cc;
47: PetscInt max_k,k, aug_dim;
48: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
51: if (ksp->pc_side == PC_SYMMETRIC) {
52: SETERRQ(PETSC_ERR_SUP,"no symmetric preconditioning for KSPLGMRES");
53: }
54: max_k = lgmres->max_k;
55: aug_dim = lgmres->aug_dim;
56: hh = (max_k + 2) * (max_k + 1);
57: hes = (max_k + 1) * (max_k + 1);
58: rs = (max_k + 2);
59: cc = (max_k + 1); /* SS and CC are the same size */
60: size = (hh + hes + rs + 2*cc) * sizeof(PetscScalar);
62: /* Allocate space and set pointers to beginning */
63: PetscMalloc(size,&lgmres->hh_origin);
64: PetscMemzero(lgmres->hh_origin,size);
65: PetscLogObjectMemory(ksp,size); /* HH - modified (by plane rotations) hessenburg */
66: lgmres->hes_origin = lgmres->hh_origin + hh; /* HES - unmodified hessenburg */
67: lgmres->rs_origin = lgmres->hes_origin + hes; /* RS - the right-hand-side of the
68: Hessenberg system */
69: lgmres->cc_origin = lgmres->rs_origin + rs; /* CC - cosines for rotations */
70: lgmres->ss_origin = lgmres->cc_origin + cc; /* SS - sines for rotations */
72: if (ksp->calc_sings) {
73: /* Allocate workspace to hold Hessenberg matrix needed by Eispack */
74: size = (max_k + 3)*(max_k + 9)*sizeof(PetscScalar);
75: PetscMalloc(size,&lgmres->Rsvd);
76: PetscMalloc(5*(max_k+2)*sizeof(PetscReal),&lgmres->Dsvd);
77: PetscLogObjectMemory(ksp,size+5*(max_k+2)*sizeof(PetscReal));
78: }
80: /* Allocate array to hold pointers to user vectors. Note that we need
81: we need it+1 vectors, and it <= max_k) - vec_offset indicates some initial work vectors*/
82: PetscMalloc((VEC_OFFSET+2+max_k)*sizeof(void*),&lgmres->vecs);
83: lgmres->vecs_allocated = VEC_OFFSET + 2 + max_k;
84: PetscMalloc((VEC_OFFSET+2+max_k)*sizeof(void*),&lgmres->user_work);
85: PetscMalloc((VEC_OFFSET+2+max_k)*sizeof(PetscInt),&lgmres->mwork_alloc);
86: PetscLogObjectMemory(ksp,(VEC_OFFSET+2+max_k)*(2*sizeof(void*)+sizeof(PetscInt)));
88: /* LGMRES_MOD: need array of pointers to augvecs*/
89: PetscMalloc((2 * aug_dim + AUG_OFFSET)*sizeof(void*),&lgmres->augvecs);
90: lgmres->aug_vecs_allocated = 2 *aug_dim + AUG_OFFSET;
91: PetscMalloc((2* aug_dim + AUG_OFFSET)*sizeof(void*),&lgmres->augvecs_user_work);
92: PetscMalloc(aug_dim*sizeof(PetscInt),&lgmres->aug_order);
93: PetscLogObjectMemory(ksp,(aug_dim)*(4*sizeof(void*) + sizeof(PetscInt)) + AUG_OFFSET*2*sizeof(void*));
95:
96: /* if q_preallocate = 0 then only allocate one "chunk" of space (for
97: 5 vectors) - additional will then be allocated from LGMREScycle()
98: as needed. Otherwise, allocate all of the space that could be needed */
99: if (lgmres->q_preallocate) {
100: lgmres->vv_allocated = VEC_OFFSET + 2 + max_k;
101: KSPGetVecs(ksp,lgmres->vv_allocated,&lgmres->user_work[0],0,PETSC_NULL);
102: PetscLogObjectParents(ksp,lgmres->vv_allocated,lgmres->user_work[0]);
103: lgmres->mwork_alloc[0] = lgmres->vv_allocated;
104: lgmres->nwork_alloc = 1;
105: for (k=0; k<lgmres->vv_allocated; k++) {
106: lgmres->vecs[k] = lgmres->user_work[0][k];
107: }
108: } else {
109: lgmres->vv_allocated = 5;
110: KSPGetVecs(ksp,5,&lgmres->user_work[0],0,PETSC_NULL);
111: PetscLogObjectParents(ksp,5,lgmres->user_work[0]);
112: lgmres->mwork_alloc[0] = 5;
113: lgmres->nwork_alloc = 1;
114: for (k=0; k<lgmres->vv_allocated; k++) {
115: lgmres->vecs[k] = lgmres->user_work[0][k];
116: }
117: }
118: /* LGMRES_MOD - for now we will preallocate the augvecs - because aug_dim << restart
119: ... also keep in mind that we need to keep augvecs from cycle to cycle*/
120: lgmres->aug_vv_allocated = 2* aug_dim + AUG_OFFSET;
121: lgmres->augwork_alloc = 2* aug_dim + AUG_OFFSET;
122: KSPGetVecs(ksp,lgmres->aug_vv_allocated,&lgmres->augvecs_user_work[0],0,PETSC_NULL);
123: PetscLogObjectParents(ksp,lgmres->aug_vv_allocated,lgmres->augvecs_user_work[0]);
124: for (k=0; k<lgmres->aug_vv_allocated; k++) {
125: lgmres->augvecs[k] = lgmres->augvecs_user_work[0][k];
126: }
127: return(0);
128: }
131: /*
133: LGMRESCycle - Run lgmres, possibly with restart. Return residual
134: history if requested.
136: input parameters:
137: . lgmres - structure containing parameters and work areas
139: output parameters:
140: . nres - residuals (from preconditioned system) at each step.
141: If restarting, consider passing nres+it. If null,
142: ignored
143: . itcount - number of iterations used. nres[0] to nres[itcount]
144: are defined. If null, ignored. If null, ignored.
145: . converged - 0 if not converged
147:
148: Notes:
149: On entry, the value in vector VEC_VV(0) should be
150: the initial residual.
153: */
156: PetscErrorCode LGMREScycle(PetscInt *itcount,KSP ksp)
157: {
159: KSP_LGMRES *lgmres = (KSP_LGMRES *)(ksp->data);
160: PetscReal res_norm, res;
161: PetscReal hapbnd, tt;
162: PetscScalar tmp;
163: PetscTruth hapend = PETSC_FALSE; /* indicates happy breakdown ending */
165: PetscInt loc_it; /* local count of # of dir. in Krylov space */
166: PetscInt max_k = lgmres->max_k; /* max approx space size */
167: PetscInt max_it = ksp->max_it; /* max # of overall iterations for the method */
168: /* LGMRES_MOD - new variables*/
169: PetscInt aug_dim = lgmres->aug_dim;
170: PetscInt spot = 0;
171: PetscInt order = 0;
172: PetscInt it_arnoldi; /* number of arnoldi steps to take */
173: PetscInt it_total; /* total number of its to take (=approx space size)*/
174: PetscInt ii, jj;
175: PetscReal tmp_norm;
176: PetscScalar inv_tmp_norm;
177: PetscScalar *avec;
180: /* Number of pseudo iterations since last restart is the number
181: of prestart directions */
182: loc_it = 0;
184: /* LGMRES_MOD: determine number of arnoldi steps to take */
185: /* if approx_constant then we keep the space the same size even if
186: we don't have the full number of aug vectors yet*/
187: if (lgmres->approx_constant) {
188: it_arnoldi = max_k - lgmres->aug_ct;
189: } else {
190: it_arnoldi = max_k - aug_dim;
191: }
193: it_total = it_arnoldi + lgmres->aug_ct;
195: /* initial residual is in VEC_VV(0) - compute its norm*/
196: VecNorm(VEC_VV(0),NORM_2,&res_norm);
197: res = res_norm;
198:
199: /* first entry in right-hand-side of hessenberg system is just
200: the initial residual norm */
201: *GRS(0) = res_norm;
203: /* check for the convergence */
204: if (!res) {
205: if (itcount) *itcount = 0;
206: ksp->reason = KSP_CONVERGED_ATOL;
207: PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
208: return(0);
209: }
211: /* scale VEC_VV (the initial residual) */
212: tmp = 1.0/res_norm; VecScale(VEC_VV(0),tmp);
214: ksp->rnorm = res;
217: /* note: (lgmres->it) is always set one less than (loc_it) It is used in
218: KSPBUILDSolution_LGMRES, where it is passed to BuildLgmresSoln.
219: Note that when BuildLgmresSoln is called from this function,
220: (loc_it -1) is passed, so the two are equivalent */
221: lgmres->it = (loc_it - 1);
223:
224: /* MAIN ITERATION LOOP BEGINNING*/
227: /* keep iterating until we have converged OR generated the max number
228: of directions OR reached the max number of iterations for the method */
229: (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
230:
231: while (!ksp->reason && loc_it < it_total && ksp->its < max_it) { /* LGMRES_MOD: changed to it_total */
232: KSPLogResidualHistory(ksp,res);
233: lgmres->it = (loc_it - 1);
234: KSPMonitor(ksp,ksp->its,res);
236: /* see if more space is needed for work vectors */
237: if (lgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
238: LGMRESGetNewVectors(ksp,loc_it+1);
239: /* (loc_it+1) is passed in as number of the first vector that should
240: be allocated */
241: }
243: /*LGMRES_MOD: decide whether this is an arnoldi step or an aug step */
244: if (loc_it < it_arnoldi) { /* Arnoldi */
245: KSP_PCApplyBAorAB(ksp,VEC_VV(loc_it),VEC_VV(1+loc_it),VEC_TEMP_MATOP);
246: } else { /*aug step */
247: order = loc_it - it_arnoldi + 1; /* which aug step */
248: for (ii=0; ii<aug_dim; ii++) {
249: if (lgmres->aug_order[ii] == order) {
250: spot = ii;
251: break; /* must have this because there will be duplicates before aug_ct = aug_dim */
252: }
253: }
255: VecCopy(A_AUGVEC(spot), VEC_VV(1+loc_it));
256: /*note: an alternate implementation choice would be to only save the AUGVECS and
257: not A_AUGVEC and then apply the PC here to the augvec */
258: }
260: /* update hessenberg matrix and do Gram-Schmidt - new direction is in
261: VEC_VV(1+loc_it)*/
262: (*lgmres->orthog)(ksp,loc_it);
264: /* new entry in hessenburg is the 2-norm of our new direction */
265: VecNorm(VEC_VV(loc_it+1),NORM_2,&tt);
266: *HH(loc_it+1,loc_it) = tt;
267: *HES(loc_it+1,loc_it) = tt;
270: /* check for the happy breakdown */
271: hapbnd = PetscAbsScalar(tt / *GRS(loc_it));/* GRS(loc_it) contains the res_norm from the last iteration */
272: if (hapbnd > lgmres->haptol) hapbnd = lgmres->haptol;
273: if (tt > hapbnd) {
274: tmp = 1.0/tt;
275: VecScale(VEC_VV(loc_it+1),tmp); /* scale new direction by its norm */
276: } else {
277: PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %G tt = %G\n",hapbnd,tt);
278: hapend = PETSC_TRUE;
279: }
281: /* Now apply rotations to new col of hessenberg (and right side of system),
282: calculate new rotation, and get new residual norm at the same time*/
283: LGMRESUpdateHessenberg(ksp,loc_it,hapend,&res);
284: if (ksp->reason) break;
286: loc_it++;
287: lgmres->it = (loc_it-1); /* Add this here in case it has converged */
288:
289: PetscObjectTakeAccess(ksp);
290: ksp->its++;
291: ksp->rnorm = res;
292: PetscObjectGrantAccess(ksp);
294: (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
296: /* Catch error in happy breakdown and signal convergence and break from loop */
297: if (hapend) {
298: if (!ksp->reason) {
299: SETERRQ1(0,"You reached the happy break down,but convergence was not indicated. Residual norm = %G",res);
300: }
301: break;
302: }
303: }
304: /* END OF ITERATION LOOP */
306: KSPLogResidualHistory(ksp,res);
308: /* Monitor if we know that we will not return for a restart */
309: if (ksp->reason || ksp->its >= max_it) {
310: KSPMonitor(ksp, ksp->its, res);
311: }
313: if (itcount) *itcount = loc_it;
315: /*
316: Down here we have to solve for the "best" coefficients of the Krylov
317: columns, add the solution values together, and possibly unwind the
318: preconditioning from the solution
319: */
320:
321: /* Form the solution (or the solution so far) */
322: /* Note: must pass in (loc_it-1) for iteration count so that BuildLgmresSoln
323: properly navigates */
325: BuildLgmresSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,loc_it-1);
328: /* LGMRES_MOD collect aug vector and A*augvector for future restarts -
329: only if we will be restarting (i.e. this cycle performed it_total
330: iterations) */
331: if (!ksp->reason && ksp->its < max_it && aug_dim > 0) {
333: /*AUG_TEMP contains the new augmentation vector (assigned in BuildLgmresSoln) */
334: if (!lgmres->aug_ct) {
335: spot = 0;
336: lgmres->aug_ct++;
337: } else if (lgmres->aug_ct < aug_dim) {
338: spot = lgmres->aug_ct;
339: lgmres->aug_ct++;
340: } else { /* truncate */
341: for (ii=0; ii<aug_dim; ii++) {
342: if (lgmres->aug_order[ii] == aug_dim) {
343: spot = ii;
344: }
345: }
346: }
348:
350: VecCopy(AUG_TEMP, AUGVEC(spot));
351: /*need to normalize */
352: VecNorm(AUGVEC(spot), NORM_2, &tmp_norm);
353: inv_tmp_norm = 1.0/tmp_norm;
354: VecScale(AUGVEC(spot),inv_tmp_norm);
356: /*set new aug vector to order 1 - move all others back one */
357: for (ii=0; ii < aug_dim; ii++) {
358: AUG_ORDER(ii)++;
359: }
360: AUG_ORDER(spot) = 1;
362: /*now add the A*aug vector to A_AUGVEC(spot) - this is independ. of preconditioning type*/
363: /* want V*H*y - y is in GRS, V is in VEC_VV and H is in HES */
365:
366: /* first do H+*y */
367: VecSet(AUG_TEMP,0.0);
368: VecGetArray(AUG_TEMP, &avec);
369: for (ii=0; ii < it_total + 1; ii++) {
370: for (jj=0; jj <= ii+1; jj++) {
371: avec[jj] += *HES(jj ,ii) * *GRS(ii);
372: }
373: }
375: /*now multiply result by V+ */
376: VecSet(VEC_TEMP,0.0);
377: VecMAXPY(VEC_TEMP, it_total+1, avec, &VEC_VV(0)); /*answer is in VEC_TEMP*/
378: VecRestoreArray(AUG_TEMP, &avec);
379:
380: /*copy answer to aug location and scale*/
381: VecCopy(VEC_TEMP, A_AUGVEC(spot));
382: VecScale(A_AUGVEC(spot),inv_tmp_norm);
385: }
386: return(0);
387: }
389: /*
390: KSPSolve_LGMRES - This routine applies the LGMRES method.
393: Input Parameter:
394: . ksp - the Krylov space object that was set to use lgmres
396: Output Parameter:
397: . outits - number of iterations used
399: */
403: PetscErrorCode KSPSolve_LGMRES(KSP ksp)
404: {
406: PetscInt cycle_its; /* iterations done in a call to LGMREScycle */
407: PetscInt itcount; /* running total of iterations, incl. those in restarts */
408: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
409: PetscTruth guess_zero = ksp->guess_zero;
410: PetscInt ii; /*LGMRES_MOD variable */
413: if (ksp->calc_sings && !lgmres->Rsvd) {
414: SETERRQ(PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
415: }
416: PetscObjectTakeAccess(ksp);
417: ksp->its = 0;
418: lgmres->aug_ct = 0;
419: lgmres->matvecs = 0;
420: PetscObjectGrantAccess(ksp);
422: /* initialize */
423: itcount = 0;
424: ksp->reason = KSP_CONVERGED_ITERATING;
425: /*LGMRES_MOD*/
426: for (ii=0; ii<lgmres->aug_dim; ii++) {
427: lgmres->aug_order[ii] = 0;
428: }
430: while (!ksp->reason) {
431: /* calc residual - puts in VEC_VV(0) */
432: KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
433: LGMREScycle(&cycle_its,ksp);
434: itcount += cycle_its;
435: if (itcount >= ksp->max_it) {
436: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
437: break;
438: }
439: ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
440: }
441: ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
442: return(0);
443: }
445: /*
447: KSPDestroy_LGMRES - Frees all memory space used by the Krylov method.
449: */
452: PetscErrorCode KSPDestroy_LGMRES(KSP ksp)
453: {
454: KSP_LGMRES *lgmres = (KSP_LGMRES*)ksp->data;
456: PetscInt i;
459: /* Free the Hessenberg matrices */
460: PetscFree(lgmres->hh_origin);
462: /* Free pointers to user variables */
463: PetscFree(lgmres->vecs);
465: /*LGMRES_MOD - free pointers for extra vectors */
466: PetscFree(lgmres->augvecs);
468: /* free work vectors */
469: for (i=0; i < lgmres->nwork_alloc; i++) {
470: VecDestroyVecs(lgmres->user_work[i],lgmres->mwork_alloc[i]);
471: }
472: PetscFree(lgmres->user_work);
474: /*LGMRES_MOD - free aug work vectors also */
475: /*this was all allocated as one "chunk" */
476: if (lgmres->augwork_alloc) {
477: VecDestroyVecs(lgmres->augvecs_user_work[0],lgmres->augwork_alloc);
478: }
479: PetscFree(lgmres->augvecs_user_work);
480: PetscFree(lgmres->aug_order);
481: PetscFree(lgmres->mwork_alloc);
482: PetscFree(lgmres->nrs);
483: if (lgmres->sol_temp) {VecDestroy(lgmres->sol_temp);}
484: PetscFree(lgmres->Rsvd);
485: PetscFree(lgmres->Dsvd);
486: PetscFree(lgmres->orthogwork);
487: PetscFree(ksp->data);
488: /* clear composed functions */
489: PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C","",PETSC_NULL);
490: PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C","",PETSC_NULL);
491: PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetRestart_C","",PETSC_NULL);
492: PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetHapTol_C","",PETSC_NULL);
493: PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C","",PETSC_NULL);
494: return(0);
495: }
497: /*
498: BuildLgmresSoln - create the solution from the starting vector and the
499: current iterates.
501: Input parameters:
502: nrs - work area of size it + 1.
503: vguess - index of initial guess
504: vdest - index of result. Note that vguess may == vdest (replace
505: guess with the solution).
506: it - HH upper triangular part is a block of size (it+1) x (it+1)
508: This is an internal routine that knows about the LGMRES internals.
509: */
512: static PetscErrorCode BuildLgmresSoln(PetscScalar* nrs,Vec vguess,Vec vdest,KSP ksp,PetscInt it)
513: {
514: PetscScalar tt;
516: PetscInt ii,k,j;
517: KSP_LGMRES *lgmres = (KSP_LGMRES *)(ksp->data);
518: /*LGMRES_MOD */
519: PetscInt it_arnoldi, it_aug;
520: PetscInt jj, spot = 0;
523: /* Solve for solution vector that minimizes the residual */
525: /* If it is < 0, no lgmres steps have been performed */
526: if (it < 0) {
527: VecCopy(vguess,vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
528: return(0);
529: }
531: /* so (it+1) lgmres steps HAVE been performed */
533: /* LGMRES_MOD - determine if we need to use augvecs for the soln - do not assume that
534: this is called after the total its allowed for an approx space */
535: if (lgmres->approx_constant) {
536: it_arnoldi = lgmres->max_k - lgmres->aug_ct;
537: } else {
538: it_arnoldi = lgmres->max_k - lgmres->aug_dim;
539: }
540: if (it_arnoldi >= it +1) {
541: it_aug = 0;
542: it_arnoldi = it+1;
543: } else {
544: it_aug = (it + 1) - it_arnoldi;
545: }
547: /* now it_arnoldi indicates the number of matvecs that took place */
548: lgmres->matvecs += it_arnoldi;
550:
551: /* solve the upper triangular system - GRS is the right side and HH is
552: the upper triangular matrix - put soln in nrs */
553: if (*HH(it,it) == 0.0) SETERRQ2(PETSC_ERR_CONV_FAILED,"HH(it,it) is identically zero; it = %D GRS(it) = %G",it,PetscAbsScalar(*GRS(it)));
554: if (*HH(it,it) != 0.0) {
555: nrs[it] = *GRS(it) / *HH(it,it);
556: } else {
557: nrs[it] = 0.0;
558: }
560: for (ii=1; ii<=it; ii++) {
561: k = it - ii;
562: tt = *GRS(k);
563: for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
564: nrs[k] = tt / *HH(k,k);
565: }
567: /* Accumulate the correction to the soln of the preconditioned prob. in VEC_TEMP */
568: VecSet(VEC_TEMP,0.0); /* set VEC_TEMP components to 0 */
570: /*LGMRES_MOD - if augmenting has happened we need to form the solution
571: using the augvecs */
572: if (!it_aug) { /* all its are from arnoldi */
573: VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));
574: } else { /*use aug vecs */
575: /*first do regular krylov directions */
576: VecMAXPY(VEC_TEMP,it_arnoldi,nrs,&VEC_VV(0));
577: /*now add augmented portions - add contribution of aug vectors one at a time*/
580: for (ii=0; ii<it_aug; ii++) {
581: for (jj=0; jj<lgmres->aug_dim; jj++) {
582: if (lgmres->aug_order[jj] == (ii+1)) {
583: spot = jj;
584: break; /* must have this because there will be duplicates before aug_ct = aug_dim */
585: }
586: }
587: VecAXPY(VEC_TEMP,nrs[it_arnoldi+ii],AUGVEC(spot));
588: }
589: }
590: /* now VEC_TEMP is what we want to keep for augmenting purposes - grab before the
591: preconditioner is "unwound" from right-precondtioning*/
592: VecCopy(VEC_TEMP, AUG_TEMP);
594: KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
596: /* add solution to previous solution */
597: /* put updated solution into vdest.*/
598: if (vdest != vguess) {
599: VecCopy(VEC_TEMP,vdest);
600: }
601: VecAXPY(vdest,1.0,VEC_TEMP);
603: return(0);
604: }
606: /*
608: LGMRESUpdateHessenberg - Do the scalar work for the orthogonalization.
609: Return new residual.
611: input parameters:
613: . ksp - Krylov space object
614: . it - plane rotations are applied to the (it+1)th column of the
615: modified hessenberg (i.e. HH(:,it))
616: . hapend - PETSC_FALSE not happy breakdown ending.
618: output parameters:
619: . res - the new residual
620:
621: */
624: static PetscErrorCode LGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscTruth hapend,PetscReal *res)
625: {
626: PetscScalar *hh,*cc,*ss,tt;
627: PetscInt j;
628: KSP_LGMRES *lgmres = (KSP_LGMRES *)(ksp->data);
631: hh = HH(0,it); /* pointer to beginning of column to update - so
632: incrementing hh "steps down" the (it+1)th col of HH*/
633: cc = CC(0); /* beginning of cosine rotations */
634: ss = SS(0); /* beginning of sine rotations */
636: /* Apply all the previously computed plane rotations to the new column
637: of the Hessenberg matrix */
638: /* Note: this uses the rotation [conj(c) s ; -s c], c= cos(theta), s= sin(theta) */
640: for (j=1; j<=it; j++) {
641: tt = *hh;
642: #if defined(PETSC_USE_COMPLEX)
643: *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
644: #else
645: *hh = *cc * tt + *ss * *(hh+1);
646: #endif
647: hh++;
648: *hh = *cc++ * *hh - (*ss++ * tt);
649: /* hh, cc, and ss have all been incremented one by end of loop */
650: }
652: /*
653: compute the new plane rotation, and apply it to:
654: 1) the right-hand-side of the Hessenberg system (GRS)
655: note: it affects GRS(it) and GRS(it+1)
656: 2) the new column of the Hessenberg matrix
657: note: it affects HH(it,it) which is currently pointed to
658: by hh and HH(it+1, it) (*(hh+1))
659: thus obtaining the updated value of the residual...
660: */
662: /* compute new plane rotation */
664: if (!hapend) {
665: #if defined(PETSC_USE_COMPLEX)
666: tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
667: #else
668: tt = PetscSqrtScalar(*hh * *hh + *(hh+1) * *(hh+1));
669: #endif
670: if (tt == 0.0) {
671: ksp->reason = KSP_DIVERGED_NULL;
672: return(0);
673: }
674: *cc = *hh / tt; /* new cosine value */
675: *ss = *(hh+1) / tt; /* new sine value */
677: /* apply to 1) and 2) */
678: *GRS(it+1) = - (*ss * *GRS(it));
679: #if defined(PETSC_USE_COMPLEX)
680: *GRS(it) = PetscConj(*cc) * *GRS(it);
681: *hh = PetscConj(*cc) * *hh + *ss * *(hh+1);
682: #else
683: *GRS(it) = *cc * *GRS(it);
684: *hh = *cc * *hh + *ss * *(hh+1);
685: #endif
687: /* residual is the last element (it+1) of right-hand side! */
688: *res = PetscAbsScalar(*GRS(it+1));
690: } else { /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply
691: another rotation matrix (so RH doesn't change). The new residual is
692: always the new sine term times the residual from last time (GRS(it)),
693: but now the new sine rotation would be zero...so the residual should
694: be zero...so we will multiply "zero" by the last residual. This might
695: not be exactly what we want to do here -could just return "zero". */
696:
697: *res = 0.0;
698: }
699: return(0);
700: }
702: /*
704: LGMRESGetNewVectors - This routine allocates more work vectors, starting from
705: VEC_VV(it)
706:
707: */
710: static PetscErrorCode LGMRESGetNewVectors(KSP ksp,PetscInt it)
711: {
712: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
713: PetscInt nwork = lgmres->nwork_alloc; /* number of work vector chunks allocated */
714: PetscInt nalloc; /* number to allocate */
716: PetscInt k;
717:
719: nalloc = lgmres->delta_allocate; /* number of vectors to allocate
720: in a single chunk */
722: /* Adjust the number to allocate to make sure that we don't exceed the
723: number of available slots (lgmres->vecs_allocated)*/
724: if (it + VEC_OFFSET + nalloc >= lgmres->vecs_allocated){
725: nalloc = lgmres->vecs_allocated - it - VEC_OFFSET;
726: }
727: if (!nalloc) return(0);
729: lgmres->vv_allocated += nalloc; /* vv_allocated is the number of vectors allocated */
731: /* work vectors */
732: KSPGetVecs(ksp,nalloc,&lgmres->user_work[nwork],0,PETSC_NULL);
733: PetscLogObjectParents(ksp,nalloc,lgmres->user_work[nwork]);
734: /* specify size of chunk allocated */
735: lgmres->mwork_alloc[nwork] = nalloc;
737: for (k=0; k < nalloc; k++) {
738: lgmres->vecs[it+VEC_OFFSET+k] = lgmres->user_work[nwork][k];
739: }
740:
742: /* LGMRES_MOD - for now we are preallocating the augmentation vectors */
743:
745: /* increment the number of work vector chunks */
746: lgmres->nwork_alloc++;
747: return(0);
748: }
750: /*
752: KSPBuildSolution_LGMRES
754: Input Parameter:
755: . ksp - the Krylov space object
756: . ptr-
758: Output Parameter:
759: . result - the solution
761: Note: this calls BuildLgmresSoln - the same function that LGMREScycle
762: calls directly.
764: */
767: PetscErrorCode KSPBuildSolution_LGMRES(KSP ksp,Vec ptr,Vec *result)
768: {
769: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
773: if (!ptr) {
774: if (!lgmres->sol_temp) {
775: VecDuplicate(ksp->vec_sol,&lgmres->sol_temp);
776: PetscLogObjectParent(ksp,lgmres->sol_temp);
777: }
778: ptr = lgmres->sol_temp;
779: }
780: if (!lgmres->nrs) {
781: /* allocate the work area */
782: PetscMalloc(lgmres->max_k*sizeof(PetscScalar),&lgmres->nrs);
783: PetscLogObjectMemory(ksp,lgmres->max_k*sizeof(PetscScalar));
784: }
785:
786: BuildLgmresSoln(lgmres->nrs,ksp->vec_sol,ptr,ksp,lgmres->it);
787: if (result) *result = ptr;
788:
789: return(0);
790: }
796: PetscErrorCode KSPView_LGMRES(KSP ksp,PetscViewer viewer)
797: {
798: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
800: PetscTruth iascii;
803: KSPView_GMRES(ksp,viewer);
804: PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);
805: if (iascii) {
806: /*LGMRES_MOD */
807: PetscViewerASCIIPrintf(viewer," LGMRES: aug. dimension=%D\n",lgmres->aug_dim);
808: if (lgmres->approx_constant) {
809: PetscViewerASCIIPrintf(viewer," LGMRES: approx. space size was kept constant.\n");
810: }
811: PetscViewerASCIIPrintf(viewer," LGMRES: number of matvecs=%D\n",lgmres->matvecs);
812: } else {
813: SETERRQ1(PETSC_ERR_SUP,"Viewer type %s not supported for KSP LGMRES",((PetscObject)viewer)->type_name);
814: }
815: return(0);
816: }
822: PetscErrorCode KSPSetFromOptions_LGMRES(KSP ksp)
823: {
825: PetscInt aug;
826: KSP_LGMRES *lgmres = (KSP_LGMRES*) ksp->data;
827: PetscTruth flg;
830: KSPSetFromOptions_GMRES(ksp);
831: PetscOptionsHead("KSP LGMRES Options");
832: PetscOptionsName("-ksp_lgmres_constant","Use constant approx. space size","KSPGMRESSetConstant",&flg);
833: if (flg) { lgmres->approx_constant = 1; }
834: PetscOptionsInt("-ksp_lgmres_augment","Number of error approximations to augment the Krylov space with","KSPLGMRESSetAugDim",lgmres->aug_dim,&aug,&flg);
835: if (flg) { KSPLGMRESSetAugDim(ksp,aug); }
836: PetscOptionsTail();
837: return(0);
838: }
841: EXTERN PetscErrorCode KSPComputeExtremeSingularValues_GMRES(KSP,PetscReal *,PetscReal *);
842: EXTERN PetscErrorCode KSPComputeEigenvalues_GMRES(KSP,PetscInt,PetscReal *,PetscReal *,PetscInt *);
844: /*functions for extra lgmres options here*/
848: PetscErrorCode KSPLGMRESSetConstant_LGMRES(KSP ksp)
849: {
850: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
852: lgmres->approx_constant = 1;
853: return(0);
854: }
860: PetscErrorCode KSPLGMRESSetAugDim_LGMRES(KSP ksp,PetscInt aug_dim)
861: {
862: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
865: if (aug_dim < 0) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Augmentation dimension must be positive");
866: if (aug_dim > (lgmres->max_k -1)) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Augmentation dimension must be <= (restart size-1)");
867: lgmres->aug_dim = aug_dim;
868: return(0);
869: }
873: /* end new lgmres functions */
876: /* use these options from gmres */
878: EXTERN PetscErrorCode KSPGMRESSetHapTol_GMRES(KSP,double);
879: EXTERN PetscErrorCode KSPGMRESSetPreAllocateVectors_GMRES(KSP);
880: EXTERN PetscErrorCode KSPGMRESSetRestart_GMRES(KSP,PetscInt);
881: EXTERN PetscErrorCode KSPGMRESSetOrthogonalization_GMRES(KSP,PetscErrorCode (*)(KSP,PetscInt));
882: EXTERN PetscErrorCode KSPGMRESSetCGSRefinementType_GMRES(KSP,KSPGMRESCGSRefinementType);
885: /*MC
886: KSPLGMRES - Augments the standard GMRES approximation space with approximations to
887: the error from previous restart cycles.
889: Options Database Keys:
890: + -ksp_gmres_restart <restart> - total approximation space size (Krylov directions + error approximations)
891: . -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
892: . -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
893: vectors are allocated as needed)
894: . -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
895: . -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
896: . -ksp_gmres_cgs_refinement_type <never,ifneeded,always> - determine if iterative refinement is used to increase the
897: stability of the classical Gram-Schmidt orthogonalization.
898: . -ksp_gmres_krylov_monitor - plot the Krylov space generated
899: . -ksp_lgmres_augment <k> - number of error approximations to augment the Krylov space with
900: - -ksp_lgmres_constant - use a constant approx. space size (only affects restart cycles < num. error approx.(k), i.e. the first k restarts)
902: Described in:
903: A. H. Baker, E.R. Jessup, and T.A. Manteuffel. A technique for
904: accelerating the convergence of restarted GMRES. SIAM
905: Journal on Matrix Analysis and Applications, 26 (2005), pp. 962-984.
907: To run LGMRES(m, k) as described in the above paper, use:
908: -ksp_gmres_restart <m+k>
909: -ksp_lgmres_augment <k>
911: Level: beginner
913: Notes: This object is subclassed off of KSPGMRES
915: Contributed by: Allison Baker
917: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPGMRES,
918: KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization()
919: KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
920: KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPLGMRESSetAugDim(),
921: KSPGMRESSetConstant()
923: M*/
928: PetscErrorCode KSPCreate_LGMRES(KSP ksp)
929: {
930: KSP_LGMRES *lgmres;
934: PetscNewLog(ksp,KSP_LGMRES,&lgmres);
935: ksp->data = (void*)lgmres;
936: ksp->ops->buildsolution = KSPBuildSolution_LGMRES;
938: ksp->ops->setup = KSPSetUp_LGMRES;
939: ksp->ops->solve = KSPSolve_LGMRES;
940: ksp->ops->destroy = KSPDestroy_LGMRES;
941: ksp->ops->view = KSPView_LGMRES;
942: ksp->ops->setfromoptions = KSPSetFromOptions_LGMRES;
943: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
944: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_GMRES;
946: PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",
947: "KSPGMRESSetPreAllocateVectors_GMRES",
948: KSPGMRESSetPreAllocateVectors_GMRES);
949: PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",
950: "KSPGMRESSetOrthogonalization_GMRES",
951: KSPGMRESSetOrthogonalization_GMRES);
952: PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetRestart_C",
953: "KSPGMRESSetRestart_GMRES",
954: KSPGMRESSetRestart_GMRES);
955: PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetHapTol_C",
956: "KSPGMRESSetHapTol_GMRES",
957: KSPGMRESSetHapTol_GMRES);
958: PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",
959: "KSPGMRESSetCGSRefinementType_GMRES",
960: KSPGMRESSetCGSRefinementType_GMRES);
962: /*LGMRES_MOD add extra functions here - like the one to set num of aug vectors */
963: PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPLGMRESSetConstant_C",
964: "KSPLGMRESSetConstant_LGMRES",
965: KSPLGMRESSetConstant_LGMRES);
967: PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPLGMRESSetAugDim_C",
968: "KSPLGMRESSetAugDim_LGMRES",
969: KSPLGMRESSetAugDim_LGMRES);
970:
972: /*defaults */
973: lgmres->haptol = 1.0e-30;
974: lgmres->q_preallocate = 0;
975: lgmres->delta_allocate = LGMRES_DELTA_DIRECTIONS;
976: lgmres->orthog = KSPGMRESClassicalGramSchmidtOrthogonalization;
977: lgmres->nrs = 0;
978: lgmres->sol_temp = 0;
979: lgmres->max_k = LGMRES_DEFAULT_MAXK;
980: lgmres->Rsvd = 0;
981: lgmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
982: lgmres->orthogwork = 0;
983: /*LGMRES_MOD - new defaults */
984: lgmres->aug_dim = LGMRES_DEFAULT_AUGDIM;
985: lgmres->aug_ct = 0; /* start with no aug vectors */
986: lgmres->approx_constant = 0;
987: lgmres->matvecs = 0;
989: return(0);
990: }