Actual source code: lgmres.c
2: #include <../src/ksp/ksp/impls/gmres/lgmres/lgmresimpl.h>
4: #define LGMRES_DELTA_DIRECTIONS 10
5: #define LGMRES_DEFAULT_MAXK 30
6: #define LGMRES_DEFAULT_AUGDIM 2 /*default number of augmentation vectors */
7: static PetscErrorCode KSPLGMRESGetNewVectors(KSP,PetscInt);
8: static PetscErrorCode KSPLGMRESUpdateHessenberg(KSP,PetscInt,PetscBool,PetscReal*);
9: static PetscErrorCode KSPLGMRESBuildSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);
11: PetscErrorCode KSPLGMRESSetAugDim(KSP ksp, PetscInt dim)
12: {
13: PetscTryMethod((ksp),"KSPLGMRESSetAugDim_C",(KSP,PetscInt),(ksp,dim));
14: return 0;
15: }
17: PetscErrorCode KSPLGMRESSetConstant(KSP ksp)
18: {
19: PetscTryMethod((ksp),"KSPLGMRESSetConstant_C",(KSP),(ksp));
20: return 0;
21: }
23: /*
24: KSPSetUp_LGMRES - Sets up the workspace needed by lgmres.
26: This is called once, usually automatically by KSPSolve() or KSPSetUp(),
27: but can be called directly by KSPSetUp().
29: */
30: PetscErrorCode KSPSetUp_LGMRES(KSP ksp)
31: {
32: PetscInt max_k,k, aug_dim;
33: KSP_LGMRES *lgmres = (KSP_LGMRES*)ksp->data;
35: max_k = lgmres->max_k;
36: aug_dim = lgmres->aug_dim;
37: KSPSetUp_GMRES(ksp);
39: /* need array of pointers to augvecs*/
40: PetscMalloc1(2*aug_dim + AUG_OFFSET,&lgmres->augvecs);
42: lgmres->aug_vecs_allocated = 2 *aug_dim + AUG_OFFSET;
44: PetscMalloc1(2*aug_dim + AUG_OFFSET,&lgmres->augvecs_user_work);
45: PetscMalloc1(aug_dim,&lgmres->aug_order);
46: PetscLogObjectMemory((PetscObject)ksp,(aug_dim)*(4*sizeof(void*) + sizeof(PetscInt)) + AUG_OFFSET*2*sizeof(void*));
48: /* for now we will preallocate the augvecs - because aug_dim << restart
49: ... also keep in mind that we need to keep augvecs from cycle to cycle*/
50: lgmres->aug_vv_allocated = 2* aug_dim + AUG_OFFSET;
51: lgmres->augwork_alloc = 2* aug_dim + AUG_OFFSET;
53: KSPCreateVecs(ksp,lgmres->aug_vv_allocated,&lgmres->augvecs_user_work[0],0,NULL);
54: PetscMalloc1(max_k+1,&lgmres->hwork);
55: PetscLogObjectParents(ksp,lgmres->aug_vv_allocated,lgmres->augvecs_user_work[0]);
56: for (k=0; k<lgmres->aug_vv_allocated; k++) {
57: lgmres->augvecs[k] = lgmres->augvecs_user_work[0][k];
58: }
59: return 0;
60: }
62: /*
64: KSPLGMRESCycle - Run lgmres, possibly with restart. Return residual
65: history if requested.
67: input parameters:
68: . lgmres - structure containing parameters and work areas
70: output parameters:
71: . nres - residuals (from preconditioned system) at each step.
72: If restarting, consider passing nres+it. If null,
73: ignored
74: . itcount - number of iterations used. nres[0] to nres[itcount]
75: are defined. If null, ignored. If null, ignored.
76: . converged - 0 if not converged
78: Notes:
79: On entry, the value in vector VEC_VV(0) should be
80: the initial residual.
82: */
83: PetscErrorCode KSPLGMRESCycle(PetscInt *itcount,KSP ksp)
84: {
85: KSP_LGMRES *lgmres = (KSP_LGMRES*)(ksp->data);
86: PetscReal res_norm, res;
87: PetscReal hapbnd, tt;
88: PetscScalar tmp;
89: PetscBool hapend = PETSC_FALSE; /* indicates happy breakdown ending */
90: PetscInt loc_it; /* local count of # of dir. in Krylov space */
91: PetscInt max_k = lgmres->max_k; /* max approx space size */
92: PetscInt max_it = ksp->max_it; /* max # of overall iterations for the method */
94: /* LGMRES_MOD - new variables*/
95: PetscInt aug_dim = lgmres->aug_dim;
96: PetscInt spot = 0;
97: PetscInt order = 0;
98: PetscInt it_arnoldi; /* number of arnoldi steps to take */
99: PetscInt it_total; /* total number of its to take (=approx space size)*/
100: PetscInt ii, jj;
101: PetscReal tmp_norm;
102: PetscScalar inv_tmp_norm;
103: PetscScalar *avec;
105: /* Number of pseudo iterations since last restart is the number
106: of prestart directions */
107: loc_it = 0;
109: /* LGMRES_MOD: determine number of arnoldi steps to take */
110: /* if approx_constant then we keep the space the same size even if
111: we don't have the full number of aug vectors yet*/
112: if (lgmres->approx_constant) it_arnoldi = max_k - lgmres->aug_ct;
113: else it_arnoldi = max_k - aug_dim;
115: it_total = it_arnoldi + lgmres->aug_ct;
117: /* initial residual is in VEC_VV(0) - compute its norm*/
118: VecNorm(VEC_VV(0),NORM_2,&res_norm);
119: KSPCheckNorm(ksp,res_norm);
120: res = res_norm;
122: /* first entry in right-hand-side of hessenberg system is just
123: the initial residual norm */
124: *GRS(0) = res_norm;
126: /* check for the convergence */
127: if (!res) {
128: if (itcount) *itcount = 0;
129: ksp->reason = KSP_CONVERGED_ATOL;
130: PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
131: return 0;
132: }
134: /* scale VEC_VV (the initial residual) */
135: tmp = 1.0/res_norm; VecScale(VEC_VV(0),tmp);
137: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
138: else ksp->rnorm = 0.0;
140: /* note: (lgmres->it) is always set one less than (loc_it) It is used in
141: KSPBUILDSolution_LGMRES, where it is passed to KSPLGMRESBuildSoln.
142: Note that when KSPLGMRESBuildSoln is called from this function,
143: (loc_it -1) is passed, so the two are equivalent */
144: lgmres->it = (loc_it - 1);
146: /* MAIN ITERATION LOOP BEGINNING*/
148: /* keep iterating until we have converged OR generated the max number
149: of directions OR reached the max number of iterations for the method */
150: (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
152: while (!ksp->reason && loc_it < it_total && ksp->its < max_it) { /* LGMRES_MOD: changed to it_total */
153: KSPLogResidualHistory(ksp,res);
154: lgmres->it = (loc_it - 1);
155: KSPMonitor(ksp,ksp->its,res);
157: /* see if more space is needed for work vectors */
158: if (lgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
159: KSPLGMRESGetNewVectors(ksp,loc_it+1);
160: /* (loc_it+1) is passed in as number of the first vector that should
161: be allocated */
162: }
164: /*LGMRES_MOD: decide whether this is an arnoldi step or an aug step */
165: if (loc_it < it_arnoldi) { /* Arnoldi */
166: KSP_PCApplyBAorAB(ksp,VEC_VV(loc_it),VEC_VV(1+loc_it),VEC_TEMP_MATOP);
167: } else { /*aug step */
168: order = loc_it - it_arnoldi + 1; /* which aug step */
169: for (ii=0; ii<aug_dim; ii++) {
170: if (lgmres->aug_order[ii] == order) {
171: spot = ii;
172: break; /* must have this because there will be duplicates before aug_ct = aug_dim */
173: }
174: }
176: VecCopy(A_AUGVEC(spot), VEC_VV(1+loc_it));
177: /*note: an alternate implementation choice would be to only save the AUGVECS and
178: not A_AUGVEC and then apply the PC here to the augvec */
179: }
181: /* update hessenberg matrix and do Gram-Schmidt - new direction is in
182: VEC_VV(1+loc_it)*/
183: (*lgmres->orthog)(ksp,loc_it);
185: /* new entry in hessenburg is the 2-norm of our new direction */
186: VecNorm(VEC_VV(loc_it+1),NORM_2,&tt);
188: *HH(loc_it+1,loc_it) = tt;
189: *HES(loc_it+1,loc_it) = tt;
191: /* check for the happy breakdown */
192: hapbnd = PetscAbsScalar(tt / *GRS(loc_it)); /* GRS(loc_it) contains the res_norm from the last iteration */
193: if (hapbnd > lgmres->haptol) hapbnd = lgmres->haptol;
194: if (tt > hapbnd) {
195: tmp = 1.0/tt;
196: VecScale(VEC_VV(loc_it+1),tmp); /* scale new direction by its norm */
197: } else {
198: PetscInfo(ksp,"Detected happy breakdown, current hapbnd = %g tt = %g\n",(double)hapbnd,(double)tt);
199: hapend = PETSC_TRUE;
200: }
202: /* Now apply rotations to new col of hessenberg (and right side of system),
203: calculate new rotation, and get new residual norm at the same time*/
204: KSPLGMRESUpdateHessenberg(ksp,loc_it,hapend,&res);
205: if (ksp->reason) break;
207: loc_it++;
208: lgmres->it = (loc_it-1); /* Add this here in case it has converged */
210: PetscObjectSAWsTakeAccess((PetscObject)ksp);
211: ksp->its++;
212: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
213: else ksp->rnorm = 0.0;
214: PetscObjectSAWsGrantAccess((PetscObject)ksp);
216: (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
218: /* Catch error in happy breakdown and signal convergence and break from loop */
219: if (hapend) {
220: if (!ksp->reason) {
222: else {
223: ksp->reason = KSP_DIVERGED_BREAKDOWN;
224: break;
225: }
226: }
227: }
228: }
229: /* END OF ITERATION LOOP */
230: KSPLogResidualHistory(ksp,res);
232: /* Monitor if we know that we will not return for a restart */
233: if (ksp->reason || ksp->its >= max_it) {
234: KSPMonitor(ksp, ksp->its, res);
235: }
237: if (itcount) *itcount = loc_it;
239: /*
240: Down here we have to solve for the "best" coefficients of the Krylov
241: columns, add the solution values together, and possibly unwind the
242: preconditioning from the solution
243: */
245: /* Form the solution (or the solution so far) */
246: /* Note: must pass in (loc_it-1) for iteration count so that KSPLGMRESBuildSoln
247: properly navigates */
249: KSPLGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,loc_it-1);
251: /* LGMRES_MOD collect aug vector and A*augvector for future restarts -
252: only if we will be restarting (i.e. this cycle performed it_total
253: iterations) */
254: if (!ksp->reason && ksp->its < max_it && aug_dim > 0) {
256: /*AUG_TEMP contains the new augmentation vector (assigned in KSPLGMRESBuildSoln) */
257: if (!lgmres->aug_ct) {
258: spot = 0;
259: lgmres->aug_ct++;
260: } else if (lgmres->aug_ct < aug_dim) {
261: spot = lgmres->aug_ct;
262: lgmres->aug_ct++;
263: } else { /* truncate */
264: for (ii=0; ii<aug_dim; ii++) {
265: if (lgmres->aug_order[ii] == aug_dim) spot = ii;
266: }
267: }
269: VecCopy(AUG_TEMP, AUGVEC(spot));
270: /*need to normalize */
271: VecNorm(AUGVEC(spot), NORM_2, &tmp_norm);
273: inv_tmp_norm = 1.0/tmp_norm;
275: VecScale(AUGVEC(spot),inv_tmp_norm);
277: /*set new aug vector to order 1 - move all others back one */
278: for (ii=0; ii < aug_dim; ii++) AUG_ORDER(ii)++;
279: AUG_ORDER(spot) = 1;
281: /*now add the A*aug vector to A_AUGVEC(spot) - this is independ. of preconditioning type*/
282: /* want V*H*y - y is in GRS, V is in VEC_VV and H is in HES */
284: /* first do H+*y */
285: avec = lgmres->hwork;
286: PetscArrayzero(avec,it_total+1);
287: for (ii=0; ii < it_total + 1; ii++) {
288: for (jj=0; jj <= ii+1 && jj < it_total+1; jj++) {
289: avec[jj] += *HES(jj ,ii) * *GRS(ii);
290: }
291: }
293: /*now multiply result by V+ */
294: VecSet(VEC_TEMP,0.0);
295: VecMAXPY(VEC_TEMP, it_total+1, avec, &VEC_VV(0)); /*answer is in VEC_TEMP*/
297: /*copy answer to aug location and scale*/
298: VecCopy(VEC_TEMP, A_AUGVEC(spot));
299: VecScale(A_AUGVEC(spot),inv_tmp_norm);
300: }
301: return 0;
302: }
304: /*
305: KSPSolve_LGMRES - This routine applies the LGMRES method.
307: Input Parameter:
308: . ksp - the Krylov space object that was set to use lgmres
310: Output Parameter:
311: . outits - number of iterations used
313: */
315: PetscErrorCode KSPSolve_LGMRES(KSP ksp)
316: {
317: PetscInt cycle_its; /* iterations done in a call to KSPLGMRESCycle */
318: PetscInt itcount; /* running total of iterations, incl. those in restarts */
319: KSP_LGMRES *lgmres = (KSP_LGMRES*)ksp->data;
320: PetscBool guess_zero = ksp->guess_zero;
321: PetscInt ii; /*LGMRES_MOD variable */
325: PetscObjectSAWsTakeAccess((PetscObject)ksp);
327: ksp->its = 0;
328: lgmres->aug_ct = 0;
329: lgmres->matvecs = 0;
331: PetscObjectSAWsGrantAccess((PetscObject)ksp);
333: /* initialize */
334: itcount = 0;
335: /*LGMRES_MOD*/
336: for (ii=0; ii<lgmres->aug_dim; ii++) lgmres->aug_order[ii] = 0;
338: while (!ksp->reason) {
339: /* calc residual - puts in VEC_VV(0) */
340: KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
341: KSPLGMRESCycle(&cycle_its,ksp);
342: itcount += cycle_its;
343: if (itcount >= ksp->max_it) {
344: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
345: break;
346: }
347: ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
348: }
349: ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
350: return 0;
351: }
353: /*
355: KSPDestroy_LGMRES - Frees all memory space used by the Krylov method.
357: */
358: PetscErrorCode KSPDestroy_LGMRES(KSP ksp)
359: {
360: KSP_LGMRES *lgmres = (KSP_LGMRES*)ksp->data;
362: PetscFree(lgmres->augvecs);
363: if (lgmres->augwork_alloc) {
364: VecDestroyVecs(lgmres->augwork_alloc,&lgmres->augvecs_user_work[0]);
365: }
366: PetscFree(lgmres->augvecs_user_work);
367: PetscFree(lgmres->aug_order);
368: PetscFree(lgmres->hwork);
369: KSPDestroy_GMRES(ksp);
370: return 0;
371: }
373: /*
374: KSPLGMRESBuildSoln - create the solution from the starting vector and the
375: current iterates.
377: Input parameters:
378: nrs - work area of size it + 1.
379: vguess - index of initial guess
380: vdest - index of result. Note that vguess may == vdest (replace
381: guess with the solution).
382: it - HH upper triangular part is a block of size (it+1) x (it+1)
384: This is an internal routine that knows about the LGMRES internals.
385: */
386: static PetscErrorCode KSPLGMRESBuildSoln(PetscScalar *nrs,Vec vguess,Vec vdest,KSP ksp,PetscInt it)
387: {
388: PetscScalar tt;
389: PetscInt ii,k,j;
390: KSP_LGMRES *lgmres = (KSP_LGMRES*)(ksp->data);
391: /*LGMRES_MOD */
392: PetscInt it_arnoldi, it_aug;
393: PetscInt jj, spot = 0;
395: /* Solve for solution vector that minimizes the residual */
397: /* If it is < 0, no lgmres steps have been performed */
398: if (it < 0) {
399: VecCopy(vguess,vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
400: return 0;
401: }
403: /* so (it+1) lgmres steps HAVE been performed */
405: /* LGMRES_MOD - determine if we need to use augvecs for the soln - do not assume that
406: this is called after the total its allowed for an approx space */
407: if (lgmres->approx_constant) {
408: it_arnoldi = lgmres->max_k - lgmres->aug_ct;
409: } else {
410: it_arnoldi = lgmres->max_k - lgmres->aug_dim;
411: }
412: if (it_arnoldi >= it +1) {
413: it_aug = 0;
414: it_arnoldi = it+1;
415: } else {
416: it_aug = (it + 1) - it_arnoldi;
417: }
419: /* now it_arnoldi indicates the number of matvecs that took place */
420: lgmres->matvecs += it_arnoldi;
422: /* solve the upper triangular system - GRS is the right side and HH is
423: the upper triangular matrix - put soln in nrs */
425: if (*HH(it,it) != 0.0) {
426: nrs[it] = *GRS(it) / *HH(it,it);
427: } else {
428: nrs[it] = 0.0;
429: }
431: for (ii=1; ii<=it; ii++) {
432: k = it - ii;
433: tt = *GRS(k);
434: for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
435: nrs[k] = tt / *HH(k,k);
436: }
438: /* Accumulate the correction to the soln of the preconditioned prob. in VEC_TEMP */
439: VecSet(VEC_TEMP,0.0); /* set VEC_TEMP components to 0 */
441: /*LGMRES_MOD - if augmenting has happened we need to form the solution
442: using the augvecs */
443: if (!it_aug) { /* all its are from arnoldi */
444: VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));
445: } else { /*use aug vecs */
446: /*first do regular krylov directions */
447: VecMAXPY(VEC_TEMP,it_arnoldi,nrs,&VEC_VV(0));
448: /*now add augmented portions - add contribution of aug vectors one at a time*/
450: for (ii=0; ii<it_aug; ii++) {
451: for (jj=0; jj<lgmres->aug_dim; jj++) {
452: if (lgmres->aug_order[jj] == (ii+1)) {
453: spot = jj;
454: break; /* must have this because there will be duplicates before aug_ct = aug_dim */
455: }
456: }
457: VecAXPY(VEC_TEMP,nrs[it_arnoldi+ii],AUGVEC(spot));
458: }
459: }
460: /* now VEC_TEMP is what we want to keep for augmenting purposes - grab before the
461: preconditioner is "unwound" from right-precondtioning*/
462: VecCopy(VEC_TEMP, AUG_TEMP);
464: KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
466: /* add solution to previous solution */
467: /* put updated solution into vdest.*/
468: VecCopy(vguess,vdest);
469: VecAXPY(vdest,1.0,VEC_TEMP);
470: return 0;
471: }
473: /*
475: KSPLGMRESUpdateHessenberg - Do the scalar work for the orthogonalization.
476: Return new residual.
478: input parameters:
480: . ksp - Krylov space object
481: . it - plane rotations are applied to the (it+1)th column of the
482: modified hessenberg (i.e. HH(:,it))
483: . hapend - PETSC_FALSE not happy breakdown ending.
485: output parameters:
486: . res - the new residual
488: */
489: static PetscErrorCode KSPLGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool hapend,PetscReal *res)
490: {
491: PetscScalar *hh,*cc,*ss,tt;
492: PetscInt j;
493: KSP_LGMRES *lgmres = (KSP_LGMRES*)(ksp->data);
495: hh = HH(0,it); /* pointer to beginning of column to update - so
496: incrementing hh "steps down" the (it+1)th col of HH*/
497: cc = CC(0); /* beginning of cosine rotations */
498: ss = SS(0); /* beginning of sine rotations */
500: /* Apply all the previously computed plane rotations to the new column
501: of the Hessenberg matrix */
502: /* Note: this uses the rotation [conj(c) s ; -s c], c= cos(theta), s= sin(theta) */
504: for (j=1; j<=it; j++) {
505: tt = *hh;
506: *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
507: hh++;
508: *hh = *cc++ * *hh - (*ss++ * tt);
509: /* hh, cc, and ss have all been incremented one by end of loop */
510: }
512: /*
513: compute the new plane rotation, and apply it to:
514: 1) the right-hand-side of the Hessenberg system (GRS)
515: note: it affects GRS(it) and GRS(it+1)
516: 2) the new column of the Hessenberg matrix
517: note: it affects HH(it,it) which is currently pointed to
518: by hh and HH(it+1, it) (*(hh+1))
519: thus obtaining the updated value of the residual...
520: */
522: /* compute new plane rotation */
524: if (!hapend) {
525: tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
526: if (tt == 0.0) {
527: ksp->reason = KSP_DIVERGED_NULL;
528: return 0;
529: }
530: *cc = *hh / tt; /* new cosine value */
531: *ss = *(hh+1) / tt; /* new sine value */
533: /* apply to 1) and 2) */
534: *GRS(it+1) = -(*ss * *GRS(it));
535: *GRS(it) = PetscConj(*cc) * *GRS(it);
536: *hh = PetscConj(*cc) * *hh + *ss * *(hh+1);
538: /* residual is the last element (it+1) of right-hand side! */
539: *res = PetscAbsScalar(*GRS(it+1));
541: } else { /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
542: another rotation matrix (so RH doesn't change). The new residual is
543: always the new sine term times the residual from last time (GRS(it)),
544: but now the new sine rotation would be zero...so the residual should
545: be zero...so we will multiply "zero" by the last residual. This might
546: not be exactly what we want to do here -could just return "zero". */
548: *res = 0.0;
549: }
550: return 0;
551: }
553: /*
555: KSPLGMRESGetNewVectors - This routine allocates more work vectors, starting from
556: VEC_VV(it)
558: */
559: static PetscErrorCode KSPLGMRESGetNewVectors(KSP ksp,PetscInt it)
560: {
561: KSP_LGMRES *lgmres = (KSP_LGMRES*)ksp->data;
562: PetscInt nwork = lgmres->nwork_alloc; /* number of work vector chunks allocated */
563: PetscInt nalloc; /* number to allocate */
564: PetscInt k;
566: nalloc = lgmres->delta_allocate; /* number of vectors to allocate
567: in a single chunk */
569: /* Adjust the number to allocate to make sure that we don't exceed the
570: number of available slots (lgmres->vecs_allocated)*/
571: if (it + VEC_OFFSET + nalloc >= lgmres->vecs_allocated) {
572: nalloc = lgmres->vecs_allocated - it - VEC_OFFSET;
573: }
574: if (!nalloc) return 0;
576: lgmres->vv_allocated += nalloc; /* vv_allocated is the number of vectors allocated */
578: /* work vectors */
579: KSPCreateVecs(ksp,nalloc,&lgmres->user_work[nwork],0,NULL);
580: PetscLogObjectParents(ksp,nalloc,lgmres->user_work[nwork]);
581: /* specify size of chunk allocated */
582: lgmres->mwork_alloc[nwork] = nalloc;
584: for (k=0; k < nalloc; k++) {
585: lgmres->vecs[it+VEC_OFFSET+k] = lgmres->user_work[nwork][k];
586: }
588: /* LGMRES_MOD - for now we are preallocating the augmentation vectors */
590: /* increment the number of work vector chunks */
591: lgmres->nwork_alloc++;
592: return 0;
593: }
595: /*
597: KSPBuildSolution_LGMRES
599: Input Parameter:
600: . ksp - the Krylov space object
601: . ptr-
603: Output Parameter:
604: . result - the solution
606: Note: this calls KSPLGMRESBuildSoln - the same function that KSPLGMRESCycle
607: calls directly.
609: */
610: PetscErrorCode KSPBuildSolution_LGMRES(KSP ksp,Vec ptr,Vec *result)
611: {
612: KSP_LGMRES *lgmres = (KSP_LGMRES*)ksp->data;
614: if (!ptr) {
615: if (!lgmres->sol_temp) {
616: VecDuplicate(ksp->vec_sol,&lgmres->sol_temp);
617: PetscLogObjectParent((PetscObject)ksp,(PetscObject)lgmres->sol_temp);
618: }
619: ptr = lgmres->sol_temp;
620: }
621: if (!lgmres->nrs) {
622: /* allocate the work area */
623: PetscMalloc1(lgmres->max_k,&lgmres->nrs);
624: PetscLogObjectMemory((PetscObject)ksp,lgmres->max_k*sizeof(PetscScalar));
625: }
627: KSPLGMRESBuildSoln(lgmres->nrs,ksp->vec_sol,ptr,ksp,lgmres->it);
628: if (result) *result = ptr;
629: return 0;
630: }
632: PetscErrorCode KSPView_LGMRES(KSP ksp,PetscViewer viewer)
633: {
634: KSP_LGMRES *lgmres = (KSP_LGMRES*)ksp->data;
635: PetscBool iascii;
637: KSPView_GMRES(ksp,viewer);
638: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
639: if (iascii) {
640: /*LGMRES_MOD */
641: PetscViewerASCIIPrintf(viewer," aug. dimension=%D\n",lgmres->aug_dim);
642: if (lgmres->approx_constant) {
643: PetscViewerASCIIPrintf(viewer," approx. space size was kept constant.\n");
644: }
645: PetscViewerASCIIPrintf(viewer," number of matvecs=%D\n",lgmres->matvecs);
646: }
647: return 0;
648: }
650: PetscErrorCode KSPSetFromOptions_LGMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
651: {
652: PetscInt aug;
653: KSP_LGMRES *lgmres = (KSP_LGMRES*) ksp->data;
654: PetscBool flg = PETSC_FALSE;
656: KSPSetFromOptions_GMRES(PetscOptionsObject,ksp);
657: PetscOptionsHead(PetscOptionsObject,"KSP LGMRES Options");
658: PetscOptionsBool("-ksp_lgmres_constant","Use constant approx. space size","KSPGMRESSetConstant",lgmres->approx_constant,&lgmres->approx_constant,NULL);
659: PetscOptionsInt("-ksp_lgmres_augment","Number of error approximations to augment the Krylov space with","KSPLGMRESSetAugDim",lgmres->aug_dim,&aug,&flg);
660: if (flg) KSPLGMRESSetAugDim(ksp,aug);
661: PetscOptionsTail();
662: return 0;
663: }
665: /*functions for extra lgmres options here*/
666: static PetscErrorCode KSPLGMRESSetConstant_LGMRES(KSP ksp)
667: {
668: KSP_LGMRES *lgmres = (KSP_LGMRES*)ksp->data;
670: lgmres->approx_constant = PETSC_TRUE;
671: return 0;
672: }
674: static PetscErrorCode KSPLGMRESSetAugDim_LGMRES(KSP ksp,PetscInt aug_dim)
675: {
676: KSP_LGMRES *lgmres = (KSP_LGMRES*)ksp->data;
680: lgmres->aug_dim = aug_dim;
681: return 0;
682: }
684: /* end new lgmres functions */
686: /*MC
687: KSPLGMRES - Augments the standard GMRES approximation space with approximations to
688: the error from previous restart cycles.
690: Options Database Keys:
691: + -ksp_gmres_restart <restart> - total approximation space size (Krylov directions + error approximations)
692: . -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
693: . -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
694: vectors are allocated as needed)
695: . -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
696: . -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
697: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
698: stability of the classical Gram-Schmidt orthogonalization.
699: . -ksp_gmres_krylov_monitor - plot the Krylov space generated
700: . -ksp_lgmres_augment <k> - number of error approximations to augment the Krylov space with
701: - -ksp_lgmres_constant - use a constant approx. space size (only affects restart cycles < num. error approx.(k), i.e. the first k restarts)
703: To run LGMRES(m, k) as described in the above paper, use:
704: -ksp_gmres_restart <m+k>
705: -ksp_lgmres_augment <k>
707: Level: beginner
709: Notes:
710: Supports both left and right preconditioning, but not symmetric.
712: References:
713: . * - A. H. Baker, E.R. Jessup, and T.A. Manteuffel. A technique for accelerating the convergence of restarted GMRES. SIAM Journal on Matrix Analysis and Applications, 26 (2005).
715: Developer Notes:
716: This object is subclassed off of KSPGMRES
718: Contributed by: Allison Baker
720: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPGMRES,
721: KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
722: KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
723: KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPLGMRESSetAugDim(),
724: KSPGMRESSetConstant()
726: M*/
728: PETSC_EXTERN PetscErrorCode KSPCreate_LGMRES(KSP ksp)
729: {
730: KSP_LGMRES *lgmres;
732: PetscNewLog(ksp,&lgmres);
734: ksp->data = (void*)lgmres;
735: ksp->ops->buildsolution = KSPBuildSolution_LGMRES;
737: ksp->ops->setup = KSPSetUp_LGMRES;
738: ksp->ops->solve = KSPSolve_LGMRES;
739: ksp->ops->destroy = KSPDestroy_LGMRES;
740: ksp->ops->view = KSPView_LGMRES;
741: ksp->ops->setfromoptions = KSPSetFromOptions_LGMRES;
742: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
743: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_GMRES;
745: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
746: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);
747: KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);
749: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
750: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
751: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",KSPGMRESGetOrthogonalization_GMRES);
752: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
753: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);
754: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",KSPGMRESSetHapTol_GMRES);
755: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
756: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",KSPGMRESGetCGSRefinementType_GMRES);
758: /*LGMRES_MOD add extra functions here - like the one to set num of aug vectors */
759: PetscObjectComposeFunction((PetscObject)ksp,"KSPLGMRESSetConstant_C",KSPLGMRESSetConstant_LGMRES);
760: PetscObjectComposeFunction((PetscObject)ksp,"KSPLGMRESSetAugDim_C",KSPLGMRESSetAugDim_LGMRES);
762: /*defaults */
763: lgmres->haptol = 1.0e-30;
764: lgmres->q_preallocate = 0;
765: lgmres->delta_allocate = LGMRES_DELTA_DIRECTIONS;
766: lgmres->orthog = KSPGMRESClassicalGramSchmidtOrthogonalization;
767: lgmres->nrs = NULL;
768: lgmres->sol_temp = NULL;
769: lgmres->max_k = LGMRES_DEFAULT_MAXK;
770: lgmres->Rsvd = NULL;
771: lgmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
772: lgmres->orthogwork = NULL;
774: /*LGMRES_MOD - new defaults */
775: lgmres->aug_dim = LGMRES_DEFAULT_AUGDIM;
776: lgmres->aug_ct = 0; /* start with no aug vectors */
777: lgmres->approx_constant = PETSC_FALSE;
778: lgmres->matvecs = 0;
779: return 0;
780: }