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);
47: /* for now we will preallocate the augvecs - because aug_dim << restart
48: ... also keep in mind that we need to keep augvecs from cycle to cycle*/
49: lgmres->aug_vv_allocated = 2 * aug_dim + AUG_OFFSET;
50: lgmres->augwork_alloc = 2 * aug_dim + AUG_OFFSET;
52: KSPCreateVecs(ksp, lgmres->aug_vv_allocated, &lgmres->augvecs_user_work[0], 0, NULL);
53: PetscMalloc1(max_k + 1, &lgmres->hwork);
54: for (k = 0; k < lgmres->aug_vv_allocated; k++) lgmres->augvecs[k] = lgmres->augvecs_user_work[0][k];
55: return 0;
56: }
58: /*
60: KSPLGMRESCycle - Run lgmres, possibly with restart. Return residual
61: history if requested.
63: input parameters:
64: . lgmres - structure containing parameters and work areas
66: output parameters:
67: . nres - residuals (from preconditioned system) at each step.
68: If restarting, consider passing nres+it. If null,
69: ignored
70: . itcount - number of iterations used. nres[0] to nres[itcount]
71: are defined. If null, ignored. If null, ignored.
72: . converged - 0 if not converged
74: Notes:
75: On entry, the value in vector VEC_VV(0) should be
76: the initial residual.
78: */
79: PetscErrorCode KSPLGMRESCycle(PetscInt *itcount, KSP ksp)
80: {
81: KSP_LGMRES *lgmres = (KSP_LGMRES *)(ksp->data);
82: PetscReal res_norm, res;
83: PetscReal hapbnd, tt;
84: PetscScalar tmp;
85: PetscBool hapend = PETSC_FALSE; /* indicates happy breakdown ending */
86: PetscInt loc_it; /* local count of # of dir. in Krylov space */
87: PetscInt max_k = lgmres->max_k; /* max approx space size */
88: PetscInt max_it = ksp->max_it; /* max # of overall iterations for the method */
90: /* LGMRES_MOD - new variables*/
91: PetscInt aug_dim = lgmres->aug_dim;
92: PetscInt spot = 0;
93: PetscInt order = 0;
94: PetscInt it_arnoldi; /* number of arnoldi steps to take */
95: PetscInt it_total; /* total number of its to take (=approx space size)*/
96: PetscInt ii, jj;
97: PetscReal tmp_norm;
98: PetscScalar inv_tmp_norm;
99: PetscScalar *avec;
101: /* Number of pseudo iterations since last restart is the number
102: of prestart directions */
103: loc_it = 0;
105: /* LGMRES_MOD: determine number of arnoldi steps to take */
106: /* if approx_constant then we keep the space the same size even if
107: we don't have the full number of aug vectors yet*/
108: if (lgmres->approx_constant) it_arnoldi = max_k - lgmres->aug_ct;
109: else it_arnoldi = max_k - aug_dim;
111: it_total = it_arnoldi + lgmres->aug_ct;
113: /* initial residual is in VEC_VV(0) - compute its norm*/
114: VecNorm(VEC_VV(0), NORM_2, &res_norm);
115: KSPCheckNorm(ksp, res_norm);
116: res = res_norm;
118: /* first entry in right-hand-side of hessenberg system is just
119: the initial residual norm */
120: *GRS(0) = res_norm;
122: /* check for the convergence */
123: if (!res) {
124: if (itcount) *itcount = 0;
125: ksp->reason = KSP_CONVERGED_ATOL;
126: PetscInfo(ksp, "Converged due to zero residual norm on entry\n");
127: return 0;
128: }
130: /* scale VEC_VV (the initial residual) */
131: tmp = 1.0 / res_norm;
132: VecScale(VEC_VV(0), tmp);
134: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
135: else ksp->rnorm = 0.0;
137: /* note: (lgmres->it) is always set one less than (loc_it) It is used in
138: KSPBUILDSolution_LGMRES, where it is passed to KSPLGMRESBuildSoln.
139: Note that when KSPLGMRESBuildSoln is called from this function,
140: (loc_it -1) is passed, so the two are equivalent */
141: lgmres->it = (loc_it - 1);
143: /* MAIN ITERATION LOOP BEGINNING*/
145: /* keep iterating until we have converged OR generated the max number
146: of directions OR reached the max number of iterations for the method */
147: (*ksp->converged)(ksp, ksp->its, res, &ksp->reason, ksp->cnvP);
149: while (!ksp->reason && loc_it < it_total && ksp->its < max_it) { /* LGMRES_MOD: changed to it_total */
150: KSPLogResidualHistory(ksp, res);
151: lgmres->it = (loc_it - 1);
152: KSPMonitor(ksp, ksp->its, res);
154: /* see if more space is needed for work vectors */
155: if (lgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
156: KSPLGMRESGetNewVectors(ksp, loc_it + 1);
157: /* (loc_it+1) is passed in as number of the first vector that should
158: be allocated */
159: }
161: /*LGMRES_MOD: decide whether this is an arnoldi step or an aug step */
162: if (loc_it < it_arnoldi) { /* Arnoldi */
163: KSP_PCApplyBAorAB(ksp, VEC_VV(loc_it), VEC_VV(1 + loc_it), VEC_TEMP_MATOP);
164: } else { /*aug step */
165: order = loc_it - it_arnoldi + 1; /* which aug step */
166: for (ii = 0; ii < aug_dim; ii++) {
167: if (lgmres->aug_order[ii] == order) {
168: spot = ii;
169: break; /* must have this because there will be duplicates before aug_ct = aug_dim */
170: }
171: }
173: VecCopy(A_AUGVEC(spot), VEC_VV(1 + loc_it));
174: /*note: an alternate implementation choice would be to only save the AUGVECS and
175: not A_AUGVEC and then apply the PC here to the augvec */
176: }
178: /* update hessenberg matrix and do Gram-Schmidt - new direction is in
179: VEC_VV(1+loc_it)*/
180: (*lgmres->orthog)(ksp, loc_it);
182: /* new entry in hessenburg is the 2-norm of our new direction */
183: VecNorm(VEC_VV(loc_it + 1), NORM_2, &tt);
185: *HH(loc_it + 1, loc_it) = tt;
186: *HES(loc_it + 1, loc_it) = tt;
188: /* check for the happy breakdown */
189: hapbnd = PetscAbsScalar(tt / *GRS(loc_it)); /* GRS(loc_it) contains the res_norm from the last iteration */
190: if (hapbnd > lgmres->haptol) hapbnd = lgmres->haptol;
191: if (tt > hapbnd) {
192: tmp = 1.0 / tt;
193: VecScale(VEC_VV(loc_it + 1), tmp); /* scale new direction by its norm */
194: } else {
195: PetscInfo(ksp, "Detected happy breakdown, current hapbnd = %g tt = %g\n", (double)hapbnd, (double)tt);
196: hapend = PETSC_TRUE;
197: }
199: /* Now apply rotations to new col of hessenberg (and right side of system),
200: calculate new rotation, and get new residual norm at the same time*/
201: KSPLGMRESUpdateHessenberg(ksp, loc_it, hapend, &res);
202: if (ksp->reason) break;
204: loc_it++;
205: lgmres->it = (loc_it - 1); /* Add this here in case it has converged */
207: PetscObjectSAWsTakeAccess((PetscObject)ksp);
208: ksp->its++;
209: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
210: else ksp->rnorm = 0.0;
211: PetscObjectSAWsGrantAccess((PetscObject)ksp);
213: (*ksp->converged)(ksp, ksp->its, res, &ksp->reason, ksp->cnvP);
215: /* Catch error in happy breakdown and signal convergence and break from loop */
216: if (hapend) {
217: if (!ksp->reason) {
219: ksp->reason = KSP_DIVERGED_BREAKDOWN;
220: break;
221: }
222: }
223: }
224: /* END OF ITERATION LOOP */
225: KSPLogResidualHistory(ksp, res);
227: /* Monitor if we know that we will not return for a restart */
228: if (ksp->reason || ksp->its >= max_it) KSPMonitor(ksp, ksp->its, res);
230: if (itcount) *itcount = loc_it;
232: /*
233: Down here we have to solve for the "best" coefficients of the Krylov
234: columns, add the solution values together, and possibly unwind the
235: preconditioning from the solution
236: */
238: /* Form the solution (or the solution so far) */
239: /* Note: must pass in (loc_it-1) for iteration count so that KSPLGMRESBuildSoln
240: properly navigates */
242: KSPLGMRESBuildSoln(GRS(0), ksp->vec_sol, ksp->vec_sol, ksp, loc_it - 1);
244: /* LGMRES_MOD collect aug vector and A*augvector for future restarts -
245: only if we will be restarting (i.e. this cycle performed it_total
246: iterations) */
247: if (!ksp->reason && ksp->its < max_it && aug_dim > 0) {
248: /*AUG_TEMP contains the new augmentation vector (assigned in KSPLGMRESBuildSoln) */
249: if (!lgmres->aug_ct) {
250: spot = 0;
251: lgmres->aug_ct++;
252: } else if (lgmres->aug_ct < aug_dim) {
253: spot = lgmres->aug_ct;
254: lgmres->aug_ct++;
255: } else { /* truncate */
256: for (ii = 0; ii < aug_dim; ii++) {
257: if (lgmres->aug_order[ii] == aug_dim) spot = ii;
258: }
259: }
261: VecCopy(AUG_TEMP, AUGVEC(spot));
262: /*need to normalize */
263: VecNorm(AUGVEC(spot), NORM_2, &tmp_norm);
265: inv_tmp_norm = 1.0 / tmp_norm;
267: VecScale(AUGVEC(spot), inv_tmp_norm);
269: /*set new aug vector to order 1 - move all others back one */
270: for (ii = 0; ii < aug_dim; ii++) AUG_ORDER(ii)++;
271: AUG_ORDER(spot) = 1;
273: /*now add the A*aug vector to A_AUGVEC(spot) - this is independ. of preconditioning type*/
274: /* want V*H*y - y is in GRS, V is in VEC_VV and H is in HES */
276: /* first do H+*y */
277: avec = lgmres->hwork;
278: PetscArrayzero(avec, it_total + 1);
279: for (ii = 0; ii < it_total + 1; ii++) {
280: for (jj = 0; jj <= ii + 1 && jj < it_total + 1; jj++) avec[jj] += *HES(jj, ii) * *GRS(ii);
281: }
283: /*now multiply result by V+ */
284: VecSet(VEC_TEMP, 0.0);
285: VecMAXPY(VEC_TEMP, it_total + 1, avec, &VEC_VV(0)); /*answer is in VEC_TEMP*/
287: /*copy answer to aug location and scale*/
288: VecCopy(VEC_TEMP, A_AUGVEC(spot));
289: VecScale(A_AUGVEC(spot), inv_tmp_norm);
290: }
291: return 0;
292: }
294: /*
295: KSPSolve_LGMRES - This routine applies the LGMRES method.
297: Input Parameter:
298: . ksp - the Krylov space object that was set to use lgmres
300: Output Parameter:
301: . outits - number of iterations used
303: */
305: PetscErrorCode KSPSolve_LGMRES(KSP ksp)
306: {
307: PetscInt cycle_its; /* iterations done in a call to KSPLGMRESCycle */
308: PetscInt itcount; /* running total of iterations, incl. those in restarts */
309: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
310: PetscBool guess_zero = ksp->guess_zero;
311: PetscInt ii; /*LGMRES_MOD variable */
315: PetscObjectSAWsTakeAccess((PetscObject)ksp);
317: ksp->its = 0;
318: lgmres->aug_ct = 0;
319: lgmres->matvecs = 0;
321: PetscObjectSAWsGrantAccess((PetscObject)ksp);
323: /* initialize */
324: itcount = 0;
325: /*LGMRES_MOD*/
326: for (ii = 0; ii < lgmres->aug_dim; ii++) lgmres->aug_order[ii] = 0;
328: while (!ksp->reason) {
329: /* calc residual - puts in VEC_VV(0) */
330: KSPInitialResidual(ksp, ksp->vec_sol, VEC_TEMP, VEC_TEMP_MATOP, VEC_VV(0), ksp->vec_rhs);
331: KSPLGMRESCycle(&cycle_its, ksp);
332: itcount += cycle_its;
333: if (itcount >= ksp->max_it) {
334: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
335: break;
336: }
337: ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
338: }
339: ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
340: return 0;
341: }
343: /*
345: KSPDestroy_LGMRES - Frees all memory space used by the Krylov method.
347: */
348: PetscErrorCode KSPDestroy_LGMRES(KSP ksp)
349: {
350: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
352: PetscFree(lgmres->augvecs);
353: if (lgmres->augwork_alloc) VecDestroyVecs(lgmres->augwork_alloc, &lgmres->augvecs_user_work[0]);
354: PetscFree(lgmres->augvecs_user_work);
355: PetscFree(lgmres->aug_order);
356: PetscFree(lgmres->hwork);
357: PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetConstant_C", NULL);
358: PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetAugDim_C", NULL);
359: KSPDestroy_GMRES(ksp);
360: return 0;
361: }
363: /*
364: KSPLGMRESBuildSoln - create the solution from the starting vector and the
365: current iterates.
367: Input parameters:
368: nrs - work area of size it + 1.
369: vguess - index of initial guess
370: vdest - index of result. Note that vguess may == vdest (replace
371: guess with the solution).
372: it - HH upper triangular part is a block of size (it+1) x (it+1)
374: This is an internal routine that knows about the LGMRES internals.
375: */
376: static PetscErrorCode KSPLGMRESBuildSoln(PetscScalar *nrs, Vec vguess, Vec vdest, KSP ksp, PetscInt it)
377: {
378: PetscScalar tt;
379: PetscInt ii, k, j;
380: KSP_LGMRES *lgmres = (KSP_LGMRES *)(ksp->data);
381: /*LGMRES_MOD */
382: PetscInt it_arnoldi, it_aug;
383: PetscInt jj, spot = 0;
385: /* Solve for solution vector that minimizes the residual */
387: /* If it is < 0, no lgmres steps have been performed */
388: if (it < 0) {
389: VecCopy(vguess, vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
390: return 0;
391: }
393: /* so (it+1) lgmres steps HAVE been performed */
395: /* LGMRES_MOD - determine if we need to use augvecs for the soln - do not assume that
396: this is called after the total its allowed for an approx space */
397: if (lgmres->approx_constant) {
398: it_arnoldi = lgmres->max_k - lgmres->aug_ct;
399: } else {
400: it_arnoldi = lgmres->max_k - lgmres->aug_dim;
401: }
402: if (it_arnoldi >= it + 1) {
403: it_aug = 0;
404: it_arnoldi = it + 1;
405: } else {
406: it_aug = (it + 1) - it_arnoldi;
407: }
409: /* now it_arnoldi indicates the number of matvecs that took place */
410: lgmres->matvecs += it_arnoldi;
412: /* solve the upper triangular system - GRS is the right side and HH is
413: the upper triangular matrix - put soln in nrs */
415: if (*HH(it, it) != 0.0) {
416: nrs[it] = *GRS(it) / *HH(it, it);
417: } else {
418: nrs[it] = 0.0;
419: }
421: for (ii = 1; ii <= it; ii++) {
422: k = it - ii;
423: tt = *GRS(k);
424: for (j = k + 1; j <= it; j++) tt = tt - *HH(k, j) * nrs[j];
425: nrs[k] = tt / *HH(k, k);
426: }
428: /* Accumulate the correction to the soln of the preconditioned prob. in VEC_TEMP */
429: VecSet(VEC_TEMP, 0.0); /* set VEC_TEMP components to 0 */
431: /*LGMRES_MOD - if augmenting has happened we need to form the solution
432: using the augvecs */
433: if (!it_aug) { /* all its are from arnoldi */
434: VecMAXPY(VEC_TEMP, it + 1, nrs, &VEC_VV(0));
435: } else { /*use aug vecs */
436: /*first do regular krylov directions */
437: VecMAXPY(VEC_TEMP, it_arnoldi, nrs, &VEC_VV(0));
438: /*now add augmented portions - add contribution of aug vectors one at a time*/
440: for (ii = 0; ii < it_aug; ii++) {
441: for (jj = 0; jj < lgmres->aug_dim; jj++) {
442: if (lgmres->aug_order[jj] == (ii + 1)) {
443: spot = jj;
444: break; /* must have this because there will be duplicates before aug_ct = aug_dim */
445: }
446: }
447: VecAXPY(VEC_TEMP, nrs[it_arnoldi + ii], AUGVEC(spot));
448: }
449: }
450: /* now VEC_TEMP is what we want to keep for augmenting purposes - grab before the
451: preconditioner is "unwound" from right-precondtioning*/
452: VecCopy(VEC_TEMP, AUG_TEMP);
454: KSPUnwindPreconditioner(ksp, VEC_TEMP, VEC_TEMP_MATOP);
456: /* add solution to previous solution */
457: /* put updated solution into vdest.*/
458: VecCopy(vguess, vdest);
459: VecAXPY(vdest, 1.0, VEC_TEMP);
460: return 0;
461: }
463: /*
465: KSPLGMRESUpdateHessenberg - Do the scalar work for the orthogonalization.
466: Return new residual.
468: input parameters:
470: . ksp - Krylov space object
471: . it - plane rotations are applied to the (it+1)th column of the
472: modified hessenberg (i.e. HH(:,it))
473: . hapend - PETSC_FALSE not happy breakdown ending.
475: output parameters:
476: . res - the new residual
478: */
479: static PetscErrorCode KSPLGMRESUpdateHessenberg(KSP ksp, PetscInt it, PetscBool hapend, PetscReal *res)
480: {
481: PetscScalar *hh, *cc, *ss, tt;
482: PetscInt j;
483: KSP_LGMRES *lgmres = (KSP_LGMRES *)(ksp->data);
485: hh = HH(0, it); /* pointer to beginning of column to update - so
486: incrementing hh "steps down" the (it+1)th col of HH*/
487: cc = CC(0); /* beginning of cosine rotations */
488: ss = SS(0); /* beginning of sine rotations */
490: /* Apply all the previously computed plane rotations to the new column
491: of the Hessenberg matrix */
492: /* Note: this uses the rotation [conj(c) s ; -s c], c= cos(theta), s= sin(theta) */
494: for (j = 1; j <= it; j++) {
495: tt = *hh;
496: *hh = PetscConj(*cc) * tt + *ss * *(hh + 1);
497: hh++;
498: *hh = *cc++ * *hh - (*ss++ * tt);
499: /* hh, cc, and ss have all been incremented one by end of loop */
500: }
502: /*
503: compute the new plane rotation, and apply it to:
504: 1) the right-hand-side of the Hessenberg system (GRS)
505: note: it affects GRS(it) and GRS(it+1)
506: 2) the new column of the Hessenberg matrix
507: note: it affects HH(it,it) which is currently pointed to
508: by hh and HH(it+1, it) (*(hh+1))
509: thus obtaining the updated value of the residual...
510: */
512: /* compute new plane rotation */
514: if (!hapend) {
515: tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh + 1)) * *(hh + 1));
516: if (tt == 0.0) {
517: ksp->reason = KSP_DIVERGED_NULL;
518: return 0;
519: }
520: *cc = *hh / tt; /* new cosine value */
521: *ss = *(hh + 1) / tt; /* new sine value */
523: /* apply to 1) and 2) */
524: *GRS(it + 1) = -(*ss * *GRS(it));
525: *GRS(it) = PetscConj(*cc) * *GRS(it);
526: *hh = PetscConj(*cc) * *hh + *ss * *(hh + 1);
528: /* residual is the last element (it+1) of right-hand side! */
529: *res = PetscAbsScalar(*GRS(it + 1));
531: } else { /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
532: another rotation matrix (so RH doesn't change). The new residual is
533: always the new sine term times the residual from last time (GRS(it)),
534: but now the new sine rotation would be zero...so the residual should
535: be zero...so we will multiply "zero" by the last residual. This might
536: not be exactly what we want to do here -could just return "zero". */
538: *res = 0.0;
539: }
540: return 0;
541: }
543: /*
545: KSPLGMRESGetNewVectors - This routine allocates more work vectors, starting from
546: VEC_VV(it)
548: */
549: static PetscErrorCode KSPLGMRESGetNewVectors(KSP ksp, PetscInt it)
550: {
551: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
552: PetscInt nwork = lgmres->nwork_alloc; /* number of work vector chunks allocated */
553: PetscInt nalloc; /* number to allocate */
554: PetscInt k;
556: nalloc = lgmres->delta_allocate; /* number of vectors to allocate
557: in a single chunk */
559: /* Adjust the number to allocate to make sure that we don't exceed the
560: number of available slots (lgmres->vecs_allocated)*/
561: if (it + VEC_OFFSET + nalloc >= lgmres->vecs_allocated) nalloc = lgmres->vecs_allocated - it - VEC_OFFSET;
562: if (!nalloc) return 0;
564: lgmres->vv_allocated += nalloc; /* vv_allocated is the number of vectors allocated */
566: /* work vectors */
567: KSPCreateVecs(ksp, nalloc, &lgmres->user_work[nwork], 0, NULL);
568: /* specify size of chunk allocated */
569: lgmres->mwork_alloc[nwork] = nalloc;
571: for (k = 0; k < nalloc; k++) lgmres->vecs[it + VEC_OFFSET + k] = lgmres->user_work[nwork][k];
573: /* LGMRES_MOD - for now we are preallocating the augmentation vectors */
575: /* increment the number of work vector chunks */
576: lgmres->nwork_alloc++;
577: return 0;
578: }
580: /*
582: KSPBuildSolution_LGMRES
584: Input Parameter:
585: . ksp - the Krylov space object
586: . ptr-
588: Output Parameter:
589: . result - the solution
591: Note: this calls KSPLGMRESBuildSoln - the same function that KSPLGMRESCycle
592: calls directly.
594: */
595: PetscErrorCode KSPBuildSolution_LGMRES(KSP ksp, Vec ptr, Vec *result)
596: {
597: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
599: if (!ptr) {
600: if (!lgmres->sol_temp) { VecDuplicate(ksp->vec_sol, &lgmres->sol_temp); }
601: ptr = lgmres->sol_temp;
602: }
603: if (!lgmres->nrs) {
604: /* allocate the work area */
605: PetscMalloc1(lgmres->max_k, &lgmres->nrs);
606: }
608: KSPLGMRESBuildSoln(lgmres->nrs, ksp->vec_sol, ptr, ksp, lgmres->it);
609: if (result) *result = ptr;
610: return 0;
611: }
613: PetscErrorCode KSPView_LGMRES(KSP ksp, PetscViewer viewer)
614: {
615: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
616: PetscBool iascii;
618: KSPView_GMRES(ksp, viewer);
619: PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii);
620: if (iascii) {
621: /*LGMRES_MOD */
622: PetscViewerASCIIPrintf(viewer, " aug. dimension=%" PetscInt_FMT "\n", lgmres->aug_dim);
623: if (lgmres->approx_constant) PetscViewerASCIIPrintf(viewer, " approx. space size was kept constant.\n");
624: PetscViewerASCIIPrintf(viewer, " number of matvecs=%" PetscInt_FMT "\n", lgmres->matvecs);
625: }
626: return 0;
627: }
629: PetscErrorCode KSPSetFromOptions_LGMRES(KSP ksp, PetscOptionItems *PetscOptionsObject)
630: {
631: PetscInt aug;
632: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
633: PetscBool flg = PETSC_FALSE;
635: KSPSetFromOptions_GMRES(ksp, PetscOptionsObject);
636: PetscOptionsHeadBegin(PetscOptionsObject, "KSP LGMRES Options");
637: PetscOptionsBool("-ksp_lgmres_constant", "Use constant approx. space size", "KSPGMRESSetConstant", lgmres->approx_constant, &lgmres->approx_constant, NULL);
638: PetscOptionsInt("-ksp_lgmres_augment", "Number of error approximations to augment the Krylov space with", "KSPLGMRESSetAugDim", lgmres->aug_dim, &aug, &flg);
639: if (flg) KSPLGMRESSetAugDim(ksp, aug);
640: PetscOptionsHeadEnd();
641: return 0;
642: }
644: /*functions for extra lgmres options here*/
645: static PetscErrorCode KSPLGMRESSetConstant_LGMRES(KSP ksp)
646: {
647: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
649: lgmres->approx_constant = PETSC_TRUE;
650: return 0;
651: }
653: static PetscErrorCode KSPLGMRESSetAugDim_LGMRES(KSP ksp, PetscInt aug_dim)
654: {
655: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
659: lgmres->aug_dim = aug_dim;
660: return 0;
661: }
663: /* end new lgmres functions */
665: /*MC
666: KSPLGMRES - Augments the standard GMRES approximation space with approximations to
667: the error from previous restart cycles.
669: Options Database Keys:
670: + -ksp_gmres_restart <restart> - total approximation space size (Krylov directions + error approximations)
671: . -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
672: . -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
673: vectors are allocated as needed)
674: . -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
675: . -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
676: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
677: stability of the classical Gram-Schmidt orthogonalization.
678: . -ksp_gmres_krylov_monitor - plot the Krylov space generated
679: . -ksp_lgmres_augment <k> - number of error approximations to augment the Krylov space with
680: - -ksp_lgmres_constant - use a constant approx. space size (only affects restart cycles < num. error approx.(k), i.e. the first k restarts)
682: To run LGMRES(m, k) as described in the above paper, use:
683: -ksp_gmres_restart <m+k>
684: -ksp_lgmres_augment <k>
686: Level: beginner
688: Notes:
689: Supports both left and right preconditioning, but not symmetric.
691: References:
692: . * - 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).
694: Developer Notes:
695: This object is subclassed off of KSPGMRES
697: Contributed by: Allison Baker
699: .seealso: `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPFGMRES`, `KSPGMRES`,
700: `KSPGMRESSetRestart()`, `KSPGMRESSetHapTol()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESGetOrthogonalization()`,
701: `KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESModifiedGramSchmidtOrthogonalization()`,
702: `KSPGMRESCGSRefinementType`, `KSPGMRESSetCGSRefinementType()`, `KSPGMRESGetCGSRefinementType()`, `KSPGMRESMonitorKrylov()`, `KSPLGMRESSetAugDim()`,
703: `KSPGMRESSetConstant()`
705: M*/
707: PETSC_EXTERN PetscErrorCode KSPCreate_LGMRES(KSP ksp)
708: {
709: KSP_LGMRES *lgmres;
711: PetscNew(&lgmres);
713: ksp->data = (void *)lgmres;
714: ksp->ops->buildsolution = KSPBuildSolution_LGMRES;
716: ksp->ops->setup = KSPSetUp_LGMRES;
717: ksp->ops->solve = KSPSolve_LGMRES;
718: ksp->ops->destroy = KSPDestroy_LGMRES;
719: ksp->ops->view = KSPView_LGMRES;
720: ksp->ops->setfromoptions = KSPSetFromOptions_LGMRES;
721: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
722: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_GMRES;
724: KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3);
725: KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2);
726: KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1);
728: PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetPreAllocateVectors_C", KSPGMRESSetPreAllocateVectors_GMRES);
729: PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetOrthogonalization_C", KSPGMRESSetOrthogonalization_GMRES);
730: PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetOrthogonalization_C", KSPGMRESGetOrthogonalization_GMRES);
731: PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetRestart_C", KSPGMRESSetRestart_GMRES);
732: PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetRestart_C", KSPGMRESGetRestart_GMRES);
733: PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetHapTol_C", KSPGMRESSetHapTol_GMRES);
734: PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetCGSRefinementType_C", KSPGMRESSetCGSRefinementType_GMRES);
735: PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetCGSRefinementType_C", KSPGMRESGetCGSRefinementType_GMRES);
737: /*LGMRES_MOD add extra functions here - like the one to set num of aug vectors */
738: PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetConstant_C", KSPLGMRESSetConstant_LGMRES);
739: PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetAugDim_C", KSPLGMRESSetAugDim_LGMRES);
741: /*defaults */
742: lgmres->haptol = 1.0e-30;
743: lgmres->q_preallocate = 0;
744: lgmres->delta_allocate = LGMRES_DELTA_DIRECTIONS;
745: lgmres->orthog = KSPGMRESClassicalGramSchmidtOrthogonalization;
746: lgmres->nrs = NULL;
747: lgmres->sol_temp = NULL;
748: lgmres->max_k = LGMRES_DEFAULT_MAXK;
749: lgmres->Rsvd = NULL;
750: lgmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
751: lgmres->orthogwork = NULL;
753: /*LGMRES_MOD - new defaults */
754: lgmres->aug_dim = LGMRES_DEFAULT_AUGDIM;
755: lgmres->aug_ct = 0; /* start with no aug vectors */
756: lgmres->approx_constant = PETSC_FALSE;
757: lgmres->matvecs = 0;
758: return 0;
759: }