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: /*
59: KSPLGMRESCycle - Run lgmres, possibly with restart. Return residual
60: history if requested.
62: input parameters:
63: . lgmres - structure containing parameters and work areas
65: output parameters:
66: . nres - residuals (from preconditioned system) at each step.
67: If restarting, consider passing nres+it. If null,
68: ignored
69: . itcount - number of iterations used. nres[0] to nres[itcount]
70: are defined. If null, ignored. If null, ignored.
71: . converged - 0 if not converged
73: Notes:
74: On entry, the value in vector VEC_VV(0) should be
75: the initial residual.
76: */
77: PetscErrorCode KSPLGMRESCycle(PetscInt *itcount, KSP ksp)
78: {
79: KSP_LGMRES *lgmres = (KSP_LGMRES *)(ksp->data);
80: PetscReal res_norm, res;
81: PetscReal hapbnd, tt;
82: PetscScalar tmp;
83: PetscBool hapend = PETSC_FALSE; /* indicates happy breakdown ending */
84: PetscInt loc_it; /* local count of # of dir. in Krylov space */
85: PetscInt max_k = lgmres->max_k; /* max approx space size */
86: PetscInt max_it = ksp->max_it; /* max # of overall iterations for the method */
88: /* LGMRES_MOD - new variables*/
89: PetscInt aug_dim = lgmres->aug_dim;
90: PetscInt spot = 0;
91: PetscInt order = 0;
92: PetscInt it_arnoldi; /* number of arnoldi steps to take */
93: PetscInt it_total; /* total number of its to take (=approx space size)*/
94: PetscInt ii, jj;
95: PetscReal tmp_norm;
96: PetscScalar inv_tmp_norm;
97: PetscScalar *avec;
99: /* Number of pseudo iterations since last restart is the number
100: of prestart directions */
101: loc_it = 0;
103: /* LGMRES_MOD: determine number of arnoldi steps to take */
104: /* if approx_constant then we keep the space the same size even if
105: we don't have the full number of aug vectors yet*/
106: if (lgmres->approx_constant) it_arnoldi = max_k - lgmres->aug_ct;
107: else it_arnoldi = max_k - aug_dim;
109: it_total = it_arnoldi + lgmres->aug_ct;
111: /* initial residual is in VEC_VV(0) - compute its norm*/
112: VecNorm(VEC_VV(0), NORM_2, &res_norm);
113: KSPCheckNorm(ksp, res_norm);
114: res = res_norm;
116: /* first entry in right-hand-side of hessenberg system is just
117: the initial residual norm */
118: *GRS(0) = res_norm;
120: /* check for the convergence */
121: if (!res) {
122: if (itcount) *itcount = 0;
123: ksp->reason = KSP_CONVERGED_ATOL;
124: PetscInfo(ksp, "Converged due to zero residual norm on entry\n");
125: return 0;
126: }
128: /* scale VEC_VV (the initial residual) */
129: tmp = 1.0 / res_norm;
130: VecScale(VEC_VV(0), tmp);
132: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
133: else ksp->rnorm = 0.0;
135: /* note: (lgmres->it) is always set one less than (loc_it) It is used in
136: KSPBUILDSolution_LGMRES, where it is passed to KSPLGMRESBuildSoln.
137: Note that when KSPLGMRESBuildSoln is called from this function,
138: (loc_it -1) is passed, so the two are equivalent */
139: lgmres->it = (loc_it - 1);
141: /* MAIN ITERATION LOOP BEGINNING*/
143: /* keep iterating until we have converged OR generated the max number
144: of directions OR reached the max number of iterations for the method */
145: (*ksp->converged)(ksp, ksp->its, res, &ksp->reason, ksp->cnvP);
147: while (!ksp->reason && loc_it < it_total && ksp->its < max_it) { /* LGMRES_MOD: changed to it_total */
148: KSPLogResidualHistory(ksp, res);
149: lgmres->it = (loc_it - 1);
150: KSPMonitor(ksp, ksp->its, res);
152: /* see if more space is needed for work vectors */
153: if (lgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
154: KSPLGMRESGetNewVectors(ksp, loc_it + 1);
155: /* (loc_it+1) is passed in as number of the first vector that should
156: be allocated */
157: }
159: /*LGMRES_MOD: decide whether this is an arnoldi step or an aug step */
160: if (loc_it < it_arnoldi) { /* Arnoldi */
161: KSP_PCApplyBAorAB(ksp, VEC_VV(loc_it), VEC_VV(1 + loc_it), VEC_TEMP_MATOP);
162: } else { /*aug step */
163: order = loc_it - it_arnoldi + 1; /* which aug step */
164: for (ii = 0; ii < aug_dim; ii++) {
165: if (lgmres->aug_order[ii] == order) {
166: spot = ii;
167: break; /* must have this because there will be duplicates before aug_ct = aug_dim */
168: }
169: }
171: VecCopy(A_AUGVEC(spot), VEC_VV(1 + loc_it));
172: /*note: an alternate implementation choice would be to only save the AUGVECS and
173: not A_AUGVEC and then apply the PC here to the augvec */
174: }
176: /* update hessenberg matrix and do Gram-Schmidt - new direction is in
177: VEC_VV(1+loc_it)*/
178: (*lgmres->orthog)(ksp, loc_it);
180: /* new entry in hessenburg is the 2-norm of our new direction */
181: VecNorm(VEC_VV(loc_it + 1), NORM_2, &tt);
183: *HH(loc_it + 1, loc_it) = tt;
184: *HES(loc_it + 1, loc_it) = tt;
186: /* check for the happy breakdown */
187: hapbnd = PetscAbsScalar(tt / *GRS(loc_it)); /* GRS(loc_it) contains the res_norm from the last iteration */
188: if (hapbnd > lgmres->haptol) hapbnd = lgmres->haptol;
189: if (tt > hapbnd) {
190: tmp = 1.0 / tt;
191: VecScale(VEC_VV(loc_it + 1), tmp); /* scale new direction by its norm */
192: } else {
193: PetscInfo(ksp, "Detected happy breakdown, current hapbnd = %g tt = %g\n", (double)hapbnd, (double)tt);
194: hapend = PETSC_TRUE;
195: }
197: /* Now apply rotations to new col of hessenberg (and right side of system),
198: calculate new rotation, and get new residual norm at the same time*/
199: KSPLGMRESUpdateHessenberg(ksp, loc_it, hapend, &res);
200: if (ksp->reason) break;
202: loc_it++;
203: lgmres->it = (loc_it - 1); /* Add this here in case it has converged */
205: PetscObjectSAWsTakeAccess((PetscObject)ksp);
206: ksp->its++;
207: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
208: else ksp->rnorm = 0.0;
209: PetscObjectSAWsGrantAccess((PetscObject)ksp);
211: (*ksp->converged)(ksp, ksp->its, res, &ksp->reason, ksp->cnvP);
213: /* Catch error in happy breakdown and signal convergence and break from loop */
214: if (hapend) {
215: if (!ksp->reason) {
217: ksp->reason = KSP_DIVERGED_BREAKDOWN;
218: break;
219: }
220: }
221: }
222: /* END OF ITERATION LOOP */
223: KSPLogResidualHistory(ksp, res);
225: /* Monitor if we know that we will not return for a restart */
226: if (ksp->reason || ksp->its >= max_it) KSPMonitor(ksp, ksp->its, res);
228: if (itcount) *itcount = loc_it;
230: /*
231: Down here we have to solve for the "best" coefficients of the Krylov
232: columns, add the solution values together, and possibly unwind the
233: preconditioning from the solution
234: */
236: /* Form the solution (or the solution so far) */
237: /* Note: must pass in (loc_it-1) for iteration count so that KSPLGMRESBuildSoln
238: properly navigates */
240: KSPLGMRESBuildSoln(GRS(0), ksp->vec_sol, ksp->vec_sol, ksp, loc_it - 1);
242: /* LGMRES_MOD collect aug vector and A*augvector for future restarts -
243: only if we will be restarting (i.e. this cycle performed it_total
244: iterations) */
245: if (!ksp->reason && ksp->its < max_it && aug_dim > 0) {
246: /*AUG_TEMP contains the new augmentation vector (assigned in KSPLGMRESBuildSoln) */
247: if (!lgmres->aug_ct) {
248: spot = 0;
249: lgmres->aug_ct++;
250: } else if (lgmres->aug_ct < aug_dim) {
251: spot = lgmres->aug_ct;
252: lgmres->aug_ct++;
253: } else { /* truncate */
254: for (ii = 0; ii < aug_dim; ii++) {
255: if (lgmres->aug_order[ii] == aug_dim) spot = ii;
256: }
257: }
259: VecCopy(AUG_TEMP, AUGVEC(spot));
260: /*need to normalize */
261: VecNorm(AUGVEC(spot), NORM_2, &tmp_norm);
263: inv_tmp_norm = 1.0 / tmp_norm;
265: VecScale(AUGVEC(spot), inv_tmp_norm);
267: /*set new aug vector to order 1 - move all others back one */
268: for (ii = 0; ii < aug_dim; ii++) AUG_ORDER(ii)++;
269: AUG_ORDER(spot) = 1;
271: /*now add the A*aug vector to A_AUGVEC(spot) - this is independent of preconditioning type*/
272: /* want V*H*y - y is in GRS, V is in VEC_VV and H is in HES */
274: /* first do H+*y */
275: avec = lgmres->hwork;
276: PetscArrayzero(avec, it_total + 1);
277: for (ii = 0; ii < it_total + 1; ii++) {
278: for (jj = 0; jj <= ii + 1 && jj < it_total + 1; jj++) avec[jj] += *HES(jj, ii) * *GRS(ii);
279: }
281: /*now multiply result by V+ */
282: VecSet(VEC_TEMP, 0.0);
283: VecMAXPY(VEC_TEMP, it_total + 1, avec, &VEC_VV(0)); /*answer is in VEC_TEMP*/
285: /*copy answer to aug location and scale*/
286: VecCopy(VEC_TEMP, A_AUGVEC(spot));
287: VecScale(A_AUGVEC(spot), inv_tmp_norm);
288: }
289: return 0;
290: }
292: /*
293: KSPSolve_LGMRES - This routine applies the LGMRES method.
295: Input Parameter:
296: . ksp - the Krylov space object that was set to use lgmres
298: Output Parameter:
299: . outits - number of iterations used
301: */
302: PetscErrorCode KSPSolve_LGMRES(KSP ksp)
303: {
304: PetscInt cycle_its; /* iterations done in a call to KSPLGMRESCycle */
305: PetscInt itcount; /* running total of iterations, incl. those in restarts */
306: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
307: PetscBool guess_zero = ksp->guess_zero;
308: PetscInt ii; /*LGMRES_MOD variable */
312: PetscObjectSAWsTakeAccess((PetscObject)ksp);
314: ksp->its = 0;
315: lgmres->aug_ct = 0;
316: lgmres->matvecs = 0;
318: PetscObjectSAWsGrantAccess((PetscObject)ksp);
320: /* initialize */
321: itcount = 0;
322: /*LGMRES_MOD*/
323: for (ii = 0; ii < lgmres->aug_dim; ii++) lgmres->aug_order[ii] = 0;
325: while (!ksp->reason) {
326: /* calc residual - puts in VEC_VV(0) */
327: KSPInitialResidual(ksp, ksp->vec_sol, VEC_TEMP, VEC_TEMP_MATOP, VEC_VV(0), ksp->vec_rhs);
328: KSPLGMRESCycle(&cycle_its, ksp);
329: itcount += cycle_its;
330: if (itcount >= ksp->max_it) {
331: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
332: break;
333: }
334: ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
335: }
336: ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
337: return 0;
338: }
340: /*
341: KSPDestroy_LGMRES - Frees all memory space used by the Krylov method.
342: */
343: PetscErrorCode KSPDestroy_LGMRES(KSP ksp)
344: {
345: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
347: PetscFree(lgmres->augvecs);
348: if (lgmres->augwork_alloc) VecDestroyVecs(lgmres->augwork_alloc, &lgmres->augvecs_user_work[0]);
349: PetscFree(lgmres->augvecs_user_work);
350: PetscFree(lgmres->aug_order);
351: PetscFree(lgmres->hwork);
352: PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetConstant_C", NULL);
353: PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetAugDim_C", NULL);
354: KSPDestroy_GMRES(ksp);
355: return 0;
356: }
358: /*
359: KSPLGMRESBuildSoln - create the solution from the starting vector and the
360: current iterates.
362: Input parameters:
363: nrs - work area of size it + 1.
364: vguess - index of initial guess
365: vdest - index of result. Note that vguess may == vdest (replace
366: guess with the solution).
367: it - HH upper triangular part is a block of size (it+1) x (it+1)
369: This is an internal routine that knows about the LGMRES internals.
370: */
371: static PetscErrorCode KSPLGMRESBuildSoln(PetscScalar *nrs, Vec vguess, Vec vdest, KSP ksp, PetscInt it)
372: {
373: PetscScalar tt;
374: PetscInt ii, k, j;
375: KSP_LGMRES *lgmres = (KSP_LGMRES *)(ksp->data);
376: /*LGMRES_MOD */
377: PetscInt it_arnoldi, it_aug;
378: PetscInt jj, spot = 0;
380: /* Solve for solution vector that minimizes the residual */
382: /* If it is < 0, no lgmres steps have been performed */
383: if (it < 0) {
384: VecCopy(vguess, vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
385: return 0;
386: }
388: /* so (it+1) lgmres steps HAVE been performed */
390: /* LGMRES_MOD - determine if we need to use augvecs for the soln - do not assume that
391: this is called after the total its allowed for an approx space */
392: if (lgmres->approx_constant) {
393: it_arnoldi = lgmres->max_k - lgmres->aug_ct;
394: } else {
395: it_arnoldi = lgmres->max_k - lgmres->aug_dim;
396: }
397: if (it_arnoldi >= it + 1) {
398: it_aug = 0;
399: it_arnoldi = it + 1;
400: } else {
401: it_aug = (it + 1) - it_arnoldi;
402: }
404: /* now it_arnoldi indicates the number of matvecs that took place */
405: lgmres->matvecs += it_arnoldi;
407: /* solve the upper triangular system - GRS is the right side and HH is
408: the upper triangular matrix - put soln in nrs */
410: if (*HH(it, it) != 0.0) {
411: nrs[it] = *GRS(it) / *HH(it, it);
412: } else {
413: nrs[it] = 0.0;
414: }
416: for (ii = 1; ii <= it; ii++) {
417: k = it - ii;
418: tt = *GRS(k);
419: for (j = k + 1; j <= it; j++) tt = tt - *HH(k, j) * nrs[j];
420: nrs[k] = tt / *HH(k, k);
421: }
423: /* Accumulate the correction to the soln of the preconditioned prob. in VEC_TEMP */
424: VecSet(VEC_TEMP, 0.0); /* set VEC_TEMP components to 0 */
426: /*LGMRES_MOD - if augmenting has happened we need to form the solution
427: using the augvecs */
428: if (!it_aug) { /* all its are from arnoldi */
429: VecMAXPY(VEC_TEMP, it + 1, nrs, &VEC_VV(0));
430: } else { /*use aug vecs */
431: /*first do regular krylov directions */
432: VecMAXPY(VEC_TEMP, it_arnoldi, nrs, &VEC_VV(0));
433: /*now add augmented portions - add contribution of aug vectors one at a time*/
435: for (ii = 0; ii < it_aug; ii++) {
436: for (jj = 0; jj < lgmres->aug_dim; jj++) {
437: if (lgmres->aug_order[jj] == (ii + 1)) {
438: spot = jj;
439: break; /* must have this because there will be duplicates before aug_ct = aug_dim */
440: }
441: }
442: VecAXPY(VEC_TEMP, nrs[it_arnoldi + ii], AUGVEC(spot));
443: }
444: }
445: /* now VEC_TEMP is what we want to keep for augmenting purposes - grab before the
446: preconditioner is "unwound" from right-precondtioning*/
447: VecCopy(VEC_TEMP, AUG_TEMP);
449: KSPUnwindPreconditioner(ksp, VEC_TEMP, VEC_TEMP_MATOP);
451: /* add solution to previous solution */
452: /* put updated solution into vdest.*/
453: VecCopy(vguess, vdest);
454: VecAXPY(vdest, 1.0, VEC_TEMP);
455: return 0;
456: }
458: /*
459: KSPLGMRESUpdateHessenberg - Do the scalar work for the orthogonalization.
460: Return new residual.
462: input parameters:
464: . ksp - Krylov space object
465: . it - plane rotations are applied to the (it+1)th column of the
466: modified hessenberg (i.e. HH(:,it))
467: . hapend - PETSC_FALSE not happy breakdown ending.
469: output parameters:
470: . res - the new residual
472: */
473: static PetscErrorCode KSPLGMRESUpdateHessenberg(KSP ksp, PetscInt it, PetscBool hapend, PetscReal *res)
474: {
475: PetscScalar *hh, *cc, *ss, tt;
476: PetscInt j;
477: KSP_LGMRES *lgmres = (KSP_LGMRES *)(ksp->data);
479: hh = HH(0, it); /* pointer to beginning of column to update - so
480: incrementing hh "steps down" the (it+1)th col of HH*/
481: cc = CC(0); /* beginning of cosine rotations */
482: ss = SS(0); /* beginning of sine rotations */
484: /* Apply all the previously computed plane rotations to the new column
485: of the Hessenberg matrix */
486: /* Note: this uses the rotation [conj(c) s ; -s c], c= cos(theta), s= sin(theta) */
488: for (j = 1; j <= it; j++) {
489: tt = *hh;
490: *hh = PetscConj(*cc) * tt + *ss * *(hh + 1);
491: hh++;
492: *hh = *cc++ * *hh - (*ss++ * tt);
493: /* hh, cc, and ss have all been incremented one by end of loop */
494: }
496: /*
497: compute the new plane rotation, and apply it to:
498: 1) the right-hand-side of the Hessenberg system (GRS)
499: note: it affects GRS(it) and GRS(it+1)
500: 2) the new column of the Hessenberg matrix
501: note: it affects HH(it,it) which is currently pointed to
502: by hh and HH(it+1, it) (*(hh+1))
503: thus obtaining the updated value of the residual...
504: */
506: /* compute new plane rotation */
508: if (!hapend) {
509: tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh + 1)) * *(hh + 1));
510: if (tt == 0.0) {
511: ksp->reason = KSP_DIVERGED_NULL;
512: return 0;
513: }
514: *cc = *hh / tt; /* new cosine value */
515: *ss = *(hh + 1) / tt; /* new sine value */
517: /* apply to 1) and 2) */
518: *GRS(it + 1) = -(*ss * *GRS(it));
519: *GRS(it) = PetscConj(*cc) * *GRS(it);
520: *hh = PetscConj(*cc) * *hh + *ss * *(hh + 1);
522: /* residual is the last element (it+1) of right-hand side! */
523: *res = PetscAbsScalar(*GRS(it + 1));
525: } else { /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
526: another rotation matrix (so RH doesn't change). The new residual is
527: always the new sine term times the residual from last time (GRS(it)),
528: but now the new sine rotation would be zero...so the residual should
529: be zero...so we will multiply "zero" by the last residual. This might
530: not be exactly what we want to do here -could just return "zero". */
532: *res = 0.0;
533: }
534: return 0;
535: }
537: /*
539: KSPLGMRESGetNewVectors - This routine allocates more work vectors, starting from
540: VEC_VV(it)
542: */
543: static PetscErrorCode KSPLGMRESGetNewVectors(KSP ksp, PetscInt it)
544: {
545: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
546: PetscInt nwork = lgmres->nwork_alloc; /* number of work vector chunks allocated */
547: PetscInt nalloc; /* number to allocate */
548: PetscInt k;
550: nalloc = lgmres->delta_allocate; /* number of vectors to allocate
551: in a single chunk */
553: /* Adjust the number to allocate to make sure that we don't exceed the
554: number of available slots (lgmres->vecs_allocated)*/
555: if (it + VEC_OFFSET + nalloc >= lgmres->vecs_allocated) nalloc = lgmres->vecs_allocated - it - VEC_OFFSET;
556: if (!nalloc) return 0;
558: lgmres->vv_allocated += nalloc; /* vv_allocated is the number of vectors allocated */
560: /* work vectors */
561: KSPCreateVecs(ksp, nalloc, &lgmres->user_work[nwork], 0, NULL);
562: /* specify size of chunk allocated */
563: lgmres->mwork_alloc[nwork] = nalloc;
565: for (k = 0; k < nalloc; k++) lgmres->vecs[it + VEC_OFFSET + k] = lgmres->user_work[nwork][k];
567: /* LGMRES_MOD - for now we are preallocating the augmentation vectors */
569: /* increment the number of work vector chunks */
570: lgmres->nwork_alloc++;
571: return 0;
572: }
574: /*
575: KSPBuildSolution_LGMRES
577: Input Parameter:
578: . ksp - the Krylov space object
579: . ptr-
581: Output Parameter:
582: . result - the solution
584: Note: this calls KSPLGMRESBuildSoln - the same function that KSPLGMRESCycle
585: calls directly.
587: */
588: PetscErrorCode KSPBuildSolution_LGMRES(KSP ksp, Vec ptr, Vec *result)
589: {
590: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
592: if (!ptr) {
593: if (!lgmres->sol_temp) { VecDuplicate(ksp->vec_sol, &lgmres->sol_temp); }
594: ptr = lgmres->sol_temp;
595: }
596: if (!lgmres->nrs) {
597: /* allocate the work area */
598: PetscMalloc1(lgmres->max_k, &lgmres->nrs);
599: }
601: KSPLGMRESBuildSoln(lgmres->nrs, ksp->vec_sol, ptr, ksp, lgmres->it);
602: if (result) *result = ptr;
603: return 0;
604: }
606: PetscErrorCode KSPView_LGMRES(KSP ksp, PetscViewer viewer)
607: {
608: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
609: PetscBool iascii;
611: KSPView_GMRES(ksp, viewer);
612: PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii);
613: if (iascii) {
614: /*LGMRES_MOD */
615: PetscViewerASCIIPrintf(viewer, " aug. dimension=%" PetscInt_FMT "\n", lgmres->aug_dim);
616: if (lgmres->approx_constant) PetscViewerASCIIPrintf(viewer, " approx. space size was kept constant.\n");
617: PetscViewerASCIIPrintf(viewer, " number of matvecs=%" PetscInt_FMT "\n", lgmres->matvecs);
618: }
619: return 0;
620: }
622: PetscErrorCode KSPSetFromOptions_LGMRES(KSP ksp, PetscOptionItems *PetscOptionsObject)
623: {
624: PetscInt aug;
625: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
626: PetscBool flg = PETSC_FALSE;
628: KSPSetFromOptions_GMRES(ksp, PetscOptionsObject);
629: PetscOptionsHeadBegin(PetscOptionsObject, "KSP LGMRES Options");
630: PetscOptionsBool("-ksp_lgmres_constant", "Use constant approx. space size", "KSPGMRESSetConstant", lgmres->approx_constant, &lgmres->approx_constant, NULL);
631: PetscOptionsInt("-ksp_lgmres_augment", "Number of error approximations to augment the Krylov space with", "KSPLGMRESSetAugDim", lgmres->aug_dim, &aug, &flg);
632: if (flg) KSPLGMRESSetAugDim(ksp, aug);
633: PetscOptionsHeadEnd();
634: return 0;
635: }
637: /*functions for extra lgmres options here*/
638: static PetscErrorCode KSPLGMRESSetConstant_LGMRES(KSP ksp)
639: {
640: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
642: lgmres->approx_constant = PETSC_TRUE;
643: return 0;
644: }
646: static PetscErrorCode KSPLGMRESSetAugDim_LGMRES(KSP ksp, PetscInt aug_dim)
647: {
648: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
652: lgmres->aug_dim = aug_dim;
653: return 0;
654: }
656: /*MC
657: KSPLGMRES - Augments the standard GMRES approximation space with approximations to
658: the error from previous restart cycles.
660: Options Database Keys:
661: + -ksp_gmres_restart <restart> - total approximation space size (Krylov directions + error approximations)
662: . -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
663: . -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
664: vectors are allocated as needed)
665: . -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
666: . -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
667: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
668: stability of the classical Gram-Schmidt orthogonalization.
669: . -ksp_gmres_krylov_monitor - plot the Krylov space generated
670: . -ksp_lgmres_augment <k> - number of error approximations to augment the Krylov space with
671: - -ksp_lgmres_constant - use a constant approx. space size (only affects restart cycles < num. error approx.(k), i.e. the first k restarts)
673: To run LGMRES(m, k) as described in [1], use:
674: -ksp_gmres_restart <m+k>
675: -ksp_lgmres_augment <k>
677: Level: beginner
679: Note:
680: Supports both left and right preconditioning, but not symmetric.
682: Developer Note:
683: This object is subclassed off of `KSPGMRES`
685: Contributed by:
686: Allison Baker
688: References:
689: . [1] - 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).
691: .seealso: [](chapter_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPFGMRES`, `KSPGMRES`,
692: `KSPGMRESSetRestart()`, `KSPGMRESSetHapTol()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESGetOrthogonalization()`,
693: `KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESModifiedGramSchmidtOrthogonalization()`,
694: `KSPGMRESCGSRefinementType`, `KSPGMRESSetCGSRefinementType()`, `KSPGMRESGetCGSRefinementType()`, `KSPGMRESMonitorKrylov()`, `KSPLGMRESSetAugDim()`,
695: `KSPGMRESSetConstant()`
696: M*/
698: PETSC_EXTERN PetscErrorCode KSPCreate_LGMRES(KSP ksp)
699: {
700: KSP_LGMRES *lgmres;
702: PetscNew(&lgmres);
704: ksp->data = (void *)lgmres;
705: ksp->ops->buildsolution = KSPBuildSolution_LGMRES;
707: ksp->ops->setup = KSPSetUp_LGMRES;
708: ksp->ops->solve = KSPSolve_LGMRES;
709: ksp->ops->destroy = KSPDestroy_LGMRES;
710: ksp->ops->view = KSPView_LGMRES;
711: ksp->ops->setfromoptions = KSPSetFromOptions_LGMRES;
712: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
713: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_GMRES;
715: KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3);
716: KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2);
717: KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1);
719: PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetPreAllocateVectors_C", KSPGMRESSetPreAllocateVectors_GMRES);
720: PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetOrthogonalization_C", KSPGMRESSetOrthogonalization_GMRES);
721: PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetOrthogonalization_C", KSPGMRESGetOrthogonalization_GMRES);
722: PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetRestart_C", KSPGMRESSetRestart_GMRES);
723: PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetRestart_C", KSPGMRESGetRestart_GMRES);
724: PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetHapTol_C", KSPGMRESSetHapTol_GMRES);
725: PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetCGSRefinementType_C", KSPGMRESSetCGSRefinementType_GMRES);
726: PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetCGSRefinementType_C", KSPGMRESGetCGSRefinementType_GMRES);
728: /*LGMRES_MOD add extra functions here - like the one to set num of aug vectors */
729: PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetConstant_C", KSPLGMRESSetConstant_LGMRES);
730: PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetAugDim_C", KSPLGMRESSetAugDim_LGMRES);
732: /*defaults */
733: lgmres->haptol = 1.0e-30;
734: lgmres->q_preallocate = 0;
735: lgmres->delta_allocate = LGMRES_DELTA_DIRECTIONS;
736: lgmres->orthog = KSPGMRESClassicalGramSchmidtOrthogonalization;
737: lgmres->nrs = NULL;
738: lgmres->sol_temp = NULL;
739: lgmres->max_k = LGMRES_DEFAULT_MAXK;
740: lgmres->Rsvd = NULL;
741: lgmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
742: lgmres->orthogwork = NULL;
744: /*LGMRES_MOD - new defaults */
745: lgmres->aug_dim = LGMRES_DEFAULT_AUGDIM;
746: lgmres->aug_ct = 0; /* start with no aug vectors */
747: lgmres->approx_constant = PETSC_FALSE;
748: lgmres->matvecs = 0;
749: return 0;
750: }