Actual source code: lgmres.c
1: #include <../src/ksp/ksp/impls/gmres/lgmres/lgmresimpl.h>
3: static PetscErrorCode KSPLGMRESGetNewVectors(KSP, PetscInt);
4: static PetscErrorCode KSPLGMRESUpdateHessenberg(KSP, PetscInt, PetscBool, PetscReal *);
5: static PetscErrorCode KSPLGMRESBuildSoln(PetscScalar *, Vec, Vec, KSP, PetscInt);
7: /*@
8: KSPLGMRESSetAugDim - Set the number of error approximations to include in the approximation space (default is 2) for `KSPLGMRES`
10: Collective
12: Input Parameters:
13: + ksp - the `KSP` context
14: - dim - the number of vectors to use
16: Options Database Key:
17: . -ksp_lgmres_augment dim - the number of error approximations to include
19: Level: intermediate
21: Note:
22: If this is set to zero, then this method is equivalent to `KSPGMRES`
24: .seealso: [](ch_ksp), `KSPLGMRES`, `KSPLGMRESSetConstant()`
25: @*/
26: PetscErrorCode KSPLGMRESSetAugDim(KSP ksp, PetscInt dim)
27: {
28: PetscFunctionBegin;
29: PetscTryMethod((ksp), "KSPLGMRESSetAugDim_C", (KSP, PetscInt), (ksp, dim));
30: PetscFunctionReturn(PETSC_SUCCESS);
31: }
33: /*@
34: KSPLGMRESSetConstant - keep the error approximation space a constant size for every restart cycle
36: Collective
38: Input Parameters:
39: . ksp - the `KSP` context
41: Options Database Key:
42: . -ksp_lgmres_constant - set the size to be constant
44: Level: intermediate
46: Note:
47: This only affects the first couple of restart cycles when the total number of desired error approximations may not
48: be available.
50: .seealso: [](ch_ksp), `KSPLGMRES`, `KSPLGMRESSetAugDim()`
51: @*/
52: PetscErrorCode KSPLGMRESSetConstant(KSP ksp)
53: {
54: PetscFunctionBegin;
55: PetscTryMethod((ksp), "KSPLGMRESSetConstant_C", (KSP), (ksp));
56: PetscFunctionReturn(PETSC_SUCCESS);
57: }
59: static PetscErrorCode KSPSetUp_LGMRES(KSP ksp)
60: {
61: PetscInt max_k, k, aug_dim;
62: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
64: PetscFunctionBegin;
65: max_k = lgmres->max_k;
66: aug_dim = lgmres->aug_dim;
67: PetscCall(KSPSetUp_GMRES(ksp));
69: /* need array of pointers to augvecs*/
70: PetscCall(PetscMalloc1(2 * aug_dim + AUG_OFFSET, &lgmres->augvecs));
72: lgmres->aug_vecs_allocated = 2 * aug_dim + AUG_OFFSET;
74: PetscCall(PetscMalloc1(2 * aug_dim + AUG_OFFSET, &lgmres->augvecs_user_work));
75: PetscCall(PetscMalloc1(aug_dim, &lgmres->aug_order));
77: /* for now we will preallocate the augvecs - because aug_dim << restart
78: ... also keep in mind that we need to keep augvecs from cycle to cycle*/
79: lgmres->aug_vv_allocated = 2 * aug_dim + AUG_OFFSET;
80: lgmres->augwork_alloc = 2 * aug_dim + AUG_OFFSET;
82: PetscCall(KSPCreateVecs(ksp, lgmres->aug_vv_allocated, &lgmres->augvecs_user_work[0], 0, NULL));
83: PetscCall(PetscMalloc1(max_k + 1, &lgmres->hwork));
84: for (k = 0; k < lgmres->aug_vv_allocated; k++) lgmres->augvecs[k] = lgmres->augvecs_user_work[0][k];
85: PetscFunctionReturn(PETSC_SUCCESS);
86: }
88: static PetscErrorCode KSPLGMRESCycle(PetscInt *itcount, KSP ksp)
89: {
90: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
91: PetscReal res_norm, res;
92: PetscReal hapbnd, tt;
93: PetscScalar tmp;
94: PetscBool hapend = PETSC_FALSE; /* indicates happy breakdown ending */
95: PetscInt loc_it; /* local count of # of dir. in Krylov space */
96: PetscInt max_k = lgmres->max_k; /* max approx space size */
97: PetscInt max_it = ksp->max_it; /* max # of overall iterations for the method */
99: /* LGMRES_MOD - new variables*/
100: PetscInt aug_dim = lgmres->aug_dim;
101: PetscInt spot = 0;
102: PetscInt order = 0;
103: PetscInt it_arnoldi; /* number of arnoldi steps to take */
104: PetscInt it_total; /* total number of its to take (=approx space size)*/
105: PetscInt ii, jj;
106: PetscReal tmp_norm;
107: PetscScalar inv_tmp_norm;
108: PetscScalar *avec;
110: PetscFunctionBegin;
111: /* Number of pseudo iterations since last restart is the number of prestart directions */
112: loc_it = 0;
114: /* LGMRES_MOD: determine number of arnoldi steps to take */
115: /* if approx_constant then we keep the space the same size even if
116: we don't have the full number of aug vectors yet*/
117: if (lgmres->approx_constant) it_arnoldi = max_k - lgmres->aug_ct;
118: else it_arnoldi = max_k - aug_dim;
120: it_total = it_arnoldi + lgmres->aug_ct;
122: /* initial residual is in VEC_VV(0) - compute its norm*/
123: PetscCall(VecNorm(VEC_VV(0), NORM_2, &res_norm));
124: KSPCheckNorm(ksp, res_norm);
125: res = res_norm;
127: /* first entry in the right-hand side of the Hessenberg system is just the initial residual norm */
128: *GRS(0) = res_norm;
130: /* check for the convergence */
131: if (!res) {
132: if (itcount) *itcount = 0;
133: ksp->reason = KSP_CONVERGED_ATOL;
134: PetscCall(PetscInfo(ksp, "Converged due to zero residual norm on entry\n"));
135: PetscFunctionReturn(PETSC_SUCCESS);
136: }
138: /* scale VEC_VV (the initial residual) */
139: tmp = 1.0 / res_norm;
140: PetscCall(VecScale(VEC_VV(0), tmp));
142: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
143: else ksp->rnorm = 0.0;
145: /* note: (lgmres->it) is always set one less than (loc_it) It is used in
146: KSPBUILDSolution_LGMRES, where it is passed to KSPLGMRESBuildSoln.
147: Note that when KSPLGMRESBuildSoln is called from this function,
148: (loc_it -1) is passed, so the two are equivalent */
149: lgmres->it = (loc_it - 1);
151: /* MAIN ITERATION LOOP BEGINNING*/
153: /* keep iterating until we have converged OR generated the max number
154: of directions OR reached the max number of iterations for the method */
155: PetscCall((*ksp->converged)(ksp, ksp->its, res, &ksp->reason, ksp->cnvP));
157: while (!ksp->reason && loc_it < it_total && ksp->its < max_it) { /* LGMRES_MOD: changed to it_total */
158: PetscCall(KSPLogResidualHistory(ksp, res));
159: lgmres->it = (loc_it - 1);
160: PetscCall(KSPMonitor(ksp, ksp->its, res));
162: /* see if more space is needed for work vectors */
163: if (lgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
164: PetscCall(KSPLGMRESGetNewVectors(ksp, loc_it + 1));
165: /* (loc_it+1) is passed in as number of the first vector that should be allocated */
166: }
168: /* LGMRES_MOD: decide whether this is an arnoldi step or an aug step */
169: if (loc_it < it_arnoldi) { /* Arnoldi */
170: PetscCall(KSP_PCApplyBAorAB(ksp, VEC_VV(loc_it), VEC_VV(1 + loc_it), VEC_TEMP_MATOP));
171: } else { /* aug step */
172: order = loc_it - it_arnoldi + 1; /* which aug step */
173: for (ii = 0; ii < aug_dim; ii++) {
174: if (lgmres->aug_order[ii] == order) {
175: spot = ii;
176: break; /* must have this because there will be duplicates before aug_ct = aug_dim */
177: }
178: }
180: PetscCall(VecCopy(A_AUGVEC(spot), VEC_VV(1 + loc_it)));
181: /* note: an alternate implementation choice would be to only save the AUGVECS and
182: not A_AUGVEC and then apply the PC here to the augvec */
183: }
185: /* update Hessenberg matrix and do Gram-Schmidt - new direction is in VEC_VV(1+loc_it)*/
186: PetscCall((*lgmres->orthog)(ksp, loc_it));
188: /* new entry in hessenburg is the 2-norm of our new direction */
189: PetscCall(VecNorm(VEC_VV(loc_it + 1), NORM_2, &tt));
191: *HH(loc_it + 1, loc_it) = tt;
192: *HES(loc_it + 1, loc_it) = tt;
194: /* check for the happy breakdown */
195: hapbnd = PetscAbsScalar(tt / *GRS(loc_it)); /* GRS(loc_it) contains the res_norm from the last iteration */
196: if (hapbnd > lgmres->haptol) hapbnd = lgmres->haptol;
197: if (tt > hapbnd) {
198: tmp = 1.0 / tt;
199: PetscCall(VecScale(VEC_VV(loc_it + 1), tmp)); /* scale new direction by its norm */
200: } else {
201: PetscCall(PetscInfo(ksp, "Detected happy breakdown, current hapbnd = %g tt = %g\n", (double)hapbnd, (double)tt));
202: hapend = PETSC_TRUE;
203: }
205: /* apply rotations to the new column of the Hessenberg (and the right-hand side of the system),
206: calculate new rotation, and get new residual norm at the same time*/
207: PetscCall(KSPLGMRESUpdateHessenberg(ksp, loc_it, hapend, &res));
208: if (ksp->reason) break;
210: loc_it++;
211: lgmres->it = (loc_it - 1); /* Add this here in case it has converged */
213: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
214: ksp->its++;
215: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
216: else ksp->rnorm = 0.0;
217: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
219: PetscCall((*ksp->converged)(ksp, ksp->its, res, &ksp->reason, ksp->cnvP));
221: /* Catch error in happy breakdown and signal convergence and break from loop */
222: if (hapend) {
223: if (!ksp->reason) {
224: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "Reached happy break down, but convergence was not indicated. Residual norm = %g", (double)res);
225: ksp->reason = KSP_DIVERGED_BREAKDOWN;
226: break;
227: }
228: }
229: }
230: /* END OF ITERATION LOOP */
231: PetscCall(KSPLogResidualHistory(ksp, res));
233: if (itcount) *itcount = loc_it;
235: /*
236: Solve for the "best" coefficients of the Krylov
237: columns, add the solution values together, and possibly unwind the
238: preconditioning from the solution
239: */
241: /* Form the solution (or the solution so far) */
242: /* Note: must pass in (loc_it-1) for iteration count so that KSPLGMRESBuildSoln properly navigates */
244: PetscCall(KSPLGMRESBuildSoln(GRS(0), ksp->vec_sol, ksp->vec_sol, ksp, loc_it - 1));
246: /* Monitor if we know that we will not return for a restart */
247: if (ksp->reason == KSP_CONVERGED_ITERATING && ksp->its >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
248: if (ksp->reason) PetscCall(KSPMonitor(ksp, ksp->its, res));
250: /* LGMRES_MOD collect aug vector and A*augvector for future restarts -
251: only if we will be restarting (i.e. this cycle performed it_total iterations) */
252: if (!ksp->reason && ksp->its < max_it && aug_dim > 0) {
253: /* AUG_TEMP contains the new augmentation vector (assigned in KSPLGMRESBuildSoln) */
254: if (!lgmres->aug_ct) {
255: spot = 0;
256: lgmres->aug_ct++;
257: } else if (lgmres->aug_ct < aug_dim) {
258: spot = lgmres->aug_ct;
259: lgmres->aug_ct++;
260: } else { /* truncate */
261: for (ii = 0; ii < aug_dim; ii++) {
262: if (lgmres->aug_order[ii] == aug_dim) spot = ii;
263: }
264: }
266: PetscCall(VecCopy(AUG_TEMP, AUGVEC(spot)));
267: /* need to normalize */
268: PetscCall(VecNorm(AUGVEC(spot), NORM_2, &tmp_norm));
270: inv_tmp_norm = 1.0 / tmp_norm;
272: PetscCall(VecScale(AUGVEC(spot), inv_tmp_norm));
274: /* set new aug vector to order 1 - move all others back one */
275: for (ii = 0; ii < aug_dim; ii++) AUG_ORDER(ii)++;
276: AUG_ORDER(spot) = 1;
278: /* now add the A*aug vector to A_AUGVEC(spot) - this is independent of preconditioning type */
279: /* want V*H*y - y is in GRS, V is in VEC_VV and H is in HES */
281: /* do H+*y */
282: avec = lgmres->hwork;
283: PetscCall(PetscArrayzero(avec, it_total + 1));
284: for (ii = 0; ii < it_total + 1; ii++) {
285: for (jj = 0; jj <= ii + 1 && jj < it_total + 1; jj++) avec[jj] += *HES(jj, ii) * *GRS(ii);
286: }
288: /* multiply result by V+ */
289: PetscCall(VecMAXPBY(VEC_TEMP, it_total + 1, avec, 0, &VEC_VV(0))); /* answer is in VEC_TEMP */
291: /* copy answer to aug location and scale */
292: PetscCall(VecCopy(VEC_TEMP, A_AUGVEC(spot)));
293: PetscCall(VecScale(A_AUGVEC(spot), inv_tmp_norm));
294: }
295: PetscFunctionReturn(PETSC_SUCCESS);
296: }
298: static PetscErrorCode KSPSolve_LGMRES(KSP ksp)
299: {
300: PetscInt itcount; /* running total of iterations, incl. those in restarts */
301: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
302: PetscBool guess_zero = ksp->guess_zero;
303: PetscInt ii; /* LGMRES_MOD variable */
305: PetscFunctionBegin;
306: PetscCheck(!ksp->calc_sings || lgmres->Rsvd, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ORDER, "Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
308: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
310: ksp->its = 0;
311: lgmres->aug_ct = 0;
312: lgmres->matvecs = 0;
314: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
316: /* initialize */
317: itcount = 0;
318: /* LGMRES_MOD */
319: for (ii = 0; ii < lgmres->aug_dim; ii++) lgmres->aug_order[ii] = 0;
321: while (!ksp->reason) {
322: PetscInt cycle_its = 0; /* iterations done in a call to KSPLGMRESCycle */
323: /* calc residual - puts in VEC_VV(0) */
324: PetscCall(KSPInitialResidual(ksp, ksp->vec_sol, VEC_TEMP, VEC_TEMP_MATOP, VEC_VV(0), ksp->vec_rhs));
325: PetscCall(KSPLGMRESCycle(&cycle_its, ksp));
326: itcount += cycle_its;
327: if (itcount >= ksp->max_it) {
328: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
329: break;
330: }
331: ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
332: }
333: ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
334: PetscFunctionReturn(PETSC_SUCCESS);
335: }
337: static PetscErrorCode KSPDestroy_LGMRES(KSP ksp)
338: {
339: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
341: PetscFunctionBegin;
342: PetscCall(PetscFree(lgmres->augvecs));
343: if (lgmres->augwork_alloc) PetscCall(VecDestroyVecs(lgmres->augwork_alloc, &lgmres->augvecs_user_work[0]));
344: PetscCall(PetscFree(lgmres->augvecs_user_work));
345: PetscCall(PetscFree(lgmres->aug_order));
346: PetscCall(PetscFree(lgmres->hwork));
347: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetConstant_C", NULL));
348: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetAugDim_C", NULL));
349: PetscCall(KSPDestroy_GMRES(ksp));
350: PetscFunctionReturn(PETSC_SUCCESS);
351: }
353: static PetscErrorCode KSPLGMRESBuildSoln(PetscScalar *nrs, Vec vguess, Vec vdest, KSP ksp, PetscInt it)
354: {
355: PetscScalar tt;
356: PetscInt ii, k, j;
357: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
358: /* LGMRES_MOD */
359: PetscInt it_arnoldi, it_aug;
360: PetscInt jj, spot = 0;
362: PetscFunctionBegin;
363: /* Solve for solution vector that minimizes the residual */
365: /* If it is < 0, no lgmres steps have been performed */
366: if (it < 0) {
367: PetscCall(VecCopy(vguess, vdest)); /* VecCopy() is smart, exists immediately if vguess == vdest */
368: PetscFunctionReturn(PETSC_SUCCESS);
369: }
371: /* so (it+1) lgmres steps HAVE been performed */
373: /* LGMRES_MOD - determine if we need to use augvecs for the soln - do not assume that
374: this is called after the total its allowed for an approx space */
375: if (lgmres->approx_constant) {
376: it_arnoldi = lgmres->max_k - lgmres->aug_ct;
377: } else {
378: it_arnoldi = lgmres->max_k - lgmres->aug_dim;
379: }
380: if (it_arnoldi >= it + 1) {
381: it_aug = 0;
382: it_arnoldi = it + 1;
383: } else {
384: it_aug = (it + 1) - it_arnoldi;
385: }
387: /* now it_arnoldi indicates the number of matvecs that took place */
388: lgmres->matvecs += it_arnoldi;
390: /* solve the upper triangular system - GRS is the right side and HH is
391: the upper triangular matrix - put soln in nrs */
392: PetscCheck(*HH(it, it) != 0.0, PETSC_COMM_SELF, PETSC_ERR_CONV_FAILED, "HH(it,it) is identically zero; it = %" PetscInt_FMT " GRS(it) = %g", it, (double)PetscAbsScalar(*GRS(it)));
393: if (*HH(it, it) != 0.0) {
394: nrs[it] = *GRS(it) / *HH(it, it);
395: } else {
396: nrs[it] = 0.0;
397: }
399: for (ii = 1; ii <= it; ii++) {
400: k = it - ii;
401: tt = *GRS(k);
402: for (j = k + 1; j <= it; j++) tt = tt - *HH(k, j) * nrs[j];
403: nrs[k] = tt / *HH(k, k);
404: }
406: /* Accumulate the correction to the soln of the preconditioned prob. in VEC_TEMP */
408: /* LGMRES_MOD - if augmenting has happened we need to form the solution using the augvecs */
409: if (!it_aug) { /* all its are from arnoldi */
410: PetscCall(VecMAXPBY(VEC_TEMP, it + 1, nrs, 0, &VEC_VV(0)));
411: } else { /* use aug vecs */
412: /* first do regular Krylov directions */
413: PetscCall(VecMAXPBY(VEC_TEMP, it_arnoldi, nrs, 0, &VEC_VV(0)));
414: /* now add augmented portions - add contribution of aug vectors one at a time*/
416: for (ii = 0; ii < it_aug; ii++) {
417: for (jj = 0; jj < lgmres->aug_dim; jj++) {
418: if (lgmres->aug_order[jj] == (ii + 1)) {
419: spot = jj;
420: break; /* must have this because there will be duplicates before aug_ct = aug_dim */
421: }
422: }
423: PetscCall(VecAXPY(VEC_TEMP, nrs[it_arnoldi + ii], AUGVEC(spot)));
424: }
425: }
426: /* now VEC_TEMP is what we want to keep for augmenting purposes - grab before the
427: preconditioner is "unwound" from right-precondtioning*/
428: PetscCall(VecCopy(VEC_TEMP, AUG_TEMP));
430: PetscCall(KSPUnwindPreconditioner(ksp, VEC_TEMP, VEC_TEMP_MATOP));
432: /* add solution to previous solution */
433: /* put updated solution into vdest.*/
434: PetscCall(VecCopy(vguess, vdest));
435: PetscCall(VecAXPY(vdest, 1.0, VEC_TEMP));
436: PetscFunctionReturn(PETSC_SUCCESS);
437: }
439: static PetscErrorCode KSPLGMRESUpdateHessenberg(KSP ksp, PetscInt it, PetscBool hapend, PetscReal *res)
440: {
441: PetscScalar *hh, *cc, *ss, tt;
442: PetscInt j;
443: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
445: PetscFunctionBegin;
446: hh = HH(0, it); /* pointer to beginning of column to update - so incrementing hh "steps down" the (it+1)th col of HH*/
447: cc = CC(0); /* beginning of cosine rotations */
448: ss = SS(0); /* beginning of sine rotations */
450: /* Apply all the previously computed plane rotations to the new column
451: of the Hessenberg matrix */
452: /* Note: this uses the rotation [conj(c) s ; -s c], c= cos(theta), s= sin(theta) */
454: for (j = 1; j <= it; j++) {
455: tt = *hh;
456: *hh = PetscConj(*cc) * tt + *ss * *(hh + 1);
457: hh++;
458: *hh = *cc++ * *hh - (*ss++ * tt);
459: /* hh, cc, and ss have all been incremented one by end of loop */
460: }
462: /*
463: compute the new plane rotation, and apply it to:
464: 1) the right-hand side of the Hessenberg system (GRS)
465: note: it affects GRS(it) and GRS(it+1)
466: 2) the new column of the Hessenberg matrix
467: note: it affects HH(it,it) which is currently pointed to
468: by hh and HH(it+1, it) (*(hh+1))
469: thus obtaining the updated value of the residual...
470: */
472: /* compute new plane rotation */
474: if (!hapend) {
475: tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh + 1)) * *(hh + 1));
476: if (tt == 0.0) {
477: ksp->reason = KSP_DIVERGED_NULL;
478: PetscFunctionReturn(PETSC_SUCCESS);
479: }
480: *cc = *hh / tt; /* new cosine value */
481: *ss = *(hh + 1) / tt; /* new sine value */
483: /* apply to 1) and 2) */
484: *GRS(it + 1) = -(*ss * *GRS(it));
485: *GRS(it) = PetscConj(*cc) * *GRS(it);
486: *hh = PetscConj(*cc) * *hh + *ss * *(hh + 1);
488: /* residual is the last element (it+1) of right-hand side! */
489: *res = PetscAbsScalar(*GRS(it + 1));
491: } else { /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
492: another rotation matrix (so RH doesn't change). The new residual is
493: always the new sine term times the residual from last time (GRS(it)),
494: but now the new sine rotation would be zero...so the residual should
495: be zero...so we will multiply "zero" by the last residual. This might
496: not be exactly what we want to do here -could just return "zero". */
498: *res = 0.0;
499: }
500: PetscFunctionReturn(PETSC_SUCCESS);
501: }
503: /*
504: KSPLGMRESGetNewVectors - Allocates more work vectors, starting from VEC_VV(it)
506: */
507: static PetscErrorCode KSPLGMRESGetNewVectors(KSP ksp, PetscInt it)
508: {
509: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
510: PetscInt nwork = lgmres->nwork_alloc; /* number of work vector chunks allocated */
511: PetscInt nalloc; /* number to allocate */
512: PetscInt k;
514: PetscFunctionBegin;
515: nalloc = lgmres->delta_allocate; /* number of vectors to allocate in a single chunk */
517: /* Adjust the number to allocate to make sure that we don't exceed the
518: number of available slots (lgmres->vecs_allocated)*/
519: if (it + VEC_OFFSET + nalloc >= lgmres->vecs_allocated) nalloc = lgmres->vecs_allocated - it - VEC_OFFSET;
520: if (!nalloc) PetscFunctionReturn(PETSC_SUCCESS);
522: lgmres->vv_allocated += nalloc; /* vv_allocated is the number of vectors allocated */
524: /* work vectors */
525: PetscCall(KSPCreateVecs(ksp, nalloc, &lgmres->user_work[nwork], 0, NULL));
526: /* specify size of chunk allocated */
527: lgmres->mwork_alloc[nwork] = nalloc;
529: for (k = 0; k < nalloc; k++) lgmres->vecs[it + VEC_OFFSET + k] = lgmres->user_work[nwork][k];
531: /* LGMRES_MOD - for now we are preallocating the augmentation vectors */
533: /* increment the number of work vector chunks */
534: lgmres->nwork_alloc++;
535: PetscFunctionReturn(PETSC_SUCCESS);
536: }
538: static PetscErrorCode KSPBuildSolution_LGMRES(KSP ksp, Vec ptr, Vec *result)
539: {
540: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
542: PetscFunctionBegin;
543: if (!ptr) {
544: if (!lgmres->sol_temp) PetscCall(VecDuplicate(ksp->vec_sol, &lgmres->sol_temp));
545: ptr = lgmres->sol_temp;
546: }
547: if (!lgmres->nrs) {
548: /* allocate the work area */
549: PetscCall(PetscMalloc1(lgmres->max_k, &lgmres->nrs));
550: }
552: PetscCall(KSPLGMRESBuildSoln(lgmres->nrs, ksp->vec_sol, ptr, ksp, lgmres->it));
553: if (result) *result = ptr;
554: PetscFunctionReturn(PETSC_SUCCESS);
555: }
557: static PetscErrorCode KSPView_LGMRES(KSP ksp, PetscViewer viewer)
558: {
559: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
560: PetscBool iascii;
562: PetscFunctionBegin;
563: PetscCall(KSPView_GMRES(ksp, viewer));
564: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
565: if (iascii) {
566: /* LGMRES_MOD */
567: PetscCall(PetscViewerASCIIPrintf(viewer, " aug. dimension=%" PetscInt_FMT "\n", lgmres->aug_dim));
568: if (lgmres->approx_constant) PetscCall(PetscViewerASCIIPrintf(viewer, " approx. space size was kept constant.\n"));
569: PetscCall(PetscViewerASCIIPrintf(viewer, " number of matvecs=%" PetscInt_FMT "\n", lgmres->matvecs));
570: }
571: PetscFunctionReturn(PETSC_SUCCESS);
572: }
574: static PetscErrorCode KSPSetFromOptions_LGMRES(KSP ksp, PetscOptionItems *PetscOptionsObject)
575: {
576: PetscInt aug;
577: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
578: PetscBool flg = PETSC_FALSE;
580: PetscFunctionBegin;
581: PetscCall(KSPSetFromOptions_GMRES(ksp, PetscOptionsObject));
582: PetscOptionsHeadBegin(PetscOptionsObject, "KSP LGMRES Options");
583: PetscCall(PetscOptionsBool("-ksp_lgmres_constant", "Use constant approx. space size", "KSPGMRESSetConstant", lgmres->approx_constant, &lgmres->approx_constant, NULL));
584: PetscCall(PetscOptionsInt("-ksp_lgmres_augment", "Number of error approximations to augment the Krylov space with", "KSPLGMRESSetAugDim", lgmres->aug_dim, &aug, &flg));
585: if (flg) PetscCall(KSPLGMRESSetAugDim(ksp, aug));
586: PetscOptionsHeadEnd();
587: PetscFunctionReturn(PETSC_SUCCESS);
588: }
590: static PetscErrorCode KSPLGMRESSetConstant_LGMRES(KSP ksp)
591: {
592: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
594: PetscFunctionBegin;
595: lgmres->approx_constant = PETSC_TRUE;
596: PetscFunctionReturn(PETSC_SUCCESS);
597: }
599: static PetscErrorCode KSPLGMRESSetAugDim_LGMRES(KSP ksp, PetscInt aug_dim)
600: {
601: KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
603: PetscFunctionBegin;
604: PetscCheck(aug_dim >= 0, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "Augmentation dimension must be nonegative");
605: PetscCheck(aug_dim <= (lgmres->max_k - 1), PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "Augmentation dimension must be <= (restart size-1)");
606: lgmres->aug_dim = aug_dim;
607: PetscFunctionReturn(PETSC_SUCCESS);
608: }
610: /*MC
611: KSPLGMRES - Augments the standard GMRES approximation space with approximations to the error from previous restart cycles as in {cite}`bjm2005`.
613: Options Database Keys:
614: + -ksp_gmres_restart <restart> - total approximation space size (Krylov directions + error approximations)
615: . -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
616: . -ksp_gmres_preallocate - preallocate all the Krylov search directions initially
617: (otherwise groups of vectors are allocated as needed)
618: . -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against
619: the Krylov space (fast) (the default)
620: . -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
621: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
622: stability of the classical Gram-Schmidt orthogonalization.
623: . -ksp_gmres_krylov_monitor - plot the Krylov space generated
624: . -ksp_lgmres_augment <k> - number of error approximations to augment the Krylov space with
625: - -ksp_lgmres_constant - use a constant approximate space size
626: (only affects restart cycles < num. error approx.(k), i.e. the first k restarts)
628: Level: beginner
630: Notes:
631: Supports both left and right preconditioning, but not symmetric.
633: Augmenting with 1,2, or 3 approximations is generally optimal.
635: This method is an accelerator for `KSPGMRES` - it is not useful for problems that stall. When gmres(m) stalls then lgmres with a size m
636: approximation space will also generally stall.
638: If gmres(m) converges in a small number of restart cycles, then lgmres also tends not to be very helpful.
640: Developer Notes:
641: To run LGMRES(m, k) as described in {cite}`bjm2005`, use\:
642: .vb
643: -ksp_gmres_restart <m+k>
644: -ksp_lgmres_augment <k>
645: .ve
647: This object is subclassed off of `KSPGMRES`, see the source code in src/ksp/ksp/impls/gmres for comments on the structure of the code
649: Contributed by:
650: Allison Baker
652: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPFGMRES`, `KSPGMRES`,
653: `KSPGMRESSetRestart()`, `KSPGMRESSetHapTol()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESGetOrthogonalization()`,
654: `KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESModifiedGramSchmidtOrthogonalization()`,
655: `KSPGMRESCGSRefinementType`, `KSPGMRESSetCGSRefinementType()`, `KSPGMRESGetCGSRefinementType()`, `KSPGMRESMonitorKrylov()`, `KSPLGMRESSetAugDim()`,
656: `KSPGMRESSetConstant()`, `KSPLGMRESSetConstant()`, `KSPLGMRESSetAugDim()`
657: M*/
659: PETSC_EXTERN PetscErrorCode KSPCreate_LGMRES(KSP ksp)
660: {
661: KSP_LGMRES *lgmres;
663: PetscFunctionBegin;
664: PetscCall(PetscNew(&lgmres));
666: ksp->data = (void *)lgmres;
667: ksp->ops->buildsolution = KSPBuildSolution_LGMRES;
669: ksp->ops->setup = KSPSetUp_LGMRES;
670: ksp->ops->solve = KSPSolve_LGMRES;
671: ksp->ops->destroy = KSPDestroy_LGMRES;
672: ksp->ops->view = KSPView_LGMRES;
673: ksp->ops->setfromoptions = KSPSetFromOptions_LGMRES;
674: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
675: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_GMRES;
677: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
678: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2));
679: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));
681: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetPreAllocateVectors_C", KSPGMRESSetPreAllocateVectors_GMRES));
682: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetOrthogonalization_C", KSPGMRESSetOrthogonalization_GMRES));
683: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetOrthogonalization_C", KSPGMRESGetOrthogonalization_GMRES));
684: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetRestart_C", KSPGMRESSetRestart_GMRES));
685: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetRestart_C", KSPGMRESGetRestart_GMRES));
686: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetHapTol_C", KSPGMRESSetHapTol_GMRES));
687: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetCGSRefinementType_C", KSPGMRESSetCGSRefinementType_GMRES));
688: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetCGSRefinementType_C", KSPGMRESGetCGSRefinementType_GMRES));
690: /* LGMRES_MOD add extra functions here - like the one to set num of aug vectors */
691: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetConstant_C", KSPLGMRESSetConstant_LGMRES));
692: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetAugDim_C", KSPLGMRESSetAugDim_LGMRES));
694: /* defaults */
695: lgmres->haptol = 1.0e-30;
696: lgmres->q_preallocate = 0;
697: lgmres->delta_allocate = LGMRES_DELTA_DIRECTIONS;
698: lgmres->orthog = KSPGMRESClassicalGramSchmidtOrthogonalization;
699: lgmres->nrs = NULL;
700: lgmres->sol_temp = NULL;
701: lgmres->max_k = LGMRES_DEFAULT_MAXK;
702: lgmres->Rsvd = NULL;
703: lgmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
704: lgmres->orthogwork = NULL;
706: /* LGMRES_MOD - new defaults */
707: lgmres->aug_dim = LGMRES_DEFAULT_AUGDIM;
708: lgmres->aug_ct = 0; /* start with no aug vectors */
709: lgmres->approx_constant = PETSC_FALSE;
710: lgmres->matvecs = 0;
711: PetscFunctionReturn(PETSC_SUCCESS);
712: }