Actual source code: dgmres.c
1: /*
2: Implements deflated GMRES.
3: */
5: #include <../src/ksp/ksp/impls/gmres/dgmres/dgmresimpl.h>
7: PetscLogEvent KSP_DGMRESComputeDeflationData, KSP_DGMRESApplyDeflation;
9: static PetscErrorCode KSPDGMRESGetNewVectors(KSP, PetscInt);
10: static PetscErrorCode KSPDGMRESUpdateHessenberg(KSP, PetscInt, PetscBool, PetscReal *);
11: static PetscErrorCode KSPDGMRESBuildSoln(PetscScalar *, Vec, Vec, KSP, PetscInt);
13: static PetscErrorCode KSPDGMRESSetEigen(KSP ksp, PetscInt nb_eig)
14: {
15: PetscFunctionBegin;
16: PetscTryMethod((ksp), "KSPDGMRESSetEigen_C", (KSP, PetscInt), (ksp, nb_eig));
17: PetscFunctionReturn(PETSC_SUCCESS);
18: }
19: static PetscErrorCode KSPDGMRESSetMaxEigen(KSP ksp, PetscInt max_neig)
20: {
21: PetscFunctionBegin;
22: PetscTryMethod((ksp), "KSPDGMRESSetMaxEigen_C", (KSP, PetscInt), (ksp, max_neig));
23: PetscFunctionReturn(PETSC_SUCCESS);
24: }
25: static PetscErrorCode KSPDGMRESComputeSchurForm(KSP ksp, PetscInt *neig)
26: {
27: PetscFunctionBegin;
28: PetscUseMethod((ksp), "KSPDGMRESComputeSchurForm_C", (KSP, PetscInt *), (ksp, neig));
29: PetscFunctionReturn(PETSC_SUCCESS);
30: }
31: PetscErrorCode KSPDGMRESComputeDeflationData(KSP ksp, PetscInt *curneigh)
32: {
33: PetscFunctionBegin;
34: PetscUseMethod((ksp), "KSPDGMRESComputeDeflationData_C", (KSP, PetscInt *), (ksp, curneigh));
35: PetscFunctionReturn(PETSC_SUCCESS);
36: }
37: static PetscErrorCode KSPDGMRESApplyDeflation(KSP ksp, Vec x, Vec y)
38: {
39: PetscFunctionBegin;
40: PetscUseMethod((ksp), "KSPDGMRESApplyDeflation_C", (KSP, Vec, Vec), (ksp, x, y));
41: PetscFunctionReturn(PETSC_SUCCESS);
42: }
44: static PetscErrorCode KSPDGMRESImproveEig(KSP ksp, PetscInt neig)
45: {
46: PetscFunctionBegin;
47: PetscUseMethod((ksp), "KSPDGMRESImproveEig_C", (KSP, PetscInt), (ksp, neig));
48: PetscFunctionReturn(PETSC_SUCCESS);
49: }
51: PetscErrorCode KSPSetUp_DGMRES(KSP ksp)
52: {
53: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
54: PetscInt neig = dgmres->neig + EIG_OFFSET;
55: PetscInt max_k = dgmres->max_k + 1;
57: PetscFunctionBegin;
58: PetscCall(KSPSetUp_GMRES(ksp));
59: if (!dgmres->neig) PetscFunctionReturn(PETSC_SUCCESS);
61: /* Allocate workspace for the Schur vectors*/
62: PetscCall(PetscMalloc1(neig * max_k, &SR));
63: dgmres->wr = NULL;
64: dgmres->wi = NULL;
65: dgmres->perm = NULL;
66: dgmres->modul = NULL;
67: dgmres->Q = NULL;
68: dgmres->Z = NULL;
70: UU = NULL;
71: XX = NULL;
72: MX = NULL;
73: AUU = NULL;
74: XMX = NULL;
75: XMU = NULL;
76: UMX = NULL;
77: AUAU = NULL;
78: TT = NULL;
79: TTF = NULL;
80: INVP = NULL;
81: X1 = NULL;
82: X2 = NULL;
83: MU = NULL;
84: PetscFunctionReturn(PETSC_SUCCESS);
85: }
87: /*
88: Run GMRES, possibly with restart. Return residual history if requested.
89: input parameters:
91: . gmres - structure containing parameters and work areas
93: output parameters:
94: . nres - residuals (from preconditioned system) at each step.
95: If restarting, consider passing nres+it. If null,
96: ignored
97: . itcount - number of iterations used. nres[0] to nres[itcount]
98: are defined. If null, ignored.
100: Notes:
101: On entry, the value in vector VEC_VV(0) should be the initial residual
102: (this allows shortcuts where the initial preconditioned residual is 0).
103: */
104: static PetscErrorCode KSPDGMRESCycle(PetscInt *itcount, KSP ksp)
105: {
106: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
107: PetscReal res_norm, res, hapbnd, tt;
108: PetscInt it = 0;
109: PetscInt max_k = dgmres->max_k;
110: PetscBool hapend = PETSC_FALSE;
111: PetscReal res_old;
112: PetscInt test = 0;
114: PetscFunctionBegin;
115: PetscCall(VecNormalize(VEC_VV(0), &res_norm));
116: KSPCheckNorm(ksp, res_norm);
117: res = res_norm;
118: *GRS(0) = res_norm;
120: /* check for the convergence */
121: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
122: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
123: else ksp->rnorm = 0.0;
124: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
125: dgmres->it = (it - 1);
126: PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
127: PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm));
128: if (!res) {
129: if (itcount) *itcount = 0;
130: ksp->reason = KSP_CONVERGED_ATOL;
131: PetscCall(PetscInfo(ksp, "Converged due to zero residual norm on entry\n"));
132: PetscFunctionReturn(PETSC_SUCCESS);
133: }
134: /* record the residual norm to test if deflation is needed */
135: res_old = res;
137: PetscCall((*ksp->converged)(ksp, ksp->its, ksp->rnorm, &ksp->reason, ksp->cnvP));
138: while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
139: if (it) {
140: PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
141: PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm));
142: }
143: dgmres->it = (it - 1);
144: if (dgmres->vv_allocated <= it + VEC_OFFSET + 1) PetscCall(KSPDGMRESGetNewVectors(ksp, it + 1));
145: if (dgmres->r > 0) {
146: if (ksp->pc_side == PC_LEFT) {
147: /* Apply the first preconditioner */
148: PetscCall(KSP_PCApplyBAorAB(ksp, VEC_VV(it), VEC_TEMP, VEC_TEMP_MATOP));
149: /* Then apply Deflation as a preconditioner */
150: PetscCall(KSPDGMRESApplyDeflation(ksp, VEC_TEMP, VEC_VV(1 + it)));
151: } else if (ksp->pc_side == PC_RIGHT) {
152: PetscCall(KSPDGMRESApplyDeflation(ksp, VEC_VV(it), VEC_TEMP));
153: PetscCall(KSP_PCApplyBAorAB(ksp, VEC_TEMP, VEC_VV(1 + it), VEC_TEMP_MATOP));
154: }
155: } else {
156: PetscCall(KSP_PCApplyBAorAB(ksp, VEC_VV(it), VEC_VV(1 + it), VEC_TEMP_MATOP));
157: }
158: dgmres->matvecs += 1;
159: /* update Hessenberg matrix and do Gram-Schmidt */
160: PetscCall((*dgmres->orthog)(ksp, it));
162: /* vv(i+1) . vv(i+1) */
163: PetscCall(VecNormalize(VEC_VV(it + 1), &tt));
164: /* save the magnitude */
165: *HH(it + 1, it) = tt;
166: *HES(it + 1, it) = tt;
168: /* check for the happy breakdown */
169: hapbnd = PetscAbsScalar(tt / *GRS(it));
170: if (hapbnd > dgmres->haptol) hapbnd = dgmres->haptol;
171: if (tt < hapbnd) {
172: PetscCall(PetscInfo(ksp, "Detected happy breakdown, current hapbnd = %g tt = %g\n", (double)hapbnd, (double)tt));
173: hapend = PETSC_TRUE;
174: }
175: PetscCall(KSPDGMRESUpdateHessenberg(ksp, it, hapend, &res));
177: it++;
178: dgmres->it = (it - 1); /* For converged */
179: ksp->its++;
180: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
181: else ksp->rnorm = 0.0;
182: if (ksp->reason) break;
184: PetscCall((*ksp->converged)(ksp, ksp->its, ksp->rnorm, &ksp->reason, ksp->cnvP));
186: /* Catch error in happy breakdown and signal convergence and break from loop */
187: if (hapend) {
188: if (!ksp->reason) {
189: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "Reached happy break down, but convergence was not indicated. Residual norm = %g", (double)res);
190: ksp->reason = KSP_DIVERGED_BREAKDOWN;
191: break;
192: }
193: }
194: }
196: if (itcount) *itcount = it;
198: /*
199: Down here we have to solve for the "best" coefficients of the Krylov
200: columns, add the solution values together, and possibly unwind the
201: preconditioning from the solution
202: */
203: /* Form the solution (or the solution so far) */
204: PetscCall(KSPDGMRESBuildSoln(GRS(0), ksp->vec_sol, ksp->vec_sol, ksp, it - 1));
206: /* Monitor if we know that we will not return for a restart */
207: if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
208: PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
209: PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm));
210: }
212: /* Compute data for the deflation to be used during the next restart */
213: if (!ksp->reason && ksp->its < ksp->max_it) {
214: test = max_k * PetscLogReal(ksp->rtol / res) / PetscLogReal(res / res_old);
215: /* Compute data for the deflation if the residual rtol will not be reached in the remaining number of steps allowed */
216: if ((test > dgmres->smv * (ksp->max_it - ksp->its)) || dgmres->force) PetscCall(KSPDGMRESComputeDeflationData(ksp, NULL));
217: }
218: PetscFunctionReturn(PETSC_SUCCESS);
219: }
221: PetscErrorCode KSPSolve_DGMRES(KSP ksp)
222: {
223: PetscInt i, its = 0, itcount;
224: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
225: PetscBool guess_zero = ksp->guess_zero;
227: PetscFunctionBegin;
228: PetscCheck(!ksp->calc_sings || dgmres->Rsvd, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ORDER, "Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
230: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
231: ksp->its = 0;
232: dgmres->matvecs = 0;
233: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
235: itcount = 0;
236: while (!ksp->reason) {
237: PetscCall(KSPInitialResidual(ksp, ksp->vec_sol, VEC_TEMP, VEC_TEMP_MATOP, VEC_VV(0), ksp->vec_rhs));
238: if (ksp->pc_side == PC_LEFT) {
239: dgmres->matvecs += 1;
240: if (dgmres->r > 0) {
241: PetscCall(KSPDGMRESApplyDeflation(ksp, VEC_VV(0), VEC_TEMP));
242: PetscCall(VecCopy(VEC_TEMP, VEC_VV(0)));
243: }
244: }
246: PetscCall(KSPDGMRESCycle(&its, ksp));
247: itcount += its;
248: if (itcount >= ksp->max_it) {
249: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
250: break;
251: }
252: ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
253: }
254: ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
256: for (i = 0; i < dgmres->r; i++) PetscCall(VecViewFromOptions(UU[i], (PetscObject)ksp, "-ksp_dgmres_view_deflation_vecs"));
257: PetscFunctionReturn(PETSC_SUCCESS);
258: }
260: PetscErrorCode KSPDestroy_DGMRES(KSP ksp)
261: {
262: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
263: PetscInt neig1 = dgmres->neig + EIG_OFFSET;
264: PetscInt max_neig = dgmres->max_neig;
266: PetscFunctionBegin;
267: if (dgmres->r) {
268: PetscCall(VecDestroyVecs(max_neig, &UU));
269: PetscCall(VecDestroyVecs(max_neig, &MU));
270: if (XX) {
271: PetscCall(VecDestroyVecs(neig1, &XX));
272: PetscCall(VecDestroyVecs(neig1, &MX));
273: }
274: PetscCall(PetscFree(TT));
275: PetscCall(PetscFree(TTF));
276: PetscCall(PetscFree(INVP));
277: PetscCall(PetscFree(XMX));
278: PetscCall(PetscFree(UMX));
279: PetscCall(PetscFree(XMU));
280: PetscCall(PetscFree(X1));
281: PetscCall(PetscFree(X2));
282: PetscCall(PetscFree(dgmres->work));
283: PetscCall(PetscFree(dgmres->iwork));
284: PetscCall(PetscFree(dgmres->wr));
285: PetscCall(PetscFree(dgmres->wi));
286: PetscCall(PetscFree(dgmres->modul));
287: PetscCall(PetscFree(dgmres->Q));
288: PetscCall(PetscFree(ORTH));
289: PetscCall(PetscFree(AUAU));
290: PetscCall(PetscFree(AUU));
291: PetscCall(PetscFree(SR2));
292: }
293: PetscCall(PetscFree(SR));
294: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetEigen_C", NULL));
295: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetMaxEigen_C", NULL));
296: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetRatio_C", NULL));
297: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESForce_C", NULL));
298: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeSchurForm_C", NULL));
299: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeDeflationData_C", NULL));
300: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESApplyDeflation_C", NULL));
301: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESImproveEig_C", NULL));
302: PetscCall(KSPDestroy_GMRES(ksp));
303: PetscFunctionReturn(PETSC_SUCCESS);
304: }
306: /*
307: KSPDGMRESBuildSoln - create the solution from the starting vector and the
308: current iterates.
310: Input parameters:
311: nrs - work area of size it + 1.
312: vs - index of initial guess
313: vdest - index of result. Note that vs may == vdest (replace
314: guess with the solution).
316: This is an internal routine that knows about the GMRES internals.
317: */
318: static PetscErrorCode KSPDGMRESBuildSoln(PetscScalar *nrs, Vec vs, Vec vdest, KSP ksp, PetscInt it)
319: {
320: PetscScalar tt;
321: PetscInt ii, k, j;
322: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
324: /* Solve for solution vector that minimizes the residual */
326: PetscFunctionBegin;
327: /* If it is < 0, no gmres steps have been performed */
328: if (it < 0) {
329: PetscCall(VecCopy(vs, vdest)); /* VecCopy() is smart, exists immediately if vguess == vdest */
330: PetscFunctionReturn(PETSC_SUCCESS);
331: }
332: PetscCheck(*HH(it, it) != 0.0, PetscObjectComm((PetscObject)ksp), PETSC_ERR_CONV_FAILED, "Likely your matrix is the zero operator. HH(it,it) is identically zero; it = %" PetscInt_FMT " GRS(it) = %g", it, (double)PetscAbsScalar(*GRS(it)));
333: if (*HH(it, it) != 0.0) nrs[it] = *GRS(it) / *HH(it, it);
334: else nrs[it] = 0.0;
336: for (ii = 1; ii <= it; ii++) {
337: k = it - ii;
338: tt = *GRS(k);
339: for (j = k + 1; j <= it; j++) tt = tt - *HH(k, j) * nrs[j];
340: PetscCheck(*HH(k, k) != 0.0, PetscObjectComm((PetscObject)ksp), PETSC_ERR_CONV_FAILED, "Likely your matrix is singular. HH(k,k) is identically zero; it = %" PetscInt_FMT " k = %" PetscInt_FMT, it, k);
341: nrs[k] = tt / *HH(k, k);
342: }
344: /* Accumulate the correction to the solution of the preconditioned problem in TEMP */
345: PetscCall(VecMAXPBY(VEC_TEMP, it + 1, nrs, 0, &VEC_VV(0)));
347: /* Apply deflation */
348: if (ksp->pc_side == PC_RIGHT && dgmres->r > 0) {
349: PetscCall(KSPDGMRESApplyDeflation(ksp, VEC_TEMP, VEC_TEMP_MATOP));
350: PetscCall(VecCopy(VEC_TEMP_MATOP, VEC_TEMP));
351: }
352: PetscCall(KSPUnwindPreconditioner(ksp, VEC_TEMP, VEC_TEMP_MATOP));
354: /* add solution to previous solution */
355: if (vdest != vs) PetscCall(VecCopy(vs, vdest));
356: PetscCall(VecAXPY(vdest, 1.0, VEC_TEMP));
357: PetscFunctionReturn(PETSC_SUCCESS);
358: }
360: /*
361: Do the scalar work for the orthogonalization. Return new residual norm.
362: */
363: static PetscErrorCode KSPDGMRESUpdateHessenberg(KSP ksp, PetscInt it, PetscBool hapend, PetscReal *res)
364: {
365: PetscScalar *hh, *cc, *ss, tt;
366: PetscInt j;
367: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
369: PetscFunctionBegin;
370: hh = HH(0, it);
371: cc = CC(0);
372: ss = SS(0);
374: /* Apply all the previously computed plane rotations to the new column
375: of the Hessenberg matrix */
376: for (j = 1; j <= it; j++) {
377: tt = *hh;
378: *hh = PetscConj(*cc) * tt + *ss * *(hh + 1);
379: hh++;
380: *hh = *cc++ * *hh - (*ss++ * tt);
381: }
383: /*
384: compute the new plane rotation, and apply it to:
385: 1) the right-hand side of the Hessenberg system
386: 2) the new column of the Hessenberg matrix
387: thus obtaining the updated value of the residual
388: */
389: if (!hapend) {
390: tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh + 1)) * *(hh + 1));
391: if (tt == 0.0) {
392: ksp->reason = KSP_DIVERGED_NULL;
393: PetscFunctionReturn(PETSC_SUCCESS);
394: }
395: *cc = *hh / tt;
396: *ss = *(hh + 1) / tt;
397: *GRS(it + 1) = -(*ss * *GRS(it));
398: *GRS(it) = PetscConj(*cc) * *GRS(it);
399: *hh = PetscConj(*cc) * *hh + *ss * *(hh + 1);
400: *res = PetscAbsScalar(*GRS(it + 1));
401: } else {
402: /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
403: another rotation matrix (so RH doesn't change). The new residual is
404: always the new sine term times the residual from last time (GRS(it)),
405: but now the new sine rotation would be zero...so the residual should
406: be zero...so we will multiply "zero" by the last residual. This might
407: not be exactly what we want to do here -could just return "zero". */
408: *res = 0.0;
409: }
410: PetscFunctionReturn(PETSC_SUCCESS);
411: }
413: /*
414: Allocates more work vectors, starting from VEC_VV(it).
415: */
416: static PetscErrorCode KSPDGMRESGetNewVectors(KSP ksp, PetscInt it)
417: {
418: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
419: PetscInt nwork = dgmres->nwork_alloc, k, nalloc;
421: PetscFunctionBegin;
422: nalloc = PetscMin(ksp->max_it, dgmres->delta_allocate);
423: /* Adjust the number to allocate to make sure that we don't exceed the
424: number of available slots */
425: if (it + VEC_OFFSET + nalloc >= dgmres->vecs_allocated) nalloc = dgmres->vecs_allocated - it - VEC_OFFSET;
426: if (!nalloc) PetscFunctionReturn(PETSC_SUCCESS);
428: dgmres->vv_allocated += nalloc;
430: PetscCall(KSPCreateVecs(ksp, nalloc, &dgmres->user_work[nwork], 0, NULL));
432: dgmres->mwork_alloc[nwork] = nalloc;
433: for (k = 0; k < nalloc; k++) dgmres->vecs[it + VEC_OFFSET + k] = dgmres->user_work[nwork][k];
434: dgmres->nwork_alloc++;
435: PetscFunctionReturn(PETSC_SUCCESS);
436: }
438: PetscErrorCode KSPBuildSolution_DGMRES(KSP ksp, Vec ptr, Vec *result)
439: {
440: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
442: PetscFunctionBegin;
443: if (!ptr) {
444: if (!dgmres->sol_temp) PetscCall(VecDuplicate(ksp->vec_sol, &dgmres->sol_temp));
445: ptr = dgmres->sol_temp;
446: }
447: if (!dgmres->nrs) {
448: /* allocate the work area */
449: PetscCall(PetscMalloc1(dgmres->max_k, &dgmres->nrs));
450: }
451: PetscCall(KSPDGMRESBuildSoln(dgmres->nrs, ksp->vec_sol, ptr, ksp, dgmres->it));
452: if (result) *result = ptr;
453: PetscFunctionReturn(PETSC_SUCCESS);
454: }
456: static PetscErrorCode KSPView_DGMRES(KSP ksp, PetscViewer viewer)
457: {
458: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
459: PetscBool iascii, isharmonic;
461: PetscFunctionBegin;
462: PetscCall(KSPView_GMRES(ksp, viewer));
463: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
464: if (iascii) {
465: PetscCall(PetscViewerASCIIPrintf(viewer, " Adaptive strategy is used: %s\n", PetscBools[dgmres->force]));
466: PetscCall(PetscOptionsHasName(((PetscObject)ksp)->options, ((PetscObject)ksp)->prefix, "-ksp_dgmres_harmonic_ritz", &isharmonic));
467: if (isharmonic) {
468: PetscCall(PetscViewerASCIIPrintf(viewer, " Frequency of extracted eigenvalues = %" PetscInt_FMT " using Harmonic Ritz values \n", dgmres->neig));
469: } else {
470: PetscCall(PetscViewerASCIIPrintf(viewer, " Frequency of extracted eigenvalues = %" PetscInt_FMT " using Ritz values \n", dgmres->neig));
471: }
472: PetscCall(PetscViewerASCIIPrintf(viewer, " Total number of extracted eigenvalues = %" PetscInt_FMT "\n", dgmres->r));
473: PetscCall(PetscViewerASCIIPrintf(viewer, " Maximum number of eigenvalues set to be extracted = %" PetscInt_FMT "\n", dgmres->max_neig));
474: PetscCall(PetscViewerASCIIPrintf(viewer, " relaxation parameter for the adaptive strategy(smv) = %g\n", (double)dgmres->smv));
475: PetscCall(PetscViewerASCIIPrintf(viewer, " Number of matvecs : %" PetscInt_FMT "\n", dgmres->matvecs));
476: }
477: PetscFunctionReturn(PETSC_SUCCESS);
478: }
480: PetscErrorCode KSPDGMRESSetEigen_DGMRES(KSP ksp, PetscInt neig)
481: {
482: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
484: PetscFunctionBegin;
485: PetscCheck(neig >= 0 && neig <= dgmres->max_k, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "The value of neig must be positive and less than the restart value ");
486: dgmres->neig = neig;
487: PetscFunctionReturn(PETSC_SUCCESS);
488: }
490: static PetscErrorCode KSPDGMRESSetMaxEigen_DGMRES(KSP ksp, PetscInt max_neig)
491: {
492: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
494: PetscFunctionBegin;
495: PetscCheck(max_neig >= 0 && max_neig <= dgmres->max_k, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "The value of max_neig must be positive and less than the restart value ");
496: dgmres->max_neig = max_neig;
497: PetscFunctionReturn(PETSC_SUCCESS);
498: }
500: static PetscErrorCode KSPDGMRESSetRatio_DGMRES(KSP ksp, PetscReal ratio)
501: {
502: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
504: PetscFunctionBegin;
505: PetscCheck(ratio > 0, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "The relaxation parameter value must be positive");
506: dgmres->smv = ratio;
507: PetscFunctionReturn(PETSC_SUCCESS);
508: }
510: static PetscErrorCode KSPDGMRESForce_DGMRES(KSP ksp, PetscBool force)
511: {
512: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
514: PetscFunctionBegin;
515: dgmres->force = force;
516: PetscFunctionReturn(PETSC_SUCCESS);
517: }
519: PetscErrorCode KSPSetFromOptions_DGMRES(KSP ksp, PetscOptionItems *PetscOptionsObject)
520: {
521: PetscInt neig;
522: PetscInt max_neig;
523: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
524: PetscBool flg;
526: PetscFunctionBegin;
527: PetscCall(KSPSetFromOptions_GMRES(ksp, PetscOptionsObject));
528: PetscOptionsHeadBegin(PetscOptionsObject, "KSP DGMRES Options");
529: PetscCall(PetscOptionsInt("-ksp_dgmres_eigen", "Number of smallest eigenvalues to extract at each restart", "KSPDGMRESSetEigen", dgmres->neig, &neig, &flg));
530: if (flg) PetscCall(KSPDGMRESSetEigen(ksp, neig));
531: PetscCall(PetscOptionsInt("-ksp_dgmres_max_eigen", "Maximum Number of smallest eigenvalues to extract ", "KSPDGMRESSetMaxEigen", dgmres->max_neig, &max_neig, &flg));
532: if (flg) PetscCall(KSPDGMRESSetMaxEigen(ksp, max_neig));
533: PetscCall(PetscOptionsReal("-ksp_dgmres_ratio", "Relaxation parameter for the smaller number of matrix-vectors product allowed", "KSPDGMRESSetRatio", dgmres->smv, &dgmres->smv, NULL));
534: PetscCall(PetscOptionsBool("-ksp_dgmres_improve", "Improve the computation of eigenvalues by solving a new generalized eigenvalue problem (experimental - not stable at this time)", NULL, dgmres->improve, &dgmres->improve, NULL));
535: PetscCall(PetscOptionsBool("-ksp_dgmres_force", "Sets DGMRES always at restart active, i.e do not use the adaptive strategy", "KSPDGMRESForce", dgmres->force, &dgmres->force, NULL));
536: PetscOptionsHeadEnd();
537: PetscFunctionReturn(PETSC_SUCCESS);
538: }
540: PetscErrorCode KSPDGMRESComputeDeflationData_DGMRES(KSP ksp, PetscInt *ExtrNeig)
541: {
542: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
543: PetscInt i, j, k;
544: PetscBLASInt nr, bmax;
545: PetscInt r = dgmres->r;
546: PetscInt neig; /* number of eigenvalues to extract at each restart */
547: PetscInt neig1 = dgmres->neig + EIG_OFFSET; /* max number of eig that can be extracted at each restart */
548: PetscInt max_neig = dgmres->max_neig; /* Max number of eigenvalues to extract during the iterative process */
549: PetscInt N = dgmres->max_k + 1;
550: PetscInt n = dgmres->it + 1;
551: PetscReal alpha;
553: PetscFunctionBegin;
554: PetscCall(PetscLogEventBegin(KSP_DGMRESComputeDeflationData, ksp, 0, 0, 0));
555: if (dgmres->neig == 0 || (max_neig < (r + neig1) && !dgmres->improve)) {
556: PetscCall(PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0, 0, 0));
557: PetscFunctionReturn(PETSC_SUCCESS);
558: }
560: PetscCall(KSPDGMRESComputeSchurForm(ksp, &neig));
561: /* Form the extended Schur vectors X=VV*Sr */
562: if (!XX) PetscCall(VecDuplicateVecs(VEC_VV(0), neig1, &XX));
563: for (j = 0; j < neig; j++) PetscCall(VecMAXPBY(XX[j], n, &SR[j * N], 0, &VEC_VV(0)));
565: /* Orthogonalize X against U */
566: if (!ORTH) PetscCall(PetscMalloc1(max_neig, &ORTH));
567: if (r > 0) {
568: /* modified Gram-Schmidt */
569: for (j = 0; j < neig; j++) {
570: for (i = 0; i < r; i++) {
571: /* First, compute U'*X[j] */
572: PetscCall(VecDot(XX[j], UU[i], &alpha));
573: /* Then, compute X(j)=X(j)-U*U'*X(j) */
574: PetscCall(VecAXPY(XX[j], -alpha, UU[i]));
575: }
576: }
577: }
578: /* Compute MX = M^{-1}*A*X */
579: if (!MX) PetscCall(VecDuplicateVecs(VEC_VV(0), neig1, &MX));
580: for (j = 0; j < neig; j++) PetscCall(KSP_PCApplyBAorAB(ksp, XX[j], MX[j], VEC_TEMP_MATOP));
581: dgmres->matvecs += neig;
583: if ((r + neig1) > max_neig && dgmres->improve) { /* Improve the approximate eigenvectors in X by solving a new generalized eigenvalue -- expensive to do this */
584: PetscCall(KSPDGMRESImproveEig(ksp, neig));
585: PetscCall(PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0, 0, 0));
586: PetscFunctionReturn(PETSC_SUCCESS); /* We return here since data for M have been improved in KSPDGMRESImproveEig()*/
587: }
589: /* Compute XMX = X'*M^{-1}*A*X -- size (neig, neig) */
590: if (!XMX) PetscCall(PetscMalloc1(neig1 * neig1, &XMX));
591: for (j = 0; j < neig; j++) PetscCall(VecMDot(MX[j], neig, XX, &XMX[j * neig1]));
593: if (r > 0) {
594: /* Compute UMX = U'*M^{-1}*A*X -- size (r, neig) */
595: if (!UMX) PetscCall(PetscMalloc1(max_neig * neig1, &UMX));
596: for (j = 0; j < neig; j++) PetscCall(VecMDot(MX[j], r, UU, &UMX[j * max_neig]));
597: /* Compute XMU = X'*M^{-1}*A*U -- size(neig, r) */
598: if (!XMU) PetscCall(PetscMalloc1(max_neig * neig1, &XMU));
599: for (j = 0; j < r; j++) PetscCall(VecMDot(MU[j], neig, XX, &XMU[j * neig1]));
600: }
602: /* Form the new matrix T = [T UMX; XMU XMX]; */
603: if (!TT) PetscCall(PetscMalloc1(max_neig * max_neig, &TT));
604: if (r > 0) {
605: /* Add XMU to T */
606: for (j = 0; j < r; j++) PetscCall(PetscArraycpy(&TT[max_neig * j + r], &XMU[neig1 * j], neig));
607: /* Add [UMX; XMX] to T */
608: for (j = 0; j < neig; j++) {
609: k = r + j;
610: PetscCall(PetscArraycpy(&TT[max_neig * k], &UMX[max_neig * j], r));
611: PetscCall(PetscArraycpy(&TT[max_neig * k + r], &XMX[neig1 * j], neig));
612: }
613: } else { /* Add XMX to T */
614: for (j = 0; j < neig; j++) PetscCall(PetscArraycpy(&TT[max_neig * j], &XMX[neig1 * j], neig));
615: }
617: dgmres->r += neig;
618: r = dgmres->r;
619: PetscCall(PetscBLASIntCast(r, &nr));
620: /*LU Factorize T with Lapack xgetrf routine */
622: PetscCall(PetscBLASIntCast(max_neig, &bmax));
623: if (!TTF) PetscCall(PetscMalloc1(bmax * bmax, &TTF));
624: PetscCall(PetscArraycpy(TTF, TT, bmax * r));
625: if (!INVP) PetscCall(PetscMalloc1(bmax, &INVP));
626: {
627: PetscBLASInt info;
628: PetscCallBLAS("LAPACKgetrf", LAPACKgetrf_(&nr, &nr, TTF, &bmax, INVP, &info));
629: PetscCheck(!info, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Error in LAPACK routine XGETRF INFO=%d", (int)info);
630: }
632: /* Save X in U and MX in MU for the next cycles and increase the size of the invariant subspace */
633: if (!UU) {
634: PetscCall(VecDuplicateVecs(VEC_VV(0), max_neig, &UU));
635: PetscCall(VecDuplicateVecs(VEC_VV(0), max_neig, &MU));
636: }
637: for (j = 0; j < neig; j++) {
638: PetscCall(VecCopy(XX[j], UU[r - neig + j]));
639: PetscCall(VecCopy(MX[j], MU[r - neig + j]));
640: }
641: PetscCall(PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0, 0, 0));
642: PetscFunctionReturn(PETSC_SUCCESS);
643: }
645: PetscErrorCode KSPDGMRESComputeSchurForm_DGMRES(KSP ksp, PetscInt *neig)
646: {
647: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
648: PetscInt N = dgmres->max_k + 1, n = dgmres->it + 1;
649: PetscBLASInt bn;
650: PetscReal *A;
651: PetscBLASInt ihi;
652: PetscBLASInt ldA = 0; /* leading dimension of A */
653: PetscBLASInt ldQ; /* leading dimension of Q */
654: PetscReal *Q; /* orthogonal matrix of (left) Schur vectors */
655: PetscReal *work; /* working vector */
656: PetscBLASInt lwork; /* size of the working vector */
657: PetscInt *perm; /* Permutation vector to sort eigenvalues */
658: PetscInt i, j;
659: PetscBLASInt NbrEig; /* Number of eigenvalues really extracted */
660: PetscReal *wr, *wi, *modul; /* Real and imaginary part and modulus of the eigenvalues of A */
661: PetscBLASInt *select;
662: PetscBLASInt *iwork;
663: PetscBLASInt liwork;
664: PetscScalar *Ht; /* Transpose of the Hessenberg matrix */
665: PetscScalar *t; /* Store the result of the solution of H^T*t=h_{m+1,m}e_m */
666: PetscBLASInt *ipiv; /* Permutation vector to be used in LAPACK */
667: PetscBool flag; /* determine whether to use Ritz vectors or harmonic Ritz vectors */
669: PetscFunctionBegin;
670: PetscCall(PetscBLASIntCast(n, &bn));
671: PetscCall(PetscBLASIntCast(N, &ldA));
672: ihi = ldQ = bn;
673: PetscCall(PetscBLASIntCast(5 * N, &lwork));
675: #if defined(PETSC_USE_COMPLEX)
676: SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "No support for complex numbers.");
677: #endif
679: PetscCall(PetscMalloc1(ldA * ldA, &A));
680: PetscCall(PetscMalloc1(ldQ * n, &Q));
681: PetscCall(PetscMalloc1(lwork, &work));
682: if (!dgmres->wr) {
683: PetscCall(PetscMalloc1(n, &dgmres->wr));
684: PetscCall(PetscMalloc1(n, &dgmres->wi));
685: }
686: wr = dgmres->wr;
687: wi = dgmres->wi;
688: PetscCall(PetscMalloc1(n, &modul));
689: PetscCall(PetscMalloc1(n, &perm));
690: /* copy the Hessenberg matrix to work space */
691: PetscCall(PetscArraycpy(A, dgmres->hes_origin, ldA * ldA));
692: PetscCall(PetscOptionsHasName(((PetscObject)ksp)->options, ((PetscObject)ksp)->prefix, "-ksp_dgmres_harmonic_ritz", &flag));
693: if (flag) {
694: /* Compute the matrix H + H^{-T}*h^2_{m+1,m}e_m*e_m^T */
695: /* Transpose the Hessenberg matrix */
696: PetscCall(PetscMalloc1(bn * bn, &Ht));
697: for (i = 0; i < bn; i++) {
698: for (j = 0; j < bn; j++) Ht[i * bn + j] = dgmres->hes_origin[j * ldA + i];
699: }
701: /* Solve the system H^T*t = h_{m+1,m}e_m */
702: PetscCall(PetscCalloc1(bn, &t));
703: t[bn - 1] = dgmres->hes_origin[(bn - 1) * ldA + bn]; /* Pick the last element H(m+1,m) */
704: PetscCall(PetscMalloc1(bn, &ipiv));
705: /* Call the LAPACK routine dgesv to solve the system Ht^-1 * t */
706: {
707: PetscBLASInt info;
708: PetscBLASInt nrhs = 1;
709: PetscCallBLAS("LAPACKgesv", LAPACKgesv_(&bn, &nrhs, Ht, &bn, ipiv, t, &bn, &info));
710: PetscCheck(!info, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Error while calling the Lapack routine DGESV");
711: }
712: /* Now form H + H^{-T}*h^2_{m+1,m}e_m*e_m^T */
713: for (i = 0; i < bn; i++) A[(bn - 1) * bn + i] += t[i];
714: PetscCall(PetscFree(t));
715: PetscCall(PetscFree(Ht));
716: }
717: /* Compute eigenvalues with the Schur form */
718: {
719: PetscBLASInt info = 0;
720: PetscBLASInt ilo = 1;
721: PetscCallBLAS("LAPACKhseqr", LAPACKhseqr_("S", "I", &bn, &ilo, &ihi, A, &ldA, wr, wi, Q, &ldQ, work, &lwork, &info));
722: PetscCheck(!info, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Error in LAPACK routine XHSEQR %d", (int)info);
723: }
724: PetscCall(PetscFree(work));
726: /* sort the eigenvalues */
727: for (i = 0; i < n; i++) modul[i] = PetscSqrtReal(wr[i] * wr[i] + wi[i] * wi[i]);
728: for (i = 0; i < n; i++) perm[i] = i;
730: PetscCall(PetscSortRealWithPermutation(n, modul, perm));
731: /* save the complex modulus of the largest eigenvalue in magnitude */
732: if (dgmres->lambdaN < modul[perm[n - 1]]) dgmres->lambdaN = modul[perm[n - 1]];
733: /* count the number of extracted eigenvalues (with complex conjugates) */
734: NbrEig = 0;
735: while (NbrEig < dgmres->neig) {
736: if (wi[perm[NbrEig]] != 0) NbrEig += 2;
737: else NbrEig += 1;
738: }
739: /* Reorder the Schur decomposition so that the cluster of smallest eigenvalues appears in the leading diagonal blocks of A */
741: PetscCall(PetscCalloc1(n, &select));
743: if (!dgmres->GreatestEig) {
744: for (j = 0; j < NbrEig; j++) select[perm[j]] = 1;
745: } else {
746: for (j = 0; j < NbrEig; j++) select[perm[n - j - 1]] = 1;
747: }
748: /* call Lapack dtrsen */
749: lwork = PetscMax(1, 4 * NbrEig * (bn - NbrEig));
750: liwork = PetscMax(1, 2 * NbrEig * (bn - NbrEig));
751: PetscCall(PetscMalloc1(lwork, &work));
752: PetscCall(PetscMalloc1(liwork, &iwork));
753: {
754: PetscBLASInt info = 0;
755: PetscReal CondEig; /* lower bound on the reciprocal condition number for the selected cluster of eigenvalues */
756: PetscReal CondSub; /* estimated reciprocal condition number of the specified invariant subspace. */
757: PetscCallBLAS("LAPACKtrsen", LAPACKtrsen_("B", "V", select, &bn, A, &ldA, Q, &ldQ, wr, wi, &NbrEig, &CondEig, &CondSub, work, &lwork, iwork, &liwork, &info));
758: PetscCheck(info != 1, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Unable to reorder the eigenvalues with the LAPACK routine: ILL-CONDITIONED PROBLEM");
759: }
760: PetscCall(PetscFree(select));
762: /* Extract the Schur vectors */
763: for (j = 0; j < NbrEig; j++) PetscCall(PetscArraycpy(&SR[j * N], &Q[j * ldQ], n));
764: *neig = NbrEig;
765: PetscCall(PetscFree(A));
766: PetscCall(PetscFree(work));
767: PetscCall(PetscFree(perm));
768: PetscCall(PetscFree(work));
769: PetscCall(PetscFree(iwork));
770: PetscCall(PetscFree(modul));
771: PetscCall(PetscFree(Q));
772: PetscFunctionReturn(PETSC_SUCCESS);
773: }
775: PetscErrorCode KSPDGMRESApplyDeflation_DGMRES(KSP ksp, Vec x, Vec y)
776: {
777: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
778: PetscInt i, r = dgmres->r;
779: PetscReal alpha = 1.0;
780: PetscInt max_neig = dgmres->max_neig;
781: PetscBLASInt br, bmax;
782: PetscReal lambda = dgmres->lambdaN;
784: PetscFunctionBegin;
785: PetscCall(PetscBLASIntCast(r, &br));
786: PetscCall(PetscBLASIntCast(max_neig, &bmax));
787: PetscCall(PetscLogEventBegin(KSP_DGMRESApplyDeflation, ksp, 0, 0, 0));
788: if (!r) {
789: PetscCall(VecCopy(x, y));
790: PetscFunctionReturn(PETSC_SUCCESS);
791: }
792: /* Compute U'*x */
793: if (!X1) {
794: PetscCall(PetscMalloc1(bmax, &X1));
795: PetscCall(PetscMalloc1(bmax, &X2));
796: }
797: PetscCall(VecMDot(x, r, UU, X1));
799: /* Solve T*X1=X2 for X1*/
800: PetscCall(PetscArraycpy(X2, X1, br));
801: {
802: PetscBLASInt info;
803: PetscBLASInt nrhs = 1;
804: PetscCallBLAS("LAPACKgetrs", LAPACKgetrs_("N", &br, &nrhs, TTF, &bmax, INVP, X1, &bmax, &info));
805: PetscCheck(!info, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Error in LAPACK routine XGETRS %d", (int)info);
806: }
807: /* Iterative refinement -- is it really necessary ?? */
808: if (!WORK) {
809: PetscCall(PetscMalloc1(3 * bmax, &WORK));
810: PetscCall(PetscMalloc1(bmax, &IWORK));
811: }
812: {
813: PetscBLASInt info;
814: PetscReal berr, ferr;
815: PetscBLASInt nrhs = 1;
816: PetscCallBLAS("LAPACKgerfs", LAPACKgerfs_("N", &br, &nrhs, TT, &bmax, TTF, &bmax, INVP, X2, &bmax, X1, &bmax, &ferr, &berr, WORK, IWORK, &info));
817: PetscCheck(!info, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Error in LAPACK routine XGERFS %d", (int)info);
818: }
820: for (i = 0; i < r; i++) X2[i] = X1[i] / lambda - X2[i];
822: /* Compute X2=U*X2 */
823: PetscCall(VecMAXPBY(y, r, X2, 0, UU));
824: PetscCall(VecAXPY(y, alpha, x));
826: PetscCall(PetscLogEventEnd(KSP_DGMRESApplyDeflation, ksp, 0, 0, 0));
827: PetscFunctionReturn(PETSC_SUCCESS);
828: }
830: static PetscErrorCode KSPDGMRESImproveEig_DGMRES(KSP ksp, PetscInt neig)
831: {
832: KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
833: PetscInt j, r_old, r = dgmres->r;
834: PetscBLASInt i = 0;
835: PetscInt neig1 = dgmres->neig + EIG_OFFSET;
836: PetscInt bmax = dgmres->max_neig;
837: PetscInt aug = r + neig; /* actual size of the augmented invariant basis */
838: PetscInt aug1 = bmax + neig1; /* maximum size of the augmented invariant basis */
839: PetscBLASInt ldA; /* leading dimension of AUAU and AUU*/
840: PetscBLASInt N; /* size of AUAU */
841: PetscReal *Q; /* orthogonal matrix of (left) schur vectors */
842: PetscReal *Z; /* orthogonal matrix of (right) schur vectors */
843: PetscReal *work; /* working vector */
844: PetscBLASInt lwork; /* size of the working vector */
845: PetscInt *perm; /* Permutation vector to sort eigenvalues */
846: PetscReal *wr, *wi, *beta, *modul; /* Real and imaginary part and modulus of the eigenvalues of A*/
847: PetscBLASInt NbrEig = 0, nr, bm;
848: PetscBLASInt *select;
849: PetscBLASInt liwork, *iwork;
851: PetscFunctionBegin;
852: /* Block construction of the matrices AUU=(AU)'*U and (AU)'*AU*/
853: if (!AUU) {
854: PetscCall(PetscMalloc1(aug1 * aug1, &AUU));
855: PetscCall(PetscMalloc1(aug1 * aug1, &AUAU));
856: }
857: /* AUU = (AU)'*U = [(MU)'*U (MU)'*X; (MX)'*U (MX)'*X]
858: * Note that MU and MX have been computed previously either in ComputeDataDeflation() or down here in a previous call to this function */
859: /* (MU)'*U size (r x r) -- store in the <r> first columns of AUU*/
860: for (j = 0; j < r; j++) PetscCall(VecMDot(UU[j], r, MU, &AUU[j * aug1]));
861: /* (MU)'*X size (r x neig) -- store in AUU from the column <r>*/
862: for (j = 0; j < neig; j++) PetscCall(VecMDot(XX[j], r, MU, &AUU[(r + j) * aug1]));
863: /* (MX)'*U size (neig x r) -- store in the <r> first columns of AUU from the row <r>*/
864: for (j = 0; j < r; j++) PetscCall(VecMDot(UU[j], neig, MX, &AUU[j * aug1 + r]));
865: /* (MX)'*X size (neig neig) -- store in AUU from the column <r> and the row <r>*/
866: for (j = 0; j < neig; j++) PetscCall(VecMDot(XX[j], neig, MX, &AUU[(r + j) * aug1 + r]));
868: /* AUAU = (AU)'*AU = [(MU)'*MU (MU)'*MX; (MX)'*MU (MX)'*MX] */
869: /* (MU)'*MU size (r x r) -- store in the <r> first columns of AUAU*/
870: for (j = 0; j < r; j++) PetscCall(VecMDot(MU[j], r, MU, &AUAU[j * aug1]));
871: /* (MU)'*MX size (r x neig) -- store in AUAU from the column <r>*/
872: for (j = 0; j < neig; j++) PetscCall(VecMDot(MX[j], r, MU, &AUAU[(r + j) * aug1]));
873: /* (MX)'*MU size (neig x r) -- store in the <r> first columns of AUAU from the row <r>*/
874: for (j = 0; j < r; j++) PetscCall(VecMDot(MU[j], neig, MX, &AUAU[j * aug1 + r]));
875: /* (MX)'*MX size (neig neig) -- store in AUAU from the column <r> and the row <r>*/
876: for (j = 0; j < neig; j++) PetscCall(VecMDot(MX[j], neig, MX, &AUAU[(r + j) * aug1 + r]));
878: /* Computation of the eigenvectors */
879: PetscCall(PetscBLASIntCast(aug1, &ldA));
880: PetscCall(PetscBLASIntCast(aug, &N));
881: lwork = 8 * N + 20; /* sizeof the working space */
882: PetscCall(PetscMalloc1(N, &wr));
883: PetscCall(PetscMalloc1(N, &wi));
884: PetscCall(PetscMalloc1(N, &beta));
885: PetscCall(PetscMalloc1(N, &modul));
886: PetscCall(PetscMalloc1(N, &perm));
887: PetscCall(PetscMalloc1(N * N, &Q));
888: PetscCall(PetscMalloc1(N * N, &Z));
889: PetscCall(PetscMalloc1(lwork, &work));
890: {
891: PetscBLASInt info = 0;
892: PetscCallBLAS("LAPACKgges", LAPACKgges_("V", "V", "N", NULL, &N, AUAU, &ldA, AUU, &ldA, &i, wr, wi, beta, Q, &N, Z, &N, work, &lwork, NULL, &info));
893: PetscCheck(!info, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Error in LAPACK routine XGGES %d", (int)info);
894: }
895: for (i = 0; i < N; i++) {
896: if (beta[i] != 0.0) {
897: wr[i] /= beta[i];
898: wi[i] /= beta[i];
899: }
900: }
901: /* sort the eigenvalues */
902: for (i = 0; i < N; i++) modul[i] = PetscSqrtReal(wr[i] * wr[i] + wi[i] * wi[i]);
903: for (i = 0; i < N; i++) perm[i] = i;
904: PetscCall(PetscSortRealWithPermutation(N, modul, perm));
905: /* Save the norm of the largest eigenvalue */
906: if (dgmres->lambdaN < modul[perm[N - 1]]) dgmres->lambdaN = modul[perm[N - 1]];
907: /* Allocate space to extract the first r schur vectors */
908: if (!SR2) PetscCall(PetscMalloc1(aug1 * bmax, &SR2));
909: /* count the number of extracted eigenvalues (complex conjugates count as 2) */
910: while (NbrEig < bmax) {
911: if (wi[perm[NbrEig]] == 0) NbrEig += 1;
912: else NbrEig += 2;
913: }
914: if (NbrEig > bmax) NbrEig = bmax - 1;
915: r_old = r; /* previous size of r */
916: dgmres->r = r = NbrEig;
918: /* Select the eigenvalues to reorder */
919: PetscCall(PetscCalloc1(N, &select));
920: if (!dgmres->GreatestEig) {
921: for (j = 0; j < NbrEig; j++) select[perm[j]] = 1;
922: } else {
923: for (j = 0; j < NbrEig; j++) select[perm[N - j - 1]] = 1;
924: }
925: /* Reorder and extract the new <r> schur vectors */
926: lwork = PetscMax(4 * N + 16, 2 * NbrEig * (N - NbrEig));
927: liwork = PetscMax(N + 6, 2 * NbrEig * (N - NbrEig));
928: PetscCall(PetscFree(work));
929: PetscCall(PetscMalloc1(lwork, &work));
930: PetscCall(PetscMalloc1(liwork, &iwork));
931: {
932: PetscBLASInt info = 0;
933: PetscReal Dif[2];
934: PetscBLASInt ijob = 2;
935: PetscBLASInt wantQ = 1, wantZ = 1;
936: PetscCallBLAS("LAPACKtgsen", LAPACKtgsen_(&ijob, &wantQ, &wantZ, select, &N, AUAU, &ldA, AUU, &ldA, wr, wi, beta, Q, &N, Z, &N, &NbrEig, NULL, NULL, &Dif[0], work, &lwork, iwork, &liwork, &info));
937: PetscCheck(info != 1, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Unable to reorder the eigenvalues with the LAPACK routine: ill-conditioned problem.");
938: }
939: PetscCall(PetscFree(select));
941: for (j = 0; j < r; j++) PetscCall(PetscArraycpy(&SR2[j * aug1], &Z[j * N], N));
943: /* Multiply the Schur vectors SR2 by U (and X) to get a new U
944: -- save it temporarily in MU */
945: for (j = 0; j < r; j++) {
946: PetscCall(VecMAXPBY(MU[j], r_old, &SR2[j * aug1], 0, UU));
947: PetscCall(VecMAXPY(MU[j], neig, &SR2[j * aug1 + r_old], XX));
948: }
949: /* Form T = U'*MU*U */
950: for (j = 0; j < r; j++) {
951: PetscCall(VecCopy(MU[j], UU[j]));
952: PetscCall(KSP_PCApplyBAorAB(ksp, UU[j], MU[j], VEC_TEMP_MATOP));
953: }
954: dgmres->matvecs += r;
955: for (j = 0; j < r; j++) PetscCall(VecMDot(MU[j], r, UU, &TT[j * bmax]));
956: /* Factorize T */
957: PetscCall(PetscArraycpy(TTF, TT, bmax * r));
958: PetscCall(PetscBLASIntCast(r, &nr));
959: PetscCall(PetscBLASIntCast(bmax, &bm));
960: {
961: PetscBLASInt info;
962: PetscCallBLAS("LAPACKgetrf", LAPACKgetrf_(&nr, &nr, TTF, &bm, INVP, &info));
963: PetscCheck(!info, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Error in LAPACK routine XGETRF INFO=%d", (int)info);
964: }
965: /* Free Memory */
966: PetscCall(PetscFree(wr));
967: PetscCall(PetscFree(wi));
968: PetscCall(PetscFree(beta));
969: PetscCall(PetscFree(modul));
970: PetscCall(PetscFree(perm));
971: PetscCall(PetscFree(Q));
972: PetscCall(PetscFree(Z));
973: PetscCall(PetscFree(work));
974: PetscCall(PetscFree(iwork));
975: PetscFunctionReturn(PETSC_SUCCESS);
976: }
978: /*MC
979: KSPDGMRES - Implements the deflated GMRES as defined in {cite}`erhel1996restarted` and {cite}`wakam2013memory`
981: Options Database Keys:
982: GMRES Options (inherited):
983: + -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
984: . -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
985: . -ksp_gmres_preallocate - preallocate all the Krylov search directions initially
986: (otherwise groups of vectors are allocated as needed)
987: . -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against
988: the Krylov space (fast) (the default)
989: . -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
990: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
991: stability of the classical Gram-Schmidt orthogonalization.
992: - -ksp_gmres_krylov_monitor - plot the Krylov space generated
994: DGMRES Options Database Keys:
995: + -ksp_dgmres_eigen <neig> - number of smallest eigenvalues to extract at each restart
996: . -ksp_dgmres_max_eigen <max_neig> - maximum number of eigenvalues that can be extracted during the iterative process
997: . -ksp_dgmres_force - use the deflation at each restart; switch off the adaptive strategy.
998: - -ksp_dgmres_view_deflation_vecs <viewerspec> - View the deflation vectors, where viewerspec is a key that can be
999: parsed by `PetscOptionsGetViewer()`. If neig > 1, viewerspec should
1000: end with ":append". No vectors will be viewed if the adaptive
1001: strategy chooses not to deflate, so -ksp_dgmres_force should also
1002: be given.
1003: The deflation vectors span a subspace that may be a good
1004: approximation of the subspace of smallest eigenvectors of the
1005: preconditioned operator, so this option can aid in understanding
1006: the performance of a preconditioner.
1008: Level: beginner
1010: Notes:
1011: Left and right preconditioning are supported, but not symmetric preconditioning. Complex arithmetic is not supported
1013: In this implementation, the adaptive strategy allows switching to deflated GMRES when the stagnation occurs.
1015: Contributed by:
1016: Desire NUENTSA WAKAM, INRIA
1018: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPFGMRES`, `KSPLGMRES`,
1019: `KSPGMRESSetRestart()`, `KSPGMRESSetHapTol()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESGetOrthogonalization()`,
1020: `KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESModifiedGramSchmidtOrthogonalization()`,
1021: `KSPGMRESCGSRefinementType`, `KSPGMRESSetCGSRefinementType()`, `KSPGMRESGetCGSRefinementType()`, `KSPGMRESMonitorKrylov()`, `KSPSetPCSide()`
1022: M*/
1024: PETSC_EXTERN PetscErrorCode KSPCreate_DGMRES(KSP ksp)
1025: {
1026: KSP_DGMRES *dgmres;
1028: PetscFunctionBegin;
1029: PetscCall(PetscNew(&dgmres));
1030: ksp->data = (void *)dgmres;
1032: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
1033: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2));
1034: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));
1036: ksp->ops->buildsolution = KSPBuildSolution_DGMRES;
1037: ksp->ops->setup = KSPSetUp_DGMRES;
1038: ksp->ops->solve = KSPSolve_DGMRES;
1039: ksp->ops->destroy = KSPDestroy_DGMRES;
1040: ksp->ops->view = KSPView_DGMRES;
1041: ksp->ops->setfromoptions = KSPSetFromOptions_DGMRES;
1042: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
1043: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_GMRES;
1045: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetPreAllocateVectors_C", KSPGMRESSetPreAllocateVectors_GMRES));
1046: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetOrthogonalization_C", KSPGMRESSetOrthogonalization_GMRES));
1047: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetRestart_C", KSPGMRESSetRestart_GMRES));
1048: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetHapTol_C", KSPGMRESSetHapTol_GMRES));
1049: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetCGSRefinementType_C", KSPGMRESSetCGSRefinementType_GMRES));
1050: /* -- New functions defined in DGMRES -- */
1051: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetEigen_C", KSPDGMRESSetEigen_DGMRES));
1052: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetMaxEigen_C", KSPDGMRESSetMaxEigen_DGMRES));
1053: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetRatio_C", KSPDGMRESSetRatio_DGMRES));
1054: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESForce_C", KSPDGMRESForce_DGMRES));
1055: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeSchurForm_C", KSPDGMRESComputeSchurForm_DGMRES));
1056: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeDeflationData_C", KSPDGMRESComputeDeflationData_DGMRES));
1057: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESApplyDeflation_C", KSPDGMRESApplyDeflation_DGMRES));
1058: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESImproveEig_C", KSPDGMRESImproveEig_DGMRES));
1060: PetscCall(PetscLogEventRegister("DGMRESCompDefl", KSP_CLASSID, &KSP_DGMRESComputeDeflationData));
1061: PetscCall(PetscLogEventRegister("DGMRESApplyDefl", KSP_CLASSID, &KSP_DGMRESApplyDeflation));
1063: dgmres->haptol = 1.0e-30;
1064: dgmres->q_preallocate = 0;
1065: dgmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
1066: dgmres->orthog = KSPGMRESClassicalGramSchmidtOrthogonalization;
1067: dgmres->nrs = NULL;
1068: dgmres->sol_temp = NULL;
1069: dgmres->max_k = GMRES_DEFAULT_MAXK;
1070: dgmres->Rsvd = NULL;
1071: dgmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
1072: dgmres->orthogwork = NULL;
1074: /* Default values for the deflation */
1075: dgmres->r = 0;
1076: dgmres->neig = DGMRES_DEFAULT_EIG;
1077: dgmres->max_neig = DGMRES_DEFAULT_MAXEIG - 1;
1078: dgmres->lambdaN = 0.0;
1079: dgmres->smv = SMV;
1080: dgmres->matvecs = 0;
1081: dgmres->GreatestEig = PETSC_FALSE; /* experimental */
1082: dgmres->HasSchur = PETSC_FALSE;
1083: PetscFunctionReturn(PETSC_SUCCESS);
1084: }