Actual source code: pgmres.c
1: /*
2: This file implements PGMRES (a Pipelined Generalized Minimal Residual method)
3: */
5: #include <../src/ksp/ksp/impls/gmres/pgmres/pgmresimpl.h>
7: static PetscErrorCode KSPPGMRESUpdateHessenberg(KSP, PetscInt, PetscBool *, PetscReal *);
8: static PetscErrorCode KSPPGMRESBuildSoln(PetscScalar *, Vec, Vec, KSP, PetscInt);
10: static PetscErrorCode KSPSetUp_PGMRES(KSP ksp)
11: {
12: PetscFunctionBegin;
13: PetscCall(KSPSetUp_GMRES(ksp));
14: PetscFunctionReturn(PETSC_SUCCESS);
15: }
17: static PetscErrorCode KSPPGMRESCycle(PetscInt *itcount, KSP ksp)
18: {
19: KSP_PGMRES *pgmres = (KSP_PGMRES *)(ksp->data);
20: PetscReal res_norm, res, newnorm;
21: PetscInt it = 0, j, k;
22: PetscBool hapend = PETSC_FALSE;
24: PetscFunctionBegin;
25: if (itcount) *itcount = 0;
26: PetscCall(VecNormalize(VEC_VV(0), &res_norm));
27: KSPCheckNorm(ksp, res_norm);
28: res = res_norm;
29: *RS(0) = res_norm;
31: /* check for the convergence */
32: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
33: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
34: else ksp->rnorm = 0;
35: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
36: pgmres->it = it - 2;
37: PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
38: PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm));
39: if (!res) {
40: ksp->reason = KSP_CONVERGED_ATOL;
41: PetscCall(PetscInfo(ksp, "Converged due to zero residual norm on entry\n"));
42: PetscFunctionReturn(PETSC_SUCCESS);
43: }
45: PetscCall((*ksp->converged)(ksp, ksp->its, ksp->rnorm, &ksp->reason, ksp->cnvP));
46: for (; !ksp->reason; it++) {
47: Vec Zcur, Znext;
48: if (pgmres->vv_allocated <= it + VEC_OFFSET + 1) PetscCall(KSPGMRESGetNewVectors(ksp, it + 1));
49: /* VEC_VV(it-1) is orthogonal, it will be normalized once the VecNorm arrives. */
50: Zcur = VEC_VV(it); /* Zcur is not yet orthogonal, but the VecMDot to orthogonalize it has been started. */
51: Znext = VEC_VV(it + 1); /* This iteration will compute Znext, update with a deferred correction once we know how
52: Zcur relates to the previous vectors, and start the reduction to orthogonalize it. */
54: if (it < pgmres->max_k + 1 && ksp->its + 1 < PetscMax(2, ksp->max_it)) { /* We don't know whether what we have computed is enough, so apply the matrix. */
55: PetscCall(KSP_PCApplyBAorAB(ksp, Zcur, Znext, VEC_TEMP_MATOP));
56: }
58: if (it > 1) { /* Complete the pending reduction */
59: PetscCall(VecNormEnd(VEC_VV(it - 1), NORM_2, &newnorm));
60: *HH(it - 1, it - 2) = newnorm;
61: }
62: if (it > 0) { /* Finish the reduction computing the latest column of H */
63: PetscCall(VecMDotEnd(Zcur, it, &(VEC_VV(0)), HH(0, it - 1)));
64: }
66: if (it > 1) {
67: /* normalize the base vector from two iterations ago, basis is complete up to here */
68: PetscCall(VecScale(VEC_VV(it - 1), 1. / *HH(it - 1, it - 2)));
70: PetscCall(KSPPGMRESUpdateHessenberg(ksp, it - 2, &hapend, &res));
71: pgmres->it = it - 2;
72: ksp->its++;
73: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
74: else ksp->rnorm = 0;
76: PetscCall((*ksp->converged)(ksp, ksp->its, ksp->rnorm, &ksp->reason, ksp->cnvP));
77: if (it < pgmres->max_k + 1 || ksp->reason || ksp->its == ksp->max_it) { /* Monitor if we are done or still iterating, but not before a restart. */
78: PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
79: PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm));
80: }
81: if (ksp->reason) break;
82: /* Catch error in happy breakdown and signal convergence and break from loop */
83: if (hapend) {
84: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "Reached happy break down, but convergence was not indicated. Residual norm = %g", (double)res);
85: ksp->reason = KSP_DIVERGED_BREAKDOWN;
86: break;
87: }
89: if (!(it < pgmres->max_k + 1 && ksp->its < ksp->max_it)) break;
91: /* The it-2 column of H was not scaled when we computed Zcur, apply correction */
92: PetscCall(VecScale(Zcur, 1. / *HH(it - 1, it - 2)));
93: /* And Znext computed in this iteration was computed using the under-scaled Zcur */
94: PetscCall(VecScale(Znext, 1. / *HH(it - 1, it - 2)));
96: /* In the previous iteration, we projected an unnormalized Zcur against the Krylov basis, so we need to fix the column of H resulting from that projection. */
97: for (k = 0; k < it; k++) *HH(k, it - 1) /= *HH(it - 1, it - 2);
98: /* When Zcur was projected against the Krylov basis, VV(it-1) was still not normalized, so fix that too. This
99: * column is complete except for HH(it,it-1) which we won't know until the next iteration. */
100: *HH(it - 1, it - 1) /= *HH(it - 1, it - 2);
101: }
103: if (it > 0) {
104: PetscScalar *work;
105: if (!pgmres->orthogwork) PetscCall(PetscMalloc1(pgmres->max_k + 2, &pgmres->orthogwork));
106: work = pgmres->orthogwork;
107: /* Apply correction computed by the VecMDot in the last iteration to Znext. The original form is
108: *
109: * Znext -= sum_{j=0}^{i-1} Z[j+1] * H[j,i-1]
110: *
111: * where
112: *
113: * Z[j] = sum_{k=0}^j V[k] * H[k,j-1]
114: *
115: * substituting
116: *
117: * Znext -= sum_{j=0}^{i-1} sum_{k=0}^{j+1} V[k] * H[k,j] * H[j,i-1]
118: *
119: * rearranging the iteration space from row-column to column-row
120: *
121: * Znext -= sum_{k=0}^i sum_{j=k-1}^{i-1} V[k] * H[k,j] * H[j,i-1]
122: *
123: * Note that column it-1 of HH is correct. For all previous columns, we must look at HES because HH has already
124: * been transformed to upper triangular form.
125: */
126: for (k = 0; k < it + 1; k++) {
127: work[k] = 0;
128: for (j = PetscMax(0, k - 1); j < it - 1; j++) work[k] -= *HES(k, j) * *HH(j, it - 1);
129: }
130: PetscCall(VecMAXPY(Znext, it + 1, work, &VEC_VV(0)));
131: PetscCall(VecAXPY(Znext, -*HH(it - 1, it - 1), Zcur));
133: /* Orthogonalize Zcur against existing basis vectors. */
134: for (k = 0; k < it; k++) work[k] = -*HH(k, it - 1);
135: PetscCall(VecMAXPY(Zcur, it, work, &VEC_VV(0)));
136: /* Zcur is now orthogonal, and will be referred to as VEC_VV(it) again, though it is still not normalized. */
137: /* Begin computing the norm of the new vector, will be normalized after the MatMult in the next iteration. */
138: PetscCall(VecNormBegin(VEC_VV(it), NORM_2, &newnorm));
139: }
141: /* Compute column of H (to the diagonal, but not the subdiagonal) to be able to orthogonalize the newest vector. */
142: PetscCall(VecMDotBegin(Znext, it + 1, &VEC_VV(0), HH(0, it)));
144: /* Start an asynchronous split-mode reduction, the result of the MDot and Norm will be collected on the next iteration. */
145: PetscCall(PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)Znext)));
146: }
147: if (itcount) *itcount = it - 1; /* Number of iterations actually completed. */
149: /*
150: Solve for the "best" coefficients of the Krylov
151: columns, add the solution values together, and possibly unwind the preconditioning from the solution
152: */
153: /* Form the solution (or the solution so far) */
154: PetscCall(KSPPGMRESBuildSoln(RS(0), ksp->vec_sol, ksp->vec_sol, ksp, it - 2));
155: PetscFunctionReturn(PETSC_SUCCESS);
156: }
158: static PetscErrorCode KSPSolve_PGMRES(KSP ksp)
159: {
160: PetscInt its, itcount;
161: KSP_PGMRES *pgmres = (KSP_PGMRES *)ksp->data;
162: PetscBool guess_zero = ksp->guess_zero;
164: PetscFunctionBegin;
165: PetscCheck(!ksp->calc_sings || pgmres->Rsvd, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ORDER, "Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
166: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
167: ksp->its = 0;
168: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
170: itcount = 0;
171: ksp->reason = KSP_CONVERGED_ITERATING;
172: while (!ksp->reason) {
173: PetscCall(KSPInitialResidual(ksp, ksp->vec_sol, VEC_TEMP, VEC_TEMP_MATOP, VEC_VV(0), ksp->vec_rhs));
174: PetscCall(KSPPGMRESCycle(&its, ksp));
175: itcount += its;
176: if (itcount >= ksp->max_it) {
177: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
178: break;
179: }
180: ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
181: }
182: ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
183: PetscFunctionReturn(PETSC_SUCCESS);
184: }
186: static PetscErrorCode KSPDestroy_PGMRES(KSP ksp)
187: {
188: PetscFunctionBegin;
189: PetscCall(KSPDestroy_GMRES(ksp));
190: PetscFunctionReturn(PETSC_SUCCESS);
191: }
193: static PetscErrorCode KSPPGMRESBuildSoln(PetscScalar *nrs, Vec vguess, Vec vdest, KSP ksp, PetscInt it)
194: {
195: PetscScalar tt;
196: PetscInt k, j;
197: KSP_PGMRES *pgmres = (KSP_PGMRES *)(ksp->data);
199: PetscFunctionBegin;
200: /* Solve for solution vector that minimizes the residual */
202: if (it < 0) { /* no pgmres steps have been performed */
203: PetscCall(VecCopy(vguess, vdest)); /* VecCopy() is smart, exits immediately if vguess == vdest */
204: PetscFunctionReturn(PETSC_SUCCESS);
205: }
207: /* solve the upper triangular system - RS is the right side and HH is
208: the upper triangular matrix - put soln in nrs */
209: if (*HH(it, it) != 0.0) nrs[it] = *RS(it) / *HH(it, it);
210: else nrs[it] = 0.0;
212: for (k = it - 1; k >= 0; k--) {
213: tt = *RS(k);
214: for (j = k + 1; j <= it; j++) tt -= *HH(k, j) * nrs[j];
215: nrs[k] = tt / *HH(k, k);
216: }
218: /* Accumulate the correction to the solution of the preconditioned problem in TEMP */
219: PetscCall(VecMAXPBY(VEC_TEMP, it + 1, nrs, 0, &VEC_VV(0)));
220: PetscCall(KSPUnwindPreconditioner(ksp, VEC_TEMP, VEC_TEMP_MATOP));
221: /* add solution to previous solution */
222: if (vdest == vguess) {
223: PetscCall(VecAXPY(vdest, 1.0, VEC_TEMP));
224: } else {
225: PetscCall(VecWAXPY(vdest, 1.0, VEC_TEMP, vguess));
226: }
227: PetscFunctionReturn(PETSC_SUCCESS);
228: }
230: static PetscErrorCode KSPPGMRESUpdateHessenberg(KSP ksp, PetscInt it, PetscBool *hapend, PetscReal *res)
231: {
232: PetscScalar *hh, *cc, *ss, *rs;
233: PetscInt j;
234: PetscReal hapbnd;
235: KSP_PGMRES *pgmres = (KSP_PGMRES *)(ksp->data);
237: PetscFunctionBegin;
238: hh = HH(0, it); /* pointer to beginning of column to update */
239: cc = CC(0); /* beginning of cosine rotations */
240: ss = SS(0); /* beginning of sine rotations */
241: rs = RS(0); /* right hand side of least squares system */
243: /* The Hessenberg matrix is now correct through column it, save that form for possible spectral analysis */
244: for (j = 0; j <= it + 1; j++) *HES(j, it) = hh[j];
246: /* check for the happy breakdown */
247: hapbnd = PetscMin(PetscAbsScalar(hh[it + 1] / rs[it]), pgmres->haptol);
248: if (PetscAbsScalar(hh[it + 1]) < hapbnd) {
249: PetscCall(PetscInfo(ksp, "Detected happy breakdown, current hapbnd = %14.12e H(%" PetscInt_FMT ",%" PetscInt_FMT ") = %14.12e\n", (double)hapbnd, it + 1, it, (double)PetscAbsScalar(*HH(it + 1, it))));
250: *hapend = PETSC_TRUE;
251: }
253: /* Apply all the previously computed plane rotations to the new column of the Hessenberg matrix */
254: /* Note: this uses the rotation [conj(c) s ; -s c], c= cos(theta), s= sin(theta),
255: and some refs have [c s ; -conj(s) c] (don't be confused!) */
257: for (j = 0; j < it; j++) {
258: PetscScalar hhj = hh[j];
259: hh[j] = PetscConj(cc[j]) * hhj + ss[j] * hh[j + 1];
260: hh[j + 1] = -ss[j] * hhj + cc[j] * hh[j + 1];
261: }
263: /*
264: compute the new plane rotation, and apply it to:
265: 1) the right-hand-side of the Hessenberg system (RS)
266: note: it affects RS(it) and RS(it+1)
267: 2) the new column of the Hessenberg matrix
268: note: it affects HH(it,it) which is currently pointed to
269: by hh and HH(it+1, it) (*(hh+1))
270: thus obtaining the updated value of the residual...
271: */
273: /* compute new plane rotation */
275: if (!*hapend) {
276: PetscReal delta = PetscSqrtReal(PetscSqr(PetscAbsScalar(hh[it])) + PetscSqr(PetscAbsScalar(hh[it + 1])));
277: if (delta == 0.0) {
278: ksp->reason = KSP_DIVERGED_NULL;
279: PetscFunctionReturn(PETSC_SUCCESS);
280: }
282: cc[it] = hh[it] / delta; /* new cosine value */
283: ss[it] = hh[it + 1] / delta; /* new sine value */
285: hh[it] = PetscConj(cc[it]) * hh[it] + ss[it] * hh[it + 1];
286: rs[it + 1] = -ss[it] * rs[it];
287: rs[it] = PetscConj(cc[it]) * rs[it];
288: *res = PetscAbsScalar(rs[it + 1]);
289: } else { /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
290: another rotation matrix (so RH doesn't change). The new residual is
291: always the new sine term times the residual from last time (RS(it)),
292: but now the new sine rotation would be zero...so the residual should
293: be zero...so we will multiply "zero" by the last residual. This might
294: not be exactly what we want to do here -could just return "zero". */
295: *res = 0.0;
296: }
297: PetscFunctionReturn(PETSC_SUCCESS);
298: }
300: static PetscErrorCode KSPBuildSolution_PGMRES(KSP ksp, Vec ptr, Vec *result)
301: {
302: KSP_PGMRES *pgmres = (KSP_PGMRES *)ksp->data;
304: PetscFunctionBegin;
305: if (!ptr) {
306: if (!pgmres->sol_temp) PetscCall(VecDuplicate(ksp->vec_sol, &pgmres->sol_temp));
307: ptr = pgmres->sol_temp;
308: }
309: if (!pgmres->nrs) {
310: /* allocate the work area */
311: PetscCall(PetscMalloc1(pgmres->max_k, &pgmres->nrs));
312: }
314: PetscCall(KSPPGMRESBuildSoln(pgmres->nrs, ksp->vec_sol, ptr, ksp, pgmres->it));
315: if (result) *result = ptr;
316: PetscFunctionReturn(PETSC_SUCCESS);
317: }
319: static PetscErrorCode KSPSetFromOptions_PGMRES(KSP ksp, PetscOptionItems *PetscOptionsObject)
320: {
321: PetscFunctionBegin;
322: PetscCall(KSPSetFromOptions_GMRES(ksp, PetscOptionsObject));
323: PetscOptionsHeadBegin(PetscOptionsObject, "KSP pipelined GMRES Options");
324: PetscOptionsHeadEnd();
325: PetscFunctionReturn(PETSC_SUCCESS);
326: }
328: static PetscErrorCode KSPReset_PGMRES(KSP ksp)
329: {
330: PetscFunctionBegin;
331: PetscCall(KSPReset_GMRES(ksp));
332: PetscFunctionReturn(PETSC_SUCCESS);
333: }
335: /*MC
336: KSPPGMRES - Implements the Pipelined Generalized Minimal Residual method. [](sec_pipelineksp)
338: Options Database Keys:
339: + -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
340: . -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
341: . -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of vectors are allocated as needed)
342: . -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
343: . -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
344: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
345: stability of the classical Gram-Schmidt orthogonalization.
346: - -ksp_gmres_krylov_monitor - plot the Krylov space generated
348: Level: beginner
350: Note:
351: MPI configuration may be necessary for reductions to make asynchronous progress, which is important for performance of pipelined methods.
352: See [](doc_faq_pipelined)
354: References:
355: . * - Ghysels, Ashby, Meerbergen, Vanroose, Hiding global communication latencies in the GMRES algorithm on massively parallel machines, 2012.
357: Developer Note:
358: 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
360: .seealso: [](ch_ksp), [](sec_pipelineksp), [](doc_faq_pipelined), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPGMRES`, `KSPLGMRES`, `KSPPIPECG`, `KSPPIPECR`,
361: `KSPGMRESSetRestart()`, `KSPGMRESSetHapTol()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESGetOrthogonalization()`,
362: `KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESModifiedGramSchmidtOrthogonalization()`,
363: `KSPGMRESCGSRefinementType`, `KSPGMRESSetCGSRefinementType()`, `KSPGMRESGetCGSRefinementType()`, `KSPGMRESMonitorKrylov()`
364: M*/
366: PETSC_EXTERN PetscErrorCode KSPCreate_PGMRES(KSP ksp)
367: {
368: KSP_PGMRES *pgmres;
370: PetscFunctionBegin;
371: PetscCall(PetscNew(&pgmres));
373: ksp->data = (void *)pgmres;
374: ksp->ops->buildsolution = KSPBuildSolution_PGMRES;
375: ksp->ops->setup = KSPSetUp_PGMRES;
376: ksp->ops->solve = KSPSolve_PGMRES;
377: ksp->ops->reset = KSPReset_PGMRES;
378: ksp->ops->destroy = KSPDestroy_PGMRES;
379: ksp->ops->view = KSPView_GMRES;
380: ksp->ops->setfromoptions = KSPSetFromOptions_PGMRES;
381: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
382: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_GMRES;
384: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
385: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2));
386: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));
388: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetPreAllocateVectors_C", KSPGMRESSetPreAllocateVectors_GMRES));
389: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetOrthogonalization_C", KSPGMRESSetOrthogonalization_GMRES));
390: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetOrthogonalization_C", KSPGMRESGetOrthogonalization_GMRES));
391: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetRestart_C", KSPGMRESSetRestart_GMRES));
392: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetRestart_C", KSPGMRESGetRestart_GMRES));
393: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetCGSRefinementType_C", KSPGMRESSetCGSRefinementType_GMRES));
394: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetCGSRefinementType_C", KSPGMRESGetCGSRefinementType_GMRES));
396: pgmres->nextra_vecs = 1;
397: pgmres->haptol = 1.0e-30;
398: pgmres->q_preallocate = 0;
399: pgmres->delta_allocate = PGMRES_DELTA_DIRECTIONS;
400: pgmres->orthog = KSPGMRESClassicalGramSchmidtOrthogonalization;
401: pgmres->nrs = NULL;
402: pgmres->sol_temp = NULL;
403: pgmres->max_k = PGMRES_DEFAULT_MAXK;
404: pgmres->Rsvd = NULL;
405: pgmres->orthogwork = NULL;
406: pgmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
407: PetscFunctionReturn(PETSC_SUCCESS);
408: }