Actual source code: gmres.c
1: /*
2: This file implements GMRES (a Generalized Minimal Residual) method.
3: Reference: Saad and Schultz, 1986.
5: Some comments on left vs. right preconditioning, and restarts.
6: Left and right preconditioning.
7: If right preconditioning is chosen, then the problem being solved
8: by GMRES is actually
9: My = AB^-1 y = f
10: so the initial residual is
11: r = f - M y
12: Note that B^-1 y = x or y = B x, and if x is non-zero, the initial
13: residual is
14: r = f - A x
15: The final solution is then
16: x = B^-1 y
18: If left preconditioning is chosen, then the problem being solved is
19: My = B^-1 A x = B^-1 f,
20: and the initial residual is
21: r = B^-1(f - Ax)
23: Restarts: Restarts are basically solves with x0 not equal to zero.
24: Note that we can eliminate an extra application of B^-1 between
25: restarts as long as we don't require that the solution at the end
26: of an unsuccessful gmres iteration always be the solution x.
27: */
29: #include <../src/ksp/ksp/impls/gmres/gmresimpl.h>
30: #define GMRES_DELTA_DIRECTIONS 10
31: #define GMRES_DEFAULT_MAXK 30
32: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP, PetscInt, PetscBool, PetscReal *);
33: static PetscErrorCode KSPGMRESBuildSoln(PetscScalar *, Vec, Vec, KSP, PetscInt);
35: PetscErrorCode KSPSetUp_GMRES(KSP ksp)
36: {
37: PetscInt hh, hes, rs, cc;
38: PetscInt max_k, k;
39: KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
41: PetscFunctionBegin;
42: max_k = gmres->max_k; /* restart size */
43: hh = (max_k + 2) * (max_k + 1);
44: hes = (max_k + 1) * (max_k + 1);
45: rs = (max_k + 2);
46: cc = (max_k + 1);
48: PetscCall(PetscCalloc5(hh, &gmres->hh_origin, hes, &gmres->hes_origin, rs, &gmres->rs_origin, cc, &gmres->cc_origin, cc, &gmres->ss_origin));
50: if (ksp->calc_sings) {
51: /* Allocate workspace to hold Hessenberg matrix needed by lapack */
52: PetscCall(PetscMalloc1((max_k + 3) * (max_k + 9), &gmres->Rsvd));
53: PetscCall(PetscMalloc1(6 * (max_k + 2), &gmres->Dsvd));
54: }
56: /* Allocate array to hold pointers to user vectors. Note that we need
57: 4 + max_k + 1 (since we need it+1 vectors, and it <= max_k) */
58: gmres->vecs_allocated = VEC_OFFSET + 2 + max_k + gmres->nextra_vecs;
60: PetscCall(PetscMalloc1(gmres->vecs_allocated, &gmres->vecs));
61: PetscCall(PetscMalloc1(VEC_OFFSET + 2 + max_k, &gmres->user_work));
62: PetscCall(PetscMalloc1(VEC_OFFSET + 2 + max_k, &gmres->mwork_alloc));
64: if (gmres->q_preallocate) {
65: gmres->vv_allocated = VEC_OFFSET + 2 + max_k;
67: PetscCall(KSPCreateVecs(ksp, gmres->vv_allocated, &gmres->user_work[0], 0, NULL));
69: gmres->mwork_alloc[0] = gmres->vv_allocated;
70: gmres->nwork_alloc = 1;
71: for (k = 0; k < gmres->vv_allocated; k++) gmres->vecs[k] = gmres->user_work[0][k];
72: } else {
73: gmres->vv_allocated = 5;
75: PetscCall(KSPCreateVecs(ksp, 5, &gmres->user_work[0], 0, NULL));
77: gmres->mwork_alloc[0] = 5;
78: gmres->nwork_alloc = 1;
79: for (k = 0; k < gmres->vv_allocated; k++) gmres->vecs[k] = gmres->user_work[0][k];
80: }
81: PetscFunctionReturn(PETSC_SUCCESS);
82: }
84: /*
85: Run gmres, possibly with restart. Return residual history if requested.
86: input parameters:
88: . gmres - structure containing parameters and work areas
90: output parameters:
91: . nres - residuals (from preconditioned system) at each step.
92: If restarting, consider passing nres+it. If null,
93: ignored
94: . itcount - number of iterations used. nres[0] to nres[itcount]
95: are defined. If null, ignored.
97: Notes:
98: On entry, the value in vector VEC_VV(0) should be the initial residual
99: (this allows shortcuts where the initial preconditioned residual is 0).
100: */
101: static PetscErrorCode KSPGMRESCycle(PetscInt *itcount, KSP ksp)
102: {
103: KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
104: PetscReal res, hapbnd, tt;
105: PetscInt it = 0, max_k = gmres->max_k;
106: PetscBool hapend = PETSC_FALSE;
108: PetscFunctionBegin;
109: if (itcount) *itcount = 0;
110: PetscCall(VecNormalize(VEC_VV(0), &res));
111: KSPCheckNorm(ksp, res);
113: /* the constant .1 is arbitrary, just some measure at how incorrect the residuals are */
114: if ((ksp->rnorm > 0.0) && (PetscAbsReal(res - ksp->rnorm) > gmres->breakdowntol * gmres->rnorm0)) {
115: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_CONV_FAILED, "Residual norm computed by GMRES recursion formula %g is far from the computed residual norm %g at restart, residual norm at start of cycle %g",
116: (double)ksp->rnorm, (double)res, (double)gmres->rnorm0);
117: PetscCall(PetscInfo(ksp, "Residual norm computed by GMRES recursion formula %g is far from the computed residual norm %g at restart, residual norm at start of cycle %g\n", (double)ksp->rnorm, (double)res, (double)gmres->rnorm0));
118: ksp->reason = KSP_DIVERGED_BREAKDOWN;
119: PetscFunctionReturn(PETSC_SUCCESS);
120: }
121: *GRS(0) = gmres->rnorm0 = res;
123: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
124: ksp->rnorm = res;
125: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
126: gmres->it = (it - 1);
127: PetscCall(KSPLogResidualHistory(ksp, res));
128: PetscCall(KSPLogErrorHistory(ksp));
129: PetscCall(KSPMonitor(ksp, ksp->its, res));
130: if (!res) {
131: ksp->reason = KSP_CONVERGED_ATOL;
132: PetscCall(PetscInfo(ksp, "Converged due to zero residual norm on entry\n"));
133: PetscFunctionReturn(PETSC_SUCCESS);
134: }
136: /* check for the convergence */
137: PetscCall((*ksp->converged)(ksp, ksp->its, res, &ksp->reason, ksp->cnvP));
138: while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
139: if (it) {
140: PetscCall(KSPLogResidualHistory(ksp, res));
141: PetscCall(KSPLogErrorHistory(ksp));
142: PetscCall(KSPMonitor(ksp, ksp->its, res));
143: }
144: gmres->it = (it - 1);
145: if (gmres->vv_allocated <= it + VEC_OFFSET + 1) PetscCall(KSPGMRESGetNewVectors(ksp, it + 1));
146: PetscCall(KSP_PCApplyBAorAB(ksp, VEC_VV(it), VEC_VV(1 + it), VEC_TEMP_MATOP));
148: /* update Hessenberg matrix and do Gram-Schmidt */
149: PetscCall((*gmres->orthog)(ksp, it));
150: if (ksp->reason) break;
152: /* vv(i+1) . vv(i+1) */
153: PetscCall(VecNormalize(VEC_VV(it + 1), &tt));
154: KSPCheckNorm(ksp, tt);
156: /* save the magnitude */
157: *HH(it + 1, it) = tt;
158: *HES(it + 1, it) = tt;
160: /* check for the happy breakdown */
161: hapbnd = PetscAbsScalar(tt / *GRS(it));
162: if (hapbnd > gmres->haptol) hapbnd = gmres->haptol;
163: if (tt < hapbnd) {
164: PetscCall(PetscInfo(ksp, "Detected happy breakdown, current hapbnd = %14.12e tt = %14.12e\n", (double)hapbnd, (double)tt));
165: hapend = PETSC_TRUE;
166: }
167: PetscCall(KSPGMRESUpdateHessenberg(ksp, it, hapend, &res));
169: it++;
170: gmres->it = (it - 1); /* For converged */
171: ksp->its++;
172: ksp->rnorm = res;
173: if (ksp->reason) break;
175: PetscCall((*ksp->converged)(ksp, ksp->its, res, &ksp->reason, ksp->cnvP));
177: /* Catch error in happy breakdown and signal convergence and break from loop */
178: if (hapend) {
179: if (ksp->normtype == KSP_NORM_NONE) { /* convergence test was skipped in this case */
180: ksp->reason = KSP_CONVERGED_HAPPY_BREAKDOWN;
181: } else if (!ksp->reason) {
182: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "Reached happy break down, but convergence was not indicated. Residual norm = %g", (double)res);
183: ksp->reason = KSP_DIVERGED_BREAKDOWN;
184: break;
185: }
186: }
187: }
189: if (itcount) *itcount = it;
191: /*
192: Down here we have to solve for the "best" coefficients of the Krylov
193: columns, add the solution values together, and possibly unwind the
194: preconditioning from the solution
195: */
196: /* Form the solution (or the solution so far) */
197: PetscCall(KSPGMRESBuildSoln(GRS(0), ksp->vec_sol, ksp->vec_sol, ksp, it - 1));
199: /* Monitor if we know that we will not return for a restart */
200: if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
201: PetscCall(KSPLogResidualHistory(ksp, res));
202: PetscCall(KSPLogErrorHistory(ksp));
203: PetscCall(KSPMonitor(ksp, ksp->its, res));
204: }
205: PetscFunctionReturn(PETSC_SUCCESS);
206: }
208: static PetscErrorCode KSPSolve_GMRES(KSP ksp)
209: {
210: PetscInt its, itcount, i;
211: KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
212: PetscBool guess_zero = ksp->guess_zero;
213: PetscInt N = gmres->max_k + 1;
215: PetscFunctionBegin;
216: PetscCheck(!ksp->calc_sings || gmres->Rsvd, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ORDER, "Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
218: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
219: ksp->its = 0;
220: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
222: itcount = 0;
223: gmres->fullcycle = 0;
224: ksp->rnorm = -1.0; /* special marker for KSPGMRESCycle() */
225: while (!ksp->reason || (ksp->rnorm == -1 && ksp->reason == KSP_DIVERGED_PC_FAILED)) {
226: PetscCall(KSPInitialResidual(ksp, ksp->vec_sol, VEC_TEMP, VEC_TEMP_MATOP, VEC_VV(0), ksp->vec_rhs));
227: PetscCall(KSPGMRESCycle(&its, ksp));
228: /* Store the Hessenberg matrix and the basis vectors of the Krylov subspace
229: if the cycle is complete for the computation of the Ritz pairs */
230: if (its == gmres->max_k) {
231: gmres->fullcycle++;
232: if (ksp->calc_ritz) {
233: if (!gmres->hes_ritz) {
234: PetscCall(PetscMalloc1(N * N, &gmres->hes_ritz));
235: PetscCall(VecDuplicateVecs(VEC_VV(0), N, &gmres->vecb));
236: }
237: PetscCall(PetscArraycpy(gmres->hes_ritz, gmres->hes_origin, N * N));
238: for (i = 0; i < gmres->max_k + 1; i++) PetscCall(VecCopy(VEC_VV(i), gmres->vecb[i]));
239: }
240: }
241: itcount += its;
242: if (itcount >= ksp->max_it) {
243: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
244: break;
245: }
246: ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
247: }
248: ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
249: PetscFunctionReturn(PETSC_SUCCESS);
250: }
252: PetscErrorCode KSPReset_GMRES(KSP ksp)
253: {
254: KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
255: PetscInt i;
257: PetscFunctionBegin;
258: /* Free the Hessenberg matrices */
259: PetscCall(PetscFree5(gmres->hh_origin, gmres->hes_origin, gmres->rs_origin, gmres->cc_origin, gmres->ss_origin));
260: PetscCall(PetscFree(gmres->hes_ritz));
262: /* free work vectors */
263: PetscCall(PetscFree(gmres->vecs));
264: for (i = 0; i < gmres->nwork_alloc; i++) PetscCall(VecDestroyVecs(gmres->mwork_alloc[i], &gmres->user_work[i]));
265: gmres->nwork_alloc = 0;
266: if (gmres->vecb) PetscCall(VecDestroyVecs(gmres->max_k + 1, &gmres->vecb));
268: PetscCall(PetscFree(gmres->user_work));
269: PetscCall(PetscFree(gmres->mwork_alloc));
270: PetscCall(PetscFree(gmres->nrs));
271: PetscCall(VecDestroy(&gmres->sol_temp));
272: PetscCall(PetscFree(gmres->Rsvd));
273: PetscCall(PetscFree(gmres->Dsvd));
274: PetscCall(PetscFree(gmres->orthogwork));
276: gmres->vv_allocated = 0;
277: gmres->vecs_allocated = 0;
278: gmres->sol_temp = NULL;
279: PetscFunctionReturn(PETSC_SUCCESS);
280: }
282: PetscErrorCode KSPDestroy_GMRES(KSP ksp)
283: {
284: PetscFunctionBegin;
285: PetscCall(KSPReset_GMRES(ksp));
286: PetscCall(PetscFree(ksp->data));
287: /* clear composed functions */
288: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetPreAllocateVectors_C", NULL));
289: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetOrthogonalization_C", NULL));
290: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetOrthogonalization_C", NULL));
291: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetRestart_C", NULL));
292: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetRestart_C", NULL));
293: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetHapTol_C", NULL));
294: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetBreakdownTolerance_C", NULL));
295: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetCGSRefinementType_C", NULL));
296: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetCGSRefinementType_C", NULL));
297: PetscFunctionReturn(PETSC_SUCCESS);
298: }
299: /*
300: KSPGMRESBuildSoln - create the solution from the starting vector and the
301: current iterates.
303: Input parameters:
304: nrs - work area of size it + 1.
305: vs - index of initial guess
306: vdest - index of result. Note that vs may == vdest (replace
307: guess with the solution).
309: This is an internal routine that knows about the GMRES internals.
310: */
311: static PetscErrorCode KSPGMRESBuildSoln(PetscScalar *nrs, Vec vs, Vec vdest, KSP ksp, PetscInt it)
312: {
313: PetscScalar tt;
314: PetscInt ii, k, j;
315: KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
317: PetscFunctionBegin;
318: /* Solve for solution vector that minimizes the residual */
320: /* If it is < 0, no gmres steps have been performed */
321: if (it < 0) {
322: PetscCall(VecCopy(vs, vdest)); /* VecCopy() is smart, exists immediately if vguess == vdest */
323: PetscFunctionReturn(PETSC_SUCCESS);
324: }
325: if (*HH(it, it) != 0.0) {
326: nrs[it] = *GRS(it) / *HH(it, it);
327: } else {
328: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "You reached the break down in GMRES; HH(it,it) = 0");
329: ksp->reason = KSP_DIVERGED_BREAKDOWN;
331: PetscCall(PetscInfo(ksp, "Likely your matrix or preconditioner is singular. HH(it,it) is identically zero; it = %" PetscInt_FMT " GRS(it) = %g\n", it, (double)PetscAbsScalar(*GRS(it))));
332: PetscFunctionReturn(PETSC_SUCCESS);
333: }
334: for (ii = 1; ii <= it; ii++) {
335: k = it - ii;
336: tt = *GRS(k);
337: for (j = k + 1; j <= it; j++) tt = tt - *HH(k, j) * nrs[j];
338: if (*HH(k, k) == 0.0) {
339: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %" PetscInt_FMT, k);
340: ksp->reason = KSP_DIVERGED_BREAKDOWN;
341: PetscCall(PetscInfo(ksp, "Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %" PetscInt_FMT "\n", k));
342: PetscFunctionReturn(PETSC_SUCCESS);
343: }
344: nrs[k] = tt / *HH(k, k);
345: }
347: /* Accumulate the correction to the solution of the preconditioned problem in TEMP */
348: PetscCall(VecMAXPBY(VEC_TEMP, it + 1, nrs, 0, &VEC_VV(0)));
350: PetscCall(KSPUnwindPreconditioner(ksp, VEC_TEMP, VEC_TEMP_MATOP));
351: /* add solution to previous solution */
352: if (vdest != vs) PetscCall(VecCopy(vs, vdest));
353: PetscCall(VecAXPY(vdest, 1.0, VEC_TEMP));
354: PetscFunctionReturn(PETSC_SUCCESS);
355: }
356: /*
357: Do the scalar work for the orthogonalization. Return new residual norm.
358: */
359: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP ksp, PetscInt it, PetscBool hapend, PetscReal *res)
360: {
361: PetscScalar *hh, *cc, *ss, tt;
362: PetscInt j;
363: KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
365: PetscFunctionBegin;
366: hh = HH(0, it);
367: cc = CC(0);
368: ss = SS(0);
370: /* Apply all the previously computed plane rotations to the new column
371: of the Hessenberg matrix */
372: for (j = 1; j <= it; j++) {
373: tt = *hh;
374: *hh = PetscConj(*cc) * tt + *ss * *(hh + 1);
375: hh++;
376: *hh = *cc++ * *hh - (*ss++ * tt);
377: }
379: /*
380: compute the new plane rotation, and apply it to:
381: 1) the right-hand side of the Hessenberg system
382: 2) the new column of the Hessenberg matrix
383: thus obtaining the updated value of the residual
384: */
385: if (!hapend) {
386: tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh + 1)) * *(hh + 1));
387: if (tt == 0.0) {
388: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "tt == 0.0");
389: ksp->reason = KSP_DIVERGED_NULL;
390: PetscFunctionReturn(PETSC_SUCCESS);
391: }
392: *cc = *hh / tt;
393: *ss = *(hh + 1) / tt;
394: *GRS(it + 1) = -(*ss * *GRS(it));
395: *GRS(it) = PetscConj(*cc) * *GRS(it);
396: *hh = PetscConj(*cc) * *hh + *ss * *(hh + 1);
397: *res = PetscAbsScalar(*GRS(it + 1));
398: } else {
399: /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
400: another rotation matrix (so RH doesn't change). The new residual is
401: always the new sine term times the residual from last time (GRS(it)),
402: but now the new sine rotation would be zero...so the residual should
403: be zero...so we will multiply "zero" by the last residual. This might
404: not be exactly what we want to do here -could just return "zero". */
406: *res = 0.0;
407: }
408: PetscFunctionReturn(PETSC_SUCCESS);
409: }
410: /*
411: This routine allocates more work vectors, starting from VEC_VV(it).
412: */
413: PetscErrorCode KSPGMRESGetNewVectors(KSP ksp, PetscInt it)
414: {
415: KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
416: PetscInt nwork = gmres->nwork_alloc, k, nalloc;
418: PetscFunctionBegin;
419: nalloc = PetscMin(ksp->max_it, gmres->delta_allocate);
420: /* Adjust the number to allocate to make sure that we don't exceed the
421: number of available slots */
422: if (it + VEC_OFFSET + nalloc >= gmres->vecs_allocated) nalloc = gmres->vecs_allocated - it - VEC_OFFSET;
423: if (!nalloc) PetscFunctionReturn(PETSC_SUCCESS);
425: gmres->vv_allocated += nalloc;
427: PetscCall(KSPCreateVecs(ksp, nalloc, &gmres->user_work[nwork], 0, NULL));
429: gmres->mwork_alloc[nwork] = nalloc;
430: for (k = 0; k < nalloc; k++) gmres->vecs[it + VEC_OFFSET + k] = gmres->user_work[nwork][k];
431: gmres->nwork_alloc++;
432: PetscFunctionReturn(PETSC_SUCCESS);
433: }
435: static PetscErrorCode KSPBuildSolution_GMRES(KSP ksp, Vec ptr, Vec *result)
436: {
437: KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
439: PetscFunctionBegin;
440: if (!ptr) {
441: if (!gmres->sol_temp) PetscCall(VecDuplicate(ksp->vec_sol, &gmres->sol_temp));
442: ptr = gmres->sol_temp;
443: }
444: if (!gmres->nrs) {
445: /* allocate the work area */
446: PetscCall(PetscMalloc1(gmres->max_k, &gmres->nrs));
447: }
449: PetscCall(KSPGMRESBuildSoln(gmres->nrs, ksp->vec_sol, ptr, ksp, gmres->it));
450: if (result) *result = ptr;
451: PetscFunctionReturn(PETSC_SUCCESS);
452: }
454: PetscErrorCode KSPView_GMRES(KSP ksp, PetscViewer viewer)
455: {
456: KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
457: const char *cstr;
458: PetscBool iascii, isstring;
460: PetscFunctionBegin;
461: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
462: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSTRING, &isstring));
463: if (gmres->orthog == KSPGMRESClassicalGramSchmidtOrthogonalization) {
464: switch (gmres->cgstype) {
465: case (KSP_GMRES_CGS_REFINE_NEVER):
466: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement";
467: break;
468: case (KSP_GMRES_CGS_REFINE_ALWAYS):
469: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement";
470: break;
471: case (KSP_GMRES_CGS_REFINE_IFNEEDED):
472: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement when needed";
473: break;
474: default:
475: SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "Unknown orthogonalization");
476: }
477: } else if (gmres->orthog == KSPGMRESModifiedGramSchmidtOrthogonalization) {
478: cstr = "Modified Gram-Schmidt Orthogonalization";
479: } else {
480: cstr = "unknown orthogonalization";
481: }
482: if (iascii) {
483: PetscCall(PetscViewerASCIIPrintf(viewer, " restart=%" PetscInt_FMT ", using %s\n", gmres->max_k, cstr));
484: PetscCall(PetscViewerASCIIPrintf(viewer, " happy breakdown tolerance %g\n", (double)gmres->haptol));
485: } else if (isstring) {
486: PetscCall(PetscViewerStringSPrintf(viewer, "%s restart %" PetscInt_FMT, cstr, gmres->max_k));
487: }
488: PetscFunctionReturn(PETSC_SUCCESS);
489: }
491: /*@C
492: KSPGMRESMonitorKrylov - Calls `VecView()` for each new direction in the `KSPGMRES` accumulated Krylov space.
494: Collective
496: Input Parameters:
497: + ksp - the `KSP` context
498: . its - iteration number
499: . fgnorm - 2-norm of residual (or gradient)
500: - dummy - a collection of viewers created with `PetscViewersCreate()`
502: Options Database Key:
503: . -ksp_gmres_krylov_monitor <bool> - Plot the Krylov directions
505: Level: intermediate
507: Note:
508: A new `PETSCVIEWERDRAW` is created for each Krylov vector so they can all be simultaneously viewed
510: .seealso: [](ch_ksp), `KSPGMRES`, `KSPMonitorSet()`, `KSPMonitorResidual()`, `VecView()`, `PetscViewersCreate()`, `PetscViewersDestroy()`
511: @*/
512: PetscErrorCode KSPGMRESMonitorKrylov(KSP ksp, PetscInt its, PetscReal fgnorm, void *dummy)
513: {
514: PetscViewers viewers = (PetscViewers)dummy;
515: KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
516: Vec x;
517: PetscViewer viewer;
518: PetscBool flg;
520: PetscFunctionBegin;
521: PetscCall(PetscViewersGetViewer(viewers, gmres->it + 1, &viewer));
522: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &flg));
523: if (!flg) {
524: PetscCall(PetscViewerSetType(viewer, PETSCVIEWERDRAW));
525: PetscCall(PetscViewerDrawSetInfo(viewer, NULL, "Krylov GMRES Monitor", PETSC_DECIDE, PETSC_DECIDE, 300, 300));
526: }
527: x = VEC_VV(gmres->it + 1);
528: PetscCall(VecView(x, viewer));
529: PetscFunctionReturn(PETSC_SUCCESS);
530: }
532: PetscErrorCode KSPSetFromOptions_GMRES(KSP ksp, PetscOptionItems *PetscOptionsObject)
533: {
534: PetscInt restart;
535: PetscReal haptol, breakdowntol;
536: KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
537: PetscBool flg;
539: PetscFunctionBegin;
540: PetscOptionsHeadBegin(PetscOptionsObject, "KSP GMRES Options");
541: PetscCall(PetscOptionsInt("-ksp_gmres_restart", "Number of Krylov search directions", "KSPGMRESSetRestart", gmres->max_k, &restart, &flg));
542: if (flg) PetscCall(KSPGMRESSetRestart(ksp, restart));
543: PetscCall(PetscOptionsReal("-ksp_gmres_haptol", "Tolerance for exact convergence (happy ending)", "KSPGMRESSetHapTol", gmres->haptol, &haptol, &flg));
544: if (flg) PetscCall(KSPGMRESSetHapTol(ksp, haptol));
545: PetscCall(PetscOptionsReal("-ksp_gmres_breakdown_tolerance", "Divergence breakdown tolerance during GMRES restart", "KSPGMRESSetBreakdownTolerance", gmres->breakdowntol, &breakdowntol, &flg));
546: if (flg) PetscCall(KSPGMRESSetBreakdownTolerance(ksp, breakdowntol));
547: flg = PETSC_FALSE;
548: PetscCall(PetscOptionsBool("-ksp_gmres_preallocate", "Preallocate Krylov vectors", "KSPGMRESSetPreAllocateVectors", flg, &flg, NULL));
549: if (flg) PetscCall(KSPGMRESSetPreAllocateVectors(ksp));
550: PetscCall(PetscOptionsBoolGroupBegin("-ksp_gmres_classicalgramschmidt", "Classical (unmodified) Gram-Schmidt (fast)", "KSPGMRESSetOrthogonalization", &flg));
551: if (flg) PetscCall(KSPGMRESSetOrthogonalization(ksp, KSPGMRESClassicalGramSchmidtOrthogonalization));
552: PetscCall(PetscOptionsBoolGroupEnd("-ksp_gmres_modifiedgramschmidt", "Modified Gram-Schmidt (slow,more stable)", "KSPGMRESSetOrthogonalization", &flg));
553: if (flg) PetscCall(KSPGMRESSetOrthogonalization(ksp, KSPGMRESModifiedGramSchmidtOrthogonalization));
554: PetscCall(PetscOptionsEnum("-ksp_gmres_cgs_refinement_type", "Type of iterative refinement for classical (unmodified) Gram-Schmidt", "KSPGMRESSetCGSRefinementType", KSPGMRESCGSRefinementTypes, (PetscEnum)gmres->cgstype, (PetscEnum *)&gmres->cgstype, &flg));
555: flg = PETSC_FALSE;
556: PetscCall(PetscOptionsBool("-ksp_gmres_krylov_monitor", "Plot the Krylov directions", "KSPMonitorSet", flg, &flg, NULL));
557: if (flg) {
558: PetscViewers viewers;
559: PetscCall(PetscViewersCreate(PetscObjectComm((PetscObject)ksp), &viewers));
560: PetscCall(KSPMonitorSet(ksp, KSPGMRESMonitorKrylov, viewers, (PetscErrorCode(*)(void **))PetscViewersDestroy));
561: }
562: PetscOptionsHeadEnd();
563: PetscFunctionReturn(PETSC_SUCCESS);
564: }
566: PetscErrorCode KSPGMRESSetHapTol_GMRES(KSP ksp, PetscReal tol)
567: {
568: KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
570: PetscFunctionBegin;
571: PetscCheck(tol >= 0.0, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "Tolerance must be non-negative");
572: gmres->haptol = tol;
573: PetscFunctionReturn(PETSC_SUCCESS);
574: }
576: static PetscErrorCode KSPGMRESSetBreakdownTolerance_GMRES(KSP ksp, PetscReal tol)
577: {
578: KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
580: PetscFunctionBegin;
581: if (tol == (PetscReal)PETSC_DEFAULT) {
582: gmres->breakdowntol = 0.1;
583: PetscFunctionReturn(PETSC_SUCCESS);
584: }
585: PetscCheck(tol >= 0.0, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "Breakdown tolerance must be non-negative");
586: gmres->breakdowntol = tol;
587: PetscFunctionReturn(PETSC_SUCCESS);
588: }
590: PetscErrorCode KSPGMRESGetRestart_GMRES(KSP ksp, PetscInt *max_k)
591: {
592: KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
594: PetscFunctionBegin;
595: *max_k = gmres->max_k;
596: PetscFunctionReturn(PETSC_SUCCESS);
597: }
599: PetscErrorCode KSPGMRESSetRestart_GMRES(KSP ksp, PetscInt max_k)
600: {
601: KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
603: PetscFunctionBegin;
604: PetscCheck(max_k >= 1, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "Restart must be positive");
605: if (!ksp->setupstage) {
606: gmres->max_k = max_k;
607: } else if (gmres->max_k != max_k) {
608: gmres->max_k = max_k;
609: ksp->setupstage = KSP_SETUP_NEW;
610: /* free the data structures, then create them again */
611: PetscCall(KSPReset_GMRES(ksp));
612: }
613: PetscFunctionReturn(PETSC_SUCCESS);
614: }
616: PetscErrorCode KSPGMRESSetOrthogonalization_GMRES(KSP ksp, FCN fcn)
617: {
618: PetscFunctionBegin;
619: ((KSP_GMRES *)ksp->data)->orthog = fcn;
620: PetscFunctionReturn(PETSC_SUCCESS);
621: }
623: PetscErrorCode KSPGMRESGetOrthogonalization_GMRES(KSP ksp, FCN *fcn)
624: {
625: PetscFunctionBegin;
626: *fcn = ((KSP_GMRES *)ksp->data)->orthog;
627: PetscFunctionReturn(PETSC_SUCCESS);
628: }
630: PetscErrorCode KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
631: {
632: KSP_GMRES *gmres;
634: PetscFunctionBegin;
635: gmres = (KSP_GMRES *)ksp->data;
636: gmres->q_preallocate = 1;
637: PetscFunctionReturn(PETSC_SUCCESS);
638: }
640: PetscErrorCode KSPGMRESSetCGSRefinementType_GMRES(KSP ksp, KSPGMRESCGSRefinementType type)
641: {
642: KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
644: PetscFunctionBegin;
645: gmres->cgstype = type;
646: PetscFunctionReturn(PETSC_SUCCESS);
647: }
649: PetscErrorCode KSPGMRESGetCGSRefinementType_GMRES(KSP ksp, KSPGMRESCGSRefinementType *type)
650: {
651: KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
653: PetscFunctionBegin;
654: *type = gmres->cgstype;
655: PetscFunctionReturn(PETSC_SUCCESS);
656: }
658: /*@
659: KSPGMRESSetCGSRefinementType - Sets the type of iterative refinement to use
660: in the classical Gram-Schmidt orthogonalization.
662: Logically Collective
664: Input Parameters:
665: + ksp - the Krylov space context
666: - type - the type of refinement
667: .vb
668: KSP_GMRES_CGS_REFINE_NEVER
669: KSP_GMRES_CGS_REFINE_IFNEEDED
670: KSP_GMRES_CGS_REFINE_ALWAYS
671: .ve
673: Options Database Key:
674: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - refinement type
676: Level: intermediate
678: .seealso: [](ch_ksp), `KSPGMRES`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESCGSRefinementType`, `KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESGetCGSRefinementType()`,
679: `KSPGMRESGetOrthogonalization()`
680: @*/
681: PetscErrorCode KSPGMRESSetCGSRefinementType(KSP ksp, KSPGMRESCGSRefinementType type)
682: {
683: PetscFunctionBegin;
686: PetscTryMethod(ksp, "KSPGMRESSetCGSRefinementType_C", (KSP, KSPGMRESCGSRefinementType), (ksp, type));
687: PetscFunctionReturn(PETSC_SUCCESS);
688: }
690: /*@
691: KSPGMRESGetCGSRefinementType - Gets the type of iterative refinement to use
692: in the classical Gram Schmidt orthogonalization.
694: Not Collective
696: Input Parameter:
697: . ksp - the Krylov space context
699: Output Parameter:
700: . type - the type of refinement
702: Level: intermediate
704: .seealso: [](ch_ksp), `KSPGMRES`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESCGSRefinementType`, `KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESSetCGSRefinementType()`,
705: `KSPGMRESGetOrthogonalization()`
706: @*/
707: PetscErrorCode KSPGMRESGetCGSRefinementType(KSP ksp, KSPGMRESCGSRefinementType *type)
708: {
709: PetscFunctionBegin;
711: PetscUseMethod(ksp, "KSPGMRESGetCGSRefinementType_C", (KSP, KSPGMRESCGSRefinementType *), (ksp, type));
712: PetscFunctionReturn(PETSC_SUCCESS);
713: }
715: /*@
716: KSPGMRESSetRestart - Sets number of iterations at which `KSPGMRES`, `KSPFGMRES` and `KSPLGMRES` restarts.
718: Logically Collective
720: Input Parameters:
721: + ksp - the Krylov space context
722: - restart - integer restart value
724: Options Database Key:
725: . -ksp_gmres_restart <positive integer> - integer restart value
727: Level: intermediate
729: Note:
730: The default value is 30.
732: .seealso: [](ch_ksp), `KSPGMRES`, `KSPSetTolerances()`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESGetRestart()`
733: @*/
734: PetscErrorCode KSPGMRESSetRestart(KSP ksp, PetscInt restart)
735: {
736: PetscFunctionBegin;
739: PetscTryMethod(ksp, "KSPGMRESSetRestart_C", (KSP, PetscInt), (ksp, restart));
740: PetscFunctionReturn(PETSC_SUCCESS);
741: }
743: /*@
744: KSPGMRESGetRestart - Gets number of iterations at which `KSPGMRES`, `KSPFGMRES` and `KSPLGMRES` restarts.
746: Not Collective
748: Input Parameter:
749: . ksp - the Krylov space context
751: Output Parameter:
752: . restart - integer restart value
754: Level: intermediate
756: .seealso: [](ch_ksp), `KSPGMRES`, `KSPSetTolerances()`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESSetRestart()`
757: @*/
758: PetscErrorCode KSPGMRESGetRestart(KSP ksp, PetscInt *restart)
759: {
760: PetscFunctionBegin;
761: PetscUseMethod(ksp, "KSPGMRESGetRestart_C", (KSP, PetscInt *), (ksp, restart));
762: PetscFunctionReturn(PETSC_SUCCESS);
763: }
765: /*@
766: KSPGMRESSetHapTol - Sets tolerance for determining happy breakdown in `KSPGMRES`, `KSPFGMRES` and `KSPLGMRES`
768: Logically Collective
770: Input Parameters:
771: + ksp - the Krylov space context
772: - tol - the tolerance
774: Options Database Key:
775: . -ksp_gmres_haptol <positive real value> - set tolerance for determining happy breakdown
777: Level: intermediate
779: Note:
780: Happy breakdown is the rare case in `KSPGMRES` where an 'exact' solution is obtained after
781: a certain number of iterations. If you attempt more iterations after this point unstable
782: things can happen hence very occasionally you may need to set this value to detect this condition
784: .seealso: [](ch_ksp), `KSPGMRES`, `KSPSetTolerances()`
785: @*/
786: PetscErrorCode KSPGMRESSetHapTol(KSP ksp, PetscReal tol)
787: {
788: PetscFunctionBegin;
790: PetscTryMethod((ksp), "KSPGMRESSetHapTol_C", (KSP, PetscReal), ((ksp), (tol)));
791: PetscFunctionReturn(PETSC_SUCCESS);
792: }
794: /*@
795: KSPGMRESSetBreakdownTolerance - Sets tolerance for determining divergence breakdown in `KSPGMRES`.
797: Logically Collective
799: Input Parameters:
800: + ksp - the Krylov space context
801: - tol - the tolerance
803: Options Database Key:
804: . -ksp_gmres_breakdown_tolerance <positive real value> - set tolerance for determining divergence breakdown
806: Level: intermediate
808: Note:
809: Divergence breakdown occurs when GMRES residual increases significantly during restart
811: .seealso: [](ch_ksp), `KSPGMRES`, `KSPSetTolerances()`, `KSPGMRESSetHapTol()`
812: @*/
813: PetscErrorCode KSPGMRESSetBreakdownTolerance(KSP ksp, PetscReal tol)
814: {
815: PetscFunctionBegin;
817: PetscTryMethod((ksp), "KSPGMRESSetBreakdownTolerance_C", (KSP, PetscReal), (ksp, tol));
818: PetscFunctionReturn(PETSC_SUCCESS);
819: }
821: /*MC
822: KSPGMRES - Implements the Generalized Minimal Residual method {cite}`saad.schultz:gmres` with restart
824: Options Database Keys:
825: + -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
826: . -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
827: . -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
828: vectors are allocated as needed)
829: . -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
830: . -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
831: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
832: stability of the classical Gram-Schmidt orthogonalization.
833: - -ksp_gmres_krylov_monitor - plot the Krylov space generated
835: Level: beginner
837: Note:
838: Left and right preconditioning are supported, but not symmetric preconditioning.
840: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPFGMRES`, `KSPLGMRES`,
841: `KSPGMRESSetRestart()`, `KSPGMRESSetHapTol()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESGetOrthogonalization()`,
842: `KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESModifiedGramSchmidtOrthogonalization()`,
843: `KSPGMRESCGSRefinementType`, `KSPGMRESSetCGSRefinementType()`, `KSPGMRESGetCGSRefinementType()`, `KSPGMRESMonitorKrylov()`, `KSPSetPCSide()`
844: M*/
846: PETSC_EXTERN PetscErrorCode KSPCreate_GMRES(KSP ksp)
847: {
848: KSP_GMRES *gmres;
850: PetscFunctionBegin;
851: PetscCall(PetscNew(&gmres));
852: ksp->data = (void *)gmres;
854: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 4));
855: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 3));
856: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_SYMMETRIC, 2));
857: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));
858: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 1));
860: ksp->ops->buildsolution = KSPBuildSolution_GMRES;
861: ksp->ops->setup = KSPSetUp_GMRES;
862: ksp->ops->solve = KSPSolve_GMRES;
863: ksp->ops->reset = KSPReset_GMRES;
864: ksp->ops->destroy = KSPDestroy_GMRES;
865: ksp->ops->view = KSPView_GMRES;
866: ksp->ops->setfromoptions = KSPSetFromOptions_GMRES;
867: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
868: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_GMRES;
869: ksp->ops->computeritz = KSPComputeRitz_GMRES;
870: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetPreAllocateVectors_C", KSPGMRESSetPreAllocateVectors_GMRES));
871: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetOrthogonalization_C", KSPGMRESSetOrthogonalization_GMRES));
872: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetOrthogonalization_C", KSPGMRESGetOrthogonalization_GMRES));
873: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetRestart_C", KSPGMRESSetRestart_GMRES));
874: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetRestart_C", KSPGMRESGetRestart_GMRES));
875: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetHapTol_C", KSPGMRESSetHapTol_GMRES));
876: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetBreakdownTolerance_C", KSPGMRESSetBreakdownTolerance_GMRES));
877: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetCGSRefinementType_C", KSPGMRESSetCGSRefinementType_GMRES));
878: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetCGSRefinementType_C", KSPGMRESGetCGSRefinementType_GMRES));
880: gmres->haptol = 1.0e-30;
881: gmres->breakdowntol = 0.1;
882: gmres->q_preallocate = 0;
883: gmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
884: gmres->orthog = KSPGMRESClassicalGramSchmidtOrthogonalization;
885: gmres->nrs = NULL;
886: gmres->sol_temp = NULL;
887: gmres->max_k = GMRES_DEFAULT_MAXK;
888: gmres->Rsvd = NULL;
889: gmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
890: gmres->orthogwork = NULL;
891: PetscFunctionReturn(PETSC_SUCCESS);
892: }