Actual source code: pipefgmres.c
1: #include <../src/ksp/ksp/impls/gmres/pipefgmres/pipefgmresimpl.h>
3: static PetscBool cited = PETSC_FALSE;
4: static const char citation[] = "@article{SSM2016,\n"
5: " author = {P. Sanan and S.M. Schnepp and D.A. May},\n"
6: " title = {Pipelined, Flexible Krylov Subspace Methods},\n"
7: " journal = {SIAM Journal on Scientific Computing},\n"
8: " volume = {38},\n"
9: " number = {5},\n"
10: " pages = {C441-C470},\n"
11: " year = {2016},\n"
12: " doi = {10.1137/15M1049130},\n"
13: " URL = {http://dx.doi.org/10.1137/15M1049130},\n"
14: " eprint = {http://dx.doi.org/10.1137/15M1049130}\n"
15: "}\n";
17: static PetscErrorCode KSPPIPEFGMRESGetNewVectors(KSP, PetscInt);
18: static PetscErrorCode KSPPIPEFGMRESUpdateHessenberg(KSP, PetscInt, PetscBool *, PetscReal *);
19: static PetscErrorCode KSPPIPEFGMRESBuildSoln(PetscScalar *, Vec, Vec, KSP, PetscInt);
20: extern PetscErrorCode KSPReset_PIPEFGMRES(KSP);
22: static PetscErrorCode KSPSetUp_PIPEFGMRES(KSP ksp)
23: {
24: PetscInt k;
25: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;
26: const PetscInt max_k = pipefgmres->max_k;
28: PetscFunctionBegin;
29: PetscCall(KSPSetUp_GMRES(ksp));
31: PetscCall(PetscMalloc1((VEC_OFFSET + max_k), &pipefgmres->prevecs));
32: PetscCall(PetscMalloc1((VEC_OFFSET + max_k), &pipefgmres->prevecs_user_work));
34: PetscCall(KSPCreateVecs(ksp, pipefgmres->vv_allocated, &pipefgmres->prevecs_user_work[0], 0, NULL));
35: for (k = 0; k < pipefgmres->vv_allocated; k++) pipefgmres->prevecs[k] = pipefgmres->prevecs_user_work[0][k];
37: PetscCall(PetscMalloc1((VEC_OFFSET + max_k), &pipefgmres->zvecs));
38: PetscCall(PetscMalloc1((VEC_OFFSET + max_k), &pipefgmres->zvecs_user_work));
40: PetscCall(PetscMalloc1((VEC_OFFSET + max_k), &pipefgmres->redux));
42: PetscCall(KSPCreateVecs(ksp, pipefgmres->vv_allocated, &pipefgmres->zvecs_user_work[0], 0, NULL));
43: for (k = 0; k < pipefgmres->vv_allocated; k++) pipefgmres->zvecs[k] = pipefgmres->zvecs_user_work[0][k];
45: PetscFunctionReturn(PETSC_SUCCESS);
46: }
48: static PetscErrorCode KSPPIPEFGMRESCycle(PetscInt *itcount, KSP ksp)
49: {
50: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)(ksp->data);
51: PetscReal res_norm;
52: PetscReal hapbnd, tt;
53: PetscScalar *hh, *hes, *lhh, shift = pipefgmres->shift;
54: PetscBool hapend = PETSC_FALSE; /* indicates happy breakdown ending */
55: PetscInt loc_it; /* local count of # of dir. in Krylov space */
56: PetscInt max_k = pipefgmres->max_k; /* max # of directions Krylov space */
57: PetscInt i, j, k;
58: Mat Amat, Pmat;
59: Vec Q, W; /* Pipelining vectors */
60: Vec *redux = pipefgmres->redux; /* workspace for single reduction */
62: PetscFunctionBegin;
63: if (itcount) *itcount = 0;
65: /* Assign simpler names to these vectors, allocated as pipelining workspace */
66: Q = VEC_Q;
67: W = VEC_W;
69: /* Allocate memory for orthogonalization work (freed in the GMRES Destroy routine)*/
70: /* Note that we add an extra value here to allow for a single reduction */
71: if (!pipefgmres->orthogwork) PetscCall(PetscMalloc1(pipefgmres->max_k + 2, &pipefgmres->orthogwork));
72: lhh = pipefgmres->orthogwork;
74: /* Number of pseudo iterations since last restart is the number
75: of prestart directions */
76: loc_it = 0;
78: /* note: (pipefgmres->it) is always set one less than (loc_it) It is used in
79: KSPBUILDSolution_PIPEFGMRES, where it is passed to KSPPIPEFGMRESBuildSoln.
80: Note that when KSPPIPEFGMRESBuildSoln is called from this function,
81: (loc_it -1) is passed, so the two are equivalent */
82: pipefgmres->it = (loc_it - 1);
84: /* initial residual is in VEC_VV(0) - compute its norm*/
85: PetscCall(VecNorm(VEC_VV(0), NORM_2, &res_norm));
87: /* first entry in right-hand-side of hessenberg system is just
88: the initial residual norm */
89: *RS(0) = res_norm;
91: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
92: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res_norm;
93: else ksp->rnorm = 0;
94: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
95: PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
96: PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm));
98: /* check for the convergence - maybe the current guess is good enough */
99: PetscCall((*ksp->converged)(ksp, ksp->its, ksp->rnorm, &ksp->reason, ksp->cnvP));
100: if (ksp->reason) {
101: if (itcount) *itcount = 0;
102: PetscFunctionReturn(PETSC_SUCCESS);
103: }
105: /* scale VEC_VV (the initial residual) */
106: PetscCall(VecScale(VEC_VV(0), 1.0 / res_norm));
108: /* Fill the pipeline */
109: PetscCall(KSP_PCApply(ksp, VEC_VV(loc_it), PREVEC(loc_it)));
110: PetscCall(PCGetOperators(ksp->pc, &Amat, &Pmat));
111: PetscCall(KSP_MatMult(ksp, Amat, PREVEC(loc_it), ZVEC(loc_it)));
112: PetscCall(VecAXPY(ZVEC(loc_it), -shift, VEC_VV(loc_it))); /* Note shift */
114: /* MAIN ITERATION LOOP BEGINNING*/
115: /* keep iterating until we have converged OR generated the max number
116: of directions OR reached the max number of iterations for the method */
117: while (!ksp->reason && loc_it < max_k && ksp->its < ksp->max_it) {
118: if (loc_it) {
119: PetscCall(KSPLogResidualHistory(ksp, res_norm));
120: PetscCall(KSPMonitor(ksp, ksp->its, res_norm));
121: }
122: pipefgmres->it = (loc_it - 1);
124: /* see if more space is needed for work vectors */
125: if (pipefgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
126: PetscCall(KSPPIPEFGMRESGetNewVectors(ksp, loc_it + 1));
127: /* (loc_it+1) is passed in as number of the first vector that should be allocated */
128: }
130: /* Note that these inner products are with "Z" now, so
131: in particular, lhh[loc_it] is the 'barred' or 'shifted' value,
132: not the value from the equivalent FGMRES run (even in exact arithmetic)
133: That is, the H we need for the Arnoldi relation is different from the
134: coefficients we use in the orthogonalization process,because of the shift */
136: /* Do some local twiddling to allow for a single reduction */
137: for (i = 0; i < loc_it + 1; i++) redux[i] = VEC_VV(i);
138: redux[loc_it + 1] = ZVEC(loc_it);
140: /* note the extra dot product which ends up in lh[loc_it+1], which computes ||z||^2 */
141: PetscCall(VecMDotBegin(ZVEC(loc_it), loc_it + 2, redux, lhh));
143: /* Start the split reduction (This actually calls the MPI_Iallreduce, otherwise, the reduction is simply delayed until the "end" call)*/
144: PetscCall(PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)ZVEC(loc_it))));
146: /* The work to be overlapped with the inner products follows.
147: This is application of the preconditioner and the operator
148: to compute intermediate quantities which will be combined (locally)
149: with the results of the inner products.
150: */
151: PetscCall(KSP_PCApply(ksp, ZVEC(loc_it), Q));
152: PetscCall(PCGetOperators(ksp->pc, &Amat, &Pmat));
153: PetscCall(KSP_MatMult(ksp, Amat, Q, W));
155: /* Compute inner products of the new direction with previous directions,
156: and the norm of the to-be-orthogonalized direction "Z".
157: This information is enough to build the required entries
158: of H. The inner product with VEC_VV(it_loc) is
159: *different* than in the standard FGMRES and need to be dealt with specially.
160: That is, for standard FGMRES the orthogonalization coefficients are the same
161: as the coefficients used in the Arnoldi relation to reconstruct, but here this
162: is not true (albeit only for the one entry of H which we "unshift" below. */
164: /* Finish the dot product, retrieving the extra entry */
165: PetscCall(VecMDotEnd(ZVEC(loc_it), loc_it + 2, redux, lhh));
166: tt = PetscRealPart(lhh[loc_it + 1]);
168: /* Hessenberg entries, and entries for (naive) classical Gram-Schmidt
169: Note that the Hessenberg entries require a shift, as these are for the
170: relation AU = VH, which is wrt unshifted basis vectors */
171: hh = HH(0, loc_it);
172: hes = HES(0, loc_it);
173: for (j = 0; j < loc_it; j++) {
174: hh[j] = lhh[j];
175: hes[j] = lhh[j];
176: }
177: hh[loc_it] = lhh[loc_it] + shift;
178: hes[loc_it] = lhh[loc_it] + shift;
180: /* we delay applying the shift here */
181: for (j = 0; j <= loc_it; j++) { lhh[j] = -lhh[j]; /* flip sign */ }
183: /* Compute the norm of the un-normalized new direction using the rearranged formula
184: Note that these are shifted ("barred") quantities */
185: for (k = 0; k <= loc_it; k++) tt -= ((PetscReal)(PetscAbsScalar(lhh[k]) * PetscAbsScalar(lhh[k])));
186: /* On AVX512 this is accumulating roundoff errors for eg: tt=-2.22045e-16 */
187: if ((tt < 0.0) && tt > -PETSC_SMALL) tt = 0.0;
188: if (tt < 0.0) {
189: /* If we detect square root breakdown in the norm, we must restart the algorithm.
190: Here this means we simply break the current loop and reconstruct the solution
191: using the basis we have computed thus far. Note that by breaking immediately,
192: we do not update the iteration count, so computation done in this iteration
193: should be disregarded.
194: */
195: PetscCall(PetscInfo(ksp, "Restart due to square root breakdown at it = %" PetscInt_FMT ", tt=%g\n", ksp->its, (double)tt));
196: break;
197: } else {
198: tt = PetscSqrtReal(tt);
199: }
201: /* new entry in hessenburg is the 2-norm of our new direction */
202: hh[loc_it + 1] = tt;
203: hes[loc_it + 1] = tt;
205: /* The recurred computation for the new direction
206: The division by tt is delayed to the happy breakdown check later
207: Note placement BEFORE the unshift
208: */
209: PetscCall(VecCopy(ZVEC(loc_it), VEC_VV(loc_it + 1)));
210: PetscCall(VecMAXPY(VEC_VV(loc_it + 1), loc_it + 1, lhh, &VEC_VV(0)));
211: /* (VEC_VV(loc_it+1) is not normalized yet) */
213: /* The recurred computation for the preconditioned vector (u) */
214: PetscCall(VecCopy(Q, PREVEC(loc_it + 1)));
215: PetscCall(VecMAXPY(PREVEC(loc_it + 1), loc_it + 1, lhh, &PREVEC(0)));
216: if (tt) PetscCall(VecScale(PREVEC(loc_it + 1), 1.0 / tt));
218: /* Unshift an entry in the GS coefficients ("removing the bar") */
219: lhh[loc_it] -= shift;
221: /* The recurred computation for z (Au)
222: Note placement AFTER the "unshift" */
223: PetscCall(VecCopy(W, ZVEC(loc_it + 1)));
224: PetscCall(VecMAXPY(ZVEC(loc_it + 1), loc_it + 1, lhh, &ZVEC(0)));
225: if (tt) PetscCall(VecScale(ZVEC(loc_it + 1), 1.0 / tt));
227: /* Happy Breakdown Check */
228: hapbnd = PetscAbsScalar((tt) / *RS(loc_it));
229: /* RS(loc_it) contains the res_norm from the last iteration */
230: hapbnd = PetscMin(pipefgmres->haptol, hapbnd);
231: if (tt > hapbnd) {
232: /* scale new direction by its norm */
233: PetscCall(VecScale(VEC_VV(loc_it + 1), 1.0 / tt));
234: } else {
235: /* This happens when the solution is exactly reached. */
236: /* So there is no new direction... */
237: PetscCall(VecSet(VEC_TEMP, 0.0)); /* set VEC_TEMP to 0 */
238: hapend = PETSC_TRUE;
239: }
240: /* note that for pipefgmres we could get HES(loc_it+1, loc_it) = 0 and the
241: current solution would not be exact if HES was singular. Note that
242: HH non-singular implies that HES is not singular, and HES is guaranteed
243: to be nonsingular when PREVECS are linearly independent and A is
244: nonsingular (in GMRES, the nonsingularity of A implies the nonsingularity
245: of HES). So we should really add a check to verify that HES is nonsingular.*/
247: /* Note that to be thorough, in debug mode, one could call a LAPACK routine
248: here to check that the hessenberg matrix is indeed non-singular (since
249: FGMRES does not guarantee this) */
251: /* Now apply rotations to new col of Hessenberg (and right side of system),
252: calculate new rotation, and get new residual norm at the same time*/
253: PetscCall(KSPPIPEFGMRESUpdateHessenberg(ksp, loc_it, &hapend, &res_norm));
254: if (ksp->reason) break;
256: loc_it++;
257: pipefgmres->it = (loc_it - 1); /* Add this here in case it has converged */
259: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
260: ksp->its++;
261: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res_norm;
262: else ksp->rnorm = 0;
263: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
265: PetscCall((*ksp->converged)(ksp, ksp->its, ksp->rnorm, &ksp->reason, ksp->cnvP));
267: /* Catch error in happy breakdown and signal convergence and break from loop */
268: if (hapend) {
269: if (!ksp->reason) {
270: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "Reached happy break down, but convergence was not indicated. Residual norm = %g", (double)res_norm);
271: ksp->reason = KSP_DIVERGED_BREAKDOWN;
272: break;
273: }
274: }
275: }
276: /* END OF ITERATION LOOP */
278: /*
279: Monitor if we know that we will not return for a restart */
280: if (loc_it && (ksp->reason || ksp->its >= ksp->max_it)) {
281: PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm));
282: PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
283: }
285: if (itcount) *itcount = loc_it;
287: /*
288: Solve for the "best" coefficients of the Krylov
289: columns, add the solution values together, and possibly unwind the
290: preconditioning from the solution
291: */
293: /* Form the solution (or the solution so far) */
294: /* Note: must pass in (loc_it-1) for iteration count so that KSPPIPEGMRESIIBuildSoln properly navigates */
296: PetscCall(KSPPIPEFGMRESBuildSoln(RS(0), ksp->vec_sol, ksp->vec_sol, ksp, loc_it - 1));
297: PetscFunctionReturn(PETSC_SUCCESS);
298: }
300: static PetscErrorCode KSPSolve_PIPEFGMRES(KSP ksp)
301: {
302: PetscInt its, itcount;
303: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;
304: PetscBool guess_zero = ksp->guess_zero;
306: PetscFunctionBegin;
307: /* We have not checked these routines for use with complex numbers. The inner products are likely not defined correctly for that case */
308: PetscCheck(!PetscDefined(USE_COMPLEX) || PetscDefined(SKIP_COMPLEX), PETSC_COMM_WORLD, PETSC_ERR_SUP, "PIPEFGMRES has not been implemented for use with complex scalars");
310: PetscCall(PetscCitationsRegister(citation, &cited));
312: PetscCheck(!ksp->calc_sings || pipefgmres->Rsvd, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ORDER, "Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
313: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
314: ksp->its = 0;
315: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
317: itcount = 0;
318: ksp->reason = KSP_CONVERGED_ITERATING;
319: while (!ksp->reason) {
320: PetscCall(KSPInitialResidual(ksp, ksp->vec_sol, VEC_TEMP, VEC_TEMP_MATOP, VEC_VV(0), ksp->vec_rhs));
321: PetscCall(KSPPIPEFGMRESCycle(&its, ksp));
322: itcount += its;
323: if (itcount >= ksp->max_it) {
324: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
325: break;
326: }
327: ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
328: }
329: ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
330: PetscFunctionReturn(PETSC_SUCCESS);
331: }
333: static PetscErrorCode KSPDestroy_PIPEFGMRES(KSP ksp)
334: {
335: PetscFunctionBegin;
336: PetscCall(KSPReset_PIPEFGMRES(ksp));
337: PetscCall(KSPDestroy_GMRES(ksp));
338: PetscFunctionReturn(PETSC_SUCCESS);
339: }
341: static PetscErrorCode KSPPIPEFGMRESBuildSoln(PetscScalar *nrs, Vec vguess, Vec vdest, KSP ksp, PetscInt it)
342: {
343: PetscScalar tt;
344: PetscInt k, j;
345: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)(ksp->data);
347: PetscFunctionBegin;
348: if (it < 0) { /* no pipefgmres steps have been performed */
349: PetscCall(VecCopy(vguess, vdest)); /* VecCopy() is smart, exits immediately if vguess == vdest */
350: PetscFunctionReturn(PETSC_SUCCESS);
351: }
353: /* Solve for solution vector that minimizes the residual */
354: /* solve the upper triangular system - RS is the right side and HH is
355: the upper triangular matrix - put soln in nrs */
356: if (*HH(it, it) != 0.0) nrs[it] = *RS(it) / *HH(it, it);
357: else nrs[it] = 0.0;
359: for (k = it - 1; k >= 0; k--) {
360: tt = *RS(k);
361: for (j = k + 1; j <= it; j++) tt -= *HH(k, j) * nrs[j];
362: nrs[k] = tt / *HH(k, k);
363: }
365: /* Accumulate the correction to the solution of the preconditioned problem in VEC_TEMP */
366: PetscCall(VecMAXPBY(VEC_TEMP, it + 1, nrs, 0, &PREVEC(0)));
368: /* add solution to previous solution */
369: if (vdest == vguess) {
370: PetscCall(VecAXPY(vdest, 1.0, VEC_TEMP));
371: } else {
372: PetscCall(VecWAXPY(vdest, 1.0, VEC_TEMP, vguess));
373: }
374: PetscFunctionReturn(PETSC_SUCCESS);
375: }
377: static PetscErrorCode KSPPIPEFGMRESUpdateHessenberg(KSP ksp, PetscInt it, PetscBool *hapend, PetscReal *res)
378: {
379: PetscScalar *hh, *cc, *ss, *rs;
380: PetscInt j;
381: PetscReal hapbnd;
382: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)(ksp->data);
384: PetscFunctionBegin;
385: hh = HH(0, it); /* pointer to beginning of column to update */
386: cc = CC(0); /* beginning of cosine rotations */
387: ss = SS(0); /* beginning of sine rotations */
388: rs = RS(0); /* right hand side of least squares system */
390: /* The Hessenberg matrix is now correct through column it, save that form for possible spectral analysis */
391: for (j = 0; j <= it + 1; j++) *HES(j, it) = hh[j];
393: /* check for the happy breakdown */
394: hapbnd = PetscMin(PetscAbsScalar(hh[it + 1] / rs[it]), pipefgmres->haptol);
395: if (PetscAbsScalar(hh[it + 1]) < hapbnd) {
396: 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))));
397: *hapend = PETSC_TRUE;
398: }
400: /* Apply all the previously computed plane rotations to the new column of the Hessenberg matrix */
401: /* Note: this uses the rotation [conj(c) s ; -s c], c= cos(theta), s= sin(theta),
402: and some refs have [c s ; -conj(s) c] (don't be confused!) */
404: for (j = 0; j < it; j++) {
405: PetscScalar hhj = hh[j];
406: hh[j] = PetscConj(cc[j]) * hhj + ss[j] * hh[j + 1];
407: hh[j + 1] = -ss[j] * hhj + cc[j] * hh[j + 1];
408: }
410: /*
411: compute the new plane rotation, and apply it to:
412: 1) the right-hand-side of the Hessenberg system (RS)
413: note: it affects RS(it) and RS(it+1)
414: 2) the new column of the Hessenberg matrix
415: note: it affects HH(it,it) which is currently pointed to
416: by hh and HH(it+1, it) (*(hh+1))
417: thus obtaining the updated value of the residual...
418: */
420: /* compute new plane rotation */
422: if (!*hapend) {
423: PetscReal delta = PetscSqrtReal(PetscSqr(PetscAbsScalar(hh[it])) + PetscSqr(PetscAbsScalar(hh[it + 1])));
424: if (delta == 0.0) {
425: ksp->reason = KSP_DIVERGED_NULL;
426: PetscFunctionReturn(PETSC_SUCCESS);
427: }
429: cc[it] = hh[it] / delta; /* new cosine value */
430: ss[it] = hh[it + 1] / delta; /* new sine value */
432: hh[it] = PetscConj(cc[it]) * hh[it] + ss[it] * hh[it + 1];
433: rs[it + 1] = -ss[it] * rs[it];
434: rs[it] = PetscConj(cc[it]) * rs[it];
435: *res = PetscAbsScalar(rs[it + 1]);
436: } else { /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
437: another rotation matrix (so RH doesn't change). The new residual is
438: always the new sine term times the residual from last time (RS(it)),
439: but now the new sine rotation would be zero...so the residual should
440: be zero...so we will multiply "zero" by the last residual. This might
441: not be exactly what we want to do here -could just return "zero". */
442: *res = 0.0;
443: }
444: PetscFunctionReturn(PETSC_SUCCESS);
445: }
447: static PetscErrorCode KSPBuildSolution_PIPEFGMRES(KSP ksp, Vec ptr, Vec *result)
448: {
449: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;
451: PetscFunctionBegin;
452: if (!ptr) {
453: if (!pipefgmres->sol_temp) PetscCall(VecDuplicate(ksp->vec_sol, &pipefgmres->sol_temp));
454: ptr = pipefgmres->sol_temp;
455: }
456: if (!pipefgmres->nrs) {
457: /* allocate the work area */
458: PetscCall(PetscMalloc1(pipefgmres->max_k, &pipefgmres->nrs));
459: }
461: PetscCall(KSPPIPEFGMRESBuildSoln(pipefgmres->nrs, ksp->vec_sol, ptr, ksp, pipefgmres->it));
462: if (result) *result = ptr;
463: PetscFunctionReturn(PETSC_SUCCESS);
464: }
466: static PetscErrorCode KSPSetFromOptions_PIPEFGMRES(KSP ksp, PetscOptionItems *PetscOptionsObject)
467: {
468: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;
469: PetscBool flg;
470: PetscScalar shift;
472: PetscFunctionBegin;
473: PetscCall(KSPSetFromOptions_GMRES(ksp, PetscOptionsObject));
474: PetscOptionsHeadBegin(PetscOptionsObject, "KSP pipelined FGMRES Options");
475: PetscCall(PetscOptionsScalar("-ksp_pipefgmres_shift", "shift parameter", "KSPPIPEFGMRESSetShift", pipefgmres->shift, &shift, &flg));
476: if (flg) PetscCall(KSPPIPEFGMRESSetShift(ksp, shift));
477: PetscOptionsHeadEnd();
478: PetscFunctionReturn(PETSC_SUCCESS);
479: }
481: static PetscErrorCode KSPView_PIPEFGMRES(KSP ksp, PetscViewer viewer)
482: {
483: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;
484: PetscBool iascii, isstring;
486: PetscFunctionBegin;
487: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
488: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSTRING, &isstring));
490: if (iascii) {
491: PetscCall(PetscViewerASCIIPrintf(viewer, " restart=%" PetscInt_FMT "\n", pipefgmres->max_k));
492: PetscCall(PetscViewerASCIIPrintf(viewer, " happy breakdown tolerance %g\n", (double)pipefgmres->haptol));
493: #if defined(PETSC_USE_COMPLEX)
494: PetscCall(PetscViewerASCIIPrintf(viewer, " shift=%g+%gi\n", (double)PetscRealPart(pipefgmres->shift), (double)PetscImaginaryPart(pipefgmres->shift)));
495: #else
496: PetscCall(PetscViewerASCIIPrintf(viewer, " shift=%g\n", (double)pipefgmres->shift));
497: #endif
498: } else if (isstring) {
499: PetscCall(PetscViewerStringSPrintf(viewer, "restart %" PetscInt_FMT, pipefgmres->max_k));
500: #if defined(PETSC_USE_COMPLEX)
501: PetscCall(PetscViewerStringSPrintf(viewer, " shift=%g+%gi\n", (double)PetscRealPart(pipefgmres->shift), (double)PetscImaginaryPart(pipefgmres->shift)));
502: #else
503: PetscCall(PetscViewerStringSPrintf(viewer, " shift=%g\n", (double)pipefgmres->shift));
504: #endif
505: }
506: PetscFunctionReturn(PETSC_SUCCESS);
507: }
509: PetscErrorCode KSPReset_PIPEFGMRES(KSP ksp)
510: {
511: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;
512: PetscInt i;
514: PetscFunctionBegin;
515: PetscCall(PetscFree(pipefgmres->prevecs));
516: PetscCall(PetscFree(pipefgmres->zvecs));
517: for (i = 0; i < pipefgmres->nwork_alloc; i++) {
518: PetscCall(VecDestroyVecs(pipefgmres->mwork_alloc[i], &pipefgmres->prevecs_user_work[i]));
519: PetscCall(VecDestroyVecs(pipefgmres->mwork_alloc[i], &pipefgmres->zvecs_user_work[i]));
520: }
521: PetscCall(PetscFree(pipefgmres->prevecs_user_work));
522: PetscCall(PetscFree(pipefgmres->zvecs_user_work));
523: PetscCall(PetscFree(pipefgmres->redux));
524: PetscCall(KSPReset_GMRES(ksp));
525: PetscFunctionReturn(PETSC_SUCCESS);
526: }
528: /*MC
529: KSPPIPEFGMRES - Implements the Pipelined (1-stage) Flexible Generalized Minimal Residual method {cite}`sananschneppmay2016`. [](sec_pipelineksp). [](sec_flexibleksp)
531: Options Database Keys:
532: + -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
533: . -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
534: . -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of vectors are allocated as needed)
535: . -ksp_pipefgmres_shift - the shift to use (defaults to 1. See `KSPPIPEFGMRESSetShift()`
536: - -ksp_gmres_krylov_monitor - plot the Krylov space generated
538: Level: intermediate
540: Notes:
541: Compare to `KSPPGMRES` and `KSPFGMRES`
543: This variant is not "explicitly normalized" like `KSPPGMRES`, and requires a shift parameter.
545: A heuristic for choosing the shift parameter is the largest eigenvalue of the preconditioned operator.
547: Only right preconditioning is supported (but this preconditioner may be nonlinear/variable/inexact, as with `KSPFGMRES`).
549: MPI configuration may be necessary for reductions to make asynchronous progress, which is important for performance of pipelined methods.
550: See [](doc_faq_pipelined)
552: Developer Note:
553: This class is subclassed off of `KSPGMRES`, see the source code in src/ksp/ksp/impls/gmres for comments on the structure of the code
555: Contributed by:
556: P. Sanan and S.M. Schnepp
558: .seealso: [](ch_ksp), [](doc_faq_pipelined), [](sec_pipelineksp), [](sec_flexibleksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPLGMRES`, `KSPPIPECG`, `KSPPIPECR`, `KSPPGMRES`, `KSPFGMRES`
559: `KSPGMRESSetRestart()`, `KSPGMRESSetHapTol()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESMonitorKrylov()`, `KSPPIPEFGMRESSetShift()`
560: M*/
562: PETSC_EXTERN PetscErrorCode KSPCreate_PIPEFGMRES(KSP ksp)
563: {
564: KSP_PIPEFGMRES *pipefgmres;
566: PetscFunctionBegin;
567: PetscCall(PetscNew(&pipefgmres));
569: ksp->data = (void *)pipefgmres;
570: ksp->ops->buildsolution = KSPBuildSolution_PIPEFGMRES;
571: ksp->ops->setup = KSPSetUp_PIPEFGMRES;
572: ksp->ops->solve = KSPSolve_PIPEFGMRES;
573: ksp->ops->reset = KSPReset_PIPEFGMRES;
574: ksp->ops->destroy = KSPDestroy_PIPEFGMRES;
575: ksp->ops->view = KSPView_PIPEFGMRES;
576: ksp->ops->setfromoptions = KSPSetFromOptions_PIPEFGMRES;
577: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
578: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_GMRES;
580: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 3));
581: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));
583: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetPreAllocateVectors_C", KSPGMRESSetPreAllocateVectors_GMRES));
584: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetRestart_C", KSPGMRESSetRestart_GMRES));
585: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetRestart_C", KSPGMRESGetRestart_GMRES));
587: pipefgmres->nextra_vecs = 1;
588: pipefgmres->haptol = 1.0e-30;
589: pipefgmres->q_preallocate = 0;
590: pipefgmres->delta_allocate = PIPEFGMRES_DELTA_DIRECTIONS;
591: pipefgmres->orthog = NULL;
592: pipefgmres->nrs = NULL;
593: pipefgmres->sol_temp = NULL;
594: pipefgmres->max_k = PIPEFGMRES_DEFAULT_MAXK;
595: pipefgmres->Rsvd = NULL;
596: pipefgmres->orthogwork = NULL;
597: pipefgmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
598: pipefgmres->shift = 1.0;
599: PetscFunctionReturn(PETSC_SUCCESS);
600: }
602: static PetscErrorCode KSPPIPEFGMRESGetNewVectors(KSP ksp, PetscInt it)
603: {
604: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;
605: PetscInt nwork = pipefgmres->nwork_alloc; /* number of work vector chunks allocated */
606: PetscInt nalloc; /* number to allocate */
607: PetscInt k;
609: PetscFunctionBegin;
610: nalloc = pipefgmres->delta_allocate; /* number of vectors to allocate
611: in a single chunk */
613: /* Adjust the number to allocate to make sure that we don't exceed the
614: number of available slots (pipefgmres->vecs_allocated)*/
615: if (it + VEC_OFFSET + nalloc >= pipefgmres->vecs_allocated) nalloc = pipefgmres->vecs_allocated - it - VEC_OFFSET;
616: if (!nalloc) PetscFunctionReturn(PETSC_SUCCESS);
618: pipefgmres->vv_allocated += nalloc; /* vv_allocated is the number of vectors allocated */
620: /* work vectors */
621: PetscCall(KSPCreateVecs(ksp, nalloc, &pipefgmres->user_work[nwork], 0, NULL));
622: for (k = 0; k < nalloc; k++) pipefgmres->vecs[it + VEC_OFFSET + k] = pipefgmres->user_work[nwork][k];
623: /* specify size of chunk allocated */
624: pipefgmres->mwork_alloc[nwork] = nalloc;
626: /* preconditioned vectors (note we don't use VEC_OFFSET) */
627: PetscCall(KSPCreateVecs(ksp, nalloc, &pipefgmres->prevecs_user_work[nwork], 0, NULL));
628: for (k = 0; k < nalloc; k++) pipefgmres->prevecs[it + k] = pipefgmres->prevecs_user_work[nwork][k];
630: PetscCall(KSPCreateVecs(ksp, nalloc, &pipefgmres->zvecs_user_work[nwork], 0, NULL));
631: for (k = 0; k < nalloc; k++) pipefgmres->zvecs[it + k] = pipefgmres->zvecs_user_work[nwork][k];
633: /* increment the number of work vector chunks */
634: pipefgmres->nwork_alloc++;
635: PetscFunctionReturn(PETSC_SUCCESS);
636: }
638: /*@
639: KSPPIPEFGMRESSetShift - Set the shift parameter for the flexible, pipelined `KSPPIPEFGMRES` solver.
641: Logically Collective
643: Input Parameters:
644: + ksp - the Krylov space context
645: - shift - the shift
647: Options Database Key:
648: . -ksp_pipefgmres_shift <shift> - set the shift parameter
650: Level: intermediate
652: Note:
653: A heuristic is to set this to be comparable to the largest eigenvalue of the preconditioned operator.
654: This can be achieved with PETSc itself by using a few iterations of a Krylov method.
655: See `KSPComputeEigenvalues()` (and note the caveats there).
657: .seealso: [](ch_ksp), `KSPPIPEFGMRES`, `KSPComputeEigenvalues()`
658: @*/
659: PetscErrorCode KSPPIPEFGMRESSetShift(KSP ksp, PetscScalar shift)
660: {
661: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;
663: PetscFunctionBegin;
666: pipefgmres->shift = shift;
667: PetscFunctionReturn(PETSC_SUCCESS);
668: }