Actual source code: pipelcg.c
1: #include <petsc/private/kspimpl.h>
2: #include <petsc/private/vecimpl.h>
4: #define offset(j) PetscMax(((j) - (2 * l)), 0)
5: #define shift(i, j) ((i)-offset((j)))
6: #define G(i, j) (plcg->G[((j) * (2 * l + 1)) + (shift((i), (j)))])
7: #define G_noshift(i, j) (plcg->G[((j) * (2 * l + 1)) + (i)])
8: #define alpha(i) (plcg->alpha[(i)])
9: #define gamma(i) (plcg->gamma[(i)])
10: #define delta(i) (plcg->delta[(i)])
11: #define sigma(i) (plcg->sigma[(i)])
12: #define req(i) (plcg->req[(i)])
14: typedef struct KSP_CG_PIPE_L_s KSP_CG_PIPE_L;
15: struct KSP_CG_PIPE_L_s {
16: PetscInt l; /* pipeline depth */
17: Vec *Z; /* Z vectors (shifted base) */
18: Vec *U; /* U vectors (unpreconditioned shifted base) */
19: Vec *V; /* V vectors (original base) */
20: Vec *Q; /* Q vectors (auxiliary bases) */
21: Vec p; /* work vector */
22: PetscScalar *G; /* such that Z = VG (band matrix)*/
23: PetscScalar *gamma, *delta, *alpha;
24: PetscReal lmin, lmax; /* min and max eigen values estimates to compute base shifts */
25: PetscReal *sigma; /* base shifts */
26: MPI_Request *req; /* request array for asynchronous global collective */
27: PetscBool show_rstrt; /* flag to show restart information in output (default: not shown) */
28: };
30: /*
31: KSPSetUp_PIPELCG - Sets up the workspace needed by the PIPELCG method.
33: This is called once, usually automatically by KSPSolve() or KSPSetUp()
34: but can be called directly by KSPSetUp()
35: */
36: static PetscErrorCode KSPSetUp_PIPELCG(KSP ksp)
37: {
38: KSP_CG_PIPE_L *plcg = (KSP_CG_PIPE_L *)ksp->data;
39: PetscInt l = plcg->l, max_it = ksp->max_it;
40: MPI_Comm comm;
42: comm = PetscObjectComm((PetscObject)ksp);
47: KSPSetWorkVecs(ksp, 1); /* get work vectors needed by PIPELCG */
48: plcg->p = ksp->work[0];
50: VecDuplicateVecs(plcg->p, PetscMax(3, l + 1), &plcg->Z);
51: VecDuplicateVecs(plcg->p, 3, &plcg->U);
52: VecDuplicateVecs(plcg->p, 3, &plcg->V);
53: VecDuplicateVecs(plcg->p, 3 * (l - 1) + 1, &plcg->Q);
54: PetscCalloc1(2, &plcg->alpha);
55: PetscCalloc1(l, &plcg->sigma);
57: return 0;
58: }
60: static PetscErrorCode KSPReset_PIPELCG(KSP ksp)
61: {
62: KSP_CG_PIPE_L *plcg = (KSP_CG_PIPE_L *)ksp->data;
63: PetscInt l = plcg->l;
65: PetscFree(plcg->sigma);
66: PetscFree(plcg->alpha);
67: VecDestroyVecs(PetscMax(3, l + 1), &plcg->Z);
68: VecDestroyVecs(3, &plcg->U);
69: VecDestroyVecs(3, &plcg->V);
70: VecDestroyVecs(3 * (l - 1) + 1, &plcg->Q);
71: return 0;
72: }
74: static PetscErrorCode KSPDestroy_PIPELCG(KSP ksp)
75: {
76: KSPReset_PIPELCG(ksp);
77: KSPDestroyDefault(ksp);
78: return 0;
79: }
81: static PetscErrorCode KSPSetFromOptions_PIPELCG(KSP ksp, PetscOptionItems *PetscOptionsObject)
82: {
83: KSP_CG_PIPE_L *plcg = (KSP_CG_PIPE_L *)ksp->data;
84: PetscBool flag = PETSC_FALSE;
86: PetscOptionsHeadBegin(PetscOptionsObject, "KSP PIPELCG options");
87: PetscOptionsInt("-ksp_pipelcg_pipel", "Pipeline length", "", plcg->l, &plcg->l, &flag);
88: if (!flag) plcg->l = 1;
89: PetscOptionsReal("-ksp_pipelcg_lmin", "Estimate for smallest eigenvalue", "", plcg->lmin, &plcg->lmin, &flag);
90: if (!flag) plcg->lmin = 0.0;
91: PetscOptionsReal("-ksp_pipelcg_lmax", "Estimate for largest eigenvalue", "", plcg->lmax, &plcg->lmax, &flag);
92: if (!flag) plcg->lmax = 0.0;
93: PetscOptionsBool("-ksp_pipelcg_monitor", "Output information on restarts when they occur? (default: 0)", "", plcg->show_rstrt, &plcg->show_rstrt, &flag);
94: if (!flag) plcg->show_rstrt = PETSC_FALSE;
95: PetscOptionsHeadEnd();
96: return 0;
97: }
99: static PetscErrorCode MPIPetsc_Iallreduce(void *sendbuf, void *recvbuf, PetscMPIInt count, MPI_Datatype datatype, MPI_Op op, MPI_Comm comm, MPI_Request *request)
100: {
101: #if defined(PETSC_HAVE_MPI_NONBLOCKING_COLLECTIVES)
102: MPI_Iallreduce(sendbuf, recvbuf, count, datatype, op, comm, request);
103: #else
104: MPIU_Allreduce(sendbuf, recvbuf, count, datatype, op, comm);
105: *request = MPI_REQUEST_NULL;
106: #endif
107: return 0;
108: }
110: static PetscErrorCode KSPView_PIPELCG(KSP ksp, PetscViewer viewer)
111: {
112: KSP_CG_PIPE_L *plcg = (KSP_CG_PIPE_L *)ksp->data;
113: PetscBool iascii = PETSC_FALSE, isstring = PETSC_FALSE;
115: PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii);
116: PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSTRING, &isstring);
117: if (iascii) {
118: PetscViewerASCIIPrintf(viewer, " Pipeline depth: %" PetscInt_FMT "\n", plcg->l);
119: PetscViewerASCIIPrintf(viewer, " Minimal eigenvalue estimate %g\n", (double)plcg->lmin);
120: PetscViewerASCIIPrintf(viewer, " Maximal eigenvalue estimate %g\n", (double)plcg->lmax);
121: } else if (isstring) {
122: PetscViewerStringSPrintf(viewer, " Pipeline depth: %" PetscInt_FMT "\n", plcg->l);
123: PetscViewerStringSPrintf(viewer, " Minimal eigenvalue estimate %g\n", (double)plcg->lmin);
124: PetscViewerStringSPrintf(viewer, " Maximal eigenvalue estimate %g\n", (double)plcg->lmax);
125: }
126: return 0;
127: }
129: static PetscErrorCode KSPSolve_InnerLoop_PIPELCG(KSP ksp)
130: {
131: KSP_CG_PIPE_L *plcg = (KSP_CG_PIPE_L *)ksp->data;
132: Mat A = NULL, Pmat = NULL;
133: PetscInt it = 0, max_it = ksp->max_it, l = plcg->l, i = 0, j = 0, k = 0;
134: PetscInt start = 0, middle = 0, end = 0;
135: Vec *Z = plcg->Z, *U = plcg->U, *V = plcg->V, *Q = plcg->Q;
136: Vec x = NULL, p = NULL, temp = NULL;
137: PetscScalar sum_dummy = 0.0, eta = 0.0, zeta = 0.0, lambda = 0.0;
138: PetscReal dp = 0.0, tmp = 0.0, beta = 0.0, invbeta2 = 0.0;
139: MPI_Comm comm;
141: x = ksp->vec_sol;
142: p = plcg->p;
144: comm = PetscObjectComm((PetscObject)ksp);
145: PCGetOperators(ksp->pc, &A, &Pmat);
147: for (it = 0; it < max_it + l; ++it) {
148: /* ----------------------------------- */
149: /* Multiplication z_{it+1} = Az_{it} */
150: /* ----------------------------------- */
151: /* Shift the U vector pointers */
152: temp = U[2];
153: for (i = 2; i > 0; i--) U[i] = U[i - 1];
154: U[0] = temp;
155: if (it < l) {
156: /* SpMV and Sigma-shift and Prec */
157: MatMult(A, Z[l - it], U[0]);
158: VecAXPY(U[0], -sigma(it), U[1]);
159: KSP_PCApply(ksp, U[0], Z[l - it - 1]);
160: if (it < l - 1) VecCopy(Z[l - it - 1], Q[3 * it]);
161: } else {
162: /* Shift the Z vector pointers */
163: temp = Z[PetscMax(l, 2)];
164: for (i = PetscMax(l, 2); i > 0; --i) Z[i] = Z[i - 1];
165: Z[0] = temp;
166: /* SpMV and Prec */
167: MatMult(A, Z[1], U[0]);
168: KSP_PCApply(ksp, U[0], Z[0]);
169: }
171: /* ----------------------------------- */
172: /* Adjust the G matrix */
173: /* ----------------------------------- */
174: if (it >= l) {
175: if (it == l) {
176: /* MPI_Wait for G(0,0),scale V0 and Z and U and Q vectors with 1/beta */
177: MPI_Wait(&req(0), MPI_STATUS_IGNORE);
178: beta = PetscSqrtReal(PetscRealPart(G(0, 0)));
179: G(0, 0) = 1.0;
180: VecAXPY(V[0], 1.0 / beta, p); /* this assumes V[0] to be zero initially */
181: for (j = 0; j <= PetscMax(l, 2); ++j) VecScale(Z[j], 1.0 / beta);
182: for (j = 0; j <= 2; ++j) VecScale(U[j], 1.0 / beta);
183: for (j = 0; j < l - 1; ++j) VecScale(Q[3 * j], 1.0 / beta);
184: }
186: /* MPI_Wait until the dot products,started l iterations ago,are completed */
187: MPI_Wait(&req(it - l + 1), MPI_STATUS_IGNORE);
188: if (it >= 2 * l) {
189: for (j = PetscMax(0, it - 3 * l + 1); j <= it - 2 * l; j++) { G(j, it - l + 1) = G(it - 2 * l + 1, j + l); /* exploit symmetry in G matrix */ }
190: }
192: if (it <= 2 * l - 1) {
193: invbeta2 = 1.0 / (beta * beta);
194: /* Scale columns 1 up to l of G with 1/beta^2 */
195: for (j = PetscMax(it - 3 * l + 1, 0); j <= it - l + 1; ++j) G(j, it - l + 1) *= invbeta2;
196: }
198: for (j = PetscMax(it - 2 * l + 2, 0); j <= it - l; ++j) {
199: sum_dummy = 0.0;
200: for (k = PetscMax(it - 3 * l + 1, 0); k <= j - 1; ++k) sum_dummy = sum_dummy + G(k, j) * G(k, it - l + 1);
201: G(j, it - l + 1) = (G(j, it - l + 1) - sum_dummy) / G(j, j);
202: }
204: sum_dummy = 0.0;
205: for (k = PetscMax(it - 3 * l + 1, 0); k <= it - l; ++k) sum_dummy = sum_dummy + G(k, it - l + 1) * G(k, it - l + 1);
207: tmp = PetscRealPart(G(it - l + 1, it - l + 1) - sum_dummy);
208: /* Breakdown check */
209: if (tmp < 0) {
210: if (plcg->show_rstrt) PetscPrintf(comm, "Sqrt breakdown in iteration %" PetscInt_FMT ": sqrt argument is %e. Iteration was restarted.\n", ksp->its + 1, (double)tmp);
211: /* End hanging dot-products in the pipeline before exiting for-loop */
212: start = it - l + 2;
213: end = PetscMin(it + 1, max_it + 1); /* !warning! 'it' can actually be greater than 'max_it' */
214: for (i = start; i < end; ++i) MPI_Wait(&req(i), MPI_STATUS_IGNORE);
215: break;
216: }
217: G(it - l + 1, it - l + 1) = PetscSqrtReal(tmp);
219: if (it < 2 * l) {
220: if (it == l) {
221: gamma(it - l) = (G(it - l, it - l + 1) + sigma(it - l) * G(it - l, it - l)) / G(it - l, it - l);
222: } else {
223: gamma(it - l) = (G(it - l, it - l + 1) + sigma(it - l) * G(it - l, it - l) - delta(it - l - 1) * G(it - l - 1, it - l)) / G(it - l, it - l);
224: }
225: delta(it - l) = G(it - l + 1, it - l + 1) / G(it - l, it - l);
226: } else {
227: gamma(it - l) = (G(it - l, it - l) * gamma(it - 2 * l) + G(it - l, it - l + 1) * delta(it - 2 * l) - G(it - l - 1, it - l) * delta(it - l - 1)) / G(it - l, it - l);
228: delta(it - l) = (G(it - l + 1, it - l + 1) * delta(it - 2 * l)) / G(it - l, it - l);
229: }
231: /* -------------------------------------------------- */
232: /* Recursively compute the next V, Q, Z and U vectors */
233: /* -------------------------------------------------- */
234: /* Shift the V vector pointers */
235: temp = V[2];
236: for (i = 2; i > 0; i--) V[i] = V[i - 1];
237: V[0] = temp;
239: /* Recurrence V vectors */
240: if (l == 1) {
241: VecCopy(Z[1], V[0]);
242: } else {
243: VecCopy(Q[0], V[0]);
244: }
245: if (it == l) {
246: VecAXPY(V[0], sigma(0) - gamma(it - l), V[1]);
247: } else {
248: alpha(0) = sigma(0) - gamma(it - l);
249: alpha(1) = -delta(it - l - 1);
250: VecMAXPY(V[0], 2, &alpha(0), &V[1]);
251: }
252: VecScale(V[0], 1.0 / delta(it - l));
254: /* Recurrence Q vectors */
255: for (j = 0; j < l - 1; ++j) {
256: /* Shift the Q vector pointers */
257: temp = Q[3 * j + 2];
258: for (i = 2; i > 0; i--) Q[3 * j + i] = Q[3 * j + i - 1];
259: Q[3 * j] = temp;
261: if (j < l - 2) {
262: VecCopy(Q[3 * (j + 1)], Q[3 * j]);
263: } else {
264: VecCopy(Z[1], Q[3 * j]);
265: }
266: if (it == l) {
267: VecAXPY(Q[3 * j], sigma(j + 1) - gamma(it - l), Q[3 * j + 1]);
268: } else {
269: alpha(0) = sigma(j + 1) - gamma(it - l);
270: alpha(1) = -delta(it - l - 1);
271: VecMAXPY(Q[3 * j], 2, &alpha(0), &Q[3 * j + 1]);
272: }
273: VecScale(Q[3 * j], 1.0 / delta(it - l));
274: }
276: /* Recurrence Z and U vectors */
277: if (it == l) {
278: VecAXPY(Z[0], -gamma(it - l), Z[1]);
279: VecAXPY(U[0], -gamma(it - l), U[1]);
280: } else {
281: alpha(0) = -gamma(it - l);
282: alpha(1) = -delta(it - l - 1);
283: VecMAXPY(Z[0], 2, &alpha(0), &Z[1]);
284: VecMAXPY(U[0], 2, &alpha(0), &U[1]);
285: }
286: VecScale(Z[0], 1.0 / delta(it - l));
287: VecScale(U[0], 1.0 / delta(it - l));
288: }
290: /* ---------------------------------------- */
291: /* Compute and communicate the dot products */
292: /* ---------------------------------------- */
293: if (it < l) {
294: for (j = 0; j < it + 2; ++j) { (*U[0]->ops->dot_local)(U[0], Z[l - j], &G(j, it + 1)); /* dot-products (U[0],Z[j]) */ }
295: MPIPetsc_Iallreduce(MPI_IN_PLACE, &G(0, it + 1), it + 2, MPIU_SCALAR, MPIU_SUM, comm, &req(it + 1));
296: } else if ((it >= l) && (it < max_it)) {
297: middle = it - l + 2;
298: end = it + 2;
299: (*U[0]->ops->dot_local)(U[0], V[0], &G(it - l + 1, it + 1)); /* dot-product (U[0],V[0]) */
300: for (j = middle; j < end; ++j) { (*U[0]->ops->dot_local)(U[0], plcg->Z[it + 1 - j], &G(j, it + 1)); /* dot-products (U[0],Z[j]) */ }
301: MPIPetsc_Iallreduce(MPI_IN_PLACE, &G(it - l + 1, it + 1), l + 1, MPIU_SCALAR, MPIU_SUM, comm, &req(it + 1));
302: }
304: /* ----------------------------------------- */
305: /* Compute solution vector and residual norm */
306: /* ----------------------------------------- */
307: if (it >= l) {
308: if (it == l) {
309: if (ksp->its != 0) ++ksp->its;
310: eta = gamma(0);
311: zeta = beta;
312: VecCopy(V[1], p);
313: VecScale(p, 1.0 / eta);
314: VecAXPY(x, zeta, p);
315: dp = beta;
316: } else if (it > l) {
317: k = it - l;
318: ++ksp->its;
319: lambda = delta(k - 1) / eta;
320: eta = gamma(k) - lambda * delta(k - 1);
321: zeta = -lambda * zeta;
322: VecScale(p, -delta(k - 1) / eta);
323: VecAXPY(p, 1.0 / eta, V[1]);
324: VecAXPY(x, zeta, p);
325: dp = PetscAbsScalar(zeta);
326: }
327: ksp->rnorm = dp;
328: KSPLogResidualHistory(ksp, dp);
329: KSPMonitor(ksp, ksp->its, dp);
330: (*ksp->converged)(ksp, ksp->its, dp, &ksp->reason, ksp->cnvP);
332: if (ksp->its >= max_it && !ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
333: if (ksp->reason) {
334: /* End hanging dot-products in the pipeline before exiting for-loop */
335: start = it - l + 2;
336: end = PetscMin(it + 2, max_it + 1); /* !warning! 'it' can actually be greater than 'max_it' */
337: for (i = start; i < end; ++i) MPI_Wait(&req(i), MPI_STATUS_IGNORE);
338: break;
339: }
340: }
341: } /* End inner for loop */
342: return 0;
343: }
345: static PetscErrorCode KSPSolve_ReInitData_PIPELCG(KSP ksp)
346: {
347: KSP_CG_PIPE_L *plcg = (KSP_CG_PIPE_L *)ksp->data;
348: PetscInt i = 0, j = 0, l = plcg->l, max_it = ksp->max_it;
350: for (i = 0; i < PetscMax(3, l + 1); ++i) VecSet(plcg->Z[i], 0.0);
351: for (i = 1; i < 3; ++i) VecSet(plcg->U[i], 0.0);
352: for (i = 0; i < 3; ++i) VecSet(plcg->V[i], 0.0);
353: for (i = 0; i < 3 * (l - 1) + 1; ++i) VecSet(plcg->Q[i], 0.0);
354: for (j = 0; j < (max_it + 1); ++j) {
355: gamma(j) = 0.0;
356: delta(j) = 0.0;
357: for (i = 0; i < (2 * l + 1); ++i) G_noshift(i, j) = 0.0;
358: }
359: return 0;
360: }
362: /*
363: KSPSolve_PIPELCG - This routine actually applies the pipelined(l) conjugate gradient method
364: */
365: static PetscErrorCode KSPSolve_PIPELCG(KSP ksp)
366: {
367: KSP_CG_PIPE_L *plcg = (KSP_CG_PIPE_L *)ksp->data;
368: Mat A = NULL, Pmat = NULL;
369: Vec b = NULL, x = NULL, p = NULL;
370: PetscInt max_it = ksp->max_it, l = plcg->l;
371: PetscInt i = 0, outer_it = 0, curr_guess_zero = 0;
372: PetscReal lmin = plcg->lmin, lmax = plcg->lmax;
373: PetscBool diagonalscale = PETSC_FALSE;
374: MPI_Comm comm;
376: comm = PetscObjectComm((PetscObject)ksp);
377: PCGetDiagonalScale(ksp->pc, &diagonalscale);
380: x = ksp->vec_sol;
381: b = ksp->vec_rhs;
382: p = plcg->p;
384: PetscCalloc1((max_it + 1) * (2 * l + 1), &plcg->G);
385: PetscCalloc1(max_it + 1, &plcg->gamma);
386: PetscCalloc1(max_it + 1, &plcg->delta);
387: PetscCalloc1(max_it + 1, &plcg->req);
389: PCGetOperators(ksp->pc, &A, &Pmat);
391: for (i = 0; i < l; ++i) sigma(i) = (0.5 * (lmin + lmax) + (0.5 * (lmax - lmin) * PetscCosReal(PETSC_PI * (2.0 * i + 1.0) / (2.0 * l))));
393: ksp->its = 0;
394: outer_it = 0;
395: curr_guess_zero = !!ksp->guess_zero;
397: while (ksp->its < max_it) { /* OUTER LOOP (gmres-like restart to handle breakdowns) */
398: /* RESTART LOOP */
399: if (!curr_guess_zero) {
400: KSP_MatMult(ksp, A, x, plcg->U[0]); /* u <- b - Ax */
401: VecAYPX(plcg->U[0], -1.0, b);
402: } else {
403: VecCopy(b, plcg->U[0]); /* u <- b (x is 0) */
404: }
405: KSP_PCApply(ksp, plcg->U[0], p); /* p <- Bu */
407: if (outer_it > 0) {
408: /* Re-initialize Z,U,V,Q,gamma,delta,G after restart occurred */
409: KSPSolve_ReInitData_PIPELCG(ksp);
410: }
412: (*plcg->U[0]->ops->dot_local)(plcg->U[0], p, &G(0, 0));
413: MPIPetsc_Iallreduce(MPI_IN_PLACE, &G(0, 0), 1, MPIU_SCALAR, MPIU_SUM, comm, &req(0));
414: VecCopy(p, plcg->Z[l]);
416: KSPSolve_InnerLoop_PIPELCG(ksp);
418: if (ksp->reason) break; /* convergence or divergence */
419: ++outer_it;
420: curr_guess_zero = 0;
421: }
423: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
424: PetscFree(plcg->G);
425: PetscFree(plcg->gamma);
426: PetscFree(plcg->delta);
427: PetscFree(plcg->req);
428: return 0;
429: }
431: /*MC
432: KSPPIPELCG - Deep pipelined (length l) Conjugate Gradient method. This method has only a single non-blocking global
433: reduction per iteration, compared to 2 blocking reductions for standard `KSPCG`. The reduction is overlapped by the
434: matrix-vector product and preconditioner application of the next l iterations. The pipeline length l is a parameter
435: of the method. [](sec_pipelineksp)
437: Options Database Keys:
438: + -ksp_pipelcg_pipel - pipelined length
439: . -ksp_pipelcg_lmin - approximation to the smallest eigenvalue of the preconditioned operator (default: 0.0)
440: . -ksp_pipelcg_lmax - approximation to the largest eigenvalue of the preconditioned operator (default: 0.0)
441: - -ksp_pipelcg_monitor - output where/why the method restarts when a sqrt breakdown occurs
443: Level: advanced
445: Notes:
446: MPI configuration may be necessary for reductions to make asynchronous progress, which is important for
447: performance of pipelined methods. See [](doc_faq_pipelined)
449: Contributed by:
450: Siegfried Cools, University of Antwerp, Dept. Mathematics and Computer Science,
451: funded by Flemish Research Foundation (FWO) grant number 12H4617N.
453: Example usage:
454: .vb
455: KSP tutorials ex2, no preconditioner, pipel = 2, lmin = 0.0, lmax = 8.0 :
456: $mpiexec -n 14 ./ex2 -m 1000 -n 1000 -ksp_type pipelcg -pc_type none -ksp_norm_type natural
457: -ksp_rtol 1e-10 -ksp_max_it 1000 -ksp_pipelcg_pipel 2 -ksp_pipelcg_lmin 0.0 -ksp_pipelcg_lmax 8.0 -log_view
458: SNES tutorials ex48, bjacobi preconditioner, pipel = 3, lmin = 0.0, lmax = 2.0, show restart information :
459: $mpiexec -n 14 ./ex48 -M 150 -P 100 -ksp_type pipelcg -pc_type bjacobi -ksp_rtol 1e-10 -ksp_pipelcg_pipel 3
460: -ksp_pipelcg_lmin 0.0 -ksp_pipelcg_lmax 2.0 -ksp_pipelcg_monitor -log_view
461: .ve
463: References:
464: + * - J. Cornelis, S. Cools and W. Vanroose,
465: "The Communication-Hiding Conjugate Gradient Method with Deep Pipelines"
466: Submitted to SIAM Journal on Scientific Computing (SISC), 2018.
467: - * - S. Cools, J. Cornelis and W. Vanroose,
468: "Numerically Stable Recurrence Relations for the Communication Hiding Pipelined Conjugate Gradient Method"
469: Submitted to IEEE Transactions on Parallel and Distributed Systems, 2019.
471: .seealso: [](chapter_ksp), [](sec_pipelineksp), [](doc_faq_pipelined), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSPCG`, `KSPPIPECG`, `KSPPIPECGRR`, `KSPPGMRES`,
472: `KSPPIPEBCGS`, `KSPSetPCSide()`, `KSPGROPPCG`
473: M*/
474: PETSC_EXTERN PetscErrorCode KSPCreate_PIPELCG(KSP ksp)
475: {
476: KSP_CG_PIPE_L *plcg = NULL;
478: PetscNew(&plcg);
479: ksp->data = (void *)plcg;
481: KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 1);
482: KSPSetSupportedNorm(ksp, KSP_NORM_NATURAL, PC_LEFT, 2);
484: ksp->ops->setup = KSPSetUp_PIPELCG;
485: ksp->ops->solve = KSPSolve_PIPELCG;
486: ksp->ops->reset = KSPReset_PIPELCG;
487: ksp->ops->destroy = KSPDestroy_PIPELCG;
488: ksp->ops->view = KSPView_PIPELCG;
489: ksp->ops->setfromoptions = KSPSetFromOptions_PIPELCG;
490: ksp->ops->buildsolution = KSPBuildSolutionDefault;
491: ksp->ops->buildresidual = KSPBuildResidualDefault;
492: return 0;
493: }