Actual source code: pipebcgs.c
1: /*
2: This file implements pipelined BiCGStab (pipe-BiCGStab).
3: */
4: #include <../src/ksp/ksp/impls/bcgs/bcgsimpl.h>
6: static PetscErrorCode KSPSetUp_PIPEBCGS(KSP ksp)
7: {
8: PetscFunctionBegin;
9: PetscCall(KSPSetWorkVecs(ksp, 15));
10: PetscFunctionReturn(PETSC_SUCCESS);
11: }
13: /* Only need a few hacks from KSPSolve_BCGS */
14: #include <petsc/private/pcimpl.h>
15: static PetscErrorCode KSPSolve_PIPEBCGS(KSP ksp)
16: {
17: PetscInt i;
18: PetscScalar rho, rhoold, alpha, beta, omega = 0.0, d1, d2, d3;
19: Vec X, B, S, R, RP, Y, Q, P2, Q2, R2, S2, W, Z, W2, Z2, T, V;
20: PetscReal dp = 0.0;
21: KSP_BCGS *bcgs = (KSP_BCGS *)ksp->data;
22: PC pc;
24: PetscFunctionBegin;
25: X = ksp->vec_sol;
26: B = ksp->vec_rhs;
27: R = ksp->work[0];
28: RP = ksp->work[1];
29: S = ksp->work[2];
30: Y = ksp->work[3];
31: Q = ksp->work[4];
32: Q2 = ksp->work[5];
33: P2 = ksp->work[6];
34: R2 = ksp->work[7];
35: S2 = ksp->work[8];
36: W = ksp->work[9];
37: Z = ksp->work[10];
38: W2 = ksp->work[11];
39: Z2 = ksp->work[12];
40: T = ksp->work[13];
41: V = ksp->work[14];
43: if (!ksp->guess_zero) {
44: if (!bcgs->guess) PetscCall(VecDuplicate(X, &bcgs->guess));
45: PetscCall(VecCopy(X, bcgs->guess));
46: } else {
47: PetscCall(VecSet(X, 0.0));
48: }
50: /* Compute initial residual */
51: PetscCall(KSPGetPC(ksp, &pc));
52: if (!ksp->guess_zero) {
53: PetscCall(KSP_MatMult(ksp, pc->mat, X, Q2));
54: PetscCall(VecCopy(B, R));
55: PetscCall(VecAXPY(R, -1.0, Q2));
56: } else {
57: PetscCall(VecCopy(B, R));
58: }
60: /* Test for nothing to do */
61: if (ksp->normtype != KSP_NORM_NONE) {
62: PetscCall(VecNorm(R, NORM_2, &dp));
63: } else dp = 0.0;
64: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
65: ksp->its = 0;
66: ksp->rnorm = dp;
67: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
68: PetscCall(KSPLogResidualHistory(ksp, dp));
69: PetscCall(KSPMonitor(ksp, 0, dp));
70: PetscCall((*ksp->converged)(ksp, 0, dp, &ksp->reason, ksp->cnvP));
71: if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);
73: /* Initialize */
74: PetscCall(VecCopy(R, RP)); /* rp <- r */
76: PetscCall(VecDotBegin(R, RP, &rho)); /* rho <- (r,rp) */
77: PetscCall(PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)R)));
78: PetscCall(KSP_PCApply(ksp, R, R2)); /* r2 <- K r */
79: PetscCall(KSP_MatMult(ksp, pc->mat, R2, W)); /* w <- A r2 */
80: PetscCall(VecDotEnd(R, RP, &rho));
82: PetscCall(VecDotBegin(W, RP, &d2)); /* d2 <- (w,rp) */
83: PetscCall(PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)W)));
84: PetscCall(KSP_PCApply(ksp, W, W2)); /* w2 <- K w */
85: PetscCall(KSP_MatMult(ksp, pc->mat, W2, T)); /* t <- A w2 */
86: PetscCall(VecDotEnd(W, RP, &d2));
88: alpha = rho / d2;
89: beta = 0.0;
91: /* Main loop */
92: i = 0;
93: do {
94: if (i == 0) {
95: PetscCall(VecCopy(R2, P2)); /* p2 <- r2 */
96: PetscCall(VecCopy(W, S)); /* s <- w */
97: PetscCall(VecCopy(W2, S2)); /* s2 <- w2 */
98: PetscCall(VecCopy(T, Z)); /* z <- t */
99: } else {
100: PetscCall(VecAXPBYPCZ(P2, 1.0, -beta * omega, beta, R2, S2)); /* p2 <- beta * p2 + r2 - beta * omega * s2 */
101: PetscCall(VecAXPBYPCZ(S, 1.0, -beta * omega, beta, W, Z)); /* s <- beta * s + w - beta * omega * z */
102: PetscCall(VecAXPBYPCZ(S2, 1.0, -beta * omega, beta, W2, Z2)); /* s2 <- beta * s2 + w2 - beta * omega * z2 */
103: PetscCall(VecAXPBYPCZ(Z, 1.0, -beta * omega, beta, T, V)); /* z <- beta * z + t - beta * omega * v */
104: }
105: PetscCall(VecWAXPY(Q, -alpha, S, R)); /* q <- r - alpha s */
106: PetscCall(VecWAXPY(Q2, -alpha, S2, R2)); /* q2 <- r2 - alpha s2 */
107: PetscCall(VecWAXPY(Y, -alpha, Z, W)); /* y <- w - alpha z */
109: PetscCall(VecDotBegin(Q, Y, &d1)); /* d1 <- (q,y) */
110: PetscCall(VecDotBegin(Y, Y, &d2)); /* d2 <- (y,y) */
112: PetscCall(PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)Q)));
113: PetscCall(KSP_PCApply(ksp, Z, Z2)); /* z2 <- K z */
114: PetscCall(KSP_MatMult(ksp, pc->mat, Z2, V)); /* v <- A z2 */
116: PetscCall(VecDotEnd(Q, Y, &d1));
117: PetscCall(VecDotEnd(Y, Y, &d2));
119: if (d2 == 0.0) {
120: /* y is 0. if q is 0, then alpha s == r, and hence alpha p may be our solution. Give it a try? */
121: PetscCall(VecDot(Q, Q, &d1));
122: if (d1 != 0.0) {
123: ksp->reason = KSP_DIVERGED_BREAKDOWN;
124: break;
125: }
126: PetscCall(VecAXPY(X, alpha, P2)); /* x <- x + alpha p2 */
127: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
128: ksp->its++;
129: ksp->rnorm = 0.0;
130: ksp->reason = KSP_CONVERGED_RTOL;
131: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
132: PetscCall(KSPLogResidualHistory(ksp, dp));
133: PetscCall(KSPMonitor(ksp, i + 1, 0.0));
134: break;
135: }
136: omega = d1 / d2; /* omega <- (y'q) / (y'y) */
137: PetscCall(VecAXPBYPCZ(X, alpha, omega, 1.0, P2, Q2)); /* x <- alpha * p2 + omega * q2 + x */
138: PetscCall(VecWAXPY(R, -omega, Y, Q)); /* r <- q - omega y */
139: PetscCall(VecWAXPY(R2, -alpha, Z2, W2)); /* r2 <- w2 - alpha z2 */
140: PetscCall(VecAYPX(R2, -omega, Q2)); /* r2 <- q2 - omega r2 */
141: PetscCall(VecWAXPY(W, -alpha, V, T)); /* w <- t - alpha v */
142: PetscCall(VecAYPX(W, -omega, Y)); /* w <- y - omega w */
143: rhoold = rho;
145: if (ksp->normtype != KSP_NORM_NONE && ksp->chknorm < i + 2) { PetscCall(VecNormBegin(R, NORM_2, &dp)); /* dp <- norm(r) */ }
146: PetscCall(VecDotBegin(R, RP, &rho)); /* rho <- (r,rp) */
147: PetscCall(VecDotBegin(S, RP, &d1)); /* d1 <- (s,rp) */
148: PetscCall(VecDotBegin(W, RP, &d2)); /* d2 <- (w,rp) */
149: PetscCall(VecDotBegin(Z, RP, &d3)); /* d3 <- (z,rp) */
151: PetscCall(PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)R)));
152: PetscCall(KSP_PCApply(ksp, W, W2)); /* w2 <- K w */
153: PetscCall(KSP_MatMult(ksp, pc->mat, W2, T)); /* t <- A w2 */
155: if (ksp->normtype != KSP_NORM_NONE && ksp->chknorm < i + 2) PetscCall(VecNormEnd(R, NORM_2, &dp));
156: PetscCall(VecDotEnd(R, RP, &rho));
157: PetscCall(VecDotEnd(S, RP, &d1));
158: PetscCall(VecDotEnd(W, RP, &d2));
159: PetscCall(VecDotEnd(Z, RP, &d3));
161: PetscCheck(d2 + beta * d1 - beta * omega * d3 != 0.0, PetscObjectComm((PetscObject)ksp), PETSC_ERR_PLIB, "Divide by zero");
163: beta = (rho / rhoold) * (alpha / omega);
164: alpha = rho / (d2 + beta * d1 - beta * omega * d3); /* alpha <- rho / (d2 + beta * d1 - beta * omega * d3) */
166: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
167: ksp->its++;
169: /* Residual replacement step */
170: if (i > 0 && i % 100 == 0 && i < 1001) {
171: PetscCall(KSP_MatMult(ksp, pc->mat, X, R));
172: PetscCall(VecAYPX(R, -1.0, B)); /* r <- b - Ax */
173: PetscCall(KSP_PCApply(ksp, R, R2)); /* r2 <- K r */
174: PetscCall(KSP_MatMult(ksp, pc->mat, R2, W)); /* w <- A r2 */
175: PetscCall(KSP_PCApply(ksp, W, W2)); /* w2 <- K w */
176: PetscCall(KSP_MatMult(ksp, pc->mat, W2, T)); /* t <- A w2 */
177: PetscCall(KSP_MatMult(ksp, pc->mat, P2, S)); /* s <- A p2 */
178: PetscCall(KSP_PCApply(ksp, S, S2)); /* s2 <- K s */
179: PetscCall(KSP_MatMult(ksp, pc->mat, S2, Z)); /* z <- A s2 */
180: PetscCall(KSP_PCApply(ksp, Z, Z2)); /* z2 <- K z */
181: PetscCall(KSP_MatMult(ksp, pc->mat, Z2, V)); /* v <- A z2 */
182: }
184: ksp->rnorm = dp;
185: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
186: PetscCall(KSPLogResidualHistory(ksp, dp));
187: PetscCall(KSPMonitor(ksp, i + 1, dp));
188: PetscCall((*ksp->converged)(ksp, i + 1, dp, &ksp->reason, ksp->cnvP));
189: if (ksp->reason) break;
190: if (rho == 0.0) {
191: ksp->reason = KSP_DIVERGED_BREAKDOWN;
192: break;
193: }
194: i++;
195: } while (i < ksp->max_it);
197: if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
198: PetscFunctionReturn(PETSC_SUCCESS);
199: }
201: /*MC
202: KSPPIPEBCGS - Implements a pipelined BiCGStab method. [](sec_pipelineksp)
204: Level: intermediate
206: Notes:
207: This method has only two non-blocking reductions per iteration, compared to 3 blocking for standard `KSPFBCGS`. The
208: non-blocking reductions are overlapped by matrix-vector products and preconditioner applications.
210: Periodic residual replacement may be used to increase robustness and maximal attainable accuracy.
212: Like `KSPFBCGS`, the `KSPPIPEBCGS` implementation only allows for right preconditioning.
214: MPI configuration may be necessary for reductions to make asynchronous progress, which is important for
215: performance of pipelined methods. See [](doc_faq_pipelined)
217: Contributed by:
218: Siegfried Cools, Universiteit Antwerpen, {cite}`cools2017communication`
219: EXA2CT European Project on EXascale Algorithms and Advanced Computational Techniques, 2016.
221: .seealso: [](ch_ksp), `KSPFBCGS`, `KSPFBCGSR`, `KSPBCGS`, `KSPBCGSL`, `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPBICG`, `KSPFBCGS`, `KSPSetPCSide()`,
222: [](sec_pipelineksp), [](doc_faq_pipelined)
223: M*/
224: PETSC_EXTERN PetscErrorCode KSPCreate_PIPEBCGS(KSP ksp)
225: {
226: KSP_BCGS *bcgs;
228: PetscFunctionBegin;
229: PetscCall(PetscNew(&bcgs));
231: ksp->data = bcgs;
232: ksp->ops->setup = KSPSetUp_PIPEBCGS;
233: ksp->ops->solve = KSPSolve_PIPEBCGS;
234: ksp->ops->destroy = KSPDestroy_BCGS;
235: ksp->ops->reset = KSPReset_BCGS;
236: ksp->ops->buildresidual = KSPBuildResidualDefault;
237: ksp->ops->setfromoptions = KSPSetFromOptions_BCGS;
239: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2));
240: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));
241: PetscFunctionReturn(PETSC_SUCCESS);
242: }