Actual source code: fbcgsr.c
1: /*
2: This file implements FBiCGStab-R.
3: FBiCGStab-R is a mathematically equivalent variant of FBiCGStab. Differences are:
4: (1) There are fewer MPI_Allreduce calls.
5: (2) The convergence occasionally is much faster than that of FBiCGStab.
6: */
7: #include <../src/ksp/ksp/impls/bcgs/bcgsimpl.h>
8: #include <petsc/private/vecimpl.h>
10: static PetscErrorCode KSPSetUp_FBCGSR(KSP ksp)
11: {
12: PetscFunctionBegin;
13: PetscCall(KSPSetWorkVecs(ksp, 8));
14: PetscFunctionReturn(PETSC_SUCCESS);
15: }
17: static PetscErrorCode KSPSolve_FBCGSR(KSP ksp)
18: {
19: PetscInt i, j, N;
20: PetscScalar tau, sigma, alpha, omega, beta;
21: PetscReal rho;
22: PetscScalar xi1, xi2, xi3, xi4;
23: Vec X, B, P, P2, RP, R, V, S, T, S2;
24: PetscScalar *PETSC_RESTRICT rp, *PETSC_RESTRICT r, *PETSC_RESTRICT p;
25: PetscScalar *PETSC_RESTRICT v, *PETSC_RESTRICT s, *PETSC_RESTRICT t, *PETSC_RESTRICT s2;
26: PetscScalar insums[4], outsums[4];
27: KSP_BCGS *bcgs = (KSP_BCGS *)ksp->data;
28: PC pc;
29: Mat mat;
31: PetscFunctionBegin;
32: PetscCheck(ksp->vec_rhs->petscnative, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Only coded for PETSc vectors");
33: PetscCall(VecGetLocalSize(ksp->vec_sol, &N));
35: X = ksp->vec_sol;
36: B = ksp->vec_rhs;
37: P2 = ksp->work[0];
39: /* The following are involved in modified inner product calculations and vector updates */
40: RP = ksp->work[1];
41: PetscCall(VecGetArray(RP, (PetscScalar **)&rp));
42: PetscCall(VecRestoreArray(RP, NULL));
43: R = ksp->work[2];
44: PetscCall(VecGetArray(R, (PetscScalar **)&r));
45: PetscCall(VecRestoreArray(R, NULL));
46: P = ksp->work[3];
47: PetscCall(VecGetArray(P, (PetscScalar **)&p));
48: PetscCall(VecRestoreArray(P, NULL));
49: V = ksp->work[4];
50: PetscCall(VecGetArray(V, (PetscScalar **)&v));
51: PetscCall(VecRestoreArray(V, NULL));
52: S = ksp->work[5];
53: PetscCall(VecGetArray(S, (PetscScalar **)&s));
54: PetscCall(VecRestoreArray(S, NULL));
55: T = ksp->work[6];
56: PetscCall(VecGetArray(T, (PetscScalar **)&t));
57: PetscCall(VecRestoreArray(T, NULL));
58: S2 = ksp->work[7];
59: PetscCall(VecGetArray(S2, (PetscScalar **)&s2));
60: PetscCall(VecRestoreArray(S2, NULL));
62: /* Only supports right preconditioning */
63: PetscCheck(ksp->pc_side == PC_RIGHT, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "KSP fbcgsr does not support %s", PCSides[ksp->pc_side]);
64: if (!ksp->guess_zero) {
65: if (!bcgs->guess) PetscCall(VecDuplicate(X, &bcgs->guess));
66: PetscCall(VecCopy(X, bcgs->guess));
67: } else {
68: PetscCall(VecSet(X, 0.0));
69: }
71: /* Compute initial residual */
72: PetscCall(KSPGetPC(ksp, &pc));
73: PetscCall(PCGetOperators(pc, &mat, NULL));
74: if (!ksp->guess_zero) {
75: PetscCall(KSP_MatMult(ksp, mat, X, P2)); /* P2 is used as temporary storage */
76: PetscCall(VecCopy(B, R));
77: PetscCall(VecAXPY(R, -1.0, P2));
78: } else {
79: PetscCall(VecCopy(B, R));
80: }
82: /* Test for nothing to do */
83: PetscCall(VecNorm(R, NORM_2, &rho));
84: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
85: ksp->its = 0;
86: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = rho;
87: else ksp->rnorm = 0;
88: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
89: PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
90: PetscCall(KSPMonitor(ksp, 0, ksp->rnorm));
91: PetscCall((*ksp->converged)(ksp, 0, ksp->rnorm, &ksp->reason, ksp->cnvP));
92: if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);
94: /* Initialize iterates */
95: PetscCall(VecCopy(R, RP)); /* rp <- r */
96: PetscCall(VecCopy(R, P)); /* p <- r */
98: /* Big loop */
99: for (i = 0; i < ksp->max_it; i++) {
100: /* matmult and pc */
101: PetscCall(KSP_PCApply(ksp, P, P2)); /* p2 <- K p */
102: PetscCall(KSP_MatMult(ksp, mat, P2, V)); /* v <- A p2 */
104: /* inner products */
105: if (i == 0) {
106: tau = rho * rho;
107: PetscCall(VecDot(V, RP, &sigma)); /* sigma <- (v,rp) */
108: } else {
109: PetscCall(PetscLogEventBegin(VEC_ReduceArithmetic, 0, 0, 0, 0));
110: tau = sigma = 0.0;
111: for (j = 0; j < N; j++) {
112: tau += r[j] * rp[j]; /* tau <- (r,rp) */
113: sigma += v[j] * rp[j]; /* sigma <- (v,rp) */
114: }
115: PetscCall(PetscLogFlops(4.0 * N));
116: PetscCall(PetscLogEventEnd(VEC_ReduceArithmetic, 0, 0, 0, 0));
117: insums[0] = tau;
118: insums[1] = sigma;
119: PetscCall(PetscLogEventBegin(VEC_ReduceCommunication, 0, 0, 0, 0));
120: PetscCall(MPIU_Allreduce(insums, outsums, 2, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)ksp)));
121: PetscCall(PetscLogEventEnd(VEC_ReduceCommunication, 0, 0, 0, 0));
122: tau = outsums[0];
123: sigma = outsums[1];
124: }
126: /* scalar update */
127: alpha = tau / sigma;
129: /* vector update */
130: PetscCall(VecWAXPY(S, -alpha, V, R)); /* s <- r - alpha v */
132: /* matmult and pc */
133: PetscCall(KSP_PCApply(ksp, S, S2)); /* s2 <- K s */
134: PetscCall(KSP_MatMult(ksp, mat, S2, T)); /* t <- A s2 */
136: /* inner products */
137: PetscCall(PetscLogEventBegin(VEC_ReduceArithmetic, 0, 0, 0, 0));
138: xi1 = xi2 = xi3 = xi4 = 0.0;
139: for (j = 0; j < N; j++) {
140: xi1 += s[j] * s[j]; /* xi1 <- (s,s) */
141: xi2 += t[j] * s[j]; /* xi2 <- (t,s) */
142: xi3 += t[j] * t[j]; /* xi3 <- (t,t) */
143: xi4 += t[j] * rp[j]; /* xi4 <- (t,rp) */
144: }
145: PetscCall(PetscLogFlops(8.0 * N));
146: PetscCall(PetscLogEventEnd(VEC_ReduceArithmetic, 0, 0, 0, 0));
148: insums[0] = xi1;
149: insums[1] = xi2;
150: insums[2] = xi3;
151: insums[3] = xi4;
153: PetscCall(PetscLogEventBegin(VEC_ReduceCommunication, 0, 0, 0, 0));
154: PetscCall(MPIU_Allreduce(insums, outsums, 4, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)ksp)));
155: PetscCall(PetscLogEventEnd(VEC_ReduceCommunication, 0, 0, 0, 0));
156: xi1 = outsums[0];
157: xi2 = outsums[1];
158: xi3 = outsums[2];
159: xi4 = outsums[3];
161: /* test denominator */
162: if ((xi3 == 0.0) || (sigma == 0.0)) {
163: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "KSPSolve has failed due to zero inner product");
164: ksp->reason = KSP_DIVERGED_BREAKDOWN;
165: PetscCall(PetscInfo(ksp, "KSPSolve has failed due to zero inner product\n"));
166: break;
167: }
169: /* scalar updates */
170: omega = xi2 / xi3;
171: beta = -xi4 / sigma;
172: rho = PetscSqrtReal(PetscAbsScalar(xi1 - omega * xi2)); /* residual norm */
174: /* vector updates */
175: PetscCall(VecAXPBYPCZ(X, alpha, omega, 1.0, P2, S2)); /* x <- alpha * p2 + omega * s2 + x */
177: /* convergence test */
178: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
179: ksp->its++;
180: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = rho;
181: else ksp->rnorm = 0;
182: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
183: PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
184: PetscCall(KSPMonitor(ksp, i + 1, ksp->rnorm));
185: PetscCall((*ksp->converged)(ksp, i + 1, ksp->rnorm, &ksp->reason, ksp->cnvP));
186: if (ksp->reason) break;
188: /* vector updates */
189: PetscCall(PetscLogEventBegin(VEC_Ops, 0, 0, 0, 0));
190: for (j = 0; j < N; j++) {
191: r[j] = s[j] - omega * t[j]; /* r <- s - omega t */
192: p[j] = r[j] + beta * (p[j] - omega * v[j]); /* p <- r + beta * (p - omega v) */
193: }
194: PetscCall(PetscLogFlops(6.0 * N));
195: PetscCall(PetscLogEventEnd(VEC_Ops, 0, 0, 0, 0));
196: }
198: if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
199: PetscFunctionReturn(PETSC_SUCCESS);
200: }
202: /*MC
203: KSPFBCGSR - Implements a mathematically equivalent variant of flexible bi-CG-stab, `KSPFBCGS`. [](sec_flexibleksp)
205: Level: beginner
207: Notes:
208: This implementation requires fewer `MPI_Allreduce()` calls than `KSPFBCGS` and may converge faster
210: See `KSPPIPEBCGS` for a pipelined version of the algorithm
212: Flexible BiCGStab, unlike most Krylov methods, allows the preconditioner to be nonlinear, that is the action of the preconditioner to a vector need not be linear
213: in the vector entries.
215: Only supports right preconditioning
217: .seealso: [](ch_ksp), [](sec_flexibleksp), `KSPFBCGSR`, `KSPPIPEBCGS`, `KSPBCGSL`, `KSPBCGS`, `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPBICG`, `KSPFBCGS`, `KSPSetPCSide()`
218: M*/
219: PETSC_EXTERN PetscErrorCode KSPCreate_FBCGSR(KSP ksp)
220: {
221: KSP_BCGS *bcgs;
223: PetscFunctionBegin;
224: PetscCall(PetscNew(&bcgs));
226: ksp->data = bcgs;
227: ksp->ops->setup = KSPSetUp_FBCGSR;
228: ksp->ops->solve = KSPSolve_FBCGSR;
229: ksp->ops->destroy = KSPDestroy_BCGS;
230: ksp->ops->reset = KSPReset_BCGS;
231: ksp->ops->buildsolution = KSPBuildSolution_BCGS;
232: ksp->ops->buildresidual = KSPBuildResidualDefault;
233: ksp->ops->setfromoptions = KSPSetFromOptions_BCGS;
234: ksp->pc_side = PC_RIGHT; /* set default PC side */
236: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
237: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2));
238: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));
239: PetscFunctionReturn(PETSC_SUCCESS);
240: }