Actual source code: qmrcgs.c
1: /*
2: This file implements QMRCGS (QMRCGStab).
3: */
4: #include <../src/ksp/ksp/impls/bcgs/bcgsimpl.h>
6: static PetscErrorCode KSPSetUp_QMRCGS(KSP ksp)
7: {
8: PetscFunctionBegin;
9: PetscCall(KSPSetWorkVecs(ksp, 14));
10: PetscFunctionReturn(PETSC_SUCCESS);
11: }
13: /* Only need a few hacks from KSPSolve_BCGS */
15: static PetscErrorCode KSPSolve_QMRCGS(KSP ksp)
16: {
17: PetscInt i;
18: PetscScalar eta, rho1, rho2, alpha, eta2, omega, beta, cf, cf1, uu;
19: Vec X, B, R, P, PH, V, D2, X2, S, SH, T, D, S2, RP, AX, Z;
20: PetscReal dp = 0.0, final, tau, tau2, theta, theta2, c, F, NV, vv;
21: KSP_BCGS *bcgs = (KSP_BCGS *)ksp->data;
22: PC pc;
23: Mat mat;
25: PetscFunctionBegin;
26: X = ksp->vec_sol;
27: B = ksp->vec_rhs;
28: R = ksp->work[0];
29: P = ksp->work[1];
30: PH = ksp->work[2];
31: V = ksp->work[3];
32: D2 = ksp->work[4];
33: X2 = ksp->work[5];
34: S = ksp->work[6];
35: SH = ksp->work[7];
36: T = ksp->work[8];
37: D = ksp->work[9];
38: S2 = ksp->work[10];
39: RP = ksp->work[11];
40: AX = ksp->work[12];
41: Z = ksp->work[13];
43: /* Only supports right preconditioning */
44: PetscCheck(ksp->pc_side == PC_RIGHT, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "KSP qmrcgs does not support %s", PCSides[ksp->pc_side]);
45: if (!ksp->guess_zero) {
46: if (!bcgs->guess) PetscCall(VecDuplicate(X, &bcgs->guess));
47: PetscCall(VecCopy(X, bcgs->guess));
48: } else {
49: PetscCall(VecSet(X, 0.0));
50: }
52: /* Compute initial residual */
53: PetscCall(KSPGetPC(ksp, &pc));
54: PetscCall(PCGetOperators(pc, &mat, NULL));
55: if (!ksp->guess_zero) {
56: PetscCall(KSP_MatMult(ksp, mat, X, S2));
57: PetscCall(VecCopy(B, R));
58: PetscCall(VecAXPY(R, -1.0, S2));
59: } else {
60: PetscCall(VecCopy(B, R));
61: }
63: /* Test for nothing to do */
64: if (ksp->normtype != KSP_NORM_NONE) PetscCall(VecNorm(R, NORM_2, &dp));
65: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
66: ksp->its = 0;
67: ksp->rnorm = dp;
68: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
69: PetscCall(KSPLogResidualHistory(ksp, dp));
70: PetscCall(KSPMonitor(ksp, 0, dp));
71: PetscCall((*ksp->converged)(ksp, 0, dp, &ksp->reason, ksp->cnvP));
72: if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);
74: /* Make the initial Rp == R */
75: PetscCall(VecCopy(R, RP));
77: eta = 1.0;
78: theta = 1.0;
79: if (dp == 0.0) {
80: PetscCall(VecNorm(R, NORM_2, &tau));
81: } else {
82: tau = dp;
83: }
85: PetscCall(VecDot(RP, RP, &rho1));
86: PetscCall(VecCopy(R, P));
88: i = 0;
89: do {
90: PetscCall(KSP_PCApply(ksp, P, PH)); /* ph <- K p */
91: PetscCall(KSP_MatMult(ksp, mat, PH, V)); /* v <- A ph */
93: PetscCall(VecDot(V, RP, &rho2)); /* rho2 <- (v,rp) */
94: if (rho2 == 0.0) {
95: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "KSPSolve has not converged due to division by zero");
96: ksp->reason = KSP_DIVERGED_NANORINF;
97: break;
98: }
100: if (rho1 == 0) {
101: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "KSPSolve has stagnated");
102: ksp->reason = KSP_DIVERGED_BREAKDOWN; /* Stagnation */
103: break;
104: }
106: alpha = rho1 / rho2;
107: PetscCall(VecWAXPY(S, -alpha, V, R)); /* s <- r - alpha v */
109: /* First quasi-minimization step */
110: PetscCall(VecNorm(S, NORM_2, &F)); /* f <- norm(s) */
111: theta2 = F / tau;
113: c = 1.0 / PetscSqrtReal(1.0 + theta2 * theta2);
115: tau2 = tau * theta2 * c;
116: eta2 = c * c * alpha;
117: cf = theta * theta * eta / alpha;
118: PetscCall(VecWAXPY(D2, cf, D, PH)); /* d2 <- ph + cf d */
119: PetscCall(VecWAXPY(X2, eta2, D2, X)); /* x2 <- x + eta2 d2 */
121: /* Apply the right preconditioner again */
122: PetscCall(KSP_PCApply(ksp, S, SH)); /* sh <- K s */
123: PetscCall(KSP_MatMult(ksp, mat, SH, T)); /* t <- A sh */
125: PetscCall(VecDotNorm2(S, T, &uu, &vv));
126: if (vv == 0.0) {
127: PetscCall(VecDot(S, S, &uu));
128: if (uu != 0.0) {
129: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "KSPSolve has not converged due to division by zero");
130: ksp->reason = KSP_DIVERGED_NANORINF;
131: break;
132: }
133: PetscCall(VecAXPY(X, alpha, SH)); /* x <- x + alpha sh */
134: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
135: ksp->its++;
136: ksp->rnorm = 0.0;
137: ksp->reason = KSP_CONVERGED_RTOL;
138: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
139: PetscCall(KSPLogResidualHistory(ksp, dp));
140: PetscCall(KSPMonitor(ksp, i + 1, 0.0));
141: break;
142: }
143: PetscCall(VecNorm(V, NORM_2, &NV)); /* nv <- norm(v) */
145: if (NV == 0) {
146: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "KSPSolve has not converged due to singular matrix");
147: ksp->reason = KSP_DIVERGED_BREAKDOWN;
148: break;
149: }
151: if (uu == 0) {
152: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "KSPSolve has stagnated");
153: ksp->reason = KSP_DIVERGED_BREAKDOWN; /* Stagnation */
154: break;
155: }
156: omega = uu / vv; /* omega <- uu/vv; */
158: /* Computing the residual */
159: PetscCall(VecWAXPY(R, -omega, T, S)); /* r <- s - omega t */
161: /* Second quasi-minimization step */
162: if (ksp->normtype != KSP_NORM_NONE && ksp->chknorm < i + 2) PetscCall(VecNorm(R, NORM_2, &dp));
164: if (tau2 == 0) {
165: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "KSPSolve has not converged due to division by zero");
166: ksp->reason = KSP_DIVERGED_NANORINF;
167: break;
168: }
169: theta = dp / tau2;
170: c = 1.0 / PetscSqrtReal(1.0 + theta * theta);
171: if (dp == 0.0) {
172: PetscCall(VecNorm(R, NORM_2, &tau));
173: } else {
174: tau = dp;
175: }
176: tau = tau * c;
177: eta = c * c * omega;
179: cf1 = theta2 * theta2 * eta2 / omega;
180: PetscCall(VecWAXPY(D, cf1, D2, SH)); /* d <- sh + cf1 d2 */
181: PetscCall(VecWAXPY(X, eta, D, X2)); /* x <- x2 + eta d */
183: PetscCall(VecDot(R, RP, &rho2));
184: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
185: ksp->its++;
186: ksp->rnorm = dp;
187: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
188: PetscCall(KSPLogResidualHistory(ksp, dp));
189: PetscCall(KSPMonitor(ksp, i + 1, dp));
191: beta = (alpha * rho2) / (omega * rho1);
192: PetscCall(VecAXPBYPCZ(P, 1.0, -omega * beta, beta, R, V)); /* p <- r - omega * beta* v + beta * p */
193: rho1 = rho2;
194: PetscCall(KSP_MatMult(ksp, mat, X, AX)); /* Ax <- A x */
195: PetscCall(VecWAXPY(Z, -1.0, AX, B)); /* r <- b - Ax */
196: PetscCall(VecNorm(Z, NORM_2, &final));
197: PetscCall((*ksp->converged)(ksp, i + 1, dp, &ksp->reason, ksp->cnvP));
198: if (ksp->reason) break;
199: i++;
200: } while (i < ksp->max_it);
202: /* mark lack of convergence */
203: if (ksp->its >= ksp->max_it && !ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
204: PetscFunctionReturn(PETSC_SUCCESS);
205: }
207: /*MC
208: KSPQMRCGS - Implements the QMRCGStab method {cite}`chan1994qmrcgs` and Ghai, Lu, and Jiao (NLAA 2019).
210: Level: beginner
212: Note:
213: Only right preconditioning is supported.
215: Contributed by:
216: Xiangmin Jiao (xiangmin.jiao@stonybrook.edu)
218: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPBICG`, `KSPFBICGS`, `KSPBCGSL`, `KSPSetPCSide()`
219: M*/
220: PETSC_EXTERN PetscErrorCode KSPCreate_QMRCGS(KSP ksp)
221: {
222: KSP_BCGS *bcgs;
223: static const char citations[] = "@article{chan1994qmrcgs,\n"
224: " title={A quasi-minimal residual variant of the {Bi-CGSTAB} algorithm for nonsymmetric systems},\n"
225: " author={Chan, Tony F and Gallopoulos, Efstratios and Simoncini, Valeria and Szeto, Tedd and Tong, Charles H},\n"
226: " journal={SIAM Journal on Scientific Computing},\n"
227: " volume={15},\n"
228: " number={2},\n"
229: " pages={338--347},\n"
230: " year={1994},\n"
231: " publisher={SIAM}\n"
232: "}\n"
233: "@article{ghai2019comparison,\n"
234: " title={A comparison of preconditioned {K}rylov subspace methods for large-scale nonsymmetric linear systems},\n"
235: " author={Ghai, Aditi and Lu, Cao and Jiao, Xiangmin},\n"
236: " journal={Numerical Linear Algebra with Applications},\n"
237: " volume={26},\n"
238: " number={1},\n"
239: " pages={e2215},\n"
240: " year={2019},\n"
241: " publisher={Wiley Online Library}\n"
242: "}\n";
243: PetscBool cite = PETSC_FALSE;
245: PetscFunctionBegin;
246: PetscCall(PetscCitationsRegister(citations, &cite));
247: PetscCall(PetscNew(&bcgs));
249: ksp->data = bcgs;
250: ksp->ops->setup = KSPSetUp_QMRCGS;
251: ksp->ops->solve = KSPSolve_QMRCGS;
252: ksp->ops->destroy = KSPDestroy_BCGS;
253: ksp->ops->reset = KSPReset_BCGS;
254: ksp->ops->buildresidual = KSPBuildResidualDefault;
255: ksp->ops->setfromoptions = KSPSetFromOptions_BCGS;
256: ksp->pc_side = PC_RIGHT; /* set default PC side */
258: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2));
259: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));
260: PetscFunctionReturn(PETSC_SUCCESS);
261: }