Actual source code: tcqmr.c
1: /*
2: This file contains an implementation of Tony Chan's transpose-free QMR.
4: Note: The vector dot products in the code have not been checked for the
5: complex numbers version, so most probably some are incorrect.
6: */
8: #include <../src/ksp/ksp/impls/tcqmr/tcqmrimpl.h>
10: static PetscErrorCode KSPSolve_TCQMR(KSP ksp)
11: {
12: PetscReal rnorm0, rnorm, dp1, Gamma;
13: PetscScalar theta, ep, cl1, sl1, cl, sl, sprod, tau_n1, f;
14: PetscScalar deltmp, rho, beta, eptmp, ta, s, c, tau_n, delta;
15: PetscScalar dp11, dp2, rhom1, alpha, tmp;
17: PetscFunctionBegin;
18: ksp->its = 0;
20: PetscCall(KSPInitialResidual(ksp, x, u, v, r, b));
21: PetscCall(VecNorm(r, NORM_2, &rnorm0)); /* rnorm0 = ||r|| */
22: KSPCheckNorm(ksp, rnorm0);
23: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = rnorm0;
24: else ksp->rnorm = 0;
25: PetscCall((*ksp->converged)(ksp, 0, ksp->rnorm, &ksp->reason, ksp->cnvP));
26: if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);
28: PetscCall(VecSet(um1, 0.0));
29: PetscCall(VecCopy(r, u));
30: rnorm = rnorm0;
31: tmp = 1.0 / rnorm;
32: PetscCall(VecScale(u, tmp));
33: PetscCall(VecSet(vm1, 0.0));
34: PetscCall(VecCopy(u, v));
35: PetscCall(VecCopy(u, v0));
36: PetscCall(VecSet(pvec1, 0.0));
37: PetscCall(VecSet(pvec2, 0.0));
38: PetscCall(VecSet(p, 0.0));
39: theta = 0.0;
40: ep = 0.0;
41: cl1 = 0.0;
42: sl1 = 0.0;
43: cl = 0.0;
44: sl = 0.0;
45: sprod = 1.0;
46: tau_n1 = rnorm0;
47: f = 1.0;
48: Gamma = 1.0;
49: rhom1 = 1.0;
51: /*
52: CALCULATE SQUARED LANCZOS vectors
53: */
54: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = rnorm;
55: else ksp->rnorm = 0;
56: PetscCall((*ksp->converged)(ksp, ksp->its, ksp->rnorm, &ksp->reason, ksp->cnvP));
57: while (!ksp->reason) {
58: PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm));
59: ksp->its++;
61: PetscCall(KSP_PCApplyBAorAB(ksp, u, y, vtmp)); /* y = A*u */
62: PetscCall(VecDot(y, v0, &dp11));
63: KSPCheckDot(ksp, dp11);
64: PetscCall(VecDot(u, v0, &dp2));
65: alpha = dp11 / dp2; /* alpha = v0'*y/v0'*u */
66: deltmp = alpha;
67: PetscCall(VecCopy(y, z));
68: PetscCall(VecAXPY(z, -alpha, u)); /* z = y - alpha u */
69: PetscCall(VecDot(u, v0, &rho));
70: beta = rho / (f * rhom1);
71: rhom1 = rho;
72: PetscCall(VecCopy(z, utmp)); /* up1 = (A-alpha*I)*
73: (z-2*beta*p) + f*beta*
74: beta*um1 */
75: PetscCall(VecAXPY(utmp, -2.0 * beta, p));
76: PetscCall(KSP_PCApplyBAorAB(ksp, utmp, up1, vtmp));
77: PetscCall(VecAXPY(up1, -alpha, utmp));
78: PetscCall(VecAXPY(up1, f * beta * beta, um1));
79: PetscCall(VecNorm(up1, NORM_2, &dp1));
80: KSPCheckNorm(ksp, dp1);
81: f = 1.0 / dp1;
82: PetscCall(VecScale(up1, f));
83: PetscCall(VecAYPX(p, -beta, z)); /* p = f*(z-beta*p) */
84: PetscCall(VecScale(p, f));
85: PetscCall(VecCopy(u, um1));
86: PetscCall(VecCopy(up1, u));
87: beta = beta / Gamma;
88: eptmp = beta;
89: PetscCall(KSP_PCApplyBAorAB(ksp, v, vp1, vtmp));
90: PetscCall(VecAXPY(vp1, -alpha, v));
91: PetscCall(VecAXPY(vp1, -beta, vm1));
92: PetscCall(VecNorm(vp1, NORM_2, &Gamma));
93: KSPCheckNorm(ksp, Gamma);
94: PetscCall(VecScale(vp1, 1.0 / Gamma));
95: PetscCall(VecCopy(v, vm1));
96: PetscCall(VecCopy(vp1, v));
98: /*
99: SOLVE Ax = b
100: */
101: /* Apply last two Given's (Gl-1 and Gl) rotations to (beta,alpha,Gamma) */
102: if (ksp->its > 2) {
103: theta = sl1 * beta;
104: eptmp = -cl1 * beta;
105: }
106: if (ksp->its > 1) {
107: ep = -cl * eptmp + sl * alpha;
108: deltmp = -sl * eptmp - cl * alpha;
109: }
110: if (PetscAbsReal(Gamma) > PetscAbsScalar(deltmp)) {
111: ta = -deltmp / Gamma;
112: s = 1.0 / PetscSqrtScalar(1.0 + ta * ta);
113: c = s * ta;
114: } else {
115: ta = -Gamma / deltmp;
116: c = 1.0 / PetscSqrtScalar(1.0 + ta * ta);
117: s = c * ta;
118: }
120: delta = -c * deltmp + s * Gamma;
121: tau_n = -c * tau_n1;
122: tau_n1 = -s * tau_n1;
123: PetscCall(VecCopy(vm1, pvec));
124: PetscCall(VecAXPY(pvec, -theta, pvec2));
125: PetscCall(VecAXPY(pvec, -ep, pvec1));
126: PetscCall(VecScale(pvec, 1.0 / delta));
127: PetscCall(VecAXPY(x, tau_n, pvec));
128: cl1 = cl;
129: sl1 = sl;
130: cl = c;
131: sl = s;
133: PetscCall(VecCopy(pvec1, pvec2));
134: PetscCall(VecCopy(pvec, pvec1));
136: /* Compute the upper bound on the residual norm r (See QMR paper p. 13) */
137: sprod = sprod * PetscAbsScalar(s);
138: rnorm = rnorm0 * PetscSqrtReal((PetscReal)ksp->its + 2.0) * PetscRealPart(sprod);
139: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = rnorm;
140: else ksp->rnorm = 0;
141: PetscCall((*ksp->converged)(ksp, ksp->its, ksp->rnorm, &ksp->reason, ksp->cnvP));
142: if (ksp->its >= ksp->max_it) {
143: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
144: break;
145: }
146: }
147: PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm));
148: PetscCall(KSPUnwindPreconditioner(ksp, x, vtmp));
149: PetscFunctionReturn(PETSC_SUCCESS);
150: }
152: static PetscErrorCode KSPSetUp_TCQMR(KSP ksp)
153: {
154: PetscFunctionBegin;
155: PetscCall(KSPSetWorkVecs(ksp, TCQMR_VECS));
156: PetscFunctionReturn(PETSC_SUCCESS);
157: }
159: /*MC
160: KSPTCQMR - A variant of QMR (quasi minimal residual) {cite}`chan1998transpose`
162: Level: beginner
164: Notes:
165: Supports either left or right preconditioning, but not symmetric
167: The "residual norm" computed in this algorithm is actually just an upper bound on the actual residual norm.
168: That is for left preconditioning it is a bound on the preconditioned residual and for right preconditioning
169: it is a bound on the true residual.
171: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPTFQMR`
172: M*/
174: PETSC_EXTERN PetscErrorCode KSPCreate_TCQMR(KSP ksp)
175: {
176: PetscFunctionBegin;
177: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
178: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2));
179: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));
181: ksp->data = (void *)0;
182: ksp->ops->buildsolution = KSPBuildSolutionDefault;
183: ksp->ops->buildresidual = KSPBuildResidualDefault;
184: ksp->ops->setup = KSPSetUp_TCQMR;
185: ksp->ops->solve = KSPSolve_TCQMR;
186: ksp->ops->destroy = KSPDestroyDefault;
187: ksp->ops->setfromoptions = NULL;
188: ksp->ops->view = NULL;
189: PetscFunctionReturn(PETSC_SUCCESS);
190: }