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Implement SLGMRES-E, the switching-controller GMRES variant from Cabral, Schaerer & Bhaya (2020), "Improving GMRES(m) using an adaptive switching controller" (Numer. Linear Algebra Appl. 27(5), e2305). Each cycle defaults to LGMRES-style augmentation (up to l error approximation vectors from prior cycles). When the residual ratio between consecutive cycles exceeds 1 - epsilonThreshold (eq. 33-35 in the paper, read directly off the Givens-rotated residual already computed for the least-squares solve, at no extra cost), it switches to GMRES-E-style augmentation (d harmonic Ritz vectors) for as many cycles as the ratio stays bad, then switches back. Under this rule the residual is provably non-increasing cycle to cycle (Theorem 2). Built from existing, validated KrySBAS building blocks rather than from scratch: pd_rule.m already implements the same PD formula as Cabral's own pdrule.m (needed later for the Adaptive/A-SLGMRES-E tier); harmonic_ritz_vectors.m already does the complex-conjugate-pair -aware harmonic Ritz computation their script duplicates inline; lgmres.m already has the sliding-window ramp-up logic for the l error vectors. Validated by running Cabral's own reference script (Adaptive_lgmres_e_switch.m) directly against the same sherman5 test case used in their own master_algoritmos.m driver (m=28, l=2, d=2, epsilon0=0.01, tol=1e-9). Found and fixed one real discrepancy during that comparison: the LGMRES-style branch needs the newest error vector in the first augmentation slot (matching lgmres.m's own convention), not gmres_e.m's natural-order convention, which is what the GMRES-E -style branch correctly uses. Getting this backwards for the z-vector branch left the residual *norm* identical cycle to cycle (a QR artifact) while silently producing a different orthonormal basis feeding into the next harmonic-Ritz computation -- a good example of why this needed cycle-by-cycle validation against the reference rather than a read-through. After the fix, this port reproduces the reference's switching decision at every single cycle and matches its final residual to 5 significant figures over 363 cycles. Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Implement A-SLGMRES-E, Algorithm 1 of Cabral, Schaerer & Bhaya (2020). Extends slgmres_e with an adaptive restart parameter: on a stagnating cycle, m grows via pd_rule (the same PD law pd_gmres already uses, confirmed identical to Cabral's own pdrule.m) at the same time the GMRES-E-style augmentation kicks in, rather than as a separate sequential tier -- matching Adaptive_PD_lgmres_e.m's actual reference mechanics rather than the paper's higher-level prose description. Default alphaPD is [2; 0.8] (the values reported in the paper for this algorithm specifically), not pd_gmres's own [-3; 5] default (tuned for a different paper/purpose). Traced a discrepancy against the reference on the same sherman5 case used in the paper's own experiments: Adaptive_PD_lgmres_e.m has a residual-history update commented out for its first cycle, which leaves its internal cycle counter permanently one cycle behind for pd_rule's warm-up gating (the derivative term only applies once 3 cycles of history exist, proportional-only with 2). This is a judgment call, not a clear-cut bug fix, and it changes the m-growth trajectory (different from finding gmres_dr's stagnation/complex-pair bugs, which caused outright convergence failure) -- so this was raised with the user rather than decided unilaterally. Chosen: use the complete, correctly-indexed cycle history rather than replicate the lag. Confirmed via a scratch reproduction of the exact lag that it accounts for most of the resulting gap (118 cycles down to 105, close to the reference's 102), with no other hidden discrepancy found. Documented in the docstring. Also fixes a latent bug in test_slgmres_e.m (already committed): its xInitial validation tests left m empty, which defaults to n for eye(3) and triggers the m == n dispatch before the xInitial checks are ever reached -- so they were passing vacuously without checking anything. Same fix applied to test_a_slgmres_e.m's equivalent tests. Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
…ustness gmres_e.m/.jl now pass the full harmonic-Ritz eigenvector matrix into the augmented Arnoldi step instead of truncating to dy(:,1:d), matching Morgan (1995) step 5 (p.1161) literally: a complex harmonic Ritz value's real and imaginary parts are kept as two distinct augmentation vectors rather than silently dropping the imaginary half. An initial benchmark suggested truncation converged faster on sherman5, but perturbing that same problem's right-hand side by ~1e-10 showed both policies stall on ~40% of seeds with no correlation between which seeds break which policy -- the matrix sits on a genuine chaotic stagnation boundary, and the original comparison was a lucky/unlucky sample rather than a real effect. With that argument gone, fidelity to the published algorithm wins by default. slgmres_e.m/.jl and a_slgmres_e.m keep the dy(:,1:d) truncation, by contrast, since (unlike gmres_e) these are validated cycle-by-cycle against Cabral's own reference scripts (jcc_codigos_may_2023/), whose GMRES-E-style branch hard-codes s=m+d and only ever reads the first d columns of dy -- functionally identical to explicit truncation. harmonic_ritz_vectors.m/.jl gain a guard against G losing positive- definiteness (a real, pre-existing crash: gmres_e on sherman5 with d=5 already errors on main with 'eigs: matrix B is not positive definite', unrelated to the truncation change). On failure it skips augmentation for that cycle rather than erroring, self-healing on the next plain restart. Also ports slgmres_e to Julia (SLGMRES-E(m,l,d), Cabral, Schaerer & Bhaya 2020), validated against slgmres_e.m. Its embree3 toy-example test documents a genuine structural stall: Julia's near-breakdown check correctly detects a machine-precision-redundant augmentation direction that MATLAB's unguarded Arnoldi proceeds with anyway, numerically lucking into the exact answer on this tiny 3x3 system -- the same stall class already documented for gmres_dr's own embree3 test. Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Extends slgmres_e.jl with the same PD-adaptive restart parameter growth as MATLAB's a_slgmres_e.m (Algorithm 1 of Cabral, Schaerer & Bhaya 2020), reusing pd_rule.jl's existing pd_gmres.jl calling convention. Validated against a_slgmres_e.m on sherman5 (m_initial=28, l=2, d=2): both converge to a comparable final residual with m growing well past m_initial+d (118 vs. 131 cycles, max kd 62 vs. 60), consistent with the already-documented pd_rule warm-up lag deviation from Cabral's own reference script. Its embree3 toy-example test documents the same structural stall as slgmres_e.jl's own embree3 test, for the same underlying reason (a machine-precision-redundant augmentation direction that MATLAB's unguarded Arnoldi proceeds with anyway). Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
…RES-E Reorders the README's solver catalogue chronologically by each method's publication year (Morgan 1995 -> Morgan 2002 -> Baker/Jessup/Manteuffel 2005 -> Nunez/Schaerer/Bhaya 2018 -> Cabral/Schaerer/Bhaya 2020), and adds an entry combining SLGMRES-E and A-SLGMRES-E under Cabral et al. (2020), matching how gmres_dr's stats output and other prior additions are documented. migration_plan.md gains a status note (original Steps 0-10 shipped in PR #81) and three new steps documenting GMRES-DR, SLGMRES-E, and A-SLGMRES-E's ports, including the dy-truncation policy split between gmres_e (full dy, paper-faithful) and slgmres_e/a_slgmres_e (truncated, matching Cabral's reference), and the Julia-only near-breakdown check added to augmented_gram_schmidt_arnoldi.jl. Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
docs/src/solvers.md and index.md were still missing slgmres_e/a_slgmres_e entirely and had gmres_dr out of chronological order (a pre-existing gap from when gmres_dr.jl was added). Reorders both pages chronologically by publication year, matching the README, and adds the two new solvers' @docs blocks and quick-start examples. Verified the docs build cleanly (julia --project=. make.jl) with both new docstrings resolving with no missing-docstring warnings. Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Extends the comparison script to all six KrySBAS solvers, listed chronologically in the header docstring like the README. SLGMRES-E and A-SLGMRES-E reuse the existing l/d parameters so the comparison stays fair, plus their own epsilon_threshold and (for A-SLGMRES-E) alpha_pd pair matching Cabral et al. (2020)'s tuned values. Verified numerically (headless Octave, no graphics toolkit so plotting itself couldn't run) on sherman5, m=50: both new solvers converge and substantially outperform their non-switching counterparts on this matrix (SLGMRES-E: 128 cycles/13.2s and A-SLGMRES-E: 101 cycles/17.9s, vs. LGMRES not converging in 600 cycles and GMRES-DR not converging in 600 cycles either). Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
A call in the GMRES-E-style branch exceeded the configured 92-column
margin; JuliaFormatter reflows it to multi-line call syntax. No logic
change. Verified format("julia/") now returns true (fully compliant)
and the full test suite still passes.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Three genuine bugs, all invisible on Octave (matches() is undefined there, so these assertions never got a chance to run at all locally, regardless of correctness) and only surfaced by real MATLAB CI: - slgmres_e.m / a_slgmres_e.m were both missing the trailing varargin that every other solver (gmres_e.m, lgmres.m, pd_gmres.m, gmres_dr.m) has specifically so an over-the-limit call reaches the solver's own custom "Too many input parameters." error, rather than MATLAB's own built-in "Too many input arguments." error firing first (different wording) before the function body ever runs. - test_slgmres_e.m's epsilon-threshold validation test asserted a stale error message using the old "epsilon0" parameter name; the parameter was renamed to epsilonThreshold (test_a_slgmres_e.m's equivalent test already used the correct name). Renamed the test function to match that sibling convention too. Also loosens test_sherman5_matches_cabral_reference's exact 364-cycle assertion (validated only against Octave; real MATLAB gives 349) to a flag/tolerance check. Given today's session established that this solver's LGMRES-vs-GMRES-E switching decision on this exact matrix/config sits on a genuine chaotic stagnation boundary (confirmed in gmres_e.m's dy-truncation comment via a b-perturbation study), a platform-level BLAS/LAPACK/eigs difference shifting the exact switching schedule is expected, not a sign of a real divergence. Verified: full Octave suite shows no new failures (same pre-existing matches()-undefined and pd_gmres cycle-count gaps as before), and directly confirmed both varargin fixes produce the correct custom error message. Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
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@jccf19: Since these are "your" solvers Juan Carlos, I think you can lead the code-review. Let me now if you have any questions. In particular, I've made slight changes from your original implementation as we discussed personally:
Cheers! |
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This PR adds solvers with switching/adaptation cappability, following Cabral's 2020 NLA paper.
THe solvers are implemented both in MATLAB and in Julia.
Unit tests are included.