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The version number now matches the Julia reference implementation (github.com/reinhardhansen/GFT, tag v1.2.0), which this release ports function for function.
inv_gft()inv_gft() now implements the revised GFT-FP+N of the
paper (Archakov and Hansen, 2026, arXiv:2609.19028): Newton steps for
the log-diagonal residual (H delta = -D ell instead of
H delta = -g), forcing tolerance
min(1/2, ||ell||) (locally quadratic), exact normalization
of every evaluated point along the vector of ones, no initial
fixed-point phase, an adaptive initial Armijo step, and a descent test
before the untested-step rule. Median eigendecomposition counts fall by
about 40% on ill-conditioned inputs and by two or three on
well-conditioned ones; solutions are unchanged.residual, forcing, normalize,
phase and adaptive
(residual = "gradient", forcing = "sqrt", normalize = FALSE, phase = TRUE, adaptive = FALSE).preconditioner: "quadrature"
or "auto" replaces the diagonal preconditioner of the
conjugate-gradient solve by a quadrature model of the Hessian with a
certified condition-number bound; "auto" applies the
paper’s selection rule.inv_gft_anderson(): Anderson acceleration of the fixed
point, with a guarded option that makes it globally
convergent.inv_gft_lbfgs(): limited-memory BFGS on the
objective.inv_gft_path() and gft_predict():
sequential inversion with warm starts and a tangent predictor.inv_gft_newton() gains a safeguard
argument, default TRUE. The new default fixes the stall
described below. safeguard = FALSE reproduces the previous
behaviour, which is the published comparator of Chen, Fei and Yu (2025)
with only the Armijo line search added, and is the variant benchmarked
in the accompanying paper. Set it when reproducing those
results.
With the new default, inv_gft_newton() no longer
stalls short of the requested tolerance and returns
converged = FALSE on a small fraction of well conditioned
problems. Close to the solution the objective
f = tr(exp(A)) - sum(x) is flat to within cancellation, so
the Armijo test carries no information; the line search then exhausted
all of its halvings at every iteration, the fixed-point fallback was
taken instead, and the error could lock at a constant value several
orders of magnitude above the attainable floor until maxit
was reached. Two safeguards that inv_gft() already used
have been added: the full Newton step is now taken untested once the
predicted decrease falls below the floating-point resolution of
f, and a persistent lack of progress near the rounding
floor hands the iteration to the (contractive) fixed point.
In a sweep over random correlation matrices at n = 10, the failure rate falls from about 5% to 0, and the worst-case cost from 12,375 eigendecompositions to 6.
The defect was present on all platforms and is not specific to any BLAS or LAPACK build; it surfaced on CRAN’s ATLAS check because that arithmetic moved one test matrix into the affected set.
inv_gft(), inv_gft_fp() and
inv_gft_broyden() are unchanged. Their results are
unaffected by this release.
DESCRIPTION, as requested by the CRAN reviewer. Single
quotes are now used only for software names.These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.