inv_gft_fp: Inverse GFT by the Archakov-Hansen Fixed Point

In GFT: Generalized Fisher Transformation of Correlation Matrices

Inverse GFT by the Archakov-Hansen Fixed Point

Description

Reconstructs the correlation matrix C with \mathrm{vecl}(\log C) = z by the fixed-point iteration of Archakov and Hansen (2021), x \leftarrow x - \log \mathrm{diag}(e^{A[x;z]}), evaluated in the log domain throughout.

Usage

inv_gft_fp(z, x0 = NULL, tol = 1e-13, maxit = 5000)

Arguments

z	numeric vector of length n(n-1)/2.
x0	optional starting value of length n; defaults to zero.
tol	convergence tolerance on \|\mathrm{diag}(e^A) - 1\|_\infty.
maxit	maximum number of iterations.

Details

Globally convergent, with one eigendecomposition per iteration. The local linear rate degrades as the spectrum of C spreads; inv_gft switches to an inexact Newton phase precisely to avoid this slowdown while retaining the fixed point's robustness.

Value

An object of class "gft_inv"; see inv_gft for the components.

References

Archakov, I. and Hansen, P. R. (2021). A new parametrization of correlation matrices. Econometrica, 89(4), 1699–1715. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3982/ECTA16910")}

See Also

inv_gft.

Examples

z <- gft(0.9^abs(outer(1:5, 1:5, "-")))
r <- inv_gft_fp(z)
r$eighs

GFT documentation built on Aug. 23, 2026, 5:10 p.m.