GFT - Generalized Fisher Transformation of Correlation Matrices

Forward and inverse generalized Fisher transformation (GFT) of correlation matrices, gamma = vecl(log C), which maps the positive definite correlation matrices one-to-one onto the Euclidean space of dimension n(n-1)/2, see Archakov and Hansen (2021) <doi:10.3982/ECTA16910>. The inverse is computed from a variational characterization by the GFT-FP+N algorithm: matrix-free inexact Newton steps for the log-diagonal residual, solved by preconditioned conjugate gradients, with fixed-point safeguards that guarantee global convergence. Sequential inversion with a tangent predictor, a certified quadrature preconditioner, and comparison solvers (the plain fixed point, Broyden's method, full Newton, Anderson acceleration, and limited-memory BFGS) are included. Uses base R only.