Finite-difference derivatives of G3 phase Phi and phi w.r.t. shape params

Computes the G3 cumulative intensity, its time derivative, and their partial derivatives with respect to log_tau, gamma, alpha, and eta using central finite differences.

Usage

.hzr_g3_phase_derivatives(time, tau, gamma, alpha, eta, h = 1e-05)

Arguments

time

Numeric vector of positive times.

tau

Positive scalar scale parameter.

gamma

Positive scalar time exponent.

alpha

Non-negative scalar shape parameter.

eta

Positive scalar outer exponent.

h

Finite-difference step (default 1e-5). It is an ABSOLUTE step in log_tau, and so relative in tau only to first order; a relative step with a 1e-10 floor for gamma and eta; and strictly proportional for alpha. No caller passes it. Accuracy degrades where the function's natural scale in log_tau, roughly alpha / gamma, is far from 1: at alpha = 0.05, gamma = 4 the tau derivative is accurate to about 1e-6 rather than the 1e-11 it reaches for ordinary shapes.

Value

Named list with Phi, phi, and 8 derivative vectors.