Function get_e2 

pub fn get_e2(a: f64, b: f64, w: f64, h1: f64, h2: f64, alpha_s: f64) -> f64

Computes the effect metric for a dual-site pharmacodynamic model.

This function calculates the maximum effect for a model where two binding sites contribute to the overall effect. The effect is computed as xm / (xm + 1) where xm is the optimal concentration that maximizes the combined effect from both sites.

Model Description

The underlying model assumes the total effect is:

Effect = a / xm^h1 + b / xm^h2 + w / xm^((h1+h2)/2)

where:

• a and b are the coefficients for the two binding sites
• h1 and h2 are the Hill coefficients for each site
• w is a cross-interaction term
• xm is the concentration

The function finds the optimal xm that makes this sum equal to 1, then returns the corresponding effect value xm / (xm + 1).

Arguments

• a - Coefficient for the first binding site (typically positive)
• b - Coefficient for the second binding site (typically positive)
• w - Cross-interaction term between the two sites
• h1 - Hill coefficient for the first binding site
• h2 - Hill coefficient for the second binding site
• alpha_s - Scaling factor used in the fallback numerical estimator

Returns

The E2 effect value in the range [0, 1), representing the maximum achievable effect. Returns 0.0 if both a and b are essentially zero.

Algorithm

1. If both coefficients are near zero, returns 0.0
2. If only one coefficient is positive, uses a closed-form solution
3. Otherwise, uses Nelder-Mead optimization in log-space to find the optimal xm
4. Falls back to an iterative numerical estimator if optimization fails to converge

Example

use pharmsol::get_e2;

// Single-site model (b = 0)
let e2 = get_e2(1.0, 0.0, 0.0, 1.0, 1.0, 0.5);
assert!((e2 - 0.5).abs() < 1e-6); // xm = 1, so E2 = 1/(1+1) = 0.5

// Dual-site model
let e2 = get_e2(1.0, 1.0, 0.0, 1.0, 2.0, 0.5);
assert!(e2 > 0.0 && e2 < 1.0);