Module numerical 

Numerical utilities for copula computations.

This module provides various numerical methods useful for copula analysis:

• Numerical integration (trapezoidal rule, Simpson’s rule)
• Root finding (bisection, Brent’s method)
• Numerical differentiation
• Interpolation methods

Example

use copula_core::numerical::{bisection, trapezoid_integrate};

// Find root of f(x) = x^2 - 2 on [0, 2]
let root = bisection(|x| x * x - 2.0, 0.0, 2.0, 1e-10, 100).unwrap();
assert!((root - 2.0_f64.sqrt()).abs() < 1e-9);

// Integrate f(x) = x^2 from 0 to 1
let integral = trapezoid_integrate(|x| x * x, 0.0, 1.0, 1000);
assert!((integral - 1.0/3.0).abs() < 1e-6);

Functions

bisection

Find a root of f(x) = 0 using the bisection method.

central_diff

Numerical derivative using central difference (more accurate).

forward_diff

Numerical derivative using forward difference.

linear_interp

Linear interpolation between two points.

log_sum_exp

Compute the log-sum-exp trick for numerical stability.

second_diff

Second derivative using central difference.

simpson_integrate

Numerical integration using Simpson’s rule.

trapezoid_integrate

Numerical integration using the trapezoidal rule.