Struct MeasureIntegral 

pub struct MeasureIntegral;

Numerical Lebesgue integration using midpoint-rule quadrature.

For a function f: ℝⁿ → ℝ on a box domain, the integral is approximated by subdividing each dimension into n_pts sub-intervals.

Implementations

impl MeasureIntegral

pub fn integrate_1d(f: &dyn Fn(f64) -> f64, a: f64, b: f64, n: usize) -> f64

Integrate f over a 1-D interval [a, b] using n midpoint sub-intervals.

pub fn integrate_2d( f: &dyn Fn(f64, f64) -> f64, a: f64, b: f64, c: f64, d: f64, n: usize, ) -> f64

Integrate f over a 2-D rectangle using n × n midpoint sub-intervals.

pub fn integrate_nd( f: &dyn Fn(&[f64]) -> f64, lower: &[f64], upper: &[f64], n_pts: usize, ) -> f64

Integrate f over an n-D box using midpoint quadrature.

The box is given as lower and upper vectors; n_pts sub-intervals per dimension. This has exponential cost in the dimension.

pub fn monte_carlo( f: &dyn Fn(&[f64]) -> f64, lower: &[f64], upper: &[f64], n_samples: usize, ) -> f64

Monte Carlo integration of f over an n-D box.

Produces an unbiased estimate with standard error O(1/√n).

pub fn importance_sampling( f: &dyn Fn(f64) -> f64, proposal_sample: &dyn Fn() -> f64, proposal_density: &dyn Fn(f64) -> f64, n_samples: usize, ) -> f64

Importance-sampling Monte Carlo: ∫ f dx = ∫ (f/g) · g dx.

Samples are drawn from the proposal density g (given as CDF inverse) and the estimate is (1/n) Σ f(xᵢ) / g(xᵢ).

pub fn riemann_stieltjes( f: &dyn Fn(f64) -> f64, g: &dyn Fn(f64) -> f64, a: f64, b: f64, n: usize, ) -> f64

Compute the Riemann–Stieltjes-style integral ∫ f dG numerically.

Approximates Σ f(xᵢ) · (G(xᵢ₊₁) − G(xᵢ)) over n sub-intervals.

pub fn monte_carlo_std_error( f: &dyn Fn(&[f64]) -> f64, lower: &[f64], upper: &[f64], n_samples: usize, ) -> (f64, f64)

Estimate the standard error of a Monte Carlo integral estimate.