Module numerical_integration 

Numerical integration methods.

Provides composite trapezoid, composite Simpson, Romberg integration, Gauss-Legendre quadrature (5-point and variable-point), adaptive Simpson, Monte Carlo integration, Clenshaw-Curtis, double-exponential (tanh-sinh), and multidimensional trapezoid rules.

Structs

QuadratureRule

A generic quadrature rule defined by nodes and weights on a reference interval.

Functions

adaptive_simpson

Approximate ∫ f(x) dx on [a, b] using recursive adaptive Simpson’s rule.

clenshaw_curtis

Approximate ∫_{-1}^{1} f(x) dx using Clenshaw-Curtis quadrature with n+1 points.

double_exponential

Approximate ∫ f(x) dx on [a, b] using the tanh-sinh (double exponential) transform.

gauss_legendre_5pt

Approximate ∫ f(x) dx on [a, b] using the 5-point Gauss-Legendre formula.

gauss_legendre_nodes_weights

Return the Gauss-Legendre nodes and weights for n points on [-1, 1].

monte_carlo_integrate

Approximate ∫ f(x) dx on [a, b] using Monte Carlo sampling with n_samples points.

multidimensional_trap

Approximate ∫ f(x) dx over a hyperrectangle using the composite trapezoid rule.

romberg_integration

Approximate ∫ f(x) dx on [a, b] using Romberg integration (Richardson extrapolation).

simpson_rule

Approximate ∫ f(x) dx on [a, b] using composite Simpson’s rule with n subintervals.

trapezoid_rule

Approximate ∫ f(x) dx on [a, b] using the composite trapezoid rule with n subintervals.