Module jacobi

Numerical integration using the Gauss-Jacobi quadrature rule.

This rule can integrate expressions of the form (1 - x)^alpha * (1 + x)^beta * f(x), where f(x) is a smooth function on a finite domain, alpha > -1 and beta > -1, and where f(x) is transformed from the domain [a, b] to the domain [-1, 1]. This enables the approximation of integrals with singularities at the end points of the domain.

Example

use gauss_quad::jacobi::GaussJacobi;
use approx::assert_abs_diff_eq;

let quad = GaussJacobi::new(10, 0.0, -1.0 / 3.0)?;

// numerically integrate sin(x) / (1 + x)^(1/3), a function with a singularity at x = -1.
let integral = quad.integrate(-1.0, 1.0, |x| x.sin());

assert_abs_diff_eq!(integral, -0.4207987746500829, epsilon = 1e-14);

Structs

• GaussJacobi
  A Gauss-Jacobi quadrature scheme.
• GaussJacobiError
  The error returned by GaussJacobi::new if given a degree, deg, less than 2 and/or an alpha and/or beta less than or equal to -1.
• GaussJacobiIntoIter
  An owning iterator over the node-weight pairs of the quadrature rule.
• GaussJacobiIter
  An iterator over the node-weight pairs of the quadrature rule.
• GaussJacobiNodes
  An iterator over the nodes of the quadrature rule.
• GaussJacobiWeights
  An iterator over the weights of the quadrature rule.

Enums

• GaussJacobiErrorReason
  The reason for the GaussJacobiError, returned by the GaussJacobiError::reason function.