Quadrature integration

Standard library

clenshaw_curtis(order[, domain, growth, ...])

Generate the quadrature nodes and weights in Clenshaw-Curtis quadrature.

fejer_1(order[, domain, growth, segments])

Generate the quadrature abscissas and weights in Fejér type I quadrature.

fejer_2(order[, domain, growth, segments])

Generate the quadrature abscissas and weights in Fejér type II quadrature.

gaussian(order, dist[, ...])

Create Gaussian quadrature nodes and weights.

grid(order[, domain, growth, segments])

Generate the quadrature abscissas and weights for simple grid.

legendre_proxy(order[, domain, segments])

Generate proxy abscissas and weights from Legendre quadrature.

leja(order, dist[, rule])

Generate Leja quadrature node.

newton_cotes(order[, domain, growth, segments])

Generate the abscissas and weights in Newton-Cotes quadrature.

Discrete densities

discrete(order[, domain, growth])

Generate quadrature abscissas and weights for discrete distributions.

Gaussian extensions

genz_keister_16(order[, dist])

Create Genz-Keister variant 16 quadrature nodes and weights.

genz_keister_18(order[, dist])

Create Genz-Keister variant 18 quadrature nodes and weights.

genz_keister_22(order[, dist])

Create Genz-Keister variant 22 quadrature nodes and weights.

genz_keister_24(order[, dist])

Create Genz-Keister variant 24 quadrature nodes and weights.

legendre(order[, lower, upper, physicist])

Gauss-Legendre quadrature rule.

kronrod(order, dist[, recurrence_algorithm, ...])

Generate Gauss-Kronrod quadrature abscissas and weights.

lobatto(order, dist[, recurrence_algorithm, ...])

Generate the abscissas and weights in Gauss-Loboto quadrature.

patterson(order, domain)

Generate Gauss-Patterson quadrature abscissa and weights.

radau(order, dist[, fixed_point, ...])

Generate the quadrature nodes and weights in Gauss-Radau quadrature.

Predefined Gaussian

chebyshev_1(order[, lower, upper, physicist])

Chebyshev-Gauss quadrature rule of the first kind.

chebyshev_2(order[, lower, upper, physicist])

Chebyshev-Gauss quadrature rule of the second kind.

gegenbauer(order, alpha[, lower, upper, ...])

Gauss-Gegenbauer quadrature rule.

hermite(order[, mu, sigma, physicist])

Gauss-Hermite quadrature rule.

jacobi(order, alpha, beta[, lower, upper, ...])

Gauss-Jacobi quadrature rule.

legendre(order[, lower, upper, physicist])

Gauss-Legendre quadrature rule.

laguerre(order[, alpha, physicist])

Generalized Gauss-Laguerre quadrature rule.

Helper functions

sparse_grid(order, dist[, growth, ...])

Smolyak sparse grid constructor.

kronrod_jacobi(order, coeffs)

Create the three-terms-recursion coefficients resulting from the Kronrod-Jacobi matrix.