pracma (version 1.2.0)

quadgk: Adaptive Gauss-Kronrod Quadrature

Description

Adaptive Gauss-Kronrod Quadrature.

Usage

quadgk(f, a, b, tol = .Machine$double.eps^0.5, ...)

Arguments

f

integrand as function, may have singularities at the endpoints.

a, b

endpoints of the integration interval.

tol

relative tolerence.

...

Additional parameters to be passed to the function f.

Value

• Value of the integration. The relative error should be of the same order of magnitude as the relative tolerance (or much smaller).

Details

Adaptive version of the (7, 15)-point Gauss-Kronrod quadrature formula, where in each recursion the error is taken as the difference between these two estimated integrals.

See Also

gauss_kronrod

Examples

##  Dilogarithm function
flog <- function(t) log(1-t)/t
quadgk(flog, 1, 0, tol = 1e-12)
# 1.644934066848128 - pi^2/6 < 1e-13