quadgk: Adaptive Gauss-Kronrod Quadrature

Description

Adaptive Gauss-Kronrod Quadrature.

Usage

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

Arguments

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.

Examples

Run this code

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