Multidimensional integration.

Adaptive integration of a multivariate function on a hyperrectangle.

adaptive-cubature

Adaptive integration of a multivariate function on an axis-aligned hyperrectangle.

This package is powered by the C library cubature. Follow the link for details.

Usage

cubature :: Char                 -- ^ cubature version, 'h' or 'p'
         -> ([Double] -> Double) -- ^ integrand
         -> Int                  -- ^ dimension (number of variables)
         -> [Double]             -- ^ lower limits of integration
         -> [Double]             -- ^ upper limits of integration
         -> Double               -- ^ desired relative error
         -> IO Result            -- ^ output: integral value and error estimate

Example

fExample :: [Double] -> Double
fExample x = exp (-0.5 * (sum $ zipWith (*) x x))

example :: IO Result -- should give 2pi ≈ 6.283185307179586
example = cubature 'h' fExample 2 [-6, -6] [6, 6] 1e-10 
-- Result {_integral = 6.283185282383672, _error = 6.280185128024888e-10}