Hello,
I have uploaded two new packages to Hackage:
Let me also mention another package of mine, older, for integration on a simplex: scubature (pure Haskell implementation).
I wonder how it compares to the integration package. I assume it has better performance and/or precision?
Ah this is “tanh-sinh”. Yes, numerical-integration is probably better. I experimented it in R (package RcppNumerical) and it gives good results even for highly oscillatory functions.
You gave my an idea: it would be interesting to compare the two packages on a couple of functions. Maybe I’ll do it.
Here are two functions whose integral is hard to compute, because the functions are highly oscillatory. The exact values of the integrals are given in the code.
import Numerical.Integration
example :: IO (Double, Double, Int) -- value, error estimate, error code
example = integration (\t -> 8 * cos(2*t/(1-t)) / (64*(1-t)**2 + t**2)) 0 1 1e-4 100000
value :: Double -- approx 1.7677e-7
value = exp (-6) * pi / (2 * exp 10)
example' :: IO (Double, Double, Int) -- value, error estimate, error code
example' = integration (\t -> 6 * cos(2*t/(1-t)) / (36*(1-t)**2 + t**2)) 0 1 1e-4 50000
value' :: Double -- approx 9.6513e-6
value' = exp (-6) * pi / (2 * exp 6)
For the first one, using 100000 subdivisions of the interval (0, 1), the result (after a while) is approximately 1.756e-7
For the second one, using 50000 subdivisions of the interval (0, 1), the result is approximately 9.649e-6.
So the results are not bad.
I didn’t try “tanh-sinh” but I would bet it provides bad results.
A note: the error code (which should be 0) is totally crazy, a huge number, I don’t know why.