The Data.Number.Dif
module contains a data type, Dif
, that allows for
automatic forward differentiation.
All the ideas are from Jerzy Karczmarczuk's work, see http://users.info.unicaen.fr/~karczma/arpap/diffalg.pdf.
A simple example, if we define
foo x = x*x
then the function
foo' = deriv foo
will behave as if its body was 2*x.
Documentation
The Dif
type is the type of differentiable numbers.
It's an instance of all the usual numeric classes.
The computed derivative of a function is is correct
except where the function is discontinuous, at these points
the derivative should be a Dirac pulse, but it isn't.
The Dif
numbers are printed with a trailing ~~ to
indicate that there is a "tail" of derivatives.
dVar :: Num a => a -> Dif aSource
The dVar
function turns a number into a variable
number. This is the number with with respect to which
the derivaticve is computed.