> Hello!
>
> I need to deal with functions of type (Double -> Double). I need Fourier
> transform, integration, + - * / operations, value of a function in a point,
> probably composition.
>
> However it is not very effective to use straightforwardly this type. Since
> functions in question are rather smooth (if not analytical), the best option
> would be to use some kind of pointwise representation (e.g. lists, arrays).
> But in this case the code wouldn't be so easy to understand and implement,
> compact and so on.
>
> Is there some libraries which allow me to work with functions as if their
> type was (Double -> Double), but indeed it was something faster?
Lazy polynomial splines: http://hackage.haskell.org/package/lazysplines
Lazy polynomial splines are potentially infinite sequences of segments
represented by polynomials. They're a very straightforward abstraction for
functions which can be treated as piecewise analytic. They provide efficient
addition, subtraction integration and differentiation. Multiplication and
composition can be more expensive, and division by a non-scalar can, if one is
not careful, be somewhat disastrous. The package was intended as much as a
proof-of-concept as for production. But the concept is simple enough that you
should be able to tune it to your needs.
Cheers,
Gershom
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