[Haskell-cafe] Hit a wall with the type system
droundy at darcs.net
Fri Nov 30 11:53:05 EST 2007
On Thu, Nov 29, 2007 at 04:25:43PM -0800, Dan Weston wrote:
> I must be missing something, because to me the contract seems to be much
> simpler to express (than the Functor + Isomorphism route you seem to me
> to be heading towards):
> diff f a = if dx == dx' then error "Zero denom" else dydx
> where a' = addEpsilon a
> dx = a' `takeAway` a
> dx' = a `takeAway` a'
> dy = f a' `takeAway` f a
> dydx = dy `divide` dx
But this is just a finite-difference derivative, which is generally
accurate to... well, a lot less than an analytic derivative. e.g try
diff cos 1e-30
you'll get a garbage answer, while AD or symbolic differentiation will give
you the correct answer, 1e-30.
So for derivatives you actually intend to use, it's much better to use AD
or symbolic differentiation, or just compute the derivatives by hand.
Anything but finite difference (except at a carefully examined check for
Department of Physics
Oregon State University
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