I understand the distinction, and I find both techniques interesting, but your AD code is a lot more convenient. All I have to do is make sure that my functions are sufficiently polymorphic, and I can get derivatives *automatically* with very little programmer effort. It seems like a good way to inject worry-free calculus wherever it's needed -- for instance, if I want gradient information about a function, I can use AD and avoid having to choose a length scale, consider accuracy issues, etc. like I would if I used a finite difference approximation.
(Of course, this assumes that the function I'm differentiating consists only of building blocks that I have AD definitions of. In particular, I'm not really sure how I want to define the Ord operations for Dual, so that a function with an if statement based on a comparison (e.g. Gaussian elimination with pivoting) can be differentiated. On the one hand, I'm not sure I want to include the infinitesimal part in the definition, because it is in some sense how fast the number is changing, not how big it is; on the other hand, if I don't include the infinitesimal part, my definition of Ord won't be consistent with equality...) One question I have, though, for anyone on the list who knows the answer -- if I give a function a polymorphic type signature, can it affect performance? That is, if I write two functions with the same definitions but different user-specified type signatures, foo1 :: (Floating a) => a -> a foo1 = ... and foo2 :: Double -> Double foo2 = ... when I apply foo1 to a Double, will the compiler (GHC, specifically) generate code that is just as efficient as if I used foo2? Regards, --Grady Lemoine On 12/19/06, Dan Piponi <[EMAIL PROTECTED]> wrote:
On 12/2/06, Chris Kuklewicz <[EMAIL PROTECTED]> wrote: > Grady Lemoine wrote: > > I've been playing around with Dan Piponi's work on automatic > > differentiation... > I played with such things, as seen on the old wiki: > http://haskell.org/hawiki/ShortExamples_2fSymbolDifferentiation I missed this while I was away on vacation so apologies for responding to something two weeks old. I just want to point out that the method I've been promoting is very distinct from symbolic differentiation. I wouldn't make a big deal about this except that besides playing well with Haskell, AD can help with many real world numerical problems, but people often dismiss it because it they confuse it with symbolic differentiation which they have already determined doesn't solve their problems. -- Dan _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
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