Hi Douglas,
Looks like it's pretty straightforward to use the "dimensional" and
"ad" packages together:
{-# LANGUAGE RankNTypes #-}
import qualified Numeric.AD as AD
import qualified Numeric.AD.Types as AD
import Numeric.Units.Dimensional.Prelude
import Numeric.Units.Dimensional
import qualified Prelude as P
diff :: (Div y x y', Num a) =>
(forall s. AD.Mode s => Dimensional v x (AD.AD s a)
-> Dimensional v y (AD.AD s a))
-> Dimensional v x a -> Dimensional v y' a
diff f z = Dimensional $ AD.diff (unD . f . Dimensional) (unD z)
unD (Dimensional a) = a
-- a dumb example
ke velocity = velocity*velocity*(1*~kilo gram)
main = print $ diff ke (3 *~ (metre/second))
-- prints 6.0 m kg s^-1
It might be nice to have a package that wraps up the rest of the
functionality in "ad" (gradients, the different modes etc.). I'm not
sure there are convenient vectors/matrices that can have each element
with a different type (units).
Regards,
Adam
On Fri, Jan 17, 2014 at 4:23 PM, Douglas McClean
Has anyone explored the intersection between automatic differentiation and dimension types (like those in the dimensional package or along the lines of any of the approaches discussed at http://www.haskell.org/haskellwiki/Physical_units)?
It's tricky because for ordinary automatic differentiation the types are all the same, but when dimensions get involved that isn't the case, you have to keep dividing by the dimension of the infinitesimal.
-Doug McClean
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