Automatic differentiation using decompressed vectors

Question

Is there a Haskell library for automatic differentiation that works with unboxed vectors? The grad function of Numeric.AD requires an instance of Traversable , which Data.Vector.Unboxed not.

Answer 1

I don’t know why the vectors of pairs are stored as pairs of vectors, but you can easily write instances for your data type to store elements in sequence.

 {-# LANGUAGE TypeFamilies, MultiParamTypeClasses #-} import qualified Data.Vector.Generic as G import qualified Data.Vector.Generic.Mutable as M import Control.Monad (liftM, zipWithM_) import Data.Vector.Unboxed.Base data Point3D = Point3D {-# UNPACK #-} !Int {-# UNPACK #-} !Int {-# UNPACK #-} !Int newtype instance MVector s Point3D = MV_Point3D (MVector s Int) newtype instance Vector Point3D = V_Point3D (Vector Int) instance Unbox Point3D 

At this point, the last line will throw an error because there are no instances for vector types for Point3D. They can be written as follows:

 instance M.MVector MVector Point3D where basicLength (MV_Point3D v) = M.basicLength v `div` 3 basicUnsafeSlice ab (MV_Point3D v) = MV_Point3D $ M.basicUnsafeSlice (a*3) (b*3) v basicOverlaps (MV_Point3D v0) (MV_Point3D v1) = M.basicOverlaps v0 v1 basicUnsafeNew n = liftM MV_Point3D (M.basicUnsafeNew (3*n)) basicUnsafeRead (MV_Point3D v) n = do [a,b,c] <- mapM (M.basicUnsafeRead v) [3*n,3*n+1,3*n+2] return $ Point3D abc basicUnsafeWrite (MV_Point3D v) n (Point3D abc) = zipWithM_ (M.basicUnsafeWrite v) [3*n,3*n+1,3*n+2] [a,b,c] instance G.Vector Vector Point3D where basicUnsafeFreeze (MV_Point3D v) = liftM V_Point3D (G.basicUnsafeFreeze v) basicUnsafeThaw (V_Point3D v) = liftM MV_Point3D (G.basicUnsafeThaw v) basicLength (V_Point3D v) = G.basicLength v `div` 3 basicUnsafeSlice ab (V_Point3D v) = V_Point3D $ G.basicUnsafeSlice (a*3) (b*3) v basicUnsafeIndexM (V_Point3D v) n = do [a,b,c] <- mapM (G.basicUnsafeIndexM v) [3*n,3*n+1,3*n+2] return $ Point3D abc 

I think most function definitions are self-evident. The vector of points is saved as the vector Ints, and the nth point is 3n, 3n + 1,3n + 2 Ints.