是否有适用于未装箱向量的自动微分 Haskell 库？来自Numeric.AD 的grad 函数需要Traversable 的实例，而Data.Vector.Unboxed 不需要。
【问题讨论】：
grad 不需要进行太多更改即可使其适用于未装箱的向量。您必须从Numeric.AD.Internal.Var 重新实现bind 和unbind。 Variable 类型未拆箱，但您可以将其替换为元组。 （我现在不能尝试，因为ad 不是基于 GHC 7.8）
我不知道为什么成对的向量被存储为成对的向量，但是您可以轻松地为您的数据类型编写实例来顺序存储元素。
{-# 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
此时最后一行将导致错误，因为没有针对 Point3D 的矢量类型的实例。它们可以写成：
instance M.MVector MVector Point3D where
basicLength (MV_Point3D v) = M.basicLength v `div` 3
basicUnsafeSlice a b (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 a b c
basicUnsafeWrite (MV_Point3D v) n (Point3D a b c) = 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 a b (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 a b c
我认为大多数函数定义都是不言自明的。点的向量存储为 Ints 的向量，第 n 个点是 3n,3n+1,3n+2 个 Ints。
【讨论】：