haskell - 与未装箱向量的自动微分

Question

是否有一个用于自动微分的 Haskell 库，可以处理未装箱的向量？ Numeric.AD 中的 grad 函数需要 Traversable 的实例，而 Data.Vector.Unboxed 则不需要。

Answer 1

我不知道为什么向量对存储为向量对，但您可以轻松地为数据类型编写实例来按顺序存储元素。

{-# 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 Point3D 向量类型的实例。它们可以写成如下:

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。点向量存储为整数向量，第 n 个点是 3n,3n+1,3n+2 个整数。