From 0ab93b8eb934167e16dbae193c4fd2b5359a184b Mon Sep 17 00:00:00 2001 From: Alberto Ruiz Date: Fri, 16 May 2014 09:20:47 +0200 Subject: instances moved to base --- packages/base/hmatrix-base.cabal | 3 + packages/base/src/Numeric/Chain.hs | 143 ++++++++++++++++++++++++++++++++ packages/base/src/Numeric/Matrix.hs | 100 +++++++++++++++++++++++ packages/base/src/Numeric/Vector.hs | 159 ++++++++++++++++++++++++++++++++++++ 4 files changed, 405 insertions(+) create mode 100644 packages/base/src/Numeric/Chain.hs create mode 100644 packages/base/src/Numeric/Matrix.hs create mode 100644 packages/base/src/Numeric/Vector.hs (limited to 'packages/base') diff --git a/packages/base/hmatrix-base.cabal b/packages/base/hmatrix-base.cabal index 8571e7a..8eeb97e 100644 --- a/packages/base/hmatrix-base.cabal +++ b/packages/base/hmatrix-base.cabal @@ -39,12 +39,15 @@ library Numeric.LinearAlgebra.LAPACK Data.Packed.Numeric Numeric.Vectorized + Numeric.Vector + Numeric.Matrix other-modules: Data.Packed.Internal, Data.Packed.Internal.Common, Data.Packed.Internal.Signatures, Data.Packed.Internal.Vector, Data.Packed.Internal.Matrix + Numeric.Chain C-sources: src/C/lapack-aux.c src/C/vector-aux.c diff --git a/packages/base/src/Numeric/Chain.hs b/packages/base/src/Numeric/Chain.hs new file mode 100644 index 0000000..fbdb01b --- /dev/null +++ b/packages/base/src/Numeric/Chain.hs @@ -0,0 +1,143 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Numeric.Chain +-- Copyright : (c) Vivian McPhail 2010 +-- License : GPL-style +-- +-- Maintainer : Vivian McPhail gmail.com> +-- Stability : provisional +-- Portability : portable +-- +-- optimisation of association order for chains of matrix multiplication +-- +----------------------------------------------------------------------------- + +module Numeric.Chain ( + optimiseMult, + ) where + +import Data.Maybe + +import Data.Packed.Matrix +import Data.Packed.Numeric + +import qualified Data.Array.IArray as A + +----------------------------------------------------------------------------- +{- | + Provide optimal association order for a chain of matrix multiplications + and apply the multiplications. + + The algorithm is the well-known O(n\^3) dynamic programming algorithm + that builds a pyramid of optimal associations. + +> m1, m2, m3, m4 :: Matrix Double +> m1 = (10><15) [1..] +> m2 = (15><20) [1..] +> m3 = (20><5) [1..] +> m4 = (5><10) [1..] + +> >>> optimiseMult [m1,m2,m3,m4] + +will perform @((m1 `multiply` (m2 `multiply` m3)) `multiply` m4)@ + +The naive left-to-right multiplication would take @4500@ scalar multiplications +whereas the optimised version performs @2750@ scalar multiplications. The complexity +in this case is 32 (= 4^3/2) * (2 comparisons, 3 scalar multiplications, 3 scalar additions, +5 lookups, 2 updates) + a constant (= three table allocations) +-} +optimiseMult :: Product t => [Matrix t] -> Matrix t +optimiseMult = chain + +----------------------------------------------------------------------------- + +type Matrices a = A.Array Int (Matrix a) +type Sizes = A.Array Int (Int,Int) +type Cost = A.Array Int (A.Array Int (Maybe Int)) +type Indexes = A.Array Int (A.Array Int (Maybe ((Int,Int),(Int,Int)))) + +update :: A.Array Int (A.Array Int a) -> (Int,Int) -> a -> A.Array Int (A.Array Int a) +update a (r,c) e = a A.// [(r,(a A.! r) A.// [(c,e)])] + +newWorkSpaceCost :: Int -> A.Array Int (A.Array Int (Maybe Int)) +newWorkSpaceCost n = A.array (1,n) $ map (\i -> (i, subArray i)) [1..n] + where subArray i = A.listArray (1,i) (repeat Nothing) + +newWorkSpaceIndexes :: Int -> A.Array Int (A.Array Int (Maybe ((Int,Int),(Int,Int)))) +newWorkSpaceIndexes n = A.array (1,n) $ map (\i -> (i, subArray i)) [1..n] + where subArray i = A.listArray (1,i) (repeat Nothing) + +matricesToSizes :: [Matrix a] -> Sizes +matricesToSizes ms = A.listArray (1,length ms) $ map (\m -> (rows m,cols m)) ms + +chain :: Product a => [Matrix a] -> Matrix a +chain [] = error "chain: zero matrices to multiply" +chain [m] = m +chain [ml,mr] = ml `multiply` mr +chain ms = let ln = length ms + ma = A.listArray (1,ln) ms + mz = matricesToSizes ms + i = chain_cost mz + in chain_paren (ln,ln) i ma + +chain_cost :: Sizes -> Indexes +chain_cost mz = let (_,u) = A.bounds mz + cost = newWorkSpaceCost u + ixes = newWorkSpaceIndexes u + (_,_,i) = foldl chain_cost' (mz,cost,ixes) (order u) + in i + +chain_cost' :: (Sizes,Cost,Indexes) -> (Int,Int) -> (Sizes,Cost,Indexes) +chain_cost' sci@(mz,cost,ixes) (r,c) + | c == 1 = let cost' = update cost (r,c) (Just 0) + ixes' = update ixes (r,c) (Just ((r,c),(r,c))) + in (mz,cost',ixes') + | otherwise = minimum_cost sci (r,c) + +minimum_cost :: (Sizes,Cost,Indexes) -> (Int,Int) -> (Sizes,Cost,Indexes) +minimum_cost sci fu = foldl (smaller_cost fu) sci (fulcrum_order fu) + +smaller_cost :: (Int,Int) -> (Sizes,Cost,Indexes) -> ((Int,Int),(Int,Int)) -> (Sizes,Cost,Indexes) +smaller_cost (r,c) (mz,cost,ixes) ix@((lr,lc),(rr,rc)) = let op_cost = fromJust ((cost A.! lr) A.! lc) + + fromJust ((cost A.! rr) A.! rc) + + fst (mz A.! (lr-lc+1)) + * snd (mz A.! lc) + * snd (mz A.! rr) + cost' = (cost A.! r) A.! c + in case cost' of + Nothing -> let cost'' = update cost (r,c) (Just op_cost) + ixes'' = update ixes (r,c) (Just ix) + in (mz,cost'',ixes'') + Just ct -> if op_cost < ct then + let cost'' = update cost (r,c) (Just op_cost) + ixes'' = update ixes (r,c) (Just ix) + in (mz,cost'',ixes'') + else (mz,cost,ixes) + + +fulcrum_order (r,c) = let fs' = zip (repeat r) [1..(c-1)] + in map (partner (r,c)) fs' + +partner (r,c) (a,b) = ((r-b, c-b), (a,b)) + +order 0 = [] +order n = order (n-1) ++ zip (repeat n) [1..n] + +chain_paren :: Product a => (Int,Int) -> Indexes -> Matrices a -> Matrix a +chain_paren (r,c) ixes ma = let ((lr,lc),(rr,rc)) = fromJust $ (ixes A.! r) A.! c + in if lr == rr && lc == rc then (ma A.! lr) + else (chain_paren (lr,lc) ixes ma) `multiply` (chain_paren (rr,rc) ixes ma) + +-------------------------------------------------------------------------- + +{- TESTS + +-- optimal association is ((m1*(m2*m3))*m4) +m1, m2, m3, m4 :: Matrix Double +m1 = (10><15) [1..] +m2 = (15><20) [1..] +m3 = (20><5) [1..] +m4 = (5><10) [1..] + +-} + diff --git a/packages/base/src/Numeric/Matrix.hs b/packages/base/src/Numeric/Matrix.hs new file mode 100644 index 0000000..3478aae --- /dev/null +++ b/packages/base/src/Numeric/Matrix.hs @@ -0,0 +1,100 @@ +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE UndecidableInstances #-} +{-# LANGUAGE MultiParamTypeClasses #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Numeric.Matrix +-- Copyright : (c) Alberto Ruiz 2010 +-- License : GPL-style +-- +-- Maintainer : Alberto Ruiz +-- Stability : provisional +-- Portability : portable +-- +-- Provides instances of standard classes 'Show', 'Read', 'Eq', +-- 'Num', 'Fractional', and 'Floating' for 'Matrix'. +-- +-- In arithmetic operations one-component +-- vectors and matrices automatically expand to match the dimensions of the other operand. + +----------------------------------------------------------------------------- + +module Numeric.Matrix ( + ) where + +------------------------------------------------------------------- + +import Data.Packed +import Data.Packed.Numeric +import qualified Data.Monoid as M +import Data.List(partition) +import Numeric.Chain + +------------------------------------------------------------------- + +instance Container Matrix a => Eq (Matrix a) where + (==) = equal + +instance (Container Matrix a, Num (Vector a)) => Num (Matrix a) where + (+) = liftMatrix2Auto (+) + (-) = liftMatrix2Auto (-) + negate = liftMatrix negate + (*) = liftMatrix2Auto (*) + signum = liftMatrix signum + abs = liftMatrix abs + fromInteger = (1><1) . return . fromInteger + +--------------------------------------------------- + +instance (Container Vector a, Fractional (Vector a), Num (Matrix a)) => Fractional (Matrix a) where + fromRational n = (1><1) [fromRational n] + (/) = liftMatrix2Auto (/) + +--------------------------------------------------------- + +instance (Floating a, Container Vector a, Floating (Vector a), Fractional (Matrix a)) => Floating (Matrix a) where + sin = liftMatrix sin + cos = liftMatrix cos + tan = liftMatrix tan + asin = liftMatrix asin + acos = liftMatrix acos + atan = liftMatrix atan + sinh = liftMatrix sinh + cosh = liftMatrix cosh + tanh = liftMatrix tanh + asinh = liftMatrix asinh + acosh = liftMatrix acosh + atanh = liftMatrix atanh + exp = liftMatrix exp + log = liftMatrix log + (**) = liftMatrix2Auto (**) + sqrt = liftMatrix sqrt + pi = (1><1) [pi] + +-------------------------------------------------------------------------------- + +isScalar m = rows m == 1 && cols m == 1 + +adaptScalarM f1 f2 f3 x y + | isScalar x = f1 (x @@>(0,0) ) y + | isScalar y = f3 x (y @@>(0,0) ) + | otherwise = f2 x y + +instance (Container Vector t, Eq t, Num (Vector t), Product t) => M.Monoid (Matrix t) + where + mempty = 1 + mappend = adaptScalarM scale mXm (flip scale) + + mconcat xs = work (partition isScalar xs) + where + work (ss,[]) = product ss + work (ss,ms) = scale' (product ss) (optimiseMult ms) + scale' x m + | isScalar x && x00 == 1 = m + | otherwise = scale x00 m + where + x00 = x @@> (0,0) + diff --git a/packages/base/src/Numeric/Vector.hs b/packages/base/src/Numeric/Vector.hs new file mode 100644 index 0000000..2769cd9 --- /dev/null +++ b/packages/base/src/Numeric/Vector.hs @@ -0,0 +1,159 @@ +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE UndecidableInstances #-} +{-# LANGUAGE MultiParamTypeClasses #-} +----------------------------------------------------------------------------- +-- | +-- Module : Numeric.Vector +-- Copyright : (c) Alberto Ruiz 2011 +-- License : GPL-style +-- +-- Maintainer : Alberto Ruiz +-- Stability : provisional +-- Portability : portable +-- +-- Provides instances of standard classes 'Show', 'Read', 'Eq', +-- 'Num', 'Fractional', and 'Floating' for 'Vector'. +-- +----------------------------------------------------------------------------- + +module Numeric.Vector () where + +import Numeric.Vectorized +import Data.Packed.Vector +import Data.Packed.Numeric + +------------------------------------------------------------------- + +adaptScalar f1 f2 f3 x y + | dim x == 1 = f1 (x@>0) y + | dim y == 1 = f3 x (y@>0) + | otherwise = f2 x y + +------------------------------------------------------------------ + +instance Num (Vector Float) where + (+) = adaptScalar addConstant add (flip addConstant) + negate = scale (-1) + (*) = adaptScalar scale mul (flip scale) + signum = vectorMapF Sign + abs = vectorMapF Abs + fromInteger = fromList . return . fromInteger + +instance Num (Vector Double) where + (+) = adaptScalar addConstant add (flip addConstant) + negate = scale (-1) + (*) = adaptScalar scale mul (flip scale) + signum = vectorMapR Sign + abs = vectorMapR Abs + fromInteger = fromList . return . fromInteger + +instance Num (Vector (Complex Double)) where + (+) = adaptScalar addConstant add (flip addConstant) + negate = scale (-1) + (*) = adaptScalar scale mul (flip scale) + signum = vectorMapC Sign + abs = vectorMapC Abs + fromInteger = fromList . return . fromInteger + +instance Num (Vector (Complex Float)) where + (+) = adaptScalar addConstant add (flip addConstant) + negate = scale (-1) + (*) = adaptScalar scale mul (flip scale) + signum = vectorMapQ Sign + abs = vectorMapQ Abs + fromInteger = fromList . return . fromInteger + +--------------------------------------------------- + +instance (Container Vector a, Num (Vector a)) => Fractional (Vector a) where + fromRational n = fromList [fromRational n] + (/) = adaptScalar f divide g where + r `f` v = scaleRecip r v + v `g` r = scale (recip r) v + +------------------------------------------------------- + +instance Floating (Vector Float) where + sin = vectorMapF Sin + cos = vectorMapF Cos + tan = vectorMapF Tan + asin = vectorMapF ASin + acos = vectorMapF ACos + atan = vectorMapF ATan + sinh = vectorMapF Sinh + cosh = vectorMapF Cosh + tanh = vectorMapF Tanh + asinh = vectorMapF ASinh + acosh = vectorMapF ACosh + atanh = vectorMapF ATanh + exp = vectorMapF Exp + log = vectorMapF Log + sqrt = vectorMapF Sqrt + (**) = adaptScalar (vectorMapValF PowSV) (vectorZipF Pow) (flip (vectorMapValF PowVS)) + pi = fromList [pi] + +------------------------------------------------------------- + +instance Floating (Vector Double) where + sin = vectorMapR Sin + cos = vectorMapR Cos + tan = vectorMapR Tan + asin = vectorMapR ASin + acos = vectorMapR ACos + atan = vectorMapR ATan + sinh = vectorMapR Sinh + cosh = vectorMapR Cosh + tanh = vectorMapR Tanh + asinh = vectorMapR ASinh + acosh = vectorMapR ACosh + atanh = vectorMapR ATanh + exp = vectorMapR Exp + log = vectorMapR Log + sqrt = vectorMapR Sqrt + (**) = adaptScalar (vectorMapValR PowSV) (vectorZipR Pow) (flip (vectorMapValR PowVS)) + pi = fromList [pi] + +------------------------------------------------------------- + +instance Floating (Vector (Complex Double)) where + sin = vectorMapC Sin + cos = vectorMapC Cos + tan = vectorMapC Tan + asin = vectorMapC ASin + acos = vectorMapC ACos + atan = vectorMapC ATan + sinh = vectorMapC Sinh + cosh = vectorMapC Cosh + tanh = vectorMapC Tanh + asinh = vectorMapC ASinh + acosh = vectorMapC ACosh + atanh = vectorMapC ATanh + exp = vectorMapC Exp + log = vectorMapC Log + sqrt = vectorMapC Sqrt + (**) = adaptScalar (vectorMapValC PowSV) (vectorZipC Pow) (flip (vectorMapValC PowVS)) + pi = fromList [pi] + +----------------------------------------------------------- + +instance Floating (Vector (Complex Float)) where + sin = vectorMapQ Sin + cos = vectorMapQ Cos + tan = vectorMapQ Tan + asin = vectorMapQ ASin + acos = vectorMapQ ACos + atan = vectorMapQ ATan + sinh = vectorMapQ Sinh + cosh = vectorMapQ Cosh + tanh = vectorMapQ Tanh + asinh = vectorMapQ ASinh + acosh = vectorMapQ ACosh + atanh = vectorMapQ ATanh + exp = vectorMapQ Exp + log = vectorMapQ Log + sqrt = vectorMapQ Sqrt + (**) = adaptScalar (vectorMapValQ PowSV) (vectorZipQ Pow) (flip (vectorMapValQ PowVS)) + pi = fromList [pi] + -- cgit v1.2.3