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{-# LANGUAGE UndecidableInstances, MultiParamTypeClasses, FlexibleInstances #-}
{-# LANGUAGE FlexibleContexts #-}
-----------------------------------------------------------------------------
{- |
Module : Numeric.LinearAlgebra.Linear
Copyright : (c) Alberto Ruiz 2006-7
License : GPL-style
Maintainer : Alberto Ruiz (aruiz at um dot es)
Stability : provisional
Portability : uses ffi
Basic optimized operations on vectors and matrices.
-}
-----------------------------------------------------------------------------
module Numeric.LinearAlgebra.Linear (
Vectors(..),
Linear(..)
) where
import Data.Packed.Vector
import Data.Packed.Matrix
import Data.Complex
import Numeric.GSL.Vector
import Control.Monad(ap)
-- | basic Vector functions
class Num e => Vectors a e where
vectorSum :: a e -> e
euclidean :: a e -> e
absSum :: a e -> e
vectorMin :: a e -> e
vectorMax :: a e -> e
minIdx :: a e -> Int
maxIdx :: a e -> Int
dot :: a e -> a e -> e
instance Vectors Vector Float where
vectorSum = sumF
euclidean = toScalarF Norm2
absSum = toScalarF AbsSum
vectorMin = toScalarF Min
vectorMax = toScalarF Max
minIdx = round . toScalarF MinIdx
maxIdx = round . toScalarF MaxIdx
dot = dotF
instance Vectors Vector Double where
vectorSum = sumR
euclidean = toScalarR Norm2
absSum = toScalarR AbsSum
vectorMin = toScalarR Min
vectorMax = toScalarR Max
minIdx = round . toScalarR MinIdx
maxIdx = round . toScalarR MaxIdx
dot = dotR
instance Vectors Vector (Complex Float) where
vectorSum = sumQ
euclidean = (:+ 0) . toScalarQ Norm2
absSum = (:+ 0) . toScalarQ AbsSum
vectorMin = ap (@>) minIdx
vectorMax = ap (@>) maxIdx
minIdx = minIdx . fst . fromComplex . (zipVector (*) `ap` mapVector conjugate)
maxIdx = maxIdx . fst . fromComplex . (zipVector (*) `ap` mapVector conjugate)
dot = dotQ
instance Vectors Vector (Complex Double) where
vectorSum = sumC
euclidean = (:+ 0) . toScalarC Norm2
absSum = (:+ 0) . toScalarC AbsSum
vectorMin = ap (@>) minIdx
vectorMax = ap (@>) maxIdx
minIdx = minIdx . fst . fromComplex . (zipVector (*) `ap` mapVector conjugate)
maxIdx = maxIdx . fst . fromComplex . (zipVector (*) `ap` mapVector conjugate)
dot = dotC
----------------------------------------------------
-- | Basic element-by-element functions.
class (Container c e) => Linear c e where
-- | create a structure with a single element
scalar :: e -> c e
scale :: e -> c e -> c e
-- | scale the element by element reciprocal of the object:
--
-- @scaleRecip 2 (fromList [5,i]) == 2 |> [0.4 :+ 0.0,0.0 :+ (-2.0)]@
scaleRecip :: e -> c e -> c e
addConstant :: e -> c e -> c e
add :: c e -> c e -> c e
sub :: c e -> c e -> c e
-- | element by element multiplication
mul :: c e -> c e -> c e
-- | element by element division
divide :: c e -> c e -> c e
equal :: c e -> c e -> Bool
instance Linear Vector Float where
scale = vectorMapValF Scale
scaleRecip = vectorMapValF Recip
addConstant = vectorMapValF AddConstant
add = vectorZipF Add
sub = vectorZipF Sub
mul = vectorZipF Mul
divide = vectorZipF Div
equal u v = dim u == dim v && vectorMax (vectorMapF Abs (sub u v)) == 0.0
scalar x = fromList [x]
instance Linear Vector Double where
scale = vectorMapValR Scale
scaleRecip = vectorMapValR Recip
addConstant = vectorMapValR AddConstant
add = vectorZipR Add
sub = vectorZipR Sub
mul = vectorZipR Mul
divide = vectorZipR Div
equal u v = dim u == dim v && vectorMax (vectorMapR Abs (sub u v)) == 0.0
scalar x = fromList [x]
instance Linear Vector (Complex Double) where
scale = vectorMapValC Scale
scaleRecip = vectorMapValC Recip
addConstant = vectorMapValC AddConstant
add = vectorZipC Add
sub = vectorZipC Sub
mul = vectorZipC Mul
divide = vectorZipC Div
equal u v = dim u == dim v && vectorMax (mapVector magnitude (sub u v)) == 0.0
scalar x = fromList [x]
instance (Linear Vector a, Container Matrix a) => (Linear Matrix a) where
scale x = liftMatrix (scale x)
scaleRecip x = liftMatrix (scaleRecip x)
addConstant x = liftMatrix (addConstant x)
add = liftMatrix2 add
sub = liftMatrix2 sub
mul = liftMatrix2 mul
divide = liftMatrix2 divide
equal a b = cols a == cols b && flatten a `equal` flatten b
scalar x = (1><1) [x]
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