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{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FunctionalDependencies #-}
-----------------------------------------------------------------------------
-- |
-- Module : Numeric.Container
-- Copyright : (c) Alberto Ruiz 2007
-- License : GPL-style
--
-- Maintainer : Alberto Ruiz <aruiz@um.es>
-- Stability : provisional
-- Portability : portable
--
-- Numeric classes for containers of numbers, including conversion routines
--
-----------------------------------------------------------------------------
module Numeric.Container (
Linear(..),
Container(..), RealElement, Precision(..), NumericContainer(..), comp,
Convert(..), --AutoReal(..),
RealOf, ComplexOf, SingleOf, DoubleOf,
-- ElementOf,
IndexOf,
module Data.Complex
) where
import Data.Packed.Vector
import Data.Packed.Matrix
import Data.Packed.Internal.Vector
--import Data.Packed.Internal.Matrix
--import qualified Data.Packed.ST as ST
--import Control.Arrow((***))
import Data.Complex
-------------------------------------------------------------------
-- | Supported single-double precision type pairs
class (Element s, Element d) => Precision s d | s -> d, d -> s where
double2FloatG :: Vector d -> Vector s
float2DoubleG :: Vector s -> Vector d
instance Precision Float Double where
double2FloatG = double2FloatV
float2DoubleG = float2DoubleV
instance Precision (Complex Float) (Complex Double) where
double2FloatG = asComplex . double2FloatV . asReal
float2DoubleG = asComplex . float2DoubleV . asReal
-- | Supported real types
class (Element t, Element (Complex t), RealFloat t
-- , RealOf t ~ t, RealOf (Complex t) ~ t
)
=> RealElement t
instance RealElement Double
instance RealElement Float
-- | Conversion utilities
class NumericContainer c where
toComplex :: (RealElement e) => (c e, c e) -> c (Complex e)
fromComplex :: (RealElement e) => c (Complex e) -> (c e, c e)
complex' :: (RealElement e) => c e -> c (Complex e)
conj :: (RealElement e) => c (Complex e) -> c (Complex e)
-- cmap :: (Element a, Element b) => (a -> b) -> c a -> c b
single' :: Precision a b => c b -> c a
double' :: Precision a b => c a -> c b
-- | a synonym for "complex'"
comp :: (NumericContainer c, RealElement e) => c e -> c (Complex e)
comp x = complex' x
-------------------------------------------------------------------
type family RealOf x
type instance RealOf Double = Double
type instance RealOf (Complex Double) = Double
type instance RealOf Float = Float
type instance RealOf (Complex Float) = Float
type family ComplexOf x
type instance ComplexOf Double = Complex Double
type instance ComplexOf (Complex Double) = Complex Double
type instance ComplexOf Float = Complex Float
type instance ComplexOf (Complex Float) = Complex Float
type family SingleOf x
type instance SingleOf Double = Float
type instance SingleOf Float = Float
type instance SingleOf (Complex a) = Complex (SingleOf a)
type family DoubleOf x
type instance DoubleOf Double = Double
type instance DoubleOf Float = Double
type instance DoubleOf (Complex a) = Complex (DoubleOf a)
type family ElementOf c
type instance ElementOf (Vector a) = a
type instance ElementOf (Matrix a) = a
type family IndexOf c
type instance IndexOf Vector = Int
type instance IndexOf Matrix = (Int,Int)
-------------------------------------------------------------------
class (Element t, Element (RealOf t)) => Convert t where
real :: NumericContainer c => c (RealOf t) -> c t
complex :: NumericContainer c => c t -> c (ComplexOf t)
single :: NumericContainer c => c t -> c (SingleOf t)
double :: NumericContainer c => c t -> c (DoubleOf t)
instance Convert Double where
real = id
complex = complex'
single = single'
double = id
instance Convert Float where
real = id
complex = complex'
single = id
double = double'
instance Convert (Complex Double) where
real = complex'
complex = id
single = single'
double = id
instance Convert (Complex Float) where
real = complex'
complex = id
single = id
double = double'
-------------------------------------------------------------------
-- | to be replaced by Convert
class Convert t => AutoReal t where
real'' :: NumericContainer c => c Double -> c t
complex'' :: NumericContainer c => c t -> c (Complex Double)
instance AutoReal Double where
real'' = real
complex'' = complex
instance AutoReal (Complex Double) where
real'' = real
complex'' = complex
instance AutoReal Float where
real'' = real . single
complex'' = double . complex
instance AutoReal (Complex Float) where
real'' = real . single
complex'' = double . complex
-------------------------------------------------------------------
-- | Basic element-by-element functions for numeric containers
class (Element e) => Container c e where
{-
-- | create a structure with a single element
scalar :: e -> c e
-- | multiply every element by a scalar
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
-- | add a constant to each element
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
-}
-- | cannot implement instance Functor because of Element class constraint
cmap :: (Element a, Element b) => (a -> b) -> c a -> c b
--
-- | indexing function
atIndex :: c e -> IndexOf c -> e
-- | index of min/max element
minIndex :: c e -> IndexOf c
maxIndex :: c e -> IndexOf c
-- | value of min/max element
minElement :: c e -> e
maxElement :: c e -> e
-- the C functions sumX/prodX are twice as fast as using foldVector
-- | the sum/product of elements (faster than using @fold@
sumElements :: c e -> e
prodElements :: c e -> e
-- | Basic element-by-element functions.
class (Element e, 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
|
