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{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
-----------------------------------------------------------------------------
-- |
-- Module : Numeric.Vector
-- Copyright : (c) Alberto Ruiz 2011
-- License : GPL-style
--
-- Maintainer : Alberto Ruiz <aruiz@um.es>
-- Stability : provisional
-- Portability : portable
--
-- Provides instances of standard classes 'Show', 'Read', 'Eq',
-- 'Num', 'Fractional', and 'Floating' for 'Vector'.
--
-----------------------------------------------------------------------------
module Numeric.Vector () where
import Numeric.GSL.Vector
import Numeric.Container
-------------------------------------------------------------------
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]
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