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{-# OPTIONS_GHC -fglasgow-exts -fallow-undecidable-instances #-}
-----------------------------------------------------------------------------
{- |
Module : LinearAlgebra.Instances
Copyright : (c) Alberto Ruiz 2006
License : GPL-style
Maintainer : Alberto Ruiz (aruiz at um dot es)
Stability : provisional
Portability : portable
Numeric instances for Vector and Matrix.
In the context of the standard numeric operators, one-component vectors and matrices automatically expand to match the dimensions of the other operand.
-}
-----------------------------------------------------------------------------
module LinearAlgebra.Instances(
) where
import LinearAlgebra.Linear
import GSL.Vector
import Data.Packed.Matrix
import Data.Packed.Vector
import Complex
adaptScalar f1 f2 f3 x y
| dim x == 1 = f1 (x@>0) y
| dim y == 1 = f3 x (y@>0)
| otherwise = f2 x y
liftMatrix2' :: (Field t, Field a, Field b) => (Vector a -> Vector b -> Vector t) -> Matrix a -> Matrix b -> Matrix t
liftMatrix2' f m1 m2 | compat' m1 m2 = reshape (max (cols m1) (cols m2)) (f (flatten m1) (flatten m2))
| otherwise = error "nonconformant matrices in liftMatrix2'"
compat' :: Matrix a -> Matrix b -> Bool
compat' m1 m2 = rows m1 == 1 && cols m1 == 1
|| rows m2 == 1 && cols m2 == 1
|| rows m1 == rows m2 && cols m1 == cols m2
instance (Eq a, Field a) => Eq (Vector a) where
a == b = dim a == dim b && toList a == toList b
instance (Linear Vector a) => Num (Vector a) where
(+) = adaptScalar addConstant add (flip addConstant)
negate = scale (-1)
(*) = adaptScalar scale mul (flip scale)
signum = liftVector signum
abs = liftVector abs
fromInteger = fromList . return . fromInteger
instance (Eq a, Field a) => Eq (Matrix a) where
a == b = cols a == cols b && flatten a == flatten b
instance (Linear Vector a) => Num (Matrix a) where
(+) = liftMatrix2' (+)
(-) = liftMatrix2' (-)
negate = liftMatrix negate
(*) = liftMatrix2' (*)
signum = liftMatrix signum
abs = liftMatrix abs
fromInteger = (1><1) . return . fromInteger
---------------------------------------------------
instance (Linear 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 (Linear Vector a, Fractional (Vector a)) => Fractional (Matrix a) where
fromRational n = (1><1) [fromRational n]
(/) = liftMatrix2' (/)
---------------------------------------------------------
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 (Linear Vector a, Floating (Vector 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
(**) = liftMatrix2' (**)
sqrt = liftMatrix sqrt
pi = (1><1) [pi]
|
