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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]