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|
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
-----------------------------------------------------------------------------
-- |
-- Module : Numeric.Matrix
-- Copyright : (c) Alberto Ruiz 2014
-- License : BSD3
--
-- Maintainer : Alberto Ruiz
-- Stability : provisional
--
-- Provides instances of standard classes 'Show', 'Read', 'Eq',
-- 'Num', 'Fractional', and 'Floating' for 'Matrix'.
--
-- In arithmetic operations one-component
-- vectors and matrices automatically expand to match the dimensions of the other operand.
-----------------------------------------------------------------------------
module Numeric.Matrix (
) where
-------------------------------------------------------------------
import Internal.Vector
import Internal.Matrix
import Internal.Element
import Internal.Numeric
import qualified Data.Monoid as M
import Data.List(partition)
import qualified Data.Foldable as F
import qualified Data.Semigroup as S
import Internal.Chain
-------------------------------------------------------------------
instance Container Matrix a => Eq (Matrix a) where
(==) = equal
instance (Container Matrix a, Num a, Num (Vector a)) => Num (Matrix a) where
(+) = liftMatrix2Auto (+)
(-) = liftMatrix2Auto (-)
negate = liftMatrix negate
(*) = liftMatrix2Auto (*)
signum = liftMatrix signum
abs = liftMatrix abs
fromInteger = (1><1) . return . fromInteger
---------------------------------------------------
instance (Container Vector a, Fractional a, Fractional (Vector a), Num (Matrix a)) => Fractional (Matrix a) where
fromRational n = (1><1) [fromRational n]
(/) = liftMatrix2Auto (/)
---------------------------------------------------------
instance (Floating a, Container Vector a, Floating (Vector a), Fractional (Matrix 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
(**) = liftMatrix2Auto (**)
sqrt = liftMatrix sqrt
pi = (1><1) [pi]
--------------------------------------------------------------------------------
isScalar m = rows m == 1 && cols m == 1
adaptScalarM f1 f2 f3 x y
| isScalar x = f1 (x @@>(0,0) ) y
| isScalar y = f3 x (y @@>(0,0) )
| otherwise = f2 x y
instance (Container Vector t, Eq t, Num (Vector t), Product t) => S.Semigroup (Matrix t)
where
(<>) = mappend
sconcat = mconcat . F.toList
instance (Container Vector t, Eq t, Num (Vector t), Product t) => M.Monoid (Matrix t)
where
mempty = 1
mappend = adaptScalarM scale mXm (flip scale)
mconcat xs = work (partition isScalar xs)
where
work (ss,[]) = product ss
work (ss,ms) = scl (product ss) (optimiseMult ms)
scl x m
| isScalar x && x00 == 1 = m
| otherwise = scale x00 m
where
x00 = x @@> (0,0)
|
