{-# 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 Data.Packed import Data.Packed.Internal.Numeric import qualified Data.Monoid as M import Data.List(partition) import Numeric.Chain ------------------------------------------------------------------- instance Container Matrix a => Eq (Matrix a) where (==) = equal instance (Container Matrix 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 (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) => 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)