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{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FunctionalDependencies #-}
-----------------------------------------------------------------------------
-- |
-- Module : Numeric.Matrix
-- Copyright : (c) Alberto Ruiz 2010
-- License : GPL-style
--
-- Maintainer : Alberto Ruiz <aruiz@um.es>
-- Stability : provisional
-- Portability : portable
--
-- Numeric instances and functions for 'Matrix'.
-- In the context of the standard numeric operators, one-component
-- vectors and matrices automatically expand to match the dimensions of the other operand.
--
-- Provides instances of standard classes 'Show', 'Read', 'Eq',
-- 'Num', 'Fractional', and 'Floating' for 'Matrix'.
--
-----------------------------------------------------------------------------
module Numeric.Matrix (
-- * Basic functions
module Data.Packed.Matrix,
module Numeric.Vector,
-- * Matrix creation
diag, ident,
-- * matrix operations
ctrans,
optimiseMult,
-- * Operators
(<>), (<\>)
) where
-------------------------------------------------------------------
import Data.Packed.Matrix
import Numeric.Vector
import Numeric.Chain
import Numeric.MatrixBoot
import Numeric.LinearAlgebra.Algorithms
-------------------------------------------------------------------
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]
--------------------------------------------------------
class Mul a b c | a b -> c where
infixl 7 <>
-- | Matrix-matrix, matrix-vector, and vector-matrix products.
(<>) :: Product t => a t -> b t -> c t
instance Mul Matrix Matrix Matrix where
(<>) = mXm
instance Mul Matrix Vector Vector where
(<>) m v = flatten $ m <> (asColumn v)
instance Mul Vector Matrix Vector where
(<>) v m = flatten $ (asRow v) <> m
--------------------------------------------------------
-- | least squares solution of a linear system, similar to the \\ operator of Matlab\/Octave (based on linearSolveSVD).
(<\>) :: (Field a) => Matrix a -> Vector a -> Vector a
infixl 7 <\>
m <\> v = flatten (linearSolveSVD m (reshape 1 v))
|
