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|
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE UndecidableInstances #-}
-----------------------------------------------------------------------------
-- |
-- Module : Numeric.Container
-- Copyright : (c) Alberto Ruiz 2010-14
-- License : GPL
--
-- Maintainer : Alberto Ruiz <aruiz@um.es>
-- Stability : provisional
-- Portability : portable
--
-- Basic numeric operations on 'Vector' and 'Matrix', including conversion routines.
--
-- The 'Container' class is used to define optimized generic functions which work
-- on 'Vector' and 'Matrix' with real or complex elements.
--
-- Some of these functions are also available in the instances of the standard
-- numeric Haskell classes provided by "Numeric.LinearAlgebra".
--
-----------------------------------------------------------------------------
module Numeric.Container (
-- * Basic functions
module Data.Packed,
konst, build,
constant, linspace,
diag, ident,
ctrans,
-- * Generic operations
Container(..),
-- * Matrix product
Product(..),
Contraction(..),
optimiseMult,
mXm,mXv,vXm,Mul(..),LSDiv(..), cdot, (⋅), dot, (<.>),
outer, kronecker,
-- * Random numbers
RandDist(..),
randomVector,
gaussianSample,
uniformSample,
meanCov,
-- * Element conversion
Convert(..),
Complexable(),
RealElement(),
RealOf, ComplexOf, SingleOf, DoubleOf,
IndexOf,
module Data.Complex,
-- * Input / Output
dispf, disps, dispcf, vecdisp, latexFormat, format,
loadMatrix, saveMatrix, fromFile, fileDimensions,
readMatrix,
fscanfVector, fprintfVector, freadVector, fwriteVector,
) where
import Data.Packed
import Data.Packed.Internal(constantD)
import Numeric.ContainerBoot
import Numeric.Chain
import Numeric.IO
import Data.Complex
import Numeric.LinearAlgebra.Algorithms(Field,linearSolveSVD)
import Data.Packed.Random
------------------------------------------------------------------
{- | creates a vector with a given number of equal components:
@> constant 2 7
7 |> [2.0,2.0,2.0,2.0,2.0,2.0,2.0]@
-}
constant :: Element a => a -> Int -> Vector a
-- constant x n = runSTVector (newVector x n)
constant = constantD-- about 2x faster
{- | Creates a real vector containing a range of values:
@\> linspace 5 (-3,7)
5 |> [-3.0,-0.5,2.0,4.5,7.0]@
Logarithmic spacing can be defined as follows:
@logspace n (a,b) = 10 ** linspace n (a,b)@
-}
linspace :: (Enum e, Container Vector e) => Int -> (e, e) -> Vector e
linspace n (a,b) = addConstant a $ scale s $ fromList [0 .. fromIntegral n-1]
where s = (b-a)/fromIntegral (n-1)
-- | dot product: @cdot u v = 'udot' ('conj' u) v@
cdot :: (Container Vector t, Product t) => Vector t -> Vector t -> t
cdot u v = udot (conj u) v
--------------------------------------------------------
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
--------------------------------------------------------
class LSDiv b c | b -> c, c->b where
infixl 7 <\>
-- | least squares solution of a linear system, similar to the \\ operator of Matlab\/Octave (based on linearSolveSVD)
(<\>) :: Field t => Matrix t -> b t -> c t
instance LSDiv Vector Vector where
m <\> v = flatten (linearSolveSVD m (reshape 1 v))
instance LSDiv Matrix Matrix where
(<\>) = linearSolveSVD
--------------------------------------------------------
-- | Compute mean vector and covariance matrix of the rows of a matrix.
meanCov :: Matrix Double -> (Vector Double, Matrix Double)
meanCov x = (med,cov) where
r = rows x
k = 1 / fromIntegral r
med = konst k r `vXm` x
meds = konst 1 r `outer` med
xc = x `sub` meds
cov = scale (recip (fromIntegral (r-1))) (trans xc `mXm` xc)
--------------------------------------------------------------------------------
-- | matrix-matrix product, matrix-vector product, unconjugated dot product, and scaling
class Contraction a b c | a b -> c
where
-- ^ 0x00d7 multiplication sign
infixl 7 ×
(×) :: a -> b -> c
instance Product t => Contraction (Vector t) (Vector t) t where
(×) = udot
instance Product t => Contraction (Matrix t) (Vector t) (Vector t) where
(×) = mXv
instance Product t => Contraction (Vector t) (Matrix t) (Vector t) where
(×) = vXm
instance Product t => Contraction (Matrix t) (Matrix t) (Matrix t) where
(×) = mXm
instance Container Vector t => Contraction t (Vector t) (Vector t) where
(×) = scale
instance Container Vector t => Contraction (Vector t) t (Vector t) where
(×) = flip scale
instance Container Matrix t => Contraction t (Matrix t) (Matrix t) where
(×) = scale
instance Container Matrix t => Contraction (Matrix t) t (Matrix t) where
(×) = flip scale
--------------------------------------------------------------------------------
-- | dot product (0x22C5): @u ⋅ v = 'cdot' u v@
(⋅) :: (Container Vector t, Product t) => Vector t -> Vector t -> t
infixl 7 ⋅
u ⋅ v = cdot u v
--------------------------------------------------------------------------------
-- bidirectional type inference
class Konst e d c | d -> c, c -> d
where
konst :: e -> d -> c e
instance Container Vector e => Konst e Int Vector
where
konst = konst'
instance Container Vector e => Konst e (Int,Int) Matrix
where
konst = konst'
class Build d f c e | d -> c, c -> d, f -> e, f -> d, f -> c, c e -> f, d e -> f
where
build :: d -> f -> c e
instance Container Vector e => Build Int (e -> e) Vector e
where
build = build'
instance Container Matrix e => Build (Int,Int) (e -> e -> e) Matrix e
where
build = build'
--------------------------------------------------------------------------------
{-# DEPRECATED dot "use udot" #-}
dot :: Product e => Vector e -> Vector e -> e
dot = udot
{-# DEPRECATED (<.>) "use udot or (×)" #-}
infixl 7 <.>
(<.>) :: Product e => Vector e -> Vector e -> e
(<.>) = udot
|
