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+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE FunctionalDependencies #-}
+{-# LANGUAGE UndecidableInstances #-}
+
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Data.Packed.Numeric
+-- Copyright   :  (c) Alberto Ruiz 2010-14
+-- License     :  BSD3
+-- Maintainer  :  Alberto Ruiz
+-- Stability   :  provisional
+--
+-- 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".
+--
+-----------------------------------------------------------------------------
+{-# OPTIONS_HADDOCK hide #-}
+
+module Data.Packed.Numeric (
+    -- * Basic functions
+    module Data.Packed,
+    Konst(..), Build(..),
+    linspace,
+    diag, ident,
+    ctrans,
+    -- * Generic operations
+    Container(..),
+    -- add, mul, sub, divide, equal, scaleRecip, addConstant,
+    scalar, conj, scale, arctan2, cmap,
+    atIndex, minIndex, maxIndex, minElement, maxElement,
+    sumElements, prodElements,
+    step, cond, find, assoc, accum,
+    Transposable(..), Linear(..),
+    -- * Matrix product
+    Product(..), udot, dot, (◇),
+    Mul(..),
+    Contraction(..),(<.>),
+    optimiseMult,
+    mXm,mXv,vXm,LSDiv,(<\>),
+    outer, kronecker,
+    -- * Random numbers
+    RandDist(..),
+    randomVector,
+    gaussianSample,
+    uniformSample,
+    meanCov,
+    -- * Element conversion
+    Convert(..),
+    Complexable(),
+    RealElement(),
+
+    RealOf, ComplexOf, SingleOf, DoubleOf,
+
+    IndexOf,
+    module Data.Complex,
+    -- * IO
+    module Data.Packed.IO,
+    -- * Misc
+    Testable(..)
+) where
+
+import Data.Packed
+import Data.Packed.Internal.Numeric
+import Data.Complex
+import Numeric.LinearAlgebra.Algorithms(Field,linearSolveSVD)
+import Data.Monoid(Monoid(mconcat))
+import Data.Packed.IO
+import Numeric.LinearAlgebra.Random
+
+------------------------------------------------------------------
+
+{- | Creates a real vector containing a range of values:
+
+>>> linspace 5 (-3,7::Double)
+fromList [-3.0,-0.5,2.0,4.5,7.0]@
+
+>>> linspace 5 (8,2+i) :: Vector (Complex Double)
+fromList [8.0 :+ 0.0,6.5 :+ 0.25,5.0 :+ 0.5,3.5 :+ 0.75,2.0 :+ 1.0]
+
+Logarithmic spacing can be defined as follows:
+
+@logspace n (a,b) = 10 ** linspace n (a,b)@
+-}
+linspace :: (Container Vector e) => Int -> (e, e) -> Vector e
+linspace 0 (a,b) = fromList[(a+b)/2]
+linspace n (a,b) = addConstant a $ scale s $ fromList $ map fromIntegral [0 .. n-1]
+    where s = (b-a)/fromIntegral (n-1)
+
+--------------------------------------------------------
+
+{- | Matrix product, matrix - vector product, and dot product (equivalent to 'contraction')
+
+(This operator can also be written using the unicode symbol ◇ (25c7).)
+
+Examples:
+
+>>> let a = (3><4)   [1..]      :: Matrix Double
+>>> let v = fromList [1,0,2,-1] :: Vector Double
+>>> let u = fromList [1,2,3]    :: Vector Double
+
+>>> a
+(3><4)
+ [ 1.0,  2.0,  3.0,  4.0
+ , 5.0,  6.0,  7.0,  8.0
+ , 9.0, 10.0, 11.0, 12.0 ]
+
+matrix × matrix:
+
+>>> disp 2 (a <.> trans a)
+3x3
+ 30   70  110
+ 70  174  278
+110  278  446
+
+matrix × vector:
+
+>>> a <.> v
+fromList [3.0,11.0,19.0]
+
+dot product:
+
+>>> u <.> fromList[3,2,1::Double]
+10
+
+For complex vectors the first argument is conjugated:
+
+>>> fromList [1,i] <.> fromList[2*i+1,3]
+1.0 :+ (-1.0)
+
+>>> fromList [1,i,1-i] <.> complex a
+fromList [10.0 :+ 4.0,12.0 :+ 4.0,14.0 :+ 4.0,16.0 :+ 4.0]
+-}
+infixl 7 <.>
+(<.>) :: Contraction a b c => a -> b -> c
+(<.>) = contraction
+
+
+class Contraction a b c | a b -> c
+  where
+    -- | Matrix product, matrix - vector product, and dot product
+    contraction :: a -> b -> c
+
+instance (Product t, Container Vector t) => Contraction (Vector t) (Vector t) t where
+    u `contraction` v = conj u `udot` v
+
+instance Product t => Contraction (Matrix t) (Vector t) (Vector t) where
+    contraction = mXv
+
+instance (Container Vector t, Product t) => Contraction (Vector t) (Matrix t) (Vector t) where
+    contraction v m = (conj v) `vXm` m
+
+instance Product t => Contraction (Matrix t) (Matrix t) (Matrix t) where
+    contraction = mXm
+
+
+--------------------------------------------------------------------------------
+
+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)
+infixl 7 <\>
+(<\>) :: (LSDiv c, Field t) => Matrix t -> c t -> c t
+(<\>) = linSolve
+
+class LSDiv c
+  where
+    linSolve :: Field t => Matrix t -> c t -> c t
+
+instance LSDiv Vector
+  where
+    linSolve m v = flatten (linearSolveSVD m (reshape 1 v))
+
+instance LSDiv Matrix
+  where
+    linSolve = linearSolveSVD
+
+--------------------------------------------------------------------------------
+
+class Konst e d c | d -> c, c -> d
+  where
+    -- |
+    -- >>> konst 7 3 :: Vector Float
+    -- fromList [7.0,7.0,7.0]
+    --
+    -- >>> konst i (3::Int,4::Int)
+    -- (3><4)
+    --  [ 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0
+    --  , 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0
+    --  , 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0 ]
+    --
+    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 5 (**2) :: Vector Double
+    -- fromList [0.0,1.0,4.0,9.0,16.0]
+    --
+    -- Hilbert matrix of order N:
+    --
+    -- >>> let hilb n = build (n,n) (\i j -> 1/(i+j+1)) :: Matrix Double
+    -- >>> putStr . dispf 2 $ hilb 3
+    -- 3x3
+    -- 1.00  0.50  0.33
+    -- 0.50  0.33  0.25
+    -- 0.33  0.25  0.20
+    --
+    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'
+
+--------------------------------------------------------------------------------
+
+-- | alternative unicode symbol (25c7) for 'contraction'
+(◇) :: Contraction a b c => a -> b -> c
+infixl 7 ◇
+(◇) = contraction
+
+-- | dot product: @cdot u v = 'udot' ('conj' u) v@
+dot :: (Container Vector t, Product t) => Vector t -> Vector t -> t
+dot u v = udot (conj u) v
+
+--------------------------------------------------------------------------------
+
+optimiseMult :: Monoid (Matrix t) => [Matrix t] -> Matrix t
+optimiseMult = mconcat
+
+--------------------------------------------------------------------------------
+
+
+{- | Compute mean vector and covariance matrix of the rows of a matrix.
+
+>>> meanCov $ gaussianSample 666 1000 (fromList[4,5]) (diagl[2,3])
+(fromList [4.010341078059521,5.0197204699640405],
+(2><2)
+ [     1.9862461923890056, -1.0127225830525157e-2
+ , -1.0127225830525157e-2,     3.0373954915729318 ])
+
+-}
+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)
+
+--------------------------------------------------------------------------------
+