backward compatibility

9 files changed, 351 insertions, 424 deletions

diff --git a/packages/base/src/Numeric/Container.hs b/packages/base/src/Numeric/Container.hs
index 067c5fa..6a841aa 100644
--- a/packages/base/src/Numeric/Container.hs
+++ b/packages/base/src/Numeric/Container.hs
@@ -1,258 +1,49 @@
-{-# LANGUAGE TypeFamilies #-}
-{-# LANGUAGE FlexibleContexts #-}
-{-# LANGUAGE FlexibleInstances #-}
-{-# LANGUAGE MultiParamTypeClasses #-}
-{-# LANGUAGE FunctionalDependencies #-}
-{-# LANGUAGE UndecidableInstances #-}
-
------------------------------------------------------------------------------
--- |
--- Module      :  Numeric.Container
--- 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 Numeric.Container (
-    -- * Basic functions
+module Numeric.Container(
     module Data.Packed,
-    konst, build,
+    constant,
     linspace,
-    diag, ident,
+    diag,
+    ident,
     ctrans,
-    -- * Generic operations
-    Container,
-    add, mul, sub, divide, equal, scaleRecip, addConstant,
-    scalar, conj, scale, arctan2, cmap,
-    atIndex, minIndex, maxIndex, minElement, maxElement,
+    Container(scaleRecip, addConstant,add, sub, mul, divide, equal),
+    scalar,
+    conj,
+    scale,
+    arctan2,
+    cmap,
+    Konst(..),
+    Build(..),
+    atIndex,
+    minIndex, maxIndex, minElement, maxElement,
     sumElements, prodElements,
     step, cond, find, assoc, accum,
-    Transposable(..), Linear(..),
-    -- * Matrix product
-    Product(..), udot, dot, (◇),
-    Mul(..),
-    Contraction(..),(<.>),
+    Element(..),
+    Product(..),
     optimiseMult,
-    mXm,mXv,vXm,LSDiv(..),
+    mXm, mXv, vXm, (<.>),
+    Mul(..),
+    LSDiv, (<\>),
     outer, kronecker,
-    -- * Random numbers
     RandDist(..),
-    randomVector,
-    gaussianSample,
-    uniformSample,
-    -- * Element conversion
+    randomVector, gaussianSample, uniformSample,
+    meanCov,
     Convert(..),
-    Complexable(),
-    RealElement(),
-
-    RealOf, ComplexOf, SingleOf, DoubleOf,
-
-    IndexOf,
+    Complexable,
+    RealElement,
+    RealOf, ComplexOf, SingleOf, DoubleOf, IndexOf,
     module Data.Complex,
-    -- * IO
-    module Data.Packed.IO,
-    -- * Misc
-    Testable(..)
+    dispf, disps, dispcf, vecdisp, latexFormat, format,
+    loadMatrix, saveMatrix, readMatrix
 ) where
 
-import Data.Packed hiding (stepD, stepF, condD, condF, conjugateC, conjugateQ)
-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
-
---------------------------------------------------------------------------------
-
-class LSDiv c where
- infixl 7 <\>
- -- | least squares solution of a linear system, similar to the \\ operator of Matlab\/Octave (based on linearSolveSVD)
- (<\>)  :: Field t => Matrix t -> c t -> c t
-
-instance LSDiv Vector where
-    m <\> v = flatten (linearSolveSVD m (reshape 1 v))
-
-instance LSDiv Matrix where
-    (<\>) = 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
-
---------------------------------------------------------------------------------
+import Data.Packed.Numeric
+import Data.Packed
+import Data.Packed.Internal(constantD)
+import Data.Complex
 
-optimiseMult :: Monoid (Matrix t) => [Matrix t] -> Matrix t
-optimiseMult = mconcat
+constant :: Element a => a -> Int -> Vector a
+constant = constantD
 
diff --git a/packages/base/src/Numeric/HMatrix.hs b/packages/base/src/Numeric/HMatrix.hs
new file mode 100644
index 0000000..a56c3d2
--- /dev/null
+++ b/packages/base/src/Numeric/HMatrix.hs
@@ -0,0 +1,158 @@
+-----------------------------------------------------------------------------
+{- |
+Module      :  Numeric.HMatrix
+Copyright   :  (c) Alberto Ruiz 2006-14
+License     :  BSD3
+Maintainer  :  Alberto Ruiz
+Stability   :  provisional
+
+-}
+-----------------------------------------------------------------------------
+module Numeric.HMatrix (
+
+    -- * Basic types and data processing    
+    module Numeric.LinearAlgebra.Data,
+    
+    -- * Arithmetic and numeric classes
+    -- |
+    -- The standard numeric classes are defined elementwise:
+    --
+    -- >>> fromList [1,2,3] * fromList [3,0,-2 :: Double]
+    -- fromList [3.0,0.0,-6.0]
+    -- 
+    -- >>> (3><3) [1..9] * ident 3 :: Matrix Double
+    -- (3><3)
+    --  [ 1.0, 0.0, 0.0
+    --  , 0.0, 5.0, 0.0
+    --  , 0.0, 0.0, 9.0 ]
+    --
+    -- In arithmetic operations single-element vectors and matrices
+    -- (created from numeric literals or using 'scalar') automatically
+    -- expand to match the dimensions of the other operand:
+    -- 
+    -- >>> 5 + 2*ident 3 :: Matrix Double
+    -- (3><3)
+    --  [ 7.0, 5.0, 5.0
+    --  , 5.0, 7.0, 5.0
+    --  , 5.0, 5.0, 7.0 ]
+    --
+
+    -- * Matrix product
+    (<.>),
+
+    -- | The overloaded multiplication operators may need type annotations to remove
+    -- ambiguity. In those cases we can also use the specific functions 'mXm', 'mXv', and 'dot'.
+    --
+    -- The matrix x matrix product is also implemented in the "Data.Monoid" instance, where
+    -- single-element matrices (created from numeric literals or using 'scalar')
+    -- are used for scaling.
+    --
+    -- >>> let m = (2><3)[1..] :: Matrix Double
+    -- >>> m <> 2 <> diagl[0.5,1,0]
+    -- (2><3)
+    -- [ 1.0,  4.0, 0.0
+    -- , 4.0, 10.0, 0.0 ]
+    --
+    -- 'mconcat' uses 'optimiseMult' to get the optimal association order.
+
+     
+    -- * Other products
+    outer, kronecker, cross,
+    scale,
+    sumElements, prodElements,
+    
+    -- * Linear Systems
+    (<\>),
+    linearSolve,
+    linearSolveLS,
+    linearSolveSVD,
+    luSolve,
+    cholSolve,
+    cgSolve,
+    cgSolve',
+    
+    -- * Inverse and pseudoinverse
+    inv, pinv, pinvTol,
+
+    -- * Determinant and rank
+    rcond, rank, ranksv, 
+    det, invlndet,
+    
+    -- * Singular value decomposition
+    svd,
+    fullSVD,
+    thinSVD,
+    compactSVD,
+    singularValues,
+    leftSV, rightSV,
+    
+    -- * Eigensystems
+    eig, eigSH, eigSH',
+    eigenvalues, eigenvaluesSH, eigenvaluesSH',
+    geigSH',
+
+    -- * QR
+    qr, rq, qrRaw, qrgr,
+
+    -- * Cholesky
+    chol, cholSH, mbCholSH,
+
+    -- * Hessenberg
+    hess,
+
+    -- * Schur
+    schur,
+
+    -- * LU
+    lu, luPacked,
+    
+    -- * Matrix functions
+    expm,
+    sqrtm,
+    matFunc,
+
+    -- * Nullspace
+    nullspacePrec,
+    nullVector,
+    nullspaceSVD,
+    null1, null1sym,
+    
+    orth,
+
+    -- * Norms
+    norm_0, norm_1, norm_2, norm_Inf,
+    mnorm_0, mnorm_1, mnorm_2, mnorm_Inf,
+    norm_Frob, norm_nuclear,
+
+    -- * Correlation and convolution
+    corr, conv, corrMin, corr2, conv2,
+
+    -- * Random arrays
+
+    RandDist(..), randomVector, rand, randn, gaussianSample, uniformSample,
+    
+    -- * Misc
+    meanCov, peps, relativeError, haussholder, optimiseMult, dot, udot, mXm, mXv, smXv, (<>), (◇), Seed, checkT,
+    -- * Auxiliary classes
+    Element, Container, Product, Contraction, LSDiv,
+    Complexable, RealElement,
+    RealOf, ComplexOf, SingleOf, DoubleOf,
+    IndexOf,
+    Field,
+    Normed,
+    CGMat, Transposable,
+    ℕ,ℤ,ℝ,ℂ,ℝn,ℂn, 𝑖, i_C --ℍ
+) where
+
+import Numeric.LinearAlgebra.Data
+
+import Numeric.Matrix()
+import Numeric.Vector()
+import Data.Packed.Numeric
+import Numeric.LinearAlgebra.Algorithms
+import Numeric.LinearAlgebra.Util
+import Numeric.LinearAlgebra.Random
+import Numeric.Sparse(smXv)
+import Numeric.LinearAlgebra.Util.CG
+
+
diff --git a/packages/base/src/Numeric/LinearAlgebra.hs b/packages/base/src/Numeric/LinearAlgebra.hs
index 242122f..ad315e4 100644
--- a/packages/base/src/Numeric/LinearAlgebra.hs
+++ b/packages/base/src/Numeric/LinearAlgebra.hs
@@ -1,4 +1,4 @@
------------------------------------------------------------------------------
+--------------------------------------------------------------------------------
 {- |
 Module      :  Numeric.LinearAlgebra
 Copyright   :  (c) Alberto Ruiz 2006-14
@@ -7,149 +7,16 @@ Maintainer  :  Alberto Ruiz
 Stability   :  provisional
 
 -}
------------------------------------------------------------------------------
-module Numeric.LinearAlgebra (
-
-    -- * Basic types and data processing    
-    module Numeric.LinearAlgebra.Data,
-    
-    -- * Arithmetic and numeric classes
-    -- |
-    -- The standard numeric classes are defined elementwise:
-    --
-    -- >>> fromList [1,2,3] * fromList [3,0,-2 :: Double]
-    -- fromList [3.0,0.0,-6.0]
-    -- 
-    -- >>> (3><3) [1..9] * ident 3 :: Matrix Double
-    -- (3><3)
-    --  [ 1.0, 0.0, 0.0
-    --  , 0.0, 5.0, 0.0
-    --  , 0.0, 0.0, 9.0 ]
-    --
-    -- In arithmetic operations single-element vectors and matrices
-    -- (created from numeric literals or using 'scalar') automatically
-    -- expand to match the dimensions of the other operand:
-    -- 
-    -- >>> 5 + 2*ident 3 :: Matrix Double
-    -- (3><3)
-    --  [ 7.0, 5.0, 5.0
-    --  , 5.0, 7.0, 5.0
-    --  , 5.0, 5.0, 7.0 ]
-    --
-
-    -- * Matrix product
-    (<.>),
-
-    -- | The overloaded multiplication operators may need type annotations to remove
-    -- ambiguity. In those cases we can also use the specific functions 'mXm', 'mXv', and 'dot'.
-    --
-    -- The matrix x matrix product is also implemented in the "Data.Monoid" instance, where
-    -- single-element matrices (created from numeric literals or using 'scalar')
-    -- are used for scaling.
-    --
-    -- >>> let m = (2><3)[1..] :: Matrix Double
-    -- >>> m <> 2 <> diagl[0.5,1,0]
-    -- (2><3)
-    -- [ 1.0,  4.0, 0.0
-    -- , 4.0, 10.0, 0.0 ]
-    --
-    -- 'mconcat' uses 'optimiseMult' to get the optimal association order.
-
-     
-    -- * Other products
-    outer, kronecker, cross,
-    scale,
-    sumElements, prodElements, absSum,
-    
-    -- * Linear Systems
-    (<\>),
-    linearSolve,
-    linearSolveLS,
-    linearSolveSVD,
-    luSolve,
-    cholSolve,
-    cgSolve,
-    cgSolve',
-    
-    -- * Inverse and pseudoinverse
-    inv, pinv, pinvTol,
-
-    -- * Determinant and rank
-    rcond, rank, ranksv, 
-    det, invlndet,
-    
-    -- * Singular value decomposition
-    svd,
-    fullSVD,
-    thinSVD,
-    compactSVD,
-    singularValues,
-    leftSV, rightSV,
-    
-    -- * Eigensystems
-    eig, eigSH, eigSH',
-    eigenvalues, eigenvaluesSH, eigenvaluesSH',
-    geigSH',
-
-    -- * QR
-    qr, rq, qrRaw, qrgr,
-
-    -- * Cholesky
-    chol, cholSH, mbCholSH,
-
-    -- * Hessenberg
-    hess,
-
-    -- * Schur
-    schur,
-
-    -- * LU
-    lu, luPacked,
-    
-    -- * Matrix functions
-    expm,
-    sqrtm,
-    matFunc,
+--------------------------------------------------------------------------------
+{-# OPTIONS_HADDOCK hide #-}
 
-    -- * Nullspace
-    nullspacePrec,
-    nullVector,
-    nullspaceSVD,
-    null1, null1sym,
-    
-    orth,
-
-    -- * Norms
-    norm1, norm2, normInf, pnorm, NormType(..),
-
-    -- * Correlation and convolution
-    corr, conv, corrMin, corr2, conv2,
-
-    -- * Random arrays
-
-    RandDist(..), randomVector, rand, randn, gaussianSample, uniformSample,
-    
-    -- * Misc
-    meanCov, peps, relativeError, haussholder, optimiseMult, dot, udot, mXm, mXv, smXv, (<>), (◇), Seed, checkT,
-    -- * Auxiliary classes
-    Element, Container, Product, Contraction, LSDiv,
-    Complexable(), RealElement(),
-    RealOf, ComplexOf, SingleOf, DoubleOf,
-    IndexOf,
-    Field, Normed,
-    CGMat, Transposable,
-    R,V
+module Numeric.LinearAlgebra (
+    module Numeric.Container,
+    module Numeric.LinearAlgebra.Algorithms
 ) where
 
-import Numeric.LinearAlgebra.Data
-
-import Numeric.Matrix()
-import Numeric.Vector()
 import Numeric.Container
 import Numeric.LinearAlgebra.Algorithms
-import Numeric.LinearAlgebra.Util
-import Numeric.LinearAlgebra.Random
-import Numeric.Sparse(smXv)
-import Numeric.LinearAlgebra.Util.CG
-
+import Numeric.Matrix()
+import Numeric.Vector()
 
diff --git a/packages/base/src/Numeric/LinearAlgebra/Algorithms.hs b/packages/base/src/Numeric/LinearAlgebra/Algorithms.hs
index c7e7043..bbcc513 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Algorithms.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Algorithms.hs
@@ -76,12 +76,12 @@ module Numeric.LinearAlgebra.Algorithms (
 ) where
 
 
-import Data.Packed.Development hiding ((//))
 import Data.Packed
 import Numeric.LinearAlgebra.LAPACK as LAPACK
 import Data.List(foldl1')
 import Data.Array
 import Data.Packed.Internal.Numeric
+import Data.Packed.Internal(shSize)
 
 
 {- | Generic linear algebra functions for double precision real and complex matrices.
diff --git a/packages/base/src/Numeric/LinearAlgebra/Data.hs b/packages/base/src/Numeric/LinearAlgebra/Data.hs
index e3cbe31..89bebbe 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Data.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Data.hs
@@ -16,13 +16,19 @@ module Numeric.LinearAlgebra.Data(
     -- * Vector
     -- | 1D arrays are storable vectors from the vector package.
     
-    Vector, (|>), dim, (@>),
-    
+    vect, (|>),
+
     -- * Matrix
-    Matrix, (><), size, (@@>), trans, ctrans,
+    
+    mat, (><), tr,
+    
+    -- * Indexing
+    
+    size,
+    Indexable(..),
     
     -- * Construction
-    scalar, konst, build, assoc, accum, linspace, -- ones, zeros,
+    scalar, Konst(..), Build(..), assoc, accum, linspace, -- ones, zeros,
 
     -- * Diagonal
     ident, diag, diagl, diagRect, takeDiag,
@@ -62,11 +68,13 @@ module Numeric.LinearAlgebra.Data(
 
     module Data.Complex,
 
+    Vector, Matrix
+
 ) where
 
 import Data.Packed.Vector
 import Data.Packed.Matrix
-import Numeric.Container
+import Data.Packed.Numeric
 import Numeric.LinearAlgebra.Util
 import Data.Complex
 import Numeric.Sparse
diff --git a/packages/base/src/Numeric/LinearAlgebra/Util.hs b/packages/base/src/Numeric/LinearAlgebra/Util.hs
index 2f91e18..a7d6946 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Util.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Util.hs
@@ -1,4 +1,9 @@
 {-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE FunctionalDependencies #-}
+
 -----------------------------------------------------------------------------
 {- |
 Module      :  Numeric.LinearAlgebra.Util
@@ -14,19 +19,24 @@ Stability   :  provisional
 module Numeric.LinearAlgebra.Util(
 
     -- * Convenience functions
-    size, disp,
+    vect, mat,
+    disp,
     zeros, ones,
     diagl,
     row,
     col,
     (&), (¦), (——), (#),
     (?), (¿),
+    Indexable(..), size,
+    rand, randn,
     cross,
     norm,
+    ℕ,ℤ,ℝ,ℂ,ℝn,ℂn,𝑖,i_C, --ℍ
+    norm_1, norm_2, norm_0, norm_Inf, norm_Frob, norm_nuclear,
+    mnorm_1, mnorm_2, mnorm_0, mnorm_Inf,
     unitary,
     mt,
     pairwiseD2,
-    meanCov,
     rowOuters,
     null1,
     null1sym,
@@ -48,13 +58,49 @@ module Numeric.LinearAlgebra.Util(
     vtrans
 ) where
 
-import Numeric.Container
+import Data.Packed.Numeric
 import Numeric.LinearAlgebra.Algorithms hiding (i)
 import Numeric.Matrix()
 import Numeric.Vector()
-
+import Numeric.LinearAlgebra.Random
 import Numeric.LinearAlgebra.Util.Convolution
 
+type ℝ = Double
+type ℕ = Int
+type ℤ = Int
+type ℂ = Complex Double
+type ℝn = Vector ℝ
+type ℂn = Vector ℂ
+--newtype ℍ m = H m
+
+i_C, 𝑖 :: ℂ
+𝑖 = 0:+1
+i_C = 𝑖
+
+{- | create a real vector
+
+>>> vect [1..5]
+fromList [1.0,2.0,3.0,4.0,5.0]
+
+-}
+vect :: [ℝ] -> ℝn
+vect = fromList
+
+{- | create a real matrix
+
+>>> mat 5 [1..15]
+(3><5)
+ [  1.0,  2.0,  3.0,  4.0,  5.0
+ ,  6.0,  7.0,  8.0,  9.0, 10.0
+ , 11.0, 12.0, 13.0, 14.0, 15.0 ]
+
+-}
+mat
+  :: Int -- ^ columns
+  -> [ℝ] -- ^ elements
+  -> Matrix ℝ
+mat c = reshape c . fromList
+
 {- | print a real matrix with given number of digits after the decimal point
 
 >>> disp 5 $ ident 2 / 3
@@ -175,38 +221,97 @@ norm :: Vector Double -> Double
 -- ^ 2-norm of real vector
 norm = pnorm PNorm2
 
+norm_2 :: Normed Vector t => Vector t -> RealOf t
+norm_2 = pnorm PNorm2
+
+norm_1 :: Normed Vector t => Vector t -> RealOf t
+norm_1 = pnorm PNorm1
+
+norm_Inf :: Normed Vector t => Vector t -> RealOf t
+norm_Inf = pnorm Infinity
+
+norm_0 :: Vector ℝ -> ℝ
+norm_0 v = sumElements (step (abs v - scalar (eps*mx)))
+  where
+    mx = norm_Inf v
+
+norm_Frob :: Normed Matrix t => Matrix t -> RealOf t
+norm_Frob = pnorm Frobenius
+
+norm_nuclear :: Field t => Matrix t -> ℝ
+norm_nuclear = sumElements . singularValues
+
+mnorm_2 :: Normed Matrix t => Matrix t -> RealOf t
+mnorm_2 = pnorm PNorm2
+
+mnorm_1 :: Normed Matrix t => Matrix t -> RealOf t
+mnorm_1 = pnorm PNorm1
+
+mnorm_Inf :: Normed Matrix t => Matrix t -> RealOf t
+mnorm_Inf = pnorm Infinity
+
+mnorm_0 :: Matrix ℝ -> ℝ
+mnorm_0 = norm_0 . flatten
 
 -- | Obtains a vector in the same direction with 2-norm=1
 unitary :: Vector Double -> Vector Double
 unitary v = v / scalar (norm v)
 
--- | ('rows' &&& 'cols')
-size :: Matrix t -> (Int, Int)
-size m = (rows m, cols m)
 
 -- | trans . inv
 mt :: Matrix Double -> Matrix Double
 mt = trans . inv
 
 --------------------------------------------------------------------------------
+{- |
+
+>>> size $ fromList[1..10::Double]
+10
+>>> size $ (2><5)[1..10::Double]
+(2,5)
+
+-}
+size :: Container c t => c t -> IndexOf c
+size = size'
 
-{- | Compute mean vector and covariance matrix of the rows of a matrix.
+{- |
+
+>>> vect [1..10] ! 3
+4.0
+
+>>> mat 5 [1..15] ! 1
+fromList [6.0,7.0,8.0,9.0,10.0]
 
->>> 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 ])
+>>> mat 5 [1..15] ! 1 ! 3
+9.0
 
 -}
-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)
+class Indexable c t | c -> t , t -> c
+  where
+    infixl 9 !
+    (!) :: c -> Int -> t
+
+instance Indexable (Vector Double) Double
+  where
+    (!) = (@>)
+
+instance Indexable (Vector Float) Float
+  where
+    (!) = (@>)
+
+instance Indexable (Vector (Complex Double)) (Complex Double)
+  where
+    (!) = (@>)
+
+instance Indexable (Vector (Complex Float)) (Complex Float)
+  where
+    (!) = (@>)
+
+instance Element t => Indexable (Matrix t) (Vector t)
+  where
+    m!j = subVector (j*c) c (flatten m)
+      where
+        c = cols m
 
 --------------------------------------------------------------------------------
 
@@ -220,7 +325,7 @@ pairwiseD2 x y | ok = x2 `outer` oy + ox `outer` y2 - 2* x <> trans y
     ox = one (rows x)
     oy = one (rows y)
     oc = one (cols x)
-    one k = constant 1 k
+    one k = konst 1 k
     x2 = x * x <> oc
     y2 = y * y <> oc
     ok = cols x == cols y
diff --git a/packages/base/src/Numeric/LinearAlgebra/Util/CG.hs b/packages/base/src/Numeric/LinearAlgebra/Util/CG.hs
index d21602d..5e2ea84 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Util/CG.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Util/CG.hs
@@ -6,7 +6,7 @@ module Numeric.LinearAlgebra.Util.CG(
     CGMat, CGState(..), R, V
 ) where
 
-import Numeric.Container
+import Data.Packed.Numeric
 import Numeric.Vector()
 
 {-
diff --git a/packages/base/src/Numeric/LinearAlgebra/Util/Convolution.hs b/packages/base/src/Numeric/LinearAlgebra/Util/Convolution.hs
index e4cba8f..c8c7536 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Util/Convolution.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Util/Convolution.hs
@@ -16,16 +16,18 @@ module Numeric.LinearAlgebra.Util.Convolution(
    corr2, conv2, separable
 ) where
 
-import Numeric.Container
+import Data.Packed.Numeric
 
 
 vectSS :: Element t => Int -> Vector t -> Matrix t
 vectSS n v = fromRows [ subVector k n v | k <- [0 .. dim v - n] ]
 
 
-corr :: Product t => Vector t -- ^ kernel
-                  -> Vector t -- ^ source
-                  -> Vector t
+corr
+  :: (Container Vector t, Product t)
+    => Vector t -- ^ kernel
+    -> Vector t -- ^ source
+    -> Vector t
 {- ^ correlation
 
 >>> corr (fromList[1,2,3]) (fromList [1..10])
@@ -33,12 +35,12 @@ fromList [14.0,20.0,26.0,32.0,38.0,44.0,50.0,56.0]
 
 -}
 corr ker v
-    | dim ker == 0 = constant 0 (dim v)
+    | dim ker == 0 = konst 0 (dim v)
     | dim ker <= dim v = vectSS (dim ker) v <> ker
     | otherwise = error $ "corr: dim kernel ("++show (dim ker)++") > dim vector ("++show (dim v)++")"
 
 
-conv :: (Product t, Num t) => Vector t -> Vector t -> Vector t
+conv :: (Container Vector t, Product t, Num t) => Vector t -> Vector t -> Vector t
 {- ^ convolution ('corr' with reversed kernel and padded input, equivalent to polynomial product)
 
 >>> conv (fromList[1,1]) (fromList [-1,1])
@@ -46,12 +48,12 @@ fromList [-1.0,0.0,1.0]
 
 -}
 conv ker v
-    | dim ker == 0 = constant 0 (dim v)
+    | dim ker == 0 = konst 0 (dim v)
     | otherwise = corr ker' v'
   where
     ker' = (flatten.fliprl.asRow) ker
     v' = vjoin [z,v,z]
-    z = constant 0 (dim ker -1)
+    z = konst 0 (dim ker -1)
 
 corrMin :: (Container Vector t, RealElement t, Product t)
         => Vector t
diff --git a/packages/base/src/Numeric/Sparse.hs b/packages/base/src/Numeric/Sparse.hs
index 1957d3a..2df4578 100644
--- a/packages/base/src/Numeric/Sparse.hs
+++ b/packages/base/src/Numeric/Sparse.hs
@@ -10,7 +10,7 @@ module Numeric.Sparse(
     smXv
 )where
 
-import Numeric.Container
+import Data.Packed.Numeric
 import qualified Data.Vector.Storable as V
 import Data.Function(on)
 import Control.Arrow((***))
@@ -133,10 +133,6 @@ instance Transposable SMatrix
     tr (CSC vs rs cs n m) = CSR vs rs cs m n
     tr (Diag v n m) = Diag v m n
 
-instance Transposable (Matrix Double)
-  where
-    tr = trans
-
 
 instance CGMat SMatrix
 instance CGMat (Matrix Double)