license changes, reexport modules

21 files changed, 289 insertions, 89 deletions

diff --git a/packages/base/hmatrix-base.cabal b/packages/base/hmatrix-base.cabal
index 3f12dad..638390a 100644
--- a/packages/base/hmatrix-base.cabal
+++ b/packages/base/hmatrix-base.cabal
@@ -39,10 +39,12 @@ library
                         Numeric.LinearAlgebra.LAPACK
                         Numeric.LinearAlgebra.Algorithms
                         Numeric.Container
-                        Numeric.LinearAlgebra
                         Numeric.LinearAlgebra.Util
                         Numeric.LinearAlgebra.Util.Convolution
                         Data.Packed.IO
+                        Numeric.LinearAlgebra.Base
+                        Numeric.LinearAlgebra.Devel
+                        Numeric.LinearAlgebra.Data
                         
     other-modules:      Data.Packed.Internal,
                         Data.Packed.Internal.Common,
diff --git a/packages/base/src/Data/Packed.hs b/packages/base/src/Data/Packed.hs
index c66718a..129bd22 100644
--- a/packages/base/src/Data/Packed.hs
+++ b/packages/base/src/Data/Packed.hs
@@ -10,6 +10,7 @@ Types for dense 'Vector' and 'Matrix' of 'Storable' elements.
 
 -}
 -----------------------------------------------------------------------------
+{-# OPTIONS_HADDOCK hide #-}
 
 module Data.Packed (
     -- * Vector
diff --git a/packages/base/src/Data/Packed/Development.hs b/packages/base/src/Data/Packed/Development.hs
index 6dfd551..1efedc9 100644
--- a/packages/base/src/Data/Packed/Development.hs
+++ b/packages/base/src/Data/Packed/Development.hs
@@ -13,6 +13,7 @@
 -- in the @examples\/devel@ folder included in the package.
 --
 -----------------------------------------------------------------------------
+{-# OPTIONS_HADDOCK hide #-}
 
 module Data.Packed.Development (
     createVector, createMatrix,
diff --git a/packages/base/src/Data/Packed/Foreign.hs b/packages/base/src/Data/Packed/Foreign.hs
index efa51ca..1ec3694 100644
--- a/packages/base/src/Data/Packed/Foreign.hs
+++ b/packages/base/src/Data/Packed/Foreign.hs
@@ -6,6 +6,7 @@
 -- @ glUniformMatrix4fv 0 1 (fromIntegral gl_TRUE) \`appMatrix\` perspective 0.01 100 (pi\/2) (4\/3) 
 -- @
 --
+{-# OPTIONS_HADDOCK hide #-}
 module Data.Packed.Foreign 
     ( app
     , appVector, appVectorLen
diff --git a/packages/base/src/Data/Packed/Internal.hs b/packages/base/src/Data/Packed/Internal.hs
index 537e51e..59a72fc 100644
--- a/packages/base/src/Data/Packed/Internal.hs
+++ b/packages/base/src/Data/Packed/Internal.hs
@@ -2,11 +2,9 @@
 -- |
 -- Module      :  Data.Packed.Internal
 -- Copyright   :  (c) Alberto Ruiz 2007
--- License     :  GPL-style
---
--- Maintainer  :  Alberto Ruiz <aruiz@um.es>
+-- License     :  BSD3
+-- Maintainer  :  Alberto Ruiz
 -- Stability   :  provisional
--- Portability :  portable
 --
 -- Reexports all internal modules
 --
diff --git a/packages/base/src/Data/Packed/Matrix.hs b/packages/base/src/Data/Packed/Matrix.hs
index d94d167..b3be823 100644
--- a/packages/base/src/Data/Packed/Matrix.hs
+++ b/packages/base/src/Data/Packed/Matrix.hs
@@ -8,9 +8,8 @@
 -- |
 -- Module      :  Data.Packed.Matrix
 -- Copyright   :  (c) Alberto Ruiz 2007-10
--- License     :  GPL
---
--- Maintainer  :  Alberto Ruiz <aruiz@um.es>
+-- License     :  BSD3
+-- Maintainer  :  Alberto Ruiz
 -- Stability   :  provisional
 --
 -- A Matrix representation suitable for numerical computations using LAPACK and GSL.
diff --git a/packages/base/src/Data/Packed/Numeric.hs b/packages/base/src/Data/Packed/Numeric.hs
index 4892089..c13e91d 100644
--- a/packages/base/src/Data/Packed/Numeric.hs
+++ b/packages/base/src/Data/Packed/Numeric.hs
@@ -10,7 +10,6 @@
 -- Module      :  Data.Packed.Numeric
 -- Copyright   :  (c) Alberto Ruiz 2010-14
 -- License     :  BSD3
---
 -- Maintainer  :  Alberto Ruiz
 -- Stability   :  provisional
 --
diff --git a/packages/base/src/Data/Packed/ST.hs b/packages/base/src/Data/Packed/ST.hs
index dae457c..5c45c7b 100644
--- a/packages/base/src/Data/Packed/ST.hs
+++ b/packages/base/src/Data/Packed/ST.hs
@@ -9,12 +9,12 @@
 -- License     :  BSD3
 -- Maintainer  :  Alberto Ruiz
 -- Stability   :  provisional
--- Portability :  portable
 --
 -- In-place manipulation inside the ST monad.
 -- See examples/inplace.hs in the distribution.
 --
 -----------------------------------------------------------------------------
+{-# OPTIONS_HADDOCK hide #-}
 
 module Data.Packed.ST (
     -- * Mutable Vectors
diff --git a/packages/base/src/Data/Packed/Vector.hs b/packages/base/src/Data/Packed/Vector.hs
index a8f6bb1..53fe563 100644
--- a/packages/base/src/Data/Packed/Vector.hs
+++ b/packages/base/src/Data/Packed/Vector.hs
@@ -4,9 +4,8 @@
 -- |
 -- Module      :  Data.Packed.Vector
 -- Copyright   :  (c) Alberto Ruiz 2007-10
--- License     :  GPL
---
--- Maintainer  :  Alberto Ruiz <aruiz@um.es>
+-- License     :  BSD3
+-- Maintainer  :  Alberto Ruiz
 -- Stability   :  provisional
 --
 -- 1D arrays suitable for numeric computations using external libraries.
diff --git a/packages/base/src/Numeric/Container.hs b/packages/base/src/Numeric/Container.hs
index b7d3b80..240e5f5 100644
--- a/packages/base/src/Numeric/Container.hs
+++ b/packages/base/src/Numeric/Container.hs
@@ -9,11 +9,9 @@
 -- |
 -- Module      :  Numeric.Container
 -- Copyright   :  (c) Alberto Ruiz 2010-14
--- License     :  GPL
---
--- Maintainer  :  Alberto Ruiz <aruiz@um.es>
+-- License     :  BSD3
+-- Maintainer  :  Alberto Ruiz
 -- Stability   :  provisional
--- Portability :  portable
 --
 -- Basic numeric operations on 'Vector' and 'Matrix', including conversion routines.
 --
diff --git a/packages/base/src/Numeric/LinearAlgebra.hs b/packages/base/src/Numeric/LinearAlgebra.hs
deleted file mode 100644
index 1db860c..0000000
--- a/packages/base/src/Numeric/LinearAlgebra.hs
+++ /dev/null
@@ -1,30 +0,0 @@
------------------------------------------------------------------------------
-{- |
-Module      :  Numeric.LinearAlgebra
-Copyright   :  (c) Alberto Ruiz 2006-10
-License     :  GPL-style
-
-Maintainer  :  Alberto Ruiz (aruiz at um dot es)
-Stability   :  provisional
-Portability :  uses ffi
-
-This module reexports all normally required functions for Linear Algebra applications.
-
-It also provides instances of standard classes 'Show', 'Read', 'Eq',
-'Num', 'Fractional', and 'Floating' for 'Vector' and 'Matrix'.
-In arithmetic operations one-component vectors and matrices automatically
-expand to match the dimensions of the other operand.
-
--}
------------------------------------------------------------------------------
-{-# OPTIONS_HADDOCK hide #-}
-
-module Numeric.LinearAlgebra (
-    module Numeric.Container,
-    module Numeric.LinearAlgebra.Algorithms
-) where
-
-import Numeric.Container
-import Numeric.LinearAlgebra.Algorithms
-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 6f40683..92761be 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Algorithms.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Algorithms.hs
@@ -7,12 +7,10 @@
 -----------------------------------------------------------------------------
 {- |
 Module      :  Numeric.LinearAlgebra.Algorithms
-Copyright   :  (c) Alberto Ruiz 2006-9
-License     :  GPL-style
-
-Maintainer  :  Alberto Ruiz (aruiz at um dot es)
+Copyright   :  (c) Alberto Ruiz 2006-14
+License     :  BSD3
+Maintainer  :  Alberto Ruiz
 Stability   :  provisional
-Portability :  uses ffi
 
 High level generic interface to common matrix computations.
 
@@ -20,6 +18,7 @@ Specific functions for particular base types can also be explicitly
 imported from "Numeric.LinearAlgebra.LAPACK".
 
 -}
+{-# OPTIONS_HADDOCK hide #-}
 -----------------------------------------------------------------------------
 
 module Numeric.LinearAlgebra.Algorithms (
diff --git a/packages/hmatrix/src/Numeric/HMatrix.hs b/packages/base/src/Numeric/LinearAlgebra/Base.hs
index fcd3e02..8aa7846 100644
--- a/packages/hmatrix/src/Numeric/HMatrix.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Base.hs
@@ -1,9 +1,8 @@
 -----------------------------------------------------------------------------
 {- |
-Module      :  Numeric.HMatrix
+Module      :  Numeric.LinearAlgebra
 Copyright   :  (c) Alberto Ruiz 2006-14
-License     :  GPL
-
+License     :  BSD3
 Maintainer  :  Alberto Ruiz
 Stability   :  provisional
 
@@ -11,10 +10,10 @@ This module reexports the most common Linear Algebra functions.
 
 -}
 -----------------------------------------------------------------------------
-module Numeric.HMatrix (
+module Numeric.LinearAlgebra.Base (
 
     -- * Basic types and data processing    
-    module Numeric.HMatrix.Data,
+    module Numeric.LinearAlgebra.Data,
     
     -- | The standard numeric classes are defined elementwise:
     --
@@ -121,19 +120,20 @@ module Numeric.HMatrix (
     corr, conv, corrMin, corr2, conv2,
 
     -- * Random arrays
-    rand, randn, RandDist(..), randomVector, gaussianSample, uniformSample,
+
+    -- |    rand, randn, RandDist(..), randomVector, gaussianSample, uniformSample
     
     -- * Misc
     meanCov, peps, relativeError, haussholder, optimiseMult, udot
 ) where
 
-import Numeric.HMatrix.Data
+import Numeric.LinearAlgebra.Data
 
---import Numeric.Matrix()
---import Numeric.Vector()
+import Numeric.Matrix()
+import Numeric.Vector()
 import Numeric.Container
 import Numeric.LinearAlgebra.Algorithms
 import Numeric.LinearAlgebra.Util
-import Numeric.Random
+
 
 
diff --git a/packages/hmatrix/src/Numeric/HMatrix/Data.hs b/packages/base/src/Numeric/LinearAlgebra/Data.hs
index 5d7ce4f..3bc88f9 100644
--- a/packages/hmatrix/src/Numeric/HMatrix/Data.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Data.hs
@@ -1,9 +1,8 @@
 --------------------------------------------------------------------------------
 {- |
-Module      :  Numeric.HMatrix.Data
+Module      :  Numeric.LinearAlgebra.Data
 Copyright   :  (c) Alberto Ruiz 2014
-License     :  GPL
-
+License     :  BSD3
 Maintainer  :  Alberto Ruiz
 Stability   :  provisional
 
@@ -12,7 +11,7 @@ Basic data processing.
 -}
 --------------------------------------------------------------------------------
 
-module Numeric.HMatrix.Data(
+module Numeric.LinearAlgebra.Data(
 
     -- * Vector
     -- | 1D arrays are storable vectors from the vector package.
@@ -44,10 +43,9 @@ module Numeric.HMatrix.Data(
     find, maxIndex, minIndex, maxElement, minElement, atIndex,
 
     -- * IO
-    disp, dispf, disps, dispcf, latexFormat, format,
-    loadMatrix, saveMatrix, fromFile, fileDimensions,
-    readMatrix,
-    fscanfVector, fprintfVector, freadVector, fwriteVector,
+    disp, dispf, disps, dispcf, latexFormat, format, readMatrix,
+
+    -- | loadMatrix, saveMatrix, fromFile, fileDimensions, fscanfVector, fprintfVector, freadVector, fwriteVector
 
 -- * Conversion
     Convert(..),
@@ -64,7 +62,7 @@ module Numeric.HMatrix.Data(
 import Data.Packed.Vector
 import Data.Packed.Matrix
 import Numeric.Container
-import Numeric.IO
+import Data.Packed.IO
 import Numeric.LinearAlgebra.Util
 import Data.Complex
 
diff --git a/packages/hmatrix/src/Numeric/HMatrix/Devel.hs b/packages/base/src/Numeric/LinearAlgebra/Devel.hs
index b921f44..c41db2d 100644
--- a/packages/hmatrix/src/Numeric/HMatrix/Devel.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Devel.hs
@@ -2,8 +2,7 @@
 {- |
 Module      :  Numeric.HMatrix.Devel
 Copyright   :  (c) Alberto Ruiz 2014
-License     :  GPL
-
+License     :  BSD3
 Maintainer  :  Alberto Ruiz
 Stability   :  provisional
 
@@ -12,7 +11,7 @@ The library can be easily extended using the tools in this module.
 -}
 --------------------------------------------------------------------------------
 
-module Numeric.HMatrix.Devel(
+module Numeric.LinearAlgebra.Devel(
     -- * FFI helpers
     -- | Sample usage, to upload a perspective matrix to a shader.
     --
diff --git a/packages/base/src/Numeric/LinearAlgebra/LAPACK.hs b/packages/base/src/Numeric/LinearAlgebra/LAPACK.hs
index 9cb67d4..40fef45 100644
--- a/packages/base/src/Numeric/LinearAlgebra/LAPACK.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/LAPACK.hs
@@ -3,7 +3,6 @@
 -- Module      :  Numeric.LinearAlgebra.LAPACK
 -- Copyright   :  (c) Alberto Ruiz 2006-14
 -- License     :  BSD3
--- 
 -- Maintainer  :  Alberto Ruiz
 -- Stability   :  provisional
 --
diff --git a/packages/base/src/Numeric/LinearAlgebra/Util.hs b/packages/base/src/Numeric/LinearAlgebra/Util.hs
index 533c54b..f0470ab 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Util.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Util.hs
@@ -3,9 +3,8 @@
 {- |
 Module      :  Numeric.LinearAlgebra.Util
 Copyright   :  (c) Alberto Ruiz 2013
-License     :  GPL
-
-Maintainer  :  Alberto Ruiz (aruiz at um dot es)
+License     :  BSD3
+Maintainer  :  Alberto Ruiz
 Stability   :  provisional
 
 -}
diff --git a/packages/base/src/Numeric/LinearAlgebra/Util/Convolution.hs b/packages/base/src/Numeric/LinearAlgebra/Util/Convolution.hs
index d04c46b..1775f14 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Util/Convolution.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Util/Convolution.hs
@@ -3,9 +3,8 @@
 {- |
 Module      :  Numeric.LinearAlgebra.Util.Convolution
 Copyright   :  (c) Alberto Ruiz 2012
-License     :  GPL
-
-Maintainer  :  Alberto Ruiz (aruiz at um dot es)
+License     :  BSD3
+Maintainer  :  Alberto Ruiz
 Stability   :  provisional
 
 -}
@@ -17,7 +16,7 @@ module Numeric.LinearAlgebra.Util.Convolution(
    corr2, conv2, separable
 ) where
 
-import Numeric.LinearAlgebra
+import Numeric.Container
 
 
 vectSS :: Element t => Int -> Vector t -> Matrix t
diff --git a/packages/base/src/Numeric/Matrix.hs b/packages/base/src/Numeric/Matrix.hs
index 3478aae..962ee84 100644
--- a/packages/base/src/Numeric/Matrix.hs
+++ b/packages/base/src/Numeric/Matrix.hs
@@ -7,12 +7,11 @@
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Numeric.Matrix
--- Copyright   :  (c) Alberto Ruiz 2010
--- License     :  GPL-style
+-- Copyright   :  (c) Alberto Ruiz 2014
+-- License     :  BSD3
 --
--- Maintainer  :  Alberto Ruiz <aruiz@um.es>
+-- Maintainer  :  Alberto Ruiz
 -- Stability   :  provisional
--- Portability :  portable
 --
 -- Provides instances of standard classes 'Show', 'Read', 'Eq',
 -- 'Num', 'Fractional', and 'Floating' for 'Matrix'.
diff --git a/packages/base/src/Numeric/Vector.hs b/packages/base/src/Numeric/Vector.hs
index 2769cd9..3a425f5 100644
--- a/packages/base/src/Numeric/Vector.hs
+++ b/packages/base/src/Numeric/Vector.hs
@@ -7,11 +7,10 @@
 -- |
 -- Module      :  Numeric.Vector
 -- Copyright   :  (c) Alberto Ruiz 2011
--- License     :  GPL-style
+-- License     :  BSD3
 --
--- Maintainer  :  Alberto Ruiz <aruiz@um.es>
+-- Maintainer  :  Alberto Ruiz
 -- Stability   :  provisional
--- Portability :  portable
 --
 -- Provides instances of standard classes 'Show', 'Read', 'Eq',
 -- 'Num', 'Fractional',  and 'Floating' for 'Vector'.
diff --git a/packages/hmatrix/src/Numeric/Container.hs b/packages/hmatrix/src/Numeric/Container.hs
new file mode 100644
index 0000000..146780d
--- /dev/null
+++ b/packages/hmatrix/src/Numeric/Container.hs
@@ -0,0 +1,241 @@
+{-# 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
+-- 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".
+--
+-----------------------------------------------------------------------------
+{-# OPTIONS_HADDOCK hide #-}
+
+module Numeric.Container (
+    -- * Basic functions
+    module Data.Packed,
+    konst, build,
+    linspace,
+    diag, ident,
+    ctrans,
+    -- * Generic operations
+    Container(..),
+    -- * Matrix product
+    Product(..), udot, dot, (◇),
+    Mul(..),
+    Contraction(..),
+    optimiseMult,
+    mXm,mXv,vXm,LSDiv(..),
+    outer, kronecker,
+    -- * Element conversion
+    Convert(..),
+    Complexable(),
+    RealElement(),
+
+    RealOf, ComplexOf, SingleOf, DoubleOf,
+
+    IndexOf,
+    module Data.Complex
+) where
+
+import Data.Packed hiding (stepD, stepF, condD, condF, conjugateC, conjugateQ)
+import Data.Packed.Numeric
+import Data.Complex
+import Numeric.LinearAlgebra.Algorithms(Field,linearSolveSVD)
+import Data.Monoid(Monoid(mconcat))
+
+------------------------------------------------------------------
+
+{- | 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)
+
+--------------------------------------------------------
+
+class Contraction a b c | a b -> c
+  where
+    infixl 7 <.>
+    {- | Matrix product, matrix vector product, and dot product
+
+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]
+
+-}
+    (<.>) :: a -> b -> c
+
+
+instance (Product t, Container Vector t) => Contraction (Vector t) (Vector t) t where
+    u <.> v = conj u `udot` v
+
+instance Product t => Contraction (Matrix t) (Vector t) (Vector t) where
+    (<.>) = mXv
+
+instance (Container Vector t, Product t) => Contraction (Vector t) (Matrix t) (Vector t) where
+    (<.>) v m = (conj v) `vXm` m
+
+instance Product t => Contraction (Matrix t) (Matrix t) (Matrix t) where
+    (<.>) = 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 operator for '(\<.\>)'
+
+x25c7, white diamond
+
+-}
+(◇) :: Contraction a b c => a -> b -> c
+infixl 7 ◇
+(◇) = (<.>)
+
+-- | 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
+