7 files changed, 125 insertions, 141 deletions

diff --git a/lib/Data/Packed/Internal/Matrix.hs b/lib/Data/Packed/Internal/Matrix.hs
index d39481d..7a17ef0 100644
--- a/lib/Data/Packed/Internal/Matrix.hs
+++ b/lib/Data/Packed/Internal/Matrix.hs
@@ -245,7 +245,7 @@ compat m1 m2 = rows m1 == rows m2 && cols m1 == cols m2
 
 ------------------------------------------------------------------
 
--- | Auxiliary class.
+-- | Supported element types for basic matrix operations.
 class (Storable a, Floating a) => Element a where
     subMatrixD :: (Int,Int) -- ^ (r0,c0) starting position 
                -> (Int,Int) -- ^ (rt,ct) dimensions of submatrix
diff --git a/lib/Numeric/Container.hs b/lib/Numeric/Container.hs
index aaa068f..e9a8f22 100644
--- a/lib/Numeric/Container.hs
+++ b/lib/Numeric/Container.hs
@@ -25,9 +25,10 @@ module Numeric.Container (
     mXm,mXv,vXm,
     outer, kronecker,
 
-    RealElement, --Precision,
-    ComplexContainer(toComplex,fromComplex,comp,conj),
-    Convert(..), --AutoReal(..),
+    Convert(..),
+    Complexable(),
+    RealElement(),
+
     RealOf, ComplexOf, SingleOf, DoubleOf,
 
     IndexOf,
@@ -54,10 +55,11 @@ type instance IndexOf Matrix = (Int,Int)
 -------------------------------------------------------------------
 
 -- | Basic element-by-element functions for numeric containers
-class (Element e) => Container c e where
-
+class (Complexable c, Element e) => Container c e where
     -- | create a structure with a single element
     scalar      :: e -> c e
+    -- | complex conjugate
+    conj        :: c e -> c e
     scale       :: e -> c e -> c e
     -- | scale the element by element reciprocal of the object:
     --
@@ -75,7 +77,7 @@ class (Element e) => Container c e where
     -- | cannot implement instance Functor because of Element class constraint
     cmap        :: (Element a, Element b) => (a -> b) -> c a -> c b
     -- | constant structure of given size
-    konst    :: e -> IndexOf c -> c e
+    konst       :: e -> IndexOf c -> c e
     --
     -- | indexing function
     atIndex     :: c e -> IndexOf c -> e
@@ -110,6 +112,7 @@ instance Container Vector Float where
     equal u v = dim u == dim v && maxElement (vectorMapF Abs (sub u v)) == 0.0
     scalar x = fromList [x]
     konst = constantD
+    conj = conjugateD
     cmap = mapVector
     atIndex = (@>)
     minIndex     = round . toScalarF MinIdx
@@ -130,6 +133,7 @@ instance Container Vector Double where
     equal u v = dim u == dim v && maxElement (vectorMapR Abs (sub u v)) == 0.0
     scalar x = fromList [x]
     konst = constantD
+    conj = conjugateD
     cmap = mapVector
     atIndex = (@>)
     minIndex     = round . toScalarR MinIdx
@@ -150,6 +154,7 @@ instance Container Vector (Complex Double) where
     equal u v = dim u == dim v && maxElement (mapVector magnitude (sub u v)) == 0.0
     scalar x = fromList [x]
     konst = constantD
+    conj = conjugateD
     cmap = mapVector
     atIndex = (@>)
     minIndex     = minIndex . fst . fromComplex . (zipVectorWith (*) `ap` mapVector conjugate)
@@ -170,6 +175,7 @@ instance Container Vector (Complex Float) where
     equal u v = dim u == dim v && maxElement (mapVector magnitude (sub u v)) == 0.0
     scalar x = fromList [x]
     konst = constantD
+    conj = conjugateD
     cmap = mapVector
     atIndex = (@>)
     minIndex     = minIndex . fst . fromComplex . (zipVectorWith (*) `ap` mapVector conjugate)
@@ -192,6 +198,7 @@ instance (Container Vector a) => Container Matrix a where
     equal a b = cols a == cols b && flatten a `equal` flatten b
     scalar x = (1><1) [x]
     konst v (r,c) = reshape c (konst v (r*c))
+    conj = liftMatrix conjugateD
     cmap f = liftMatrix (mapVector f)
     atIndex = (@@>)
     minIndex m = let (r,c) = (rows m,cols m)
@@ -208,7 +215,7 @@ instance (Container Vector a) => Container Matrix a where
 ----------------------------------------------------
 
 
--- | Linear algebraic properties of objects
+-- | Matrix product and related functions
 class Element e => Product e where
     -- | matrix product
     multiply :: Matrix e -> Matrix e -> Matrix e
@@ -309,4 +316,84 @@ kronecker a b = fromBlocks
               . toRows
               $ flatten a `outer` flatten b
 
-----------------------------------------------------------
+-------------------------------------------------------------------
+
+
+class Convert t where
+    real    :: Container c t => c (RealOf t) -> c t
+    complex :: Container c t => c t -> c (ComplexOf t)
+    single  :: Container c t => c t -> c (SingleOf t)
+    double  :: Container c t => c t -> c (DoubleOf t)
+    toComplex   :: (Container c t, RealElement t) => (c t, c t) -> c (Complex t)
+    fromComplex :: (Container c t, RealElement t) => c (Complex t) -> (c t, c t)
+
+
+instance Convert Double where
+    real = id
+    complex = comp'
+    single = single'
+    double = id
+    toComplex = toComplex'
+    fromComplex = fromComplex'
+
+instance Convert Float where
+    real = id
+    complex = comp'
+    single = id
+    double = double'
+    toComplex = toComplex'
+    fromComplex = fromComplex'
+
+instance Convert (Complex Double) where
+    real = comp'
+    complex = id
+    single = single'
+    double = id
+    toComplex = toComplex'
+    fromComplex = fromComplex'
+
+instance Convert (Complex Float) where
+    real = comp'
+    complex = id
+    single = id
+    double = double'
+    toComplex = toComplex'
+    fromComplex = fromComplex'
+
+-------------------------------------------------------------------
+
+type family RealOf x
+
+type instance RealOf Double = Double
+type instance RealOf (Complex Double) = Double
+
+type instance RealOf Float = Float
+type instance RealOf (Complex Float) = Float
+
+type family ComplexOf x
+
+type instance ComplexOf Double = Complex Double
+type instance ComplexOf (Complex Double) = Complex Double
+
+type instance ComplexOf Float = Complex Float
+type instance ComplexOf (Complex Float) = Complex Float
+
+type family SingleOf x
+
+type instance SingleOf Double = Float
+type instance SingleOf Float  = Float
+
+type instance SingleOf (Complex a) = Complex (SingleOf a)
+
+type family DoubleOf x
+
+type instance DoubleOf Double = Double
+type instance DoubleOf Float  = Double
+
+type instance DoubleOf (Complex a) = Complex (DoubleOf a)
+
+type family ElementOf c
+
+type instance ElementOf (Vector a) = a
+type instance ElementOf (Matrix a) = a
+
diff --git a/lib/Numeric/Conversion.hs b/lib/Numeric/Conversion.hs
index 809ac51..fbf608a 100644
--- a/lib/Numeric/Conversion.hs
+++ b/lib/Numeric/Conversion.hs
@@ -20,24 +20,15 @@
 -----------------------------------------------------------------------------
 
 module Numeric.Conversion (
-    RealElement, --Precision,
-    ComplexContainer(toComplex,fromComplex,conj,comp),
-    Convert(..), --AutoReal(..),
-    RealOf, ComplexOf, SingleOf, DoubleOf,
+    Complexable(..), RealElement,
     module Data.Complex
 ) where
 
-
 import Data.Packed.Internal.Vector
 import Data.Packed.Internal.Matrix
---import Numeric.GSL.Vector
-
 import Data.Complex
---import Control.Monad(ap)
 import Control.Arrow((***))
 
---import Numeric.LinearAlgebra.LAPACK(multiplyR,multiplyC,multiplyF,multiplyQ)
-
 -------------------------------------------------------------------
 
 -- | Supported single-double precision type pairs
@@ -60,24 +51,22 @@ class (Element t, Element (Complex t), RealFloat t
     => RealElement t
 
 instance RealElement Double
-
 instance RealElement Float
 
--- | Conversion utilities
-class ComplexContainer c where
-    toComplex   :: (RealElement e) => (c e, c e) -> c (Complex e)
-    fromComplex :: (RealElement e) => c (Complex e) -> (c e, c e)
-    comp        :: (RealElement e) => c e -> c (Complex e)
-    conj        :: (RealElement e) => c (Complex e) -> c (Complex e)
+
+-- | Structures that may contain complex numbers
+class Complexable c where
+    toComplex'   :: (RealElement e) => (c e, c e) -> c (Complex e)
+    fromComplex' :: (RealElement e) => c (Complex e) -> (c e, c e)
+    comp'        :: (RealElement e) => c e -> c (Complex e)
     single'      :: Precision a b => c b -> c a
     double'      :: Precision a b => c a -> c b
 
 
-instance ComplexContainer Vector where
-    toComplex = toComplexV
-    fromComplex = fromComplexV
-    comp v = toComplex (v,constantD 0 (dim v))
-    conj = conjugateD
+instance Complexable Vector where
+    toComplex' = toComplexV
+    fromComplex' = fromComplexV
+    comp' v = toComplex' (v,constantD 0 (dim v))
     single' = double2FloatG
     double' = float2DoubleG
 
@@ -92,107 +81,11 @@ fromComplexV z = (r,i) where
     [r,i] = toColumns $ reshape 2 $ asReal z
 
 
-instance ComplexContainer Matrix where
-    toComplex = uncurry $ liftMatrix2 $ curry toComplex
-    fromComplex z = (reshape c *** reshape c) . fromComplex . flatten $ z
+instance Complexable Matrix where
+    toComplex' = uncurry $ liftMatrix2 $ curry toComplex'
+    fromComplex' z = (reshape c *** reshape c) . fromComplex' . flatten $ z
         where c = cols z
-    comp = liftMatrix comp
-    conj = liftMatrix conj
+    comp' = liftMatrix comp'
     single' = liftMatrix single'
     double' = liftMatrix double'
 
--------------------------------------------------------------------
-
-type family RealOf x
-
-type instance RealOf Double = Double
-type instance RealOf (Complex Double) = Double
-
-type instance RealOf Float = Float
-type instance RealOf (Complex Float) = Float
-
-type family ComplexOf x
-
-type instance ComplexOf Double = Complex Double
-type instance ComplexOf (Complex Double) = Complex Double
-
-type instance ComplexOf Float = Complex Float
-type instance ComplexOf (Complex Float) = Complex Float
-
-type family SingleOf x
-
-type instance SingleOf Double = Float
-type instance SingleOf Float  = Float
-
-type instance SingleOf (Complex a) = Complex (SingleOf a)
-
-type family DoubleOf x
-
-type instance DoubleOf Double = Double
-type instance DoubleOf Float  = Double
-
-type instance DoubleOf (Complex a) = Complex (DoubleOf a)
-
-type family ElementOf c
-
-type instance ElementOf (Vector a) = a
-type instance ElementOf (Matrix a) = a
-
-
--------------------------------------------------------------------
-
-class (Element t, Element (RealOf t)) => Convert t where
-    real    :: ComplexContainer c => c (RealOf t) -> c t
-    complex :: ComplexContainer c => c t -> c (ComplexOf t)
-    single  :: ComplexContainer c => c t -> c (SingleOf t)
-    double  :: ComplexContainer c => c t -> c (DoubleOf t)
-
-
-instance Convert Double where
-    real = id
-    complex = comp
-    single = single'
-    double = id
-
-instance Convert Float where
-    real = id
-    complex = comp
-    single = id
-    double = double'
-
-instance Convert (Complex Double) where
-    real = comp
-    complex = id
-    single = single'
-    double = id
-
-instance Convert (Complex Float) where
-    real = comp
-    complex = id
-    single = id
-    double = double'
-
--------------------------------------------------------------------
-
--- | to be replaced by Convert
-class Convert t => AutoReal t where
-    real'' :: ComplexContainer c => c Double -> c t
-    complex'' :: ComplexContainer c => c t -> c (Complex Double)
-
-
-instance AutoReal Double where
-    real'' = real
-    complex'' = complex
-
-instance AutoReal (Complex Double) where
-    real'' = real
-    complex'' = complex
-
-instance AutoReal Float where
-    real'' = real . single
-    complex'' = double . complex
-
-instance AutoReal (Complex Float) where
-    real'' = real . single
-    complex'' = double . complex
-
diff --git a/lib/Numeric/LinearAlgebra/Algorithms.hs b/lib/Numeric/LinearAlgebra/Algorithms.hs
index f2f5473..3cd200e 100644
--- a/lib/Numeric/LinearAlgebra/Algorithms.hs
+++ b/lib/Numeric/LinearAlgebra/Algorithms.hs
@@ -82,7 +82,7 @@ import Data.Array
 import Numeric.Container
 
 -- | Auxiliary typeclass used to define generic computations for both real and complex matrices.
-class (Product t, Container Vector t, Container Matrix t) => Field t where
+class (Product t, Convert t, Container Vector t, Container Matrix t) => Field t where
     svd'         :: Matrix t -> (Matrix t, Vector Double, Matrix t)
     thinSVD'     :: Matrix t -> (Matrix t, Vector Double, Matrix t)
     sv'          :: Matrix t -> Vector Double
diff --git a/lib/Numeric/LinearAlgebra/LAPACK.hs b/lib/Numeric/LinearAlgebra/LAPACK.hs
index cb48571..fbc5460 100644
--- a/lib/Numeric/LinearAlgebra/LAPACK.hs
+++ b/lib/Numeric/LinearAlgebra/LAPACK.hs
@@ -259,14 +259,14 @@ eigRaux m = unsafePerformIO $ do
   where r = rows m
         g ra ca pa = dgeev ra ca pa 0 0 nullPtr
 
-fixeig1 s = toComplex (subVector 0 r (asReal s), subVector r r (asReal s))
+fixeig1 s = toComplex' (subVector 0 r (asReal s), subVector r r (asReal s))
     where r = dim s
 
 fixeig  []  _ =  []
-fixeig [_] [v] = [comp v]
+fixeig [_] [v] = [comp' v]
 fixeig ((r1:+i1):(r2:+i2):r) (v1:v2:vs)
-    | r1 == r2 && i1 == (-i2) = toComplex (v1,v2) : toComplex (v1,scale (-1) v2) : fixeig r vs
-    | otherwise = comp v1 : fixeig ((r2:+i2):r) (v2:vs)
+    | r1 == r2 && i1 == (-i2) = toComplex' (v1,v2) : toComplex' (v1,scale (-1) v2) : fixeig r vs
+    | otherwise = comp' v1 : fixeig ((r2:+i2):r) (v2:vs)
   where scale = vectorMapValR Scale
 fixeig _ _ = error "fixeig with impossible inputs"
 
diff --git a/lib/Numeric/LinearAlgebra/Tests.hs b/lib/Numeric/LinearAlgebra/Tests.hs
index aa7b01c..0df29a8 100644
--- a/lib/Numeric/LinearAlgebra/Tests.hs
+++ b/lib/Numeric/LinearAlgebra/Tests.hs
@@ -453,7 +453,7 @@ runTests n = do
         , utest "randomGaussian" randomTestGaussian
         , utest "randomUniform" randomTestUniform
         , utest "buildVector/Matrix" $
-                        comp (10 |> [0::Double ..]) == buildVector 10 fromIntegral
+                        complex (10 |> [0::Double ..]) == buildVector 10 fromIntegral
                      && ident 5 == buildMatrix 5 5 (\(r,c) -> if r==c then 1::Double else 0)
         , utest "rank" $  rank ((2><3)[1,0,0,1,6*eps,0]) == 1
                        && rank ((2><3)[1,0,0,1,7*eps,0]) == 2
diff --git a/lib/Numeric/LinearAlgebra/Tests/Instances.hs b/lib/Numeric/LinearAlgebra/Tests/Instances.hs
index 6046ccb..804c481 100644
--- a/lib/Numeric/LinearAlgebra/Tests/Instances.hs
+++ b/lib/Numeric/LinearAlgebra/Tests/Instances.hs
@@ -1,4 +1,4 @@
-{-# LANGUAGE FlexibleContexts, UndecidableInstances, CPP #-}
+{-# LANGUAGE FlexibleContexts, UndecidableInstances, CPP, FlexibleInstances #-}
 {-# OPTIONS_GHC -fno-warn-unused-imports #-}
 -----------------------------------------------------------------------------
 {- |
@@ -135,10 +135,14 @@ instance (Field a, Arbitrary a, Num (Vector a)) => Arbitrary (Her a) where
     coarbitrary = undefined
 #endif
 
+class (Field a, Arbitrary a, Element (RealOf a), Random (RealOf a)) => ArbitraryField a
+instance ArbitraryField Double
+instance ArbitraryField (Complex Double)
+
 
 -- a well-conditioned general matrix (the singular values are between 1 and 100)
 newtype (WC a) = WC (Matrix a) deriving Show
-instance (Convert a, Field a, Arbitrary a, Random (RealOf a)) => Arbitrary (WC a) where
+instance (ArbitraryField a) => Arbitrary (WC a) where
     arbitrary = do
         m <- arbitrary
         let (u,_,v) = svd m
@@ -157,7 +161,7 @@ instance (Convert a, Field a, Arbitrary a, Random (RealOf a)) => Arbitrary (WC a
 
 -- a well-conditioned square matrix (the singular values are between 1 and 100)
 newtype (SqWC a) = SqWC (Matrix a) deriving Show
-instance (Convert a, Field a, Arbitrary a, Random (RealOf a)) => Arbitrary (SqWC a) where
+instance (ArbitraryField a) => Arbitrary (SqWC a) where
     arbitrary = do
         Sq m <- arbitrary
         let (u,_,v) = svd m
@@ -174,7 +178,7 @@ instance (Convert a, Field a, Arbitrary a, Random (RealOf a)) => Arbitrary (SqWC
 
 -- a positive definite square matrix (the eigenvalues are between 0 and 100)
 newtype (PosDef a) = PosDef (Matrix a) deriving Show
-instance (Convert a, Field a, Arbitrary a, Num (Vector a), Random (RealOf a)) 
+instance (ArbitraryField a, Num (Vector a)) 
     => Arbitrary (PosDef a) where
     arbitrary = do
         Her m <- arbitrary