static dimensions, cont.

10 files changed, 536 insertions, 229 deletions

diff --git a/packages/base/hmatrix.cabal b/packages/base/hmatrix.cabal
index e958de0..3ca6659 100644
--- a/packages/base/hmatrix.cabal
+++ b/packages/base/hmatrix.cabal
@@ -47,7 +47,7 @@ library
                         Numeric.HMatrix
                         Numeric.LinearAlgebra.Devel
                         Numeric.LinearAlgebra.Data
-
+                        Numeric.LinearAlgebra.Real
 
 
     other-modules:      Data.Packed.Internal,
@@ -67,7 +67,6 @@ library
                         Numeric.LinearAlgebra.Random
                         Numeric.Conversion
                         Numeric.Sparse
-                        Numeric.LinearAlgebra.Util.Static
 
     C-sources:          src/C/lapack-aux.c
                         src/C/vector-aux.c
diff --git a/packages/base/src/Data/Packed/Internal/Numeric.hs b/packages/base/src/Data/Packed/Internal/Numeric.hs
index 3c1c1d0..0205a17 100644
--- a/packages/base/src/Data/Packed/Internal/Numeric.hs
+++ b/packages/base/src/Data/Packed/Internal/Numeric.hs
@@ -3,6 +3,7 @@
 {-# LANGUAGE FlexibleContexts #-}
 {-# LANGUAGE FlexibleInstances #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE FunctionalDependencies #-}
 {-# LANGUAGE UndecidableInstances #-}
 
 -----------------------------------------------------------------------------
@@ -692,12 +693,12 @@ condV f a b l e t = f a' b' l' e' t'
 
 --------------------------------------------------------------------------------
 
-class Transposable t
+class Transposable m mt | m -> mt, mt -> m
   where
     -- | (conjugate) transpose
-    tr :: t -> t
+    tr :: m -> mt
 
-instance (Container Vector t) => Transposable (Matrix t)
+instance (Container Vector t) => Transposable (Matrix t) (Matrix t)
   where
     tr = ctrans
 
diff --git a/packages/base/src/Data/Packed/Numeric.hs b/packages/base/src/Data/Packed/Numeric.hs
index 01cf6c5..7d88cbc 100644
--- a/packages/base/src/Data/Packed/Numeric.hs
+++ b/packages/base/src/Data/Packed/Numeric.hs
@@ -32,7 +32,7 @@ module Data.Packed.Numeric (
     diag, ident,
     ctrans,
     -- * Generic operations
-    Container(..),
+    Container(..), Numeric,
     -- add, mul, sub, divide, equal, scaleRecip, addConstant,
     scalar, conj, scale, arctan2, cmap,
     atIndex, minIndex, maxIndex, minElement, maxElement,
@@ -40,7 +40,7 @@ module Data.Packed.Numeric (
     step, cond, find, assoc, accum,
     Transposable(..), Linear(..),
     -- * Matrix product
-    Product(..), udot, dot, (◇),
+    Product(..), udot, dot, (◇), (<·>), (#>),
     Mul(..),
     Contraction(..),(<.>),
     optimiseMult,
@@ -96,7 +96,7 @@ linspace n (a,b) = addConstant a $ scale s $ fromList $ map fromIntegral [0 .. n
 
 --------------------------------------------------------
 
-{- | Matrix product, matrix - vector product, and dot product (equivalent to 'contraction')
+{- Matrix product, matrix - vector product, and dot product (equivalent to 'contraction')
 
 (This operator can also be written using the unicode symbol ◇ (25c7).)
 
@@ -138,9 +138,8 @@ For complex vectors the first argument is conjugated:
 >>> 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
@@ -160,6 +159,23 @@ instance (Container Vector t, Product t) => Contraction (Vector t) (Matrix t) (V
 instance Product t => Contraction (Matrix t) (Matrix t) (Matrix t) where
     contraction = mXm
 
+--------------------------------------------------------------------------------
+
+infixl 7 <.>
+-- | An infix synonym for 'dot'
+(<.>) :: Numeric t => Vector t -> Vector t -> t
+(<.>) = dot
+
+
+infixr 8 <·>, #>
+-- | dot product
+(<·>) :: Numeric t => Vector t -> Vector t -> t
+(<·>) = dot
+
+
+-- | matrix-vector product
+(#>) :: Numeric t => Matrix t -> Vector t -> Vector t
+(#>) = mXv
 
 --------------------------------------------------------------------------------
 
@@ -286,3 +302,16 @@ meanCov x = (med,cov) where
 
 --------------------------------------------------------------------------------
 
+class ( Container Vector t
+      , Container Matrix t
+      , Konst t Int Vector
+      , Konst t (Int,Int) Matrix
+      , Product t
+      ) => Numeric t
+
+instance Numeric Double
+instance Numeric (Complex Double)
+instance Numeric Float
+instance Numeric (Complex Float)
+
+--------------------------------------------------------------------------------
diff --git a/packages/base/src/Numeric/HMatrix.hs b/packages/base/src/Numeric/HMatrix.hs
index d5c66fb..1c70ef6 100644
--- a/packages/base/src/Numeric/HMatrix.hs
+++ b/packages/base/src/Numeric/HMatrix.hs
@@ -10,16 +10,16 @@ Stability   :  provisional
 -----------------------------------------------------------------------------
 module Numeric.HMatrix (
 
-    -- * Basic types and data processing    
+    -- * 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
@@ -29,7 +29,7 @@ module Numeric.HMatrix (
     -- 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
@@ -37,13 +37,14 @@ module Numeric.HMatrix (
     --  , 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
+    -- * Products
+    -- ** dot
+    (<·>),
+    -- ** matrix-vector
+     (#>),(!#>),
+    -- ** matrix-matrix
+     (<>),
+    -- | 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.
     --
@@ -55,12 +56,12 @@ module Numeric.HMatrix (
     --
     -- 'mconcat' uses 'optimiseMult' to get the optimal association order.
 
-     
-    -- * Other products
+
+    -- ** other
     outer, kronecker, cross,
     scale,
     sumElements, prodElements,
-    
+
     -- * Linear Systems
     (<\>),
     linearSolve,
@@ -70,14 +71,14 @@ module Numeric.HMatrix (
     cholSolve,
     cgSolve,
     cgSolve',
-    
+
     -- * Inverse and pseudoinverse
     inv, pinv, pinvTol,
 
     -- * Determinant and rank
-    rcond, rank, ranksv, 
+    rcond, rank, ranksv,
     det, invlndet,
-    
+
     -- * Singular value decomposition
     svd,
     fullSVD,
@@ -85,7 +86,7 @@ module Numeric.HMatrix (
     compactSVD,
     singularValues,
     leftSV, rightSV,
-    
+
     -- * Eigensystems
     eig, eigSH, eigSH',
     eigenvalues, eigenvaluesSH, eigenvaluesSH',
@@ -105,7 +106,7 @@ module Numeric.HMatrix (
 
     -- * LU
     lu, luPacked,
-    
+
     -- * Matrix functions
     expm,
     sqrtm,
@@ -116,7 +117,7 @@ module Numeric.HMatrix (
     nullVector,
     nullspaceSVD,
     null1, null1sym,
-    
+
     orth,
 
     -- * Norms
@@ -129,30 +130,36 @@ module Numeric.HMatrix (
 
     -- * Random arrays
 
-    RandDist(..), randomVector, rand, randn, gaussianSample, uniformSample,
-    
+    Seed, RandDist(..), randomVector, rand, randn, gaussianSample, uniformSample,
+
     -- * Misc
-    meanCov, peps, relativeError, haussholder, optimiseMult, dot, udot, mXm, mXv, smXv, (<>), (◇), Seed, checkT,
+    meanCov, peps, relativeError, haussholder, optimiseMult, udot,
     -- * Auxiliary classes
-    Element, Container, Product, Numeric, Contraction, LSDiv,
+    Element, Container, Product, Contraction(..), Numeric, LSDiv,
     Complexable, RealElement,
     RealOf, ComplexOf, SingleOf, DoubleOf,
     IndexOf,
     Field,
     Normed,
-    CGMat, Transposable,
-    ℕ,ℤ,ℝ,ℂ,ℝn,ℂn, 𝑖, i_C --ℍ
+    Transposable,
+    CGState(..),
+    Testable(..),
+    ℕ,ℤ,ℝ,ℂ, 𝑖, i_C --ℍ
 ) where
 
 import Numeric.LinearAlgebra.Data
 
 import Numeric.Matrix()
 import Numeric.Vector()
-import Data.Packed.Numeric
+import Data.Packed.Numeric hiding ((<>))
 import Numeric.LinearAlgebra.Algorithms
 import Numeric.LinearAlgebra.Util
 import Numeric.LinearAlgebra.Random
-import Numeric.Sparse(smXv)
+import Numeric.Sparse((!#>))
 import Numeric.LinearAlgebra.Util.CG
 
+-- | matrix product
+(<>) :: Numeric t => Matrix t -> Matrix t -> Matrix t
+(<>) = mXm
+infixr 8 <>
 
diff --git a/packages/base/src/Numeric/LinearAlgebra/Data.hs b/packages/base/src/Numeric/LinearAlgebra/Data.hs
index 3128a24..3417a5e 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Data.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Data.hs
@@ -49,13 +49,9 @@ module Numeric.LinearAlgebra.Data(
     find, maxIndex, minIndex, maxElement, minElement, atIndex,
 
     -- * Sparse
-    SMatrix, AssocMatrix, mkCSR, toDense,
-    mkDiag,
-
-    -- * Static dimensions
+    GMatrix, AssocMatrix, mkSparse, toDense,
+    mkDiagR, dense,
     
-    Static, ddata, R, vect0, sScalar, vect2, vect3, (&),
-
     -- * IO
     disp,
     loadMatrix, saveMatrix,
@@ -79,9 +75,8 @@ module Numeric.LinearAlgebra.Data(
 import Data.Packed.Vector
 import Data.Packed.Matrix
 import Data.Packed.Numeric
-import Numeric.LinearAlgebra.Util hiding ((&))
+import Numeric.LinearAlgebra.Util hiding ((&),(#))
 import Data.Complex
 import Numeric.Sparse
-import Numeric.LinearAlgebra.Util.Static
 
 
diff --git a/packages/base/src/Numeric/LinearAlgebra/Real.hs b/packages/base/src/Numeric/LinearAlgebra/Real.hs
new file mode 100644
index 0000000..db15705
--- /dev/null
+++ b/packages/base/src/Numeric/LinearAlgebra/Real.hs
@@ -0,0 +1,337 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE KindSignatures #-}
+{-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE FunctionalDependencies #-}
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE EmptyDataDecls #-}
+{-# LANGUAGE Rank2Types #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE ViewPatterns #-}
+{-# LANGUAGE GADTs #-}
+
+
+{- |
+Module      :  Numeric.LinearAlgebra.Real
+Copyright   :  (c) Alberto Ruiz 2006-14
+License     :  BSD3
+Stability   :  provisional
+
+Experimental interface for real arrays with statically checked dimensions.
+
+-}
+
+module Numeric.LinearAlgebra.Real(
+    -- * Vector
+    R,
+    vec2, vec3, vec4, 𝕧, (&),
+    -- * Matrix
+    L, Sq,
+    𝕞,
+    (#),(¦),(——),
+     Konst(..),
+     eye,
+     diagR, diag,
+     blockAt,
+    -- * Products
+     (<>),(#>),(<·>),
+     -- * Pretty printing
+     Disp(..),
+     -- * Misc
+     Dim, unDim,
+    module Numeric.HMatrix
+) where
+
+
+import GHC.TypeLits
+import Numeric.HMatrix hiding ((<>),(#>),(<·>),Konst(..),diag, disp,(¦),(——))
+import qualified Numeric.HMatrix as LA
+import Data.Packed.ST
+
+newtype Dim (n :: Nat) t = Dim t
+  deriving Show
+
+unDim :: Dim n t -> t
+unDim (Dim x) = x
+
+data Proxy :: Nat -> *
+
+
+lift1F
+  :: (c t -> c t)
+  -> Dim n (c t) -> Dim n (c t)
+lift1F f (Dim v) = Dim (f v)
+
+lift2F
+  :: (c t -> c t -> c t)
+  -> Dim n (c t) -> Dim n (c t) -> Dim n (c t)
+lift2F f (Dim u) (Dim v) = Dim (f u v)
+
+
+
+type R n = Dim n (Vector ℝ)
+
+type L m n = Dim m (Dim n (Matrix ℝ))
+
+
+infixl 4 &
+(&) :: forall n . KnownNat n
+    => R n -> ℝ -> R (n+1)
+Dim v & x = Dim (vjoin [v', scalar x])
+  where
+    d = fromIntegral . natVal $ (undefined :: Proxy n)
+    v' | d > 1 && size v == 1 = LA.konst (v!0) d
+       | otherwise = v
+
+
+-- vect0 :: R 0
+-- vect0 = Dim (fromList[])
+
+𝕧 :: ℝ -> R 1
+𝕧 = Dim . scalar
+
+
+vec2 :: ℝ -> ℝ -> R 2
+vec2 a b = Dim $ runSTVector $ do
+    v <- newUndefinedVector 2
+    writeVector v 0 a
+    writeVector v 1 b
+    return v
+
+vec3 :: ℝ -> ℝ -> ℝ -> R 3
+vec3 a b c = Dim $ runSTVector $ do
+    v <- newUndefinedVector 3
+    writeVector v 0 a
+    writeVector v 1 b
+    writeVector v 2 c
+    return v
+
+
+vec4 :: ℝ -> ℝ -> ℝ -> ℝ -> R 4
+vec4 a b c d = Dim $ runSTVector $ do
+    v <- newUndefinedVector 4
+    writeVector v 0 a
+    writeVector v 1 b
+    writeVector v 2 c
+    writeVector v 3 d
+    return v
+
+
+
+
+instance forall n t . (Num (Vector t), Numeric t )=> Num (Dim n (Vector t))
+  where
+    (+) = lift2F (+)
+    (*) = lift2F (*)
+    (-) = lift2F (-)
+    abs = lift1F abs
+    signum = lift1F signum
+    negate = lift1F negate
+    fromInteger x = Dim (fromInteger x)
+
+instance (Num (Matrix t), Numeric t) => Num (Dim m (Dim n (Matrix t)))
+  where
+    (+) = (lift2F . lift2F) (+)
+    (*) = (lift2F . lift2F) (*)
+    (-) = (lift2F . lift2F) (-)
+    abs = (lift1F . lift1F) abs
+    signum = (lift1F . lift1F) signum
+    negate = (lift1F . lift1F) negate
+    fromInteger x = Dim (Dim (fromInteger x))
+
+--------------------------------------------------------------------------------
+
+class Konst t
+  where
+    konst :: ℝ -> t
+
+instance forall n. KnownNat n => Konst (R n)
+  where
+    konst x = Dim (LA.konst x d)
+      where
+        d = fromIntegral . natVal $ (undefined :: Proxy n)
+
+instance forall m n . (KnownNat m, KnownNat n) => Konst (L m n)
+  where
+    konst x = Dim (Dim (LA.konst x (m',n')))
+      where
+        m' = fromIntegral . natVal $ (undefined :: Proxy m)
+        n' = fromIntegral . natVal $ (undefined :: Proxy n)
+
+--------------------------------------------------------------------------------
+
+diagR :: forall m n k . (KnownNat m, KnownNat n) => ℝ -> R k -> L m n
+diagR x v = Dim (Dim (diagRect x (unDim v) m' n'))
+  where
+    m' = fromIntegral . natVal $ (undefined :: Proxy m)
+    n' = fromIntegral . natVal $ (undefined :: Proxy n)
+
+diag :: KnownNat n => R n -> Sq n
+diag = diagR 0
+
+--------------------------------------------------------------------------------
+
+blockAt :: forall m n . (KnownNat m, KnownNat n) =>  ℝ -> Int -> Int -> Matrix Double -> L m n
+blockAt x r c a = Dim (Dim res)
+  where
+    z = scalar x
+    z1 = LA.konst x (r,c)
+    z2 = LA.konst x (max 0 (m'-(ra+r)), max 0 (n'-(ca+c)))
+    ra = min (rows a) . max 0 $ m'-r
+    ca = min (cols a) . max 0 $ n'-c
+    sa = subMatrix (0,0) (ra, ca) a
+    m' = fromIntegral . natVal $ (undefined :: Proxy m)
+    n' = fromIntegral . natVal $ (undefined :: Proxy n)
+    res = fromBlocks [[z1,z,z],[z,sa,z],[z,z,z2]]
+
+{-
+matrix :: (KnownNat m, KnownNat n) => Matrix Double -> L n m
+matrix = blockAt 0 0 0
+-}
+
+--------------------------------------------------------------------------------
+
+class Disp t
+  where
+    disp :: Int -> t -> IO ()
+
+instance Disp (L n m)
+  where
+    disp n (d2 -> a) = do
+        if rows a == 1 && cols a == 1
+            then putStrLn $ "Const " ++ (last . words . LA.dispf n $ a)
+            else putStr "Dim " >> LA.disp n a
+
+instance Disp (R n)
+  where
+    disp n (unDim -> v) = do
+        let su = LA.dispf n (asRow v)
+        if LA.size v == 1
+            then putStrLn $ "Const " ++ (last . words $ su )
+            else putStr "Dim " >> putStr (tail . dropWhile (/='x') $ su)
+
+--------------------------------------------------------------------------------
+
+infixl 3 #
+(#) :: L r c -> R c -> L (r+1) c
+Dim (Dim m) # Dim v = Dim (Dim (m LA.—— asRow v))
+
+
+𝕞  :: forall n . KnownNat n => L 0 n
+𝕞  = Dim (Dim (LA.konst 0 (0,d)))
+  where
+    d = fromIntegral . natVal $ (undefined :: Proxy n)
+
+infixl 3 ¦
+(¦) :: L r c1 -> L r c2 -> L r (c1+c2)
+Dim (Dim a) ¦ Dim (Dim b) = Dim (Dim (a LA.¦ b))
+
+infixl 2 ——
+(——) :: L r1 c -> L r2 c -> L (r1+r2) c
+Dim (Dim a) —— Dim (Dim b) = Dim (Dim (a LA.—— b))
+
+
+{-
+
+-}
+
+type Sq n = L n n
+
+type GL = (KnownNat n, KnownNat m) => L m n
+type GSq = KnownNat n => Sq n
+
+infixr 8 <>
+(<>) :: L m k -> L k n -> L m n
+(d2 -> a) <> (d2 -> b) = Dim (Dim (a LA.<> b))
+
+infixr 8 #>
+(#>) :: L m n -> R n -> R m
+(d2 -> m) #> (unDim -> v) = Dim (m LA.#> v)
+
+infixr 8 <·>
+(<·>) :: R n -> R n -> ℝ
+(unDim -> u) <·> (unDim -> v) = udot u v
+
+
+d2 :: forall c (n :: Nat) (n1 :: Nat). Dim n1 (Dim n c) -> c
+d2 = unDim . unDim
+
+
+instance Transposable (L m n) (L n m)
+  where
+    tr (Dim (Dim a)) = Dim (Dim (tr a))
+
+
+eye :: forall n . KnownNat n => Sq n
+eye = Dim (Dim (ident d))
+  where
+    d = fromIntegral . natVal $ (undefined :: Proxy n)
+
+
+--------------------------------------------------------------------------------
+
+test :: (Bool, IO ())
+test = (ok,info)
+  where
+    ok =   d2 (eye :: Sq 5) == ident 5
+           && d2 (mTm sm :: Sq 3) == tr ((3><3)[1..]) LA.<> (3><3)[1..]
+           && d2 (tm :: L 3 5) == mat 5 [1..15]
+           && thingS == thingD
+           && precS == precD
+
+    info = do
+        print $ u
+        print $ v
+        print (eye :: Sq 3)
+        print $ ((u & 5) + 1) <·> v
+        print (tm :: L 2 5)
+        print (tm <> sm :: L 2 3)
+        print thingS
+        print thingD
+        print precS
+        print precD
+
+    u = vec2 3 5
+
+    v = 𝕧 2 & 4 & 7
+
+    mTm :: L n m -> Sq m
+    mTm a = tr a <> a
+
+    tm :: GL
+    tm = lmat 0 [1..]
+
+    lmat :: forall m n . (KnownNat m, KnownNat n) => ℝ -> [ℝ] -> L m n
+    lmat z xs = Dim . Dim . reshape n' . fromList . take (m'*n') $ xs ++ repeat z
+      where
+        m' = fromIntegral . natVal $ (undefined :: Proxy m)
+        n' = fromIntegral . natVal $ (undefined :: Proxy n)
+
+    sm :: GSq
+    sm = lmat 0 [1..]
+
+    thingS = (u & 1) <·> tr q #> q #> v
+      where
+        q = tm :: L 10 3
+
+    thingD = vjoin [unDim u, 1] LA.<·> tr m LA.#> m LA.#> unDim v
+      where
+        m = mat 3 [1..30]
+
+    precS = (1::Double) + (2::Double) * ((1 :: R 3) * (u & 6)) <·> konst 2 #> v
+    precD = 1 + 2 * vjoin[unDim u, 6] LA.<·> LA.konst 2 (size (unDim u) +1, size (unDim v)) LA.#> unDim v
+
+
+instance (KnownNat n', KnownNat m') => Testable (L n' m')
+  where
+    checkT _ = test
+
+{-
+do (snd test)
+fst test
+-}
+
+
+
diff --git a/packages/base/src/Numeric/LinearAlgebra/Util.hs b/packages/base/src/Numeric/LinearAlgebra/Util.hs
index a319785..47b1090 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Util.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Util.hs
@@ -32,7 +32,7 @@ module Numeric.LinearAlgebra.Util(
     rand, randn,
     cross,
     norm,
-    ℕ,ℤ,ℝ,ℂ,ℝn,ℂn,𝑖,i_C, --ℍ
+    ℕ,ℤ,ℝ,ℂ,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,
@@ -70,8 +70,8 @@ type ℝ = Double
 type ℕ = Int
 type ℤ = Int
 type ℂ = Complex Double
-type ℝn = Vector ℝ
-type ℂn = Vector ℂ
+--type ℝn = Vector ℝ
+--type ℂn = Vector ℂ
 --newtype ℍ m = H m
 
 i_C, 𝑖 :: ℂ
@@ -84,7 +84,7 @@ i_C = 𝑖
 fromList [1.0,2.0,3.0,4.0,5.0]
 
 -}
-vect :: [ℝ] -> ℝn
+vect :: [ℝ] -> Vector ℝ
 vect = fromList
 
 {- | create a real matrix
@@ -103,18 +103,6 @@ mat
 mat c = reshape c . fromList
 
 
-
-class ( Container Vector t
-      , Container Matrix t
-      , Konst t Int Vector
-      , Konst t (Int,Int) Matrix
-      ) => Numeric t
-
-instance Numeric Double
-instance Numeric (Complex Double)
-
-
-
 {- | print a real matrix with given number of digits after the decimal point
 
 >>> disp 5 $ ident 2 / 3
diff --git a/packages/base/src/Numeric/LinearAlgebra/Util/CG.hs b/packages/base/src/Numeric/LinearAlgebra/Util/CG.hs
index 5e2ea84..50372f1 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Util/CG.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Util/CG.hs
@@ -3,11 +3,14 @@
 
 module Numeric.LinearAlgebra.Util.CG(
     cgSolve, cgSolve',
-    CGMat, CGState(..), R, V
+    CGState(..), R, V
 ) where
 
 import Data.Packed.Numeric
+import Numeric.Sparse
 import Numeric.Vector()
+import Numeric.LinearAlgebra.Algorithms(linearSolveLS, relativeError, NormType(..))
+import Control.Arrow((***))
 
 {-
 import Util.Misc(debug, debugMat)
@@ -51,7 +54,7 @@ cg sym at a (CGState p r r2 x _) = CGState p' r' r'2 x' rdx
     rdx = norm2 dx / max 1 (norm2 x)
 
 conjugrad
-  :: (Transposable m, Contraction m V V)
+  :: (Transposable m mt, Contraction m V V, Contraction mt V V)
   => Bool -> m -> V -> V -> R -> R -> [CGState]
 conjugrad sym a b = solveG (tr a ◇) (a ◇) (cg sym) b
 
@@ -82,27 +85,88 @@ takeUntil q xs = a++ take 1 b
   where
     (a,b) = break q xs
 
-class (Transposable m, Contraction m V V) => CGMat m
-
 cgSolve
-  :: CGMat m
-  => Bool     -- ^ is symmetric
-  -> m        -- ^ coefficient matrix
+  :: Bool          -- ^ is symmetric
+  -> GMatrix       -- ^ coefficient matrix
   -> Vector Double -- ^ right-hand side
-  -> Vector Double        -- ^ solution
+  -> Vector Double -- ^ solution
 cgSolve sym a b  = cgx $ last $ cgSolve' sym 1E-4 1E-3 n a b 0
   where
     n = max 10 (round $ sqrt (fromIntegral (dim b) :: Double))
 
 cgSolve'
-  :: CGMat m
-  => Bool      -- ^ symmetric
+  :: Bool      -- ^ symmetric
   -> R         -- ^ relative tolerance for the residual (e.g. 1E-4)
   -> R         -- ^ relative tolerance for δx (e.g. 1E-3)
   -> Int       -- ^ maximum number of iterations
-  -> m         -- ^ coefficient matrix
+  -> GMatrix   -- ^ coefficient matrix
   -> V         -- ^ initial solution
   -> V         -- ^ right-hand side
   -> [CGState] -- ^ solution
 cgSolve' sym er es n a b x = take n $ conjugrad sym a b x er es
 
+
+--------------------------------------------------------------------------------
+
+instance Testable GMatrix
+  where
+    checkT _ = (ok,info)
+      where
+        sma = convo2 20 3
+        x1 = vect [1..20]
+        x2 = vect [1..40]
+        sm = mkSparse sma
+        dm = toDense sma
+
+        s1 = sm !#> x1
+        d1 = dm #> x1
+
+        s2 = tr sm !#> x2
+        d2 = tr dm #> x2
+
+        sdia = mkDiagR 40 20 (vect [1..10])
+        s3 =    sdia !#> x1
+        s4 = tr sdia !#> x2
+        ddia = diagRect 0 (vect [1..10])  40 20
+        d3 = ddia #> x1
+        d4 = tr ddia #> x2
+
+        v = testb 40
+        s5 = cgSolve False sm v
+        d5 = denseSolve dm v
+
+        info = do
+            print sm
+            disp (toDense sma)
+            print s1; print d1
+            print s2; print d2
+            print s3; print d3
+            print s4; print d4
+            print s5; print d5
+            print $ relativeError Infinity s5 d5
+
+        ok = s1==d1
+          && s2==d2
+          && s3==d3
+          && s4==d4
+          && relativeError Infinity s5 d5 < 1E-10
+
+        disp = putStr . dispf 2
+
+        vect = fromList :: [Double] -> Vector Double
+
+        convomat :: Int -> Int -> AssocMatrix
+        convomat n k = [ ((i,j `mod` n),1) | i<-[0..n-1], j <- [i..i+k-1]]
+
+        convo2 :: Int -> Int -> AssocMatrix
+        convo2 n k = m1 ++ m2
+          where
+            m1 = convomat n k
+            m2 = map (((+n) *** id) *** id) m1
+            
+        testb n = vect $ take n $ cycle ([0..10]++[9,8..1])
+        
+        denseSolve a = flatten . linearSolveLS a . asColumn
+
+        -- mkDiag v = mkDiagR (dim v) (dim v) v
+
diff --git a/packages/base/src/Numeric/LinearAlgebra/Util/Static.hs b/packages/base/src/Numeric/LinearAlgebra/Util/Static.hs
deleted file mode 100644
index a3f8eb0..0000000
--- a/packages/base/src/Numeric/LinearAlgebra/Util/Static.hs
+++ /dev/null
@@ -1,70 +0,0 @@
-{-# LANGUAGE DataKinds #-}
-{-# LANGUAGE KindSignatures #-}
-{-# LANGUAGE GeneralizedNewtypeDeriving #-}
-{-# LANGUAGE MultiParamTypeClasses #-}
-{-# LANGUAGE FlexibleContexts #-}
-{-# LANGUAGE ScopedTypeVariables #-}
-{-# LANGUAGE EmptyDataDecls #-}
-{-# LANGUAGE Rank2Types #-}
-{-# LANGUAGE FlexibleInstances #-}
-{-# LANGUAGE TypeOperators #-}
-
-module Numeric.LinearAlgebra.Util.Static(
-    Static (ddata),
-    R,
-    vect0, sScalar, vect2, vect3, (&)
-) where
-
-
-import GHC.TypeLits
-import Data.Packed.Numeric
-import Numeric.Vector()
-import Numeric.LinearAlgebra.Util(Numeric,ℝ)
-
-lift1F :: (Vector t -> Vector t) -> Static n (Vector t) -> Static n (Vector t)
-lift1F f (Static v) = Static (f v)
-
-lift2F :: (Vector t -> Vector t -> Vector t) -> Static n (Vector t) -> Static n (Vector t) -> Static n (Vector t)
-lift2F f (Static u) (Static v) = Static (f u v)
-
-newtype Static (n :: Nat) t = Static { ddata :: t } deriving Show
-
-type R n = Static n (Vector ℝ)
-
-
-infixl 4 &
-(&) :: R n -> ℝ -> R (n+1)
-Static v & x = Static (vjoin [v, scalar x])
-
-vect0 :: R 0
-vect0 = Static (fromList[])
-
-sScalar :: ℝ -> R 1
-sScalar = Static . scalar
-
-
-vect2 :: ℝ -> ℝ -> R 2
-vect2 x1 x2 = Static (fromList [x1,x2])
-
-vect3 :: ℝ -> ℝ -> ℝ -> R 3
-vect3 x1 x2 x3 = Static (fromList [x1,x2,x3])
-
-
-
-
-
-
-instance forall n t . (KnownNat n, Num (Vector t), Numeric t )=> Num (Static n (Vector t))
-  where
-    (+) = lift2F add
-    (*) = lift2F mul
-    (-) = lift2F sub
-    abs = lift1F abs
-    signum = lift1F signum
-    negate = lift1F (scale (-1))
-    fromInteger x = Static (konst (fromInteger x) d)
-      where
-        d = fromIntegral . natVal $ (undefined :: Proxy n)
-
-data Proxy :: Nat -> *
-
diff --git a/packages/base/src/Numeric/Sparse.hs b/packages/base/src/Numeric/Sparse.hs
index 2df4578..4d05bdc 100644
--- a/packages/base/src/Numeric/Sparse.hs
+++ b/packages/base/src/Numeric/Sparse.hs
@@ -3,11 +3,11 @@
 {-# LANGUAGE FlexibleInstances #-}
 
 module Numeric.Sparse(
-    SMatrix(..),
-    mkCSR, mkDiag,
+    GMatrix(..),
+    mkSparse, mkDiagR, dense,
     AssocMatrix,
     toDense,
-    smXv
+    gmXv, (!#>)
 )where
 
 import Data.Packed.Numeric
@@ -17,8 +17,7 @@ import Control.Arrow((***))
 import Control.Monad(when)
 import Data.List(groupBy, sort)
 import Foreign.C.Types(CInt(..))
-import Numeric.LinearAlgebra.Util.CG(CGMat,cgSolve)
-import Numeric.LinearAlgebra.Algorithms(linearSolveLS, relativeError, NormType(..))
+
 import Data.Packed.Development
 import System.IO.Unsafe(unsafePerformIO)
 import Foreign(Ptr)
@@ -29,7 +28,7 @@ c ~!~ msg = when c (error msg)
 
 type AssocMatrix = [((Int,Int),Double)]
 
-data SMatrix
+data GMatrix
     = CSR
         { csrVals :: Vector Double
         , csrCols :: Vector CInt
@@ -46,14 +45,26 @@ data SMatrix
         }
     | Diag
         { diagVals :: Vector Double
+        , nRows    :: Int
+        , nCols    :: Int
+        }
+    | Dense
+        { gmDense :: Matrix Double
         , nRows   :: Int
         , nCols   :: Int
         }
 --    | Banded
     deriving Show
 
-mkCSR :: AssocMatrix -> SMatrix
-mkCSR sm' = CSR{..}
+dense :: Matrix Double -> GMatrix
+dense m = Dense{..}
+  where
+    gmDense = m
+    nRows = rows m
+    nCols = cols m
+
+mkSparse :: AssocMatrix -> GMatrix
+mkSparse sm' = CSR{..}
   where
     sm = sort sm'
     rws = map ((fromList *** fromList)
@@ -78,37 +89,47 @@ mkDiagR r c v
     nCols = c
     diagVals = v
 
-mkDiag v = mkDiagR (dim v) (dim v) v
-
 
 type IV t = CInt -> Ptr CInt   -> t
 type  V t = CInt -> Ptr Double -> t
 type SMxV = V (IV (IV (V (V (IO CInt)))))
 
-smXv :: SMatrix -> Vector Double -> Vector Double
-smXv CSR{..} v = unsafePerformIO $ do
-    dim v /= nCols ~!~ printf "smXv (CSR): incorrect sizes: (%d,%d) x %d" nRows nCols (dim v)
+gmXv :: GMatrix -> Vector Double -> Vector Double
+gmXv CSR{..} v = unsafePerformIO $ do
+    dim v /= nCols ~!~ printf "gmXv (CSR): incorrect sizes: (%d,%d) x %d" nRows nCols (dim v)
     r <- createVector nRows
     app5 c_smXv vec csrVals vec csrCols vec csrRows vec v vec r "CSRXv"
     return r
 
-smXv CSC{..} v = unsafePerformIO $ do
-    dim v /= nCols ~!~ printf "smXv (CSC): incorrect sizes: (%d,%d) x %d" nRows nCols (dim v)
+gmXv CSC{..} v = unsafePerformIO $ do
+    dim v /= nCols ~!~ printf "gmXv (CSC): incorrect sizes: (%d,%d) x %d" nRows nCols (dim v)
     r <- createVector nRows
     app5 c_smTXv vec cscVals vec cscRows vec cscCols vec v vec r "CSCXv"
     return r
 
-smXv Diag{..} v
+gmXv Diag{..} v
     | dim v == nCols
         = vjoin [ subVector 0 (dim diagVals) v `mul` diagVals
                 , konst 0 (nRows - dim diagVals) ]
-    | otherwise = error $ printf "smXv (Diag): incorrect sizes: (%d,%d) [%d] x %d"
+    | otherwise = error $ printf "gmXv (Diag): incorrect sizes: (%d,%d) [%d] x %d"
                                  nRows nCols (dim diagVals) (dim v)
 
+gmXv Dense{..} v
+    | dim v == nCols
+        = mXv gmDense v
+    | otherwise = error $ printf "gmXv (Dense): incorrect sizes: (%d,%d) x %d"
+                                 nRows nCols (dim v)
+
 
-instance Contraction SMatrix (Vector Double) (Vector Double)
+-- | general matrix - vector product
+infixr 8 !#>
+(!#>) :: GMatrix -> Vector Double -> Vector Double
+(!#>) = gmXv
+
+
+instance Contraction GMatrix (Vector Double) (Vector Double)
   where
-    contraction = smXv
+    contraction = gmXv
 
 --------------------------------------------------------------------------------
 
@@ -127,75 +148,11 @@ toDense asm = assoc (r+1,c+1) 0 asm
 
 
 
-instance Transposable SMatrix
+instance Transposable GMatrix GMatrix
   where
     tr (CSR vs cs rs n m) = CSC vs cs rs m n
     tr (CSC vs rs cs n m) = CSR vs rs cs m n
     tr (Diag v n m) = Diag v m n
+    tr (Dense a n m) = Dense (tr a) m n
 
 
-instance CGMat SMatrix
-instance CGMat (Matrix Double)
-
---------------------------------------------------------------------------------
-
-instance Testable SMatrix
-  where
-    checkT _ = (ok,info)
-      where
-        sma = convo2 20 3
-        x1 = vect [1..20]
-        x2 = vect [1..40]
-        sm = mkCSR sma
-        dm = toDense sma
-
-        s1 = sm ◇ x1
-        d1 = dm  ◇  x1
-
-        s2 = tr sm  ◇  x2
-        d2 = tr dm  ◇  x2
-
-        sdia = mkDiagR 40 20 (vect [1..10])
-        s3 =    sdia  ◇  x1
-        s4 = tr sdia  ◇  x2
-        ddia = diagRect 0 (vect [1..10])  40 20
-        d3 = ddia  ◇  x1
-        d4 = tr ddia  ◇  x2
-
-        v = testb 40
-        s5 = cgSolve False sm v
-        d5 = denseSolve dm v
-
-        info = do
-            print sm
-            disp (toDense sma)
-            print s1; print d1
-            print s2; print d2
-            print s3; print d3
-            print s4; print d4
-            print s5; print d5
-            print $ relativeError Infinity s5 d5
-
-        ok = s1==d1
-          && s2==d2
-          && s3==d3
-          && s4==d4
-          && relativeError Infinity s5 d5 < 1E-10
-
-        disp = putStr . dispf 2
-
-        vect = fromList :: [Double] -> Vector Double
-
-        convomat :: Int -> Int -> AssocMatrix
-        convomat n k = [ ((i,j `mod` n),1) | i<-[0..n-1], j <- [i..i+k-1]]
-
-        convo2 :: Int -> Int -> AssocMatrix
-        convo2 n k = m1 ++ m2
-          where
-            m1 = convomat n k
-            m2 = map (((+n) *** id) *** id) m1
-            
-        testb n = vect $ take n $ cycle ([0..10]++[9,8..1])
-        
-        denseSolve a = flatten . linearSolveLS a . asColumn
-