9 files changed, 272 insertions, 37 deletions

diff --git a/lib/Data/Packed/Internal.hs b/lib/Data/Packed/Internal.hs
index a7fca1a..a5a77c5 100644
--- a/lib/Data/Packed/Internal.hs
+++ b/lib/Data/Packed/Internal.hs
@@ -15,9 +15,11 @@
 module Data.Packed.Internal (
     module Data.Packed.Internal.Common,
     module Data.Packed.Internal.Vector,
-    module Data.Packed.Internal.Matrix
+    module Data.Packed.Internal.Matrix,
+    module Data.Packed.Internal.Tensor
 ) where
 
 import Data.Packed.Internal.Common
 import Data.Packed.Internal.Vector
 import Data.Packed.Internal.Matrix
+import Data.Packed.Internal.Tensor
\ No newline at end of file
diff --git a/lib/Data/Packed/Internal/Common.hs b/lib/Data/Packed/Internal/Common.hs
index bdd7f34..1bfed6d 100644
--- a/lib/Data/Packed/Internal/Common.hs
+++ b/lib/Data/Packed/Internal/Common.hs
@@ -40,6 +40,7 @@ instance (Storable a, RealFloat a) => Storable (Complex a) where    --
     poke p (a :+ b) = pokeArray (castPtr p) [a,b]                   --
 ----------------------------------------------------------------------
 
+on :: (a -> a -> b) -> (t -> a) -> t -> t -> b
 on f g = \x y -> f (g x) (g y)
 
 partit :: Int -> [a] -> [[a]]
@@ -54,12 +55,14 @@ common f = commonval . map f where
     commonval [a] = Just a
     commonval (a:b:xs) = if a==b then commonval (b:xs) else Nothing
 
+xor :: Bool -> Bool -> Bool
 xor a b = a && not b || b && not a
 
 (//) :: x -> (x -> y) -> y
 infixl 0 //
 (//) = flip ($)
 
+errorCode :: Int -> String
 errorCode 1000 = "bad size"
 errorCode 1001 = "bad function code"
 errorCode 1002 = "memory problem"
@@ -68,6 +71,7 @@ errorCode 1004 = "singular"
 errorCode 1005 = "didn't converge"
 errorCode n    = "code "++show n
 
+check :: String -> [Vector a] -> IO Int -> IO ()
 check msg ls f = do
     err <- f
     when (err/=0) (error (msg++": "++errorCode err))
@@ -77,7 +81,10 @@ check msg ls f = do
 class (Storable a, Typeable a) => Field a
 instance (Storable a, Typeable a) => Field a
 
+isReal :: (Data.Typeable.Typeable a) => (t -> a) -> t -> Bool
 isReal w x   = typeOf (undefined :: Double) == typeOf (w x)
+
+isComp :: (Data.Typeable.Typeable a) => (t -> a) -> t -> Bool
 isComp w x = typeOf (undefined :: Complex Double) == typeOf (w x)
 
 scast :: forall a . forall b . (Typeable a, Typeable b) => a -> b
diff --git a/lib/Data/Packed/Internal/Matrix.hs b/lib/Data/Packed/Internal/Matrix.hs
index 2925fc0..32dc603 100644
--- a/lib/Data/Packed/Internal/Matrix.hs
+++ b/lib/Data/Packed/Internal/Matrix.hs
@@ -194,7 +194,9 @@ multiplyD order a b
 
 ----------------------------------------------------------------------
 
-outer u v = dat (multiply RowMajor r c)
+outer' u v = dat (outer u v)
+
+outer u v = multiply RowMajor r c
     where r = matrixFromVector RowMajor 1 u
           c = matrixFromVector RowMajor (dim v) v
 
@@ -212,8 +214,7 @@ subMatrixR (r0,c0) (rt,ct) x = unsafePerformIO $ do
     r <- createMatrix RowMajor rt ct
     c_submatrixR r0 (r0+rt-1) c0 (c0+ct-1) // mat cdat x // mat cdat r // check "subMatrixR" [dat r]
     return r
-foreign import ccall "aux.h submatrixR"
-    c_submatrixR :: Int -> Int -> Int -> Int -> TMM
+foreign import ccall "aux.h submatrixR" c_submatrixR :: Int -> Int -> Int -> Int -> TMM
 
 -- | extraction of a submatrix of a complex matrix
 subMatrixC :: (Int,Int) -- ^ (r0,c0) starting position
diff --git a/lib/Data/Packed/Internal/Tensor.hs b/lib/Data/Packed/Internal/Tensor.hs
index 27fce6a..c4faf49 100644
--- a/lib/Data/Packed/Internal/Tensor.hs
+++ b/lib/Data/Packed/Internal/Tensor.hs
@@ -14,18 +14,25 @@
 
 module Data.Packed.Internal.Tensor where
 
-import Data.Packed.Internal
+import Data.Packed.Internal.Common
 import Data.Packed.Internal.Vector
 import Data.Packed.Internal.Matrix
 import Foreign.Storable
 import Data.List(sort,elemIndex,nub)
 
-data IdxTp = Covariant | Contravariant deriving (Show,Eq)
+data IdxType = Covariant | Contravariant deriving (Show,Eq)
 
-data Tensor t = T { dims   :: [(Int,(IdxTp,String))]
+type IdxName = String
+
+data IdxDesc = IdxDesc { idxDim  :: Int,
+                         idxType :: IdxType,
+                         idxName :: IdxName }
+
+data Tensor t = T { dims   :: [IdxDesc]
                   , ten    :: Vector t
                   }
 
+rank :: Tensor t -> Int
 rank = length . dims
 
 instance (Show a,Storable a) => Show (Tensor a) where
@@ -33,41 +40,49 @@ instance (Show a,Storable a) => Show (Tensor a) where
     show T {dims = ds, ten = t} = "("++shdims ds ++") "++ show (toList t)
 
 
-shdims [(n,(t,name))] = name ++ sym t ++"["++show n++"]"
+shdims :: [IdxDesc] -> String
+shdims [IdxDesc n t name] = name ++ sym t ++"["++show n++"]"
     where sym Covariant     = "_"
           sym Contravariant = "^"
 shdims (d:ds) = shdims [d] ++ "><"++ shdims ds
 
 
-
+findIdx :: (Field t) => IdxName -> Tensor t
+        -> (([IdxDesc], [IdxDesc]), Matrix t)
 findIdx name t = ((d1,d2),m) where
-    (d1,d2) = span (\(_,(_,n)) -> n /=name) (dims t)
-    c = product (map fst d2)
+    (d1,d2) = span (\d -> idxName d /= name) (dims t)
+    c = product (map idxDim d2)
     m = matrixFromVector RowMajor c (ten t)
 
+putFirstIdx :: (Field t) => String -> Tensor t -> ([IdxDesc], Matrix t)
 putFirstIdx name t = (nd,m')
     where ((d1,d2),m) = findIdx name t
           m' = matrixFromVector RowMajor c $ cdat $ trans m
           nd = d2++d1
-          c = dim (ten t) `div` (fst $ head d2)
+          c = dim (ten t) `div` (idxDim $ head d2)
 
+part :: (Field t) => Tensor t -> (IdxName, Int) -> Tensor t
 part t (name,k) = if k<0 || k>=l
-                    then error $ "part "++show (name,k)++" out of range in "++show t
+                    then error $ "part "++show (name,k)++" out of range" -- in "++show t
                     else T {dims = ds, ten = toRows m !! k}
     where (d:ds,m) = putFirstIdx name t
-          (l,_) = d
+          l = idxDim d
 
+parts :: (Field t) => Tensor t -> IdxName -> [Tensor t]
 parts t name = map f (toRows m)
     where (d:ds,m) = putFirstIdx name t
-          (l,_) = d
+          l = idxDim d
           f t = T {dims=ds, ten=t}
 
+concatRename :: [IdxDesc] -> [IdxDesc] -> [IdxDesc]
 concatRename l1 l2 = l1 ++ map ren l2 where
-    ren (n,(t,s)) = if {- s `elem` fs -} True then (n,(t,s++"'")) else (n,(t,s))
-    fs = map (snd.snd) l1
+    ren idx = if {- s `elem` fs -} True then idx {idxName = idxName idx ++ "'"} else idx
+    fs = map idxName l1
 
-prod (T d1 v1) (T d2 v2) = T (concatRename d1 d2) (outer v1 v2)
+prod :: (Field t, Num t) => Tensor t -> Tensor t -> Tensor t
+prod (T d1 v1) (T d2 v2) = T (concatRename d1 d2) (outer' v1 v2)
 
+contraction :: (Field t, Num t) => Tensor t -> IdxName -> Tensor t -> IdxName -> Tensor t
 contraction t1 n1 t2 n2 =
     if compatIdx t1 n1 t2 n2
         then T (concatRename (tail d1) (tail d2)) (cdat m)
@@ -76,18 +91,22 @@ contraction t1 n1 t2 n2 =
         (d2,m2) = putFirstIdx n2 t2
         m = multiply RowMajor (trans m1) m2
 
+sumT :: (Storable t, Enum t, Num t) => [Tensor t] -> [t]
 sumT ls = foldl (zipWith (+)) [0,0..] (map (toList.ten) ls)
 
+contract1 :: (Num t, Enum t, Field t) => Tensor t -> IdxName -> IdxName -> Tensor t
 contract1 t name1 name2 = T d $ fromList $ sumT y
     where d = dims (head y)
           x = (map (flip parts name2) (parts t name1))
           y = map head $ zipWith drop [0..] x
 
+contraction' :: (Field t, Enum t, Num t) => Tensor t -> IdxName -> Tensor t -> IdxName -> Tensor t
 contraction' t1 n1 t2 n2 =
     if compatIdx t1 n1 t2 n2
         then contract1 (prod t1 t2) n1 (n2++"'")
         else error "wrong contraction'"
 
+tridx :: (Field t) => [IdxName] -> Tensor t -> Tensor t
 tridx [] t = t
 tridx (name:rest) t = T (d:ds) (join ts) where
     ((_,d:_),_) = findIdx name t
@@ -95,30 +114,38 @@ tridx (name:rest) t = T (d:ds) (join ts) where
     ts = map ten ps
     ds = dims (head ps)
 
-compatIdxAux (n1,(t1,_)) (n2, (t2,_)) = t1 /= t2 && n1 == n2
+compatIdxAux :: IdxDesc -> IdxDesc -> Bool
+compatIdxAux IdxDesc {idxDim = n1, idxType = t1}
+             IdxDesc {idxDim = n2, idxType = t2}
+    = t1 /= t2 && n1 == n2
 
+compatIdx :: (Field t1, Field t) => Tensor t1 -> IdxName -> Tensor t -> IdxName -> Bool
 compatIdx t1 n1 t2 n2 = compatIdxAux d1 d2 where
     d1 = head $ snd $ fst $ findIdx n1 t1
     d2 = head $ snd $ fst $ findIdx n2 t2
 
-names t = sort $ map (snd.snd) (dims t)
+names :: Tensor t -> [IdxName]
+names t = sort $ map idxName (dims t)
 
+normal :: (Field t) => Tensor t -> Tensor t
 normal t = tridx (names t) t
 
+contractions :: (Num t, Field t) => Tensor t -> Tensor t -> [Tensor t]
 contractions t1 t2 = [ contraction t1 n1 t2 n2 | n1 <- names t1, n2 <- names t2, compatIdx t1 n1 t2 n2 ]
 
 -- sent to Haskell-Cafe by Sebastian Sylvan
+perms :: [t] -> [[t]]
 perms [x] = [[x]]
 perms xs = [y:ps | (y,ys) <- selections xs , ps <- perms ys]
 selections []     = []
 selections (x:xs) = (x,xs) : [(y,x:ys) | (y,ys) <- selections xs]
 
-
+interchanges :: (Ord a) => [a] -> Int
 interchanges ls = sum (map (count ls) ls)
-    where count l p = n
+    where count l p = length $ filter (>p) $ take pel l
               where Just pel = elemIndex p l
-                    n = length $ filter (>p) $ take pel l
 
+signature :: (Num t, Ord a) => [a] -> t
 signature l | length (nub l) < length l =  0
             | even (interchanges l)     =  1
             | otherwise                 = -1
diff --git a/lib/Data/Packed/Internal/Vector.hs b/lib/Data/Packed/Internal/Vector.hs
index 8848062..25e848d 100644
--- a/lib/Data/Packed/Internal/Vector.hs
+++ b/lib/Data/Packed/Internal/Vector.hs
@@ -103,15 +103,15 @@ asComplex :: Vector Double -> Vector (Complex Double)
 asComplex v = V { dim = dim v `div` 2, fptr =  castForeignPtr (fptr v), ptr = castPtr (ptr v) }
 
 
-constantG n x = fromList (replicate n x)
+constantG x n = fromList (replicate n x)
 
-constantR :: Int -> Double -> Vector Double
+constantR :: Double -> Int -> Vector Double
 constantR = constantAux cconstantR
 
-constantC :: Int -> Complex Double -> Vector (Complex Double)
+constantC :: Complex Double -> Int -> Vector (Complex Double)
 constantC = constantAux cconstantC
 
-constantAux fun n x = unsafePerformIO $ do
+constantAux fun x n = unsafePerformIO $ do
     v <- createVector n
     px <- newArray [x]
     fun px // vec v // check "constantAux" []
@@ -124,8 +124,8 @@ foreign import ccall safe "aux.h constantR"
 foreign import ccall safe "aux.h constantC"
     cconstantC :: Ptr (Complex Double) -> TCV -- Complex Double :> IO Int
 
-constant :: Field a => Int -> a -> Vector a
-constant n x | isReal id x = scast $ constantR n (scast x)
-             | isComp id x = scast $ constantC n (scast x)
-             | otherwise   = constantG n x
+constant :: Field a => a -> Int -> Vector a
+constant x n | isReal id x = scast $ constantR (scast x) n
+             | isComp id x = scast $ constantC (scast x) n
+             | otherwise   = constantG x n
 
diff --git a/lib/Data/Packed/Matrix.hs b/lib/Data/Packed/Matrix.hs
index ec5744d..c7d5cfa 100644
--- a/lib/Data/Packed/Matrix.hs
+++ b/lib/Data/Packed/Matrix.hs
@@ -16,12 +16,13 @@ module Data.Packed.Matrix (
     Matrix(rows,cols), Field,
     toLists, (><), (>|<), (@@>),
     trans,
-    reshape,
+    reshape, flatten,
     fromRows, toRows, fromColumns, toColumns,
     joinVert, joinHoriz,
     flipud, fliprl,
     liftMatrix, liftMatrix2,
     multiply,
+    outer,
     subMatrix,
     takeRows, dropRows, takeColumns, dropColumns,
     diag, takeDiag, diagRect, ident
@@ -54,11 +55,11 @@ diagRect s r c
     | r == c    = diag s
     | r < c     = trans $ diagRect s c r
     | r > c     = joinVert  [diag s , zeros (r-c,c)]
-    where zeros (r,c) = reshape c $ constant (r*c) 0
+    where zeros (r,c) = reshape c $ constant 0 (r*c)
 
 takeDiag m = fromList [cdat m `at` (k*cols m+k) | k <- [0 .. min (rows m) (cols m) -1]]
 
-ident n = diag (constant n 1)
+ident n = diag (constant 1 n)
 
 r >< c = f where
     f l | dim v == r*c = matrixFromVector RowMajor c v
@@ -88,3 +89,5 @@ dropColumns :: Field t => Int -> Matrix t -> Matrix t
 dropColumns n mat = subMatrix (0,n) (rows mat, cols mat - n) mat
 
 ----------------------------------------------------------------
+
+flatten = cdat
diff --git a/lib/Data/Packed/Plot.hs b/lib/Data/Packed/Plot.hs
new file mode 100644
index 0000000..9eddc9f
--- /dev/null
+++ b/lib/Data/Packed/Plot.hs
@@ -0,0 +1,167 @@
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Data.Packed.Plot
+-- Copyright   :  (c) Alberto Ruiz 2005
+-- License     :  GPL-style
+-- 
+-- Maintainer  :  Alberto Ruiz (aruiz at um dot es)
+-- Stability   :  provisional
+-- Portability :  uses gnuplot and ImageMagick
+--
+-- Very basic (and provisional) drawing tools.
+--
+-----------------------------------------------------------------------------
+
+module Data.Packed.Plot(
+
+    gnuplotX, mplot,
+
+    plot, parametricPlot, 
+
+    splot, mesh, mesh', meshdom,
+
+    matrixToPGM, imshow,
+
+) where
+
+import Data.Packed.Vector
+import Data.Packed.Matrix
+import GSL.Vector(FunCodeS(Max,Min),toScalarR)
+import Data.List(intersperse)
+import System
+import Data.IORef
+import System.Exit
+import Foreign hiding (rotate)
+
+
+size = dim
+
+-- | Loads a real matrix from a formatted ASCII text file 
+--fromFile :: FilePath -> IO Matrix
+--fromFile filename = readFile filename >>= return . readMatrix read
+
+-- | Saves a real matrix to a formatted ascii text file
+toFile :: FilePath -> Matrix Double -> IO ()
+toFile filename matrix = writeFile filename (unlines . map unwords. map (map show) . toLists $ matrix)
+
+------------------------------------------------------------------------
+
+
+-- | From vectors x and y, it generates a pair of matrices to be used as x and y arguments for matrix functions.
+meshdom :: Vector Double -> Vector Double -> (Matrix Double , Matrix Double)
+meshdom r1 r2 = (outer r1 (constant 1 (size r2)), outer (constant 1 (size r1)) r2)
+
+
+gnuplotX command = do {system cmdstr; return()} where
+    cmdstr = "echo \""++command++"\" | gnuplot -persist"
+
+datafollows = "\\\"-\\\""
+
+prep = (++"e\n\n") . unlines . map (unwords . (map show))
+
+
+{- | Draws a 3D surface representation of a real matrix.
+
+> > mesh (hilb 20)
+
+In certain versions you can interactively rotate the graphic using the mouse.
+
+-}
+mesh :: Matrix Double -> IO ()
+mesh m = gnuplotX (command++dat) where
+    command = "splot "++datafollows++" matrix with lines\n"
+    dat = prep $ toLists $ m
+
+mesh' m = do
+    writeFile "splot-gnu-command" "splot \"splot-tmp.txt\" matrix with lines; pause -1"; 
+    toFile "splot-tmp.txt" m
+    putStr "Press [Return] to close the graphic and continue... "
+    system "gnuplot -persist splot-gnu-command"
+    system "rm splot-tmp.txt splot-gnu-command"
+    return ()
+
+{- | Draws the surface represented by the function f in the desired ranges and number of points, internally using 'mesh'.
+
+> > let f x y = cos (x + y) 
+> > splot f (0,pi) (0,2*pi) 50    
+
+-}
+splot :: (Matrix Double->Matrix Double->Matrix Double) -> (Double,Double) -> (Double,Double) -> Int -> IO () 
+splot f rx ry n = mesh' z where
+    (x,y) = meshdom (linspace n rx) (linspace n ry)
+    z = f x y
+
+{- | plots several vectors against the first one -}
+mplot :: [Vector Double] -> IO ()
+mplot m = gnuplotX (commands++dats) where
+    commands = if length m == 1 then command1 else commandmore
+    command1 = "plot "++datafollows++" with lines\n" ++ dat
+    commandmore = "plot " ++ plots ++ "\n"
+    plots = concat $ intersperse ", " (map cmd [2 .. length m])
+    cmd k = datafollows++" using 1:"++show k++" with lines"
+    dat = prep $ toLists $ fromColumns m
+    dats = concat (replicate (length m-1) dat)
+
+
+
+
+
+
+mplot' m = do
+    writeFile "plot-gnu-command" (commands++endcmd)
+    toFile "plot-tmp.txt" (fromColumns m)
+    putStr "Press [Return] to close the graphic and continue... "
+    system "gnuplot plot-gnu-command"
+    system "rm plot-tmp.txt plot-gnu-command"
+    return ()
+ where
+    commands = if length m == 1 then command1 else commandmore
+    command1 = "plot \"plot-tmp.txt\" with lines\n"
+    commandmore = "plot " ++ plots ++ "\n"
+    plots = concat $ intersperse ", " (map cmd [2 .. length m])
+    cmd k = "\"plot-tmp.txt\" using 1:"++show k++" with lines"
+    endcmd = "pause -1"
+
+-- apply several functions to one object
+mapf fs x = map ($ x) fs
+
+{- | Draws a list of functions over a desired range and with a desired number of points 
+
+> > plot [sin, cos, sin.(3*)] (0,2*pi) 1000
+
+-}
+plot :: [Vector Double->Vector Double] -> (Double,Double) -> Int -> IO ()
+plot fs rx n = mplot (x: mapf fs x)
+    where x = linspace n rx  
+
+{- | Draws a parametric curve. For instance, to draw a spiral we can do something like:
+
+> > parametricPlot (\t->(t * sin t, t * cos t)) (0,10*pi) 1000
+
+-}
+parametricPlot :: (Vector Double->(Vector Double,Vector Double)) -> (Double, Double) -> Int -> IO ()
+parametricPlot f rt n = mplot [fx, fy]
+    where t = linspace n rt
+          (fx,fy) = f t
+
+
+-- | writes a matrix to pgm image file
+matrixToPGM :: Matrix Double -> String
+matrixToPGM m = header ++ unlines (map unwords ll) where
+    c = cols m
+    r = rows m
+    header = "P2 "++show c++" "++show r++" "++show (round maxgray :: Int)++"\n"
+    maxgray = 255.0
+    maxval = toScalarR Max $ flatten $ m
+    minval = toScalarR Min $ flatten $ m
+    scale = if (maxval == minval) 
+        then 0.0
+        else maxgray / (maxval - minval)
+    f x = show ( round ( scale *(x - minval) ) :: Int )
+    ll = map (map f) (toLists m)
+
+-- | imshow shows a representation of a matrix as a gray level image using ImageMagick's display.
+imshow :: Matrix Double -> IO ()
+imshow m = do
+    system $ "echo \""++ matrixToPGM m ++"\"| display -antialias -resize 300 - &"
+    return ()
diff --git a/lib/Data/Packed/Tensor.hs b/lib/Data/Packed/Tensor.hs
index 8d1c8b6..75a9288 100644
--- a/lib/Data/Packed/Tensor.hs
+++ b/lib/Data/Packed/Tensor.hs
@@ -1 +1,20 @@
- 
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Data.Packed.Tensor
+-- Copyright   :  (c) Alberto Ruiz 2007
+-- License     :  GPL-style
+--
+-- Maintainer  :  Alberto Ruiz <aruiz@um.es>
+-- Stability   :  provisional
+-- Portability :  portable
+--
+-- Tensors
+--
+-----------------------------------------------------------------------------
+
+module Data.Packed.Tensor (
+
+) where
+
+import Data.Packed.Internal
+import Complex
diff --git a/lib/Data/Packed/Vector.hs b/lib/Data/Packed/Vector.hs
index 992301a..aa1b489 100644
--- a/lib/Data/Packed/Vector.hs
+++ b/lib/Data/Packed/Vector.hs
@@ -20,7 +20,8 @@ module Data.Packed.Vector (
     constant,
     toComplex, comp,
     conj,
-    dot
+    dot,
+    linspace
 ) where
 
 import Data.Packed.Internal
@@ -35,6 +36,14 @@ conj :: Vector (Complex Double) -> Vector (Complex Double)
 conj v = asComplex $ cdat $ reshape 2 (asReal v) `mulC` diag (fromList [1,-1])
     where mulC = multiply RowMajor
 
-comp v = toComplex (v,constant (dim v) 0)
+comp v = toComplex (v,constant 0 (dim v))
 
+{- | Creates a real vector containing a range of values:
 
+> > linspace 10 (-2,2)
+>-2. -1.556 -1.111 -0.667 -0.222 0.222 0.667 1.111 1.556 2.
+
+-}
+linspace :: Int -> (Double, Double) -> Vector Double
+linspace n (a,b) = fromList [a::Double,a+delta .. b]
+    where delta = (b-a)/(fromIntegral n -1)