From 89651db9f2577ba42dbbb91c85565a12f34d0fb2 Mon Sep 17 00:00:00 2001
From: Alberto Ruiz <aruiz@um.es>
Date: Mon, 10 Sep 2007 09:13:20 +0000
Subject: simplified

---
 lib/Data/Packed/Internal/Matrix.hs | 398 +++++++++++++++----------------------
 1 file changed, 163 insertions(+), 235 deletions(-)

(limited to 'lib/Data')

diff --git a/lib/Data/Packed/Internal/Matrix.hs b/lib/Data/Packed/Internal/Matrix.hs
index 6ba2d06..ba32a67 100644
--- a/lib/Data/Packed/Internal/Matrix.hs
+++ b/lib/Data/Packed/Internal/Matrix.hs
@@ -1,4 +1,4 @@
-{-# OPTIONS_GHC -fglasgow-exts -fallow-overlapping-instances #-}
+{-# OPTIONS_GHC -fglasgow-exts #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Data.Packed.Internal.Matrix
@@ -22,65 +22,10 @@ import Foreign hiding (xor)
 import Complex
 import Control.Monad(when)
 import Data.List(transpose,intersperse)
---import Data.Typeable
 import Data.Maybe(fromJust)
 
-----------------------------------------------------------------
-
--- the condition Storable a => Field a means that we can only put
--- in Field types that are in Storable, and therefore Storable a
--- is not required in signatures if we have a Field a.
-
-class Storable a => Field a where
-    constant :: a -> Int -> Vector a
-    transdata :: Int -> Vector a -> Int -> Vector a
-    multiplyD :: MatrixOrder -> Matrix a -> Matrix a -> Matrix a
-    subMatrix :: (Int,Int) -- ^ (r0,c0) starting position 
-              -> (Int,Int) -- ^ (rt,ct) dimensions of submatrix
-              -> Matrix a -> Matrix a
-    diag :: Vector a -> Matrix a
-
-instance Field Double where
-    constant  = constantR
-    transdata = transdataR
-    multiplyD = multiplyR
-    subMatrix = subMatrixR
-    diag      = diagR
-
-instance Field (Complex Double) where
-    constant  = constantC
-    transdata = transdataC
-    multiplyD = multiplyC
-    subMatrix = subMatrixC
-    diag      = diagC
-
 -----------------------------------------------------------------
 
-transdataR :: Int -> Vector Double -> Int -> Vector Double
-transdataR = transdataAux ctransR
-
-transdataC :: Int -> Vector (Complex Double) -> Int -> Vector (Complex Double)
-transdataC = transdataAux ctransC
-
-transdataAux fun c1 d c2 =
-    if noneed
-        then d
-        else unsafePerformIO $ do
-            v <- createVector (dim d)
-            fun r1 c1 (ptr d) r2 c2 (ptr v) // check "transdataAux" [d]
-            --putStrLn "---> transdataAux"
-            return v
-  where r1 = dim d `div` c1
-        r2 = dim d `div` c2
-        noneed = r1 == 1 || c1 == 1
-
-foreign import ccall safe "aux.h transR"
-    ctransR :: TMM -- Double ::> Double ::> IO Int
-foreign import ccall safe "aux.h transC"
-    ctransC :: TCMCM -- Complex Double ::> Complex Double ::> IO Int
-
-transdataG c1 d c2 = fromList . concat . transpose . partit c1 . toList $ d
-
 {- Design considerations for the Matrix Type
    -----------------------------------------
 
@@ -111,103 +56,79 @@ transdataG c1 d c2 = fromList . concat . transpose . partit c1 . toList $ d
 
 data MatrixOrder = RowMajor | ColumnMajor deriving (Show,Eq)
 
-{-
-
-
-
-data Matrix t = M { rows    :: Int
-                  , cols    :: Int
-                  , dat     :: Vector t
-                  , tdat    :: Vector t
-                  , isTrans :: Bool
-                  , order   :: MatrixOrder
-                  } -- deriving Typeable
--}
-
-data Matrix t = MC { rows :: Int, cols :: Int, dat :: Vector t } -- row major order
-              | MF { rows :: Int, cols :: Int, dat :: Vector t } -- column major order
+data Matrix t = MC { rows :: Int, cols :: Int, cdat :: Vector t, fdat :: Vector t }
+              | MF { rows :: Int, cols :: Int, fdat :: Vector t, cdat :: Vector t }
 
 -- transposition just changes the data order
 trans :: Matrix t -> Matrix t
-trans MC {rows = r, cols = c, dat = d} = MF {rows = c, cols = r, dat = d}
-trans MF {rows = r, cols = c, dat = d} = MC {rows = c, cols = r, dat = d}
-
-viewC m@MC{} = m
-viewC MF {rows = r, cols = c, dat = d} = MC {rows = r, cols = c, dat = transdata r d c}
+trans MC {rows = r, cols = c, cdat = d, fdat = dt } = MF {rows = c, cols = r, fdat = d, cdat = dt }
+trans MF {rows = r, cols = c, fdat = d, cdat = dt } = MC {rows = c, cols = r, cdat = d, fdat = dt }
 
-viewF m@MF{} = m
-viewF MC {rows = r, cols = c, dat = d} = MF {rows = r, cols = c, dat = transdata c d r}
+dat MC { cdat = d } = d
+dat MF { fdat = d } = d
 
---fortran m = order m == ColumnMajor
-
-cdat m = dat (viewC m)
-fdat m = dat (viewF m)
+mat d m f = f (rows m) (cols m) (ptr (d m))
 
 type Mt t s = Int -> Int -> Ptr t -> s
 -- not yet admitted by my haddock version
 -- infixr 6 ::>
 -- type t ::> s = Mt t s
 
-mat d m f = f (rows m) (cols m) (ptr (d m))
---mat m f = f (rows m) (cols m) (ptr (dat m))
---matC m f = f (rows m) (cols m) (ptr (cdat m))
+-- | the inverse of 'fromLists'
+toLists :: (Field t) => Matrix t -> [[t]]
+toLists m = partit (cols m) . toList . cdat $ m
 
+-- | creates a Matrix from a list of vectors
+fromRows :: Field t => [Vector t] -> Matrix t
+fromRows vs = case common dim vs of
+    Nothing -> error "fromRows applied to [] or to vectors with different sizes"
+    Just c  -> reshape c (join vs)
 
---toLists :: (Storable t) => Matrix t -> [[t]]
-toLists m = partit (cols m) . toList . cdat $ m
+-- | extracts the rows of a matrix as a list of vectors
+toRows :: Field t => Matrix t -> [Vector t]
+toRows m = toRows' 0 where
+    v = cdat m
+    r = rows m
+    c = cols m
+    toRows' k | k == r*c  = []
+              | otherwise = subVector k c v : toRows' (k+c)
 
-instance (Show a, Field a) => (Show (Matrix a)) where
-    show m = (sizes++) . dsp . map (map show) . toLists $ m
-        where sizes = "("++show (rows m)++"><"++show (cols m)++")\n"
+-- | Creates a matrix from a list of vectors, as columns
+fromColumns :: Field t => [Vector t] -> Matrix t
+fromColumns m = trans . fromRows $ m
 
-dsp as = (++" ]") . (" ["++) . init . drop 2 . unlines . map (" , "++) . map unwords' $ transpose mtp
-    where
-        mt = transpose as
-        longs = map (maximum . map length) mt
-        mtp = zipWith (\a b -> map (pad a) b) longs mt
-        pad n str = replicate (n - length str) ' ' ++ str
-        unwords' = concat . intersperse ", "
+-- | Creates a list of vectors from the columns of a matrix
+toColumns :: Field t => Matrix t -> [Vector t]
+toColumns m = toRows . trans $ m
 
-{-
-matrixFromVector RowMajor c v =
-    M { rows = r
-      , cols = c
-      , dat  = v
-      , tdat = transdata c v r
-      , order = RowMajor
-      , isTrans = False
-      } where (d,m) = dim v `divMod` c
-              r | m==0 = d
-                | otherwise = error "matrixFromVector"
-
-matrixFromVector ColumnMajor c v =
-    M { rows = r
-      , cols = c
-      , dat  = v
-      , tdat = transdata r v c
-      , order = ColumnMajor
-      , isTrans = False
-      } where (d,m) = dim v `divMod` c
-              r | m==0 = d
-                | otherwise = error "matrixFromVector"
 
--}
+-- | Reads a matrix position.
+(@@>) :: Storable t => Matrix t -> (Int,Int) -> t
+infixl 9 @@>
+--m@M {rows = r, cols = c} @@> (i,j)
+--    | i<0 || i>=r || j<0 || j>=c = error "matrix indexing out of range"
+--    | otherwise   = cdat m `at` (i*c+j)
 
-matrixFromVector RowMajor c v = MC { rows = r, cols = c, dat = v}
+MC {rows = r, cols = c, cdat = v} @@> (i,j)
+    | i<0 || i>=r || j<0 || j>=c = error "matrix indexing out of range"
+    | otherwise                  = v `at` (i*c+j)
+
+MF {rows = r, cols = c, fdat = v} @@> (i,j)
+    | i<0 || i>=r || j<0 || j>=c = error "matrix indexing out of range"
+    | otherwise                  = v `at` (j*r+i)
+
+------------------------------------------------------------------
+
+matrixFromVector RowMajor c v = MC { rows = r, cols = c, cdat = v, fdat = transdata c v r }
     where (d,m) = dim v `divMod` c
           r | m==0 = d
             | otherwise = error "matrixFromVector"
 
-matrixFromVector ColumnMajor c v = MF { rows = r, cols = c, dat = v}
+matrixFromVector ColumnMajor c v = MF { rows = r, cols = c, fdat = v, cdat = transdata r v c }
     where (d,m) = dim v `divMod` c
           r | m==0 = d
             | otherwise = error "matrixFromVector"
 
-
-
-
-
-
 createMatrix order r c = do
     p <- createVector (r*c)
     return (matrixFromVector order c p)
@@ -226,45 +147,94 @@ reshape c v = matrixFromVector RowMajor c v
 
 singleton x = reshape 1 (fromList [x])
 
---liftMatrix :: (Field a, Field b) => (Vector a -> Vector b) -> Matrix a -> Matrix b
-liftMatrix f m = reshape (cols m) (f (cdat m))
+liftMatrix :: (Field a, Field b) => (Vector a -> Vector b) -> Matrix a -> Matrix b
+liftMatrix f MC { cols = c, cdat = d } = matrixFromVector RowMajor    c (f d)
+liftMatrix f MF { cols = c, fdat = d } = matrixFromVector ColumnMajor c (f d)
+
+
+liftMatrix2 :: (Field t, Field a, Field b) => (Vector a -> Vector b -> Vector t) -> Matrix a -> Matrix b -> Matrix t
+liftMatrix2 f m1 m2
+    | not (compat m1 m2) = error "nonconformant matrices in liftMatrix2"
+    | otherwise = case m1 of
+        MC {} -> matrixFromVector RowMajor    (cols m1) (f (cdat m1) (cdat m2))
+        MF {} -> matrixFromVector ColumnMajor (cols m1) (f (fdat m1) (fdat m2))
 
---liftMatrix2 :: (Field t) => (Vector a -> Vector b -> Vector t) -> Matrix a -> Matrix b -> Matrix t
-liftMatrix2 f m1 m2 | compat m1 m2 = reshape (cols m1) (f (cdat m1) (cdat m2))
-                    | otherwise    = error "nonconformant matrices in liftMatrix2"
-------------------------------------------------------------------
 
 compat :: Matrix a -> Matrix b -> Bool
 compat m1 m2 = rows m1 == rows m2 && cols m1 == cols m2
 
-dotL a b = sum (zipWith (*) a b)
+----------------------------------------------------------------
 
-multiplyL a b | ok = [[dotL x y | y <- transpose b] | x <- a]
-              | otherwise = error "inconsistent dimensions in contraction "
-    where ok = case common length a of
-                   Nothing -> False
-                   Just c  -> c == length b
+-- | element types for which optimized matrix computations are provided
+class Storable a => Field a where
+    -- | @constant val n@ creates a vector with @n@ elements, all equal to @val@.
+    constant :: a -> Int -> Vector a
+    transdata :: Int -> Vector a -> Int -> Vector a
+    multiplyD :: MatrixOrder -> Matrix a -> Matrix a -> Matrix a
+    -- | extracts a submatrix froma a matrix
+    subMatrix :: (Int,Int) -- ^ (r0,c0) starting position 
+              -> (Int,Int) -- ^ (rt,ct) dimensions of submatrix
+              -> Matrix a -> Matrix a
+    -- | creates a square matrix with the given diagonal
+    diag :: Vector a -> Matrix a
 
-transL m = matrixFromVector RowMajor (rows m) $ transdata (cols m) (cdat m) (rows m)
+instance Field Double where
+    constant  = constantR
+    transdata = transdataR
+    multiplyD = multiplyR
+    subMatrix = subMatrixR
+    diag      = diagR
 
-multiplyG a b = matrixFromVector RowMajor (cols b) $ fromList $ concat $ multiplyL (toLists a) (toLists b)
+instance Field (Complex Double) where
+    constant  = constantC
+    transdata = transdataC
+    multiplyD = multiplyC
+    subMatrix = subMatrixC
+    diag      = diagC
 
 ------------------------------------------------------------------
 
-{-
-gmatC m f | fortran m =
-                if (isTrans m)
-                    then f 0 (rows m) (cols m) (ptr (dat m))
-                    else f 1 (cols m) (rows m) (ptr (dat m))
-         | otherwise =
-                if isTrans m
-                    then f 1 (cols m) (rows m) (ptr (dat m))
-                    else f 0 (rows m) (cols m) (ptr (dat m))
--}
+instance (Show a, Field a) => (Show (Matrix a)) where
+    show m = (sizes++) . dsp . map (map show) . toLists $ m
+        where sizes = "("++show (rows m)++"><"++show (cols m)++")\n"
+
+dsp as = (++" ]") . (" ["++) . init . drop 2 . unlines . map (" , "++) . map unwords' $ transpose mtp
+    where
+        mt = transpose as
+        longs = map (maximum . map length) mt
+        mtp = zipWith (\a b -> map (pad a) b) longs mt
+        pad n str = replicate (n - length str) ' ' ++ str
+        unwords' = concat . intersperse ", "
 
-gmatC MF {rows = r, cols = c, dat = d} f = f 1 c r (ptr d)
-gmatC MC {rows = r, cols = c, dat = d} f = f 0 r c (ptr d)
-{-# INLINE gmatC #-}
+------------------------------------------------------------------
+
+transdataR :: Int -> Vector Double -> Int -> Vector Double
+transdataR = transdataAux ctransR
+
+transdataC :: Int -> Vector (Complex Double) -> Int -> Vector (Complex Double)
+transdataC = transdataAux ctransC
+
+transdataAux fun c1 d c2 =
+    if noneed
+        then d
+        else unsafePerformIO $ do
+            v <- createVector (dim d)
+            fun r1 c1 (ptr d) r2 c2 (ptr v) // check "transdataAux" [d]
+            --putStrLn "---> transdataAux"
+            return v
+  where r1 = dim d `div` c1
+        r2 = dim d `div` c2
+        noneed = r1 == 1 || c1 == 1
+
+foreign import ccall safe "aux.h transR"
+    ctransR :: TMM -- Double ::> Double ::> IO Int
+foreign import ccall safe "aux.h transC"
+    ctransC :: TCMCM -- Complex Double ::> Complex Double ::> IO Int
+
+------------------------------------------------------------------
+
+gmatC MF {rows = r, cols = c, fdat = d} f = f 1 c r (ptr d)
+gmatC MC {rows = r, cols = c, cdat = d} f = f 0 r c (ptr d)
 
 multiplyAux fun order a b = unsafePerformIO $ do
     when (cols a /= rows b) $ error $ "inconsistent dimensions in contraction "++
@@ -272,14 +242,15 @@ multiplyAux fun order a b = unsafePerformIO $ do
     r <- createMatrix order (rows a) (cols b)
     fun // gmatC a // gmatC b // mat dat r // check "multiplyAux" [dat a, dat b]
     return r
-{-# INLINE multiplyAux #-}
 
+multiplyR = multiplyAux cmultiplyR
 foreign import ccall safe "aux.h multiplyR"
     cmultiplyR :: Int -> Int -> Int -> Ptr Double
                -> Int -> Int -> Int -> Ptr Double
                -> Int -> Int -> Ptr Double
                -> IO Int
 
+multiplyC = multiplyAux cmultiplyC
 foreign import ccall safe "aux.h multiplyC"
     cmultiplyC :: Int -> Int -> Int -> Ptr (Complex Double)
                -> Int -> Int -> Int -> Ptr (Complex Double)
@@ -288,14 +259,9 @@ foreign import ccall safe "aux.h multiplyC"
 
 multiply :: (Field a) => MatrixOrder -> Matrix a -> Matrix a -> Matrix a
 multiply RowMajor a b    = multiplyD RowMajor a b
-multiply ColumnMajor a b = MF {rows = c, cols = r, dat = d}
-    where MC {rows = r, cols = c, dat = d } = multiplyD RowMajor (trans b) (trans a)
-
-
-multiplyR = multiplyAux cmultiplyR'
-multiplyC = multiplyAux cmultiplyC
-
-cmultiplyR' p1 p2 p3 p4 q1 q2 q3 q4 r1 r2 r3 = {-# SCC "mulR" #-} cmultiplyR p1 p2 p3 p4 q1 q2 q3 q4 r1 r2 r3
+multiply ColumnMajor a b = MF {rows = c, cols = r, fdat = d, cdat = dt }
+    where MC {rows = r, cols = c, cdat = d, fdat = dt } = multiplyD RowMajor (trans b) (trans a)
+-- FIXME using MatrixFromVector
 
 ----------------------------------------------------------------------
 
@@ -318,18 +284,6 @@ subMatrixC (r0,c0) (rt,ct) x =
     subMatrixR (r0,2*c0) (rt,2*ct) .
     reshape (2*cols x) . asReal . cdat $ x
 
---subMatrix :: (Field a) 
---          => (Int,Int) -- ^ (r0,c0) starting position 
---          -> (Int,Int) -- ^ (rt,ct) dimensions of submatrix
---          -> Matrix a -> Matrix a
---subMatrix st sz m
---    | isReal (baseOf.dat) m = scast $ subMatrixR st sz (scast m)
---    | isComp (baseOf.dat) m = scast $ subMatrixC st sz (scast m)
---    | otherwise             = subMatrixG st sz m
-
-subMatrixG (r0,c0) (rt,ct) x = reshape ct $ fromList $ concat $ map (subList c0 ct) (subList r0 rt (toLists x))
-    where subList s n = take n . drop s
-
 ---------------------------------------------------------------------
 
 diagAux fun msg (v@V {dim = n}) = unsafePerformIO $ do
@@ -347,66 +301,7 @@ diagC :: Vector (Complex Double) -> Matrix (Complex Double)
 diagC = diagAux c_diagC "diagC"
 foreign import ccall "aux.h diagC" c_diagC :: TCVCM
 
--- | diagonal matrix from a vector
---diag :: (Num a, Field a) => Vector a -> Matrix a
---diag v
---    | isReal (baseOf) v = scast $ diagR (scast v)
---    | isComp (baseOf) v = scast $ diagC (scast v)
---    | otherwise             = diagG v
-
-diagG v = reshape c $ fromList $ [ l!!(i-1) * delta k i | k <- [1..c], i <- [1..c]]
-    where c = dim v
-          l = toList v
-          delta i j | i==j      = 1
-                    | otherwise = 0
-
--- | creates a Matrix from a list of vectors
---fromRows :: Field t => [Vector t] -> Matrix t
-fromRows vs = case common dim vs of
-    Nothing -> error "fromRows applied to [] or to vectors with different sizes"
-    Just c  -> reshape c (join vs)
-
--- | extracts the rows of a matrix as a list of vectors
---toRows :: Storable t => Matrix t -> [Vector t]
-toRows m = toRows' 0 where
-    v = cdat m
-    r = rows m
-    c = cols m
-    toRows' k | k == r*c  = []
-              | otherwise = subVector k c v : toRows' (k+c)
-
--- | Creates a matrix from a list of vectors, as columns
-fromColumns :: Field t => [Vector t] -> Matrix t
-fromColumns m = trans . fromRows $ m
-
--- | Creates a list of vectors from the columns of a matrix
-toColumns :: Field t => Matrix t -> [Vector t]
-toColumns m = toRows . trans $ m
-
-
--- | Reads a matrix position.
-(@@>) :: Storable t => Matrix t -> (Int,Int) -> t
-infixl 9 @@>
---m@M {rows = r, cols = c} @@> (i,j)
---    | i<0 || i>=r || j<0 || j>=c = error "matrix indexing out of range"
---    | otherwise   = cdat m `at` (i*c+j)
-
-MC {rows = r, cols = c, dat = v} @@> (i,j)
-    | i<0 || i>=r || j<0 || j>=c = error "matrix indexing out of range"
-    | otherwise                  = v `at` (i*c+j)
-
-MF {rows = r, cols = c, dat = v} @@> (i,j)
-    | i<0 || i>=r || j<0 || j>=c = error "matrix indexing out of range"
-    | otherwise                  = v `at` (j*r+i)
-
-
-------------------------------------------------------------------
-
-constantR :: Double -> Int -> Vector Double
-constantR = constantAux cconstantR
-
-constantC :: Complex Double -> Int -> Vector (Complex Double)
-constantC = constantAux cconstantC
+------------------------------------------------------------------------
 
 constantAux fun x n = unsafePerformIO $ do
     v <- createVector n
@@ -415,8 +310,41 @@ constantAux fun x n = unsafePerformIO $ do
     free px
     return v
 
+constantR :: Double -> Int -> Vector Double
+constantR = constantAux cconstantR
 foreign import ccall safe "aux.h constantR"
     cconstantR :: Ptr Double -> TV -- Double :> IO Int
 
+constantC :: Complex Double -> Int -> Vector (Complex Double)
+constantC = constantAux cconstantC
 foreign import ccall safe "aux.h constantC"
     cconstantC :: Ptr (Complex Double) -> TCV -- Complex Double :> IO Int
+
+-------------------------------------------------------------------------
+
+-- Generic definitions
+
+{-
+transL m = matrixFromVector RowMajor (rows m) $ transdata (cols m) (cdat m) (rows m)
+
+subMatrixG (r0,c0) (rt,ct) x = matrixFromVector RowMajor ct $ fromList $ concat $ map (subList c0 ct) (subList r0 rt (toLists x))
+    where subList s n = take n . drop s
+
+diagG v = matrixFromVector RowMajor c $ fromList $ [ l!!(i-1) * delta k i | k <- [1..c], i <- [1..c]]
+    where c = dim v
+          l = toList v
+          delta i j | i==j      = 1
+                    | otherwise = 0
+-}
+
+transdataG c1 d c2 = fromList . concat . transpose . partit c1 . toList $ d
+
+dotL a b = sum (zipWith (*) a b)
+
+multiplyG a b = matrixFromVector RowMajor (cols b) $ fromList $ concat $ multiplyL (toLists a) (toLists b)
+
+multiplyL a b | ok = [[dotL x y | y <- transpose b] | x <- a]
+              | otherwise = error "inconsistent dimensions in contraction "
+    where ok = case common length a of
+                   Nothing -> False
+                   Just c  -> c == length b
-- 
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