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|
{-# OPTIONS_GHC -fglasgow-exts #-}
-----------------------------------------------------------------------------
-- |
-- Module : Data.Packed.Matrix
-- Copyright : (c) Alberto Ruiz 2007
-- License : GPL-style
--
-- Maintainer : Alberto Ruiz <aruiz@um.es>
-- Stability : provisional
-- Portability : portable
--
-- Matrices
--
-----------------------------------------------------------------------------
module Data.Packed.Matrix (
Field,
Matrix,rows,cols,
(><), reshape, flatten,
fromLists, toLists,
(@@>),
trans, conjTrans,
asRow, asColumn,
fromRows, toRows, fromColumns, toColumns,
fromBlocks,
flipud, fliprl,
subMatrix, takeRows, dropRows, takeColumns, dropColumns,
ident, diag, diagRect, takeDiag,
liftMatrix, liftMatrix2,
format, dispR, readMatrix, fromArray2D
) where
import Data.Packed.Internal
import Foreign(Storable)
import Complex
import Data.Packed.Vector
import Numeric(showGFloat)
import Data.List(transpose,intersperse)
import Data.Array
-- | creates a matrix from a vertical list of matrices
joinVert :: Field t => [Matrix t] -> Matrix t
joinVert ms = case common cols ms of
Nothing -> error "joinVert on matrices with different number of columns"
Just c -> reshape c $ join (map cdat ms)
-- | creates a matrix from a horizontal list of matrices
joinHoriz :: Field t => [Matrix t] -> Matrix t
joinHoriz ms = trans. joinVert . map trans $ ms
{- | Creates a matrix from blocks given as a list of lists of matrices:
@\> let a = 'diag' $ 'fromList' [5,7,2]
\> let b = 'reshape' 4 $ 'constant' (-1) 12
\> fromBlocks [[a,b],[b,a]]
(6><7)
[ 5.0, 0.0, 0.0, -1.0, -1.0, -1.0, -1.0
, 0.0, 7.0, 0.0, -1.0, -1.0, -1.0, -1.0
, 0.0, 0.0, 2.0, -1.0, -1.0, -1.0, -1.0
, -1.0, -1.0, -1.0, -1.0, 5.0, 0.0, 0.0
, -1.0, -1.0, -1.0, -1.0, 0.0, 7.0, 0.0
, -1.0, -1.0, -1.0, -1.0, 0.0, 0.0, 2.0 ]@
-}
fromBlocks :: Field t => [[Matrix t]] -> Matrix t
fromBlocks = joinVert . map joinHoriz
-- | Reverse rows
flipud :: Field t => Matrix t -> Matrix t
flipud m = fromRows . reverse . toRows $ m
-- | Reverse columns
fliprl :: Field t => Matrix t -> Matrix t
fliprl m = fromColumns . reverse . toColumns $ m
------------------------------------------------------------
{- | creates a rectangular diagonal matrix
@> diagRect (constant 5 3) 3 4
(3><4)
[ 5.0, 0.0, 0.0, 0.0
, 0.0, 5.0, 0.0, 0.0
, 0.0, 0.0, 5.0, 0.0 ]@
-}
diagRect :: (Field t, Num t) => Vector t -> Int -> Int -> Matrix t
diagRect s r c
| dim s < min r c = error "diagRect"
| 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 $ constantD 0 (r*c)
-- | extracts the diagonal from a rectangular matrix
takeDiag :: (Field t) => Matrix t -> Vector t
takeDiag m = fromList [cdat m `at` (k*cols m+k) | k <- [0 .. min (rows m) (cols m) -1]]
-- | creates the identity matrix of given dimension
ident :: Field a => Int -> Matrix a
ident n = diag (constant 1 n)
------------------------------------------------------------
{- | An easy way to create a matrix:
@\> (2><3)[1..6]
(2><3)
[ 1.0, 2.0, 3.0
, 4.0, 5.0, 6.0 ]@
This is the format produced by the instances of Show (Matrix a), which
can also be used for input.
-}
(><) :: (Field a) => Int -> Int -> [a] -> Matrix a
r >< c = f where
f l | dim v == r*c = matrixFromVector RowMajor c v
| otherwise = error $ "inconsistent list size = "
++show (dim v) ++" in ("++show r++"><"++show c++")"
where v = fromList l
----------------------------------------------------------------
-- | Creates a matrix with the first n rows of another matrix
takeRows :: Field t => Int -> Matrix t -> Matrix t
takeRows n mat = subMatrix (0,0) (n, cols mat) mat
-- | Creates a copy of a matrix without the first n rows
dropRows :: Field t => Int -> Matrix t -> Matrix t
dropRows n mat = subMatrix (n,0) (rows mat - n, cols mat) mat
-- |Creates a matrix with the first n columns of another matrix
takeColumns :: Field t => Int -> Matrix t -> Matrix t
takeColumns n mat = subMatrix (0,0) (rows mat, n) mat
-- | Creates a copy of a matrix without the first n columns
dropColumns :: Field t => Int -> Matrix t -> Matrix t
dropColumns n mat = subMatrix (0,n) (rows mat, cols mat - n) mat
----------------------------------------------------------------
{- | Creates a vector by concatenation of rows
@\> flatten ('ident' 3)
9 |> [1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0]@
-}
flatten :: Field t => Matrix t -> Vector t
flatten = cdat
{- | Creates a 'Matrix' from a list of lists (considered as rows).
@\> fromLists [[1,2],[3,4],[5,6]]
(3><2)
[ 1.0, 2.0
, 3.0, 4.0
, 5.0, 6.0 ]@
-}
fromLists :: Field t => [[t]] -> Matrix t
fromLists = fromRows . map fromList
-- | conjugate transpose
conjTrans :: Matrix (Complex Double) -> Matrix (Complex Double)
conjTrans = trans . liftMatrix conj
-- | creates a 1-row matrix from a vector
asRow :: Field a => Vector a -> Matrix a
asRow v = reshape (dim v) v
-- | creates a 1-column matrix from a vector
asColumn :: Field a => Vector a -> Matrix a
asColumn v = reshape 1 v
-----------------------------------------------------
fromArray2D :: (Field e) => Array (Int, Int) e -> Matrix e
fromArray2D m = (r><c) (elems m)
where ((r0,c0),(r1,c1)) = bounds m
r = r1-r0+1
c = c1-c0+1
------------------------------------------------------
-- shows a Double with n digits after the decimal point
shf :: (RealFloat a) => Int -> a -> String
shf dec n | abs n < 1e-10 = "0."
| abs (n - (fromIntegral.round $ n)) < 1e-10 = show (round n) ++"."
| otherwise = showGFloat (Just dec) n ""
-- shows a Complex Double as a pair, with n digits after the decimal point
shfc n z@ (a:+b)
| magnitude z <1e-10 = "0."
| abs b < 1e-10 = shf n a
| abs a < 1e-10 = shf n b ++"i"
| b > 0 = shf n a ++"+"++shf n b ++"i"
| otherwise = shf n a ++shf n b ++"i"
dsp' :: String -> [[String]] -> String
dsp' sep as = unlines . 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 sep
format :: (Field t) => String -> (t -> String) -> Matrix t -> String
format sep f m = dsp' sep . map (map f) . toLists $ m
disp m f = putStrLn $ "matrix ("++show (rows m) ++"x"++ show (cols m) ++")\n"++format " | " f m
dispR :: Int -> Matrix Double -> IO ()
dispR d m = disp m (shf d)
dispC :: Int -> Matrix (Complex Double) -> IO ()
dispC d m = disp m (shfc d)
-- | creates a matrix from a table of numbers.
readMatrix :: String -> Matrix Double
readMatrix = fromLists . map (map read). map words . filter (not.null) . lines
|
