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|
-----------------------------------------------------------------------------
-- |
-- 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 (
Matrix(rows,cols),
fromLists, toLists, (><), (>|<), (@@>),
trans, conjTrans,
reshape, flatten, asRow, asColumn,
fromRows, toRows, fromColumns, toColumns, fromBlocks,
joinVert, joinHoriz,
flipud, fliprl,
liftMatrix, liftMatrix2,
multiply,
outer,
subMatrix,
takeRows, dropRows, takeColumns, dropColumns,
diag, takeDiag, diagRect, ident
) where
import Data.Packed.Internal
import Foreign(Storable)
import Complex
import Data.Packed.Vector
-- | 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
------------------------------------------------------------
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 $ constant 0 (r*c)
takeDiag :: (Storable t) => Matrix t -> Vector t
takeDiag m = fromList [cdat m `at` (k*cols m+k) | k <- [0 .. min (rows m) (cols m) -1]]
ident :: (Num t, Field t) => Int -> Matrix t
ident n = diag (constant 1 n)
(><) :: (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
(>|<) :: (Field a) => Int -> Int -> [a] -> Matrix a
r >|< c = f where
f l | dim v == r*c = matrixFromVector ColumnMajor 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 :: Matrix t -> Vector t
flatten = cdat
-- | Creates a 'Matrix' from a list of lists (considered as rows).
fromLists :: Field t => [[t]] -> Matrix t
fromLists = fromRows . map fromList
conjTrans :: Matrix (Complex Double) -> Matrix (Complex Double)
conjTrans = trans . liftMatrix conj
asRow :: Field a => Vector a -> Matrix a
asRow v = reshape (dim v) v
asColumn :: Field a => Vector a -> Matrix a
asColumn v = reshape 1 v
|
