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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 (
Field,
Matrix,rows,cols,
(><), reshape, flatten,
fromLists, toLists,
(@@>),
trans, conjTrans,
asRow, asColumn,
fromRows, toRows, fromColumns, toColumns,
fromBlocks, joinVert, joinHoriz,
flipud, fliprl,
subMatrix, takeRows, dropRows, takeColumns, dropColumns,
ident, diag, diagRect, takeDiag,
liftMatrix, liftMatrix2,
) 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
------------------------------------------------------------
{- | 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 :: Int -> Matrix Double
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
------------------------------------------------
|
