--
-- Copyright (c) 2009-2010, ERICSSON AB All rights reserved.
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--
-- | Operations on matrices (doubly-nested parallel vectors). All operations in
-- this module assume rectangular matrices.
module Feldspar.Matrix where
import qualified Prelude as P
import Feldspar.Prelude
import Feldspar.Utils
import Feldspar.Core
import Feldspar.Vector
type Matrix a = Vector (Vector (Data a))
-- | Converts a matrix to a core array.
freezeMatrix :: Storable a => Matrix a -> Data [[a]]
freezeMatrix = freezeVector . map freezeVector
-- | Converts a core array to a matrix. The first length argument is the number
-- of rows (outer vector), and the second argument is the number of columns
-- (inner argument).
unfreezeMatrix :: Storable a => Data Length -> Data Length -> Data [[a]] -> Matrix a
unfreezeMatrix y x = map (unfreezeVector x) . (unfreezeVector y)
-- | Constructs a matrix. The elements are stored in a core array.
matrix :: Storable a => [[a]] -> Matrix a
matrix as
| allEqual xs = unfreezeMatrix y x (value as)
| otherwise = error "matrix: Not rectangular"
where
xs = P.map P.length as
y = value $ P.length as
x = value $ P.head (xs P.++ [0])
-- | Constructing a matrix from an index function.
--
-- @indexedMat m n ixf@:
--
-- * @m@ is the number of rows.
--
-- * @n@ is the number of columns.
--
-- * @ifx@ is a function mapping indexes to elements (first argument is row
-- index; second argument is column index).
indexedMat ::
Data Int -> Data Int -> (Data Int -> Data Int -> Data a) -> Matrix a
indexedMat m n idx = indexed m $ \k -> indexed n $ \l -> idx k l
-- | Transpose of a matrix
transpose :: Matrix a -> Matrix a
transpose a = indexedMat (length $ head a) (length a) $ \y x -> a ! x ! y
-- XXX This assumes that (head a) can be used even if a is empty. Might this
-- violate size constraints on the index?
-- See the conditional in 'flatten'.
-- | Concatenates the rows of a matrix.
flatten :: Matrix a -> Vector (Data a)
flatten matr = Indexed (m*n) ixf
where
m = length matr
n = (m==0) ? (0, length (head matr))
ixf i = matr ! y ! x
where
y = i `div` n
x = i `mod` n
-- XXX Should use "linear indexing"
-- | The diagonal vector of a square matrix. It happens to work if the number of
-- rows is less than the number of columns, but not the other way around (this
-- would require some overhead).
diagonal :: Matrix a -> Vector (Data a)
diagonal m = zipWith (!) m (0 ... (length m - 1))
distributeL :: (a -> b -> c) -> a -> Vector b -> Vector c
distributeL f = map . f
distributeR :: (a -> b -> c) -> Vector a -> b -> Vector c
distributeR = flip . distributeL . flip
{-# DEPRECATED mul "Please use `(**)` instead." #-}
-- | Matrix multiplication
mul :: Numeric a => Matrix a -> Matrix a -> Matrix a
mul = (**)
class Mul a b
where
type Prod a b
-- | General multiplication operator
(**) :: a -> b -> Prod a b
-- XXX This symbol should probably be used for exponentiation instead.
instance Numeric a => Mul (Data a) (Data a)
where
type Prod (Data a) (Data a) = Data a
(**) = (*)
instance Numeric a => Mul (Data a) (DVector a)
where
type Prod (Data a) (DVector a) = DVector a
(**) = distributeL (**)
instance Numeric a => Mul (DVector a) (Data a)
where
type Prod (DVector a) (Data a) = DVector a
(**) = distributeR (**)
instance Numeric a => Mul (Data a) (Matrix a)
where
type Prod (Data a) (Matrix a) = Matrix a
(**) = distributeL (**)
instance Numeric a => Mul (Matrix a) (Data a)
where
type Prod (Matrix a) (Data a) = Matrix a
(**) = distributeR (**)
instance Numeric a => Mul (DVector a) (DVector a)
where
type Prod (DVector a) (DVector a) = Data a
(**) = scalarProd
instance Numeric a => Mul (DVector a) (Matrix a)
where
type Prod (DVector a) (Matrix a) = (DVector a)
vec ** mat = distributeL (**) vec (transpose mat)
instance Numeric a => Mul (Matrix a) (DVector a)
where
type Prod (Matrix a) (DVector a) = (DVector a)
(**) = distributeR (**)
instance Numeric a => Mul (Matrix a) (Matrix a)
where
type Prod (Matrix a) (Matrix a) = (Matrix a)
a ** b = distributeR (**) a (transpose b)
class ElemWise a
where
type Elem a
-- | Operator for general element-wise multiplication
elemWise :: (Elem a -> Elem a -> Elem a) -> a -> a -> a
instance ElemWise (Data a)
where
type Elem (Data a) = Data a
elemWise = id
instance ElemWise (DVector a)
where
type Elem (DVector a) = Data a
elemWise = zipWith
instance ElemWise (Matrix a)
where
type Elem (Matrix a) = Data a
elemWise = elemWise . elemWise
(.+) :: (ElemWise a, Numeric (Elem a)) => a -> a -> a
(.+) = elemWise (+)
(.-) :: (ElemWise a, Numeric (Elem a)) => a -> a -> a
(.-) = elemWise (-)
(.*) :: (ElemWise a, Numeric (Elem a)) => a -> a -> a
(.*) = elemWise (*)