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{-# LANGUAGE FlexibleContexts #-}
-----------------------------------------------------------------------------
{- |
Module : Numeric.LinearAlgebra.Util
Copyright : (c) Alberto Ruiz 2012
License : GPL
Maintainer : Alberto Ruiz (aruiz at um dot es)
Stability : provisional
-}
-----------------------------------------------------------------------------
module Numeric.LinearAlgebra.Util(
-- * Convenience functions
size, disp,
zeros, ones,
diagl,
row,
col,
(&),(!), (#),
rand, randn,
cross,
norm,
unitary,
mt,
-- * Convolution
-- ** 1D
corr, conv, corrMin,
-- ** 2D
corr2, conv2, separable,
-- * Tools for the Kronecker product
--
-- | (see A. Fusiello, A matter of notation: Several uses of the Kronecker product in
-- 3d computer vision, Pattern Recognition Letters 28 (15) (2007) 2127-2132)
--
-- | @`vec` (a \<> x \<> b) == ('trans' b ` 'kronecker' ` a) \<> 'vec' x@
vec,
vech,
dup,
vtrans
) where
import Numeric.LinearAlgebra hiding (i)
import System.Random(randomIO)
import Numeric.LinearAlgebra.Util.Convolution
disp :: Int -> Matrix Double -> IO ()
-- ^ show a matrix with given number of digits after the decimal point
disp n = putStrLn . dispf n
-- | pseudorandom matrix with uniform elements between 0 and 1
randm :: RandDist
-> Int -- ^ rows
-> Int -- ^ columns
-> IO (Matrix Double)
randm d r c = do
seed <- randomIO
return (reshape c $ randomVector seed d (r*c))
-- | pseudorandom matrix with uniform elements between 0 and 1
rand :: Int -> Int -> IO (Matrix Double)
rand = randm Uniform
-- | pseudorandom matrix with normal elements
randn :: Int -> Int -> IO (Matrix Double)
randn = randm Gaussian
-- | create a real diagonal matrix from a list
diagl :: [Double] -> Matrix Double
diagl = diag . fromList
-- | a real matrix of zeros
zeros :: Int -- ^ rows
-> Int -- ^ columns
-> Matrix Double
zeros r c = konst 0 (r,c)
-- | a real matrix of ones
ones :: Int -- ^ rows
-> Int -- ^ columns
-> Matrix Double
ones r c = konst 1 (r,c)
-- | concatenation of real vectors
infixl 3 &
(&) :: Vector Double -> Vector Double -> Vector Double
a & b = join [a,b]
-- | horizontal concatenation of real matrices
infixl 3 !
(!) :: Matrix Double -> Matrix Double -> Matrix Double
a ! b = fromBlocks [[a,b]]
-- | vertical concatenation of real matrices
(#) :: Matrix Double -> Matrix Double -> Matrix Double
infixl 2 #
a # b = fromBlocks [[a],[b]]
-- | create a single row real matrix from a list
row :: [Double] -> Matrix Double
row = asRow . fromList
-- | create a single column real matrix from a list
col :: [Double] -> Matrix Double
col = asColumn . fromList
cross :: Vector Double -> Vector Double -> Vector Double
-- ^ cross product (for three-element real vectors)
cross x y | dim x == 3 && dim y == 3 = fromList [z1,z2,z3]
| otherwise = error $ "cross ("++show x++") ("++show y++")"
where
[x1,x2,x3] = toList x
[y1,y2,y3] = toList y
z1 = x2*y3-x3*y2
z2 = x3*y1-x1*y3
z3 = x1*y2-x2*y1
norm :: Vector Double -> Double
-- ^ 2-norm of real vector
norm = pnorm PNorm2
-- | Obtains a vector in the same direction with 2-norm=1
unitary :: Vector Double -> Vector Double
unitary v = v / scalar (norm v)
-- | (rows &&& cols)
size :: Matrix t -> (Int, Int)
size m = (rows m, cols m)
-- | trans . inv
mt :: Matrix Double -> Matrix Double
mt = trans . inv
----------------------------------------------------------------------
--------------------------------------------------------------------------------
vec :: Element t => Matrix t -> Vector t
-- ^ stacking of columns
vec = flatten . trans
vech :: Element t => Matrix t -> Vector t
-- ^ half-vectorization (of the lower triangular part)
vech m = join . zipWith f [0..] . toColumns $ m
where
f k v = subVector k (dim v - k) v
dup :: (Num t, Num (Vector t), Element t) => Int -> Matrix t
-- ^ duplication matrix (@'dup' k \<> 'vech' m == 'vec' m@, for symmetric m of 'dim' k)
dup k = trans $ fromRows $ map f es
where
rs = zip [0..] (toRows (ident (k^(2::Int))))
es = [(i,j) | j <- [0..k-1], i <- [0..k-1], i>=j ]
f (i,j) | i == j = g (k*j + i)
| otherwise = g (k*j + i) + g (k*i + j)
g j = v
where
Just v = lookup j rs
vtrans :: Element t => Int -> Matrix t -> Matrix t
-- ^ generalized \"vector\" transposition: @'vtrans' 1 == 'trans'@, and @'vtrans' ('rows' m) m == 'asColumn' ('vec' m)@
vtrans p m | r == 0 = fromBlocks . map (map asColumn . takesV (replicate q p)) . toColumns $ m
| otherwise = error $ "vtrans " ++ show p ++ " of matrix with " ++ show (rows m) ++ " rows"
where
(q,r) = divMod (rows m) p
|
