linear algebra moved

1 files changed, 0 insertions, 290 deletions

diff --git a/packages/hmatrix/src/Numeric/LinearAlgebra/Util.hs b/packages/hmatrix/src/Numeric/LinearAlgebra/Util.hs
deleted file mode 100644
index e4f21b0..0000000
--- a/packages/hmatrix/src/Numeric/LinearAlgebra/Util.hs
+++ /dev/null
@@ -1,290 +0,0 @@
-{-# LANGUAGE FlexibleContexts #-}
------------------------------------------------------------------------------
-{- |
-Module      :  Numeric.LinearAlgebra.Util
-Copyright   :  (c) Alberto Ruiz 2013
-License     :  GPL
-
-Maintainer  :  Alberto Ruiz (aruiz at um dot es)
-Stability   :  provisional
-
--}
------------------------------------------------------------------------------
-{-# OPTIONS_HADDOCK hide #-}
-
-module Numeric.LinearAlgebra.Util(
-
-    -- * Convenience functions
-    size, disp,
-    zeros, ones,
-    diagl,
-    row,
-    col,
-    (&), (¦), (——), (#),
-    (?), (¿),
-    cross,
-    norm,
-    unitary,
-    mt,
-    pairwiseD2,
-    meanCov,
-    rowOuters,
-    null1,
-    null1sym,
-    -- * 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,
-    -- * Plot
-    mplot,
-    plot, parametricPlot,
-    splot, mesh, meshdom,
-    matrixToPGM, imshow,
-    gnuplotX, gnuplotpdf, gnuplotWin
-) where
-
-import Numeric.Container
-import Numeric.IO
-import Numeric.LinearAlgebra.Algorithms hiding (i)
-import Numeric.Matrix()
-import Numeric.Vector()
-
-import Numeric.LinearAlgebra.Util.Convolution
-import Graphics.Plot
-
-
-{- | print a real matrix with given number of digits after the decimal point
-
->>> disp 5 $ ident 2 / 3
-2x2
-0.33333  0.00000
-0.00000  0.33333
-
--}
-disp :: Int -> Matrix Double -> IO ()
-
-disp n = putStrLn . dispf n
-
-
-{- | create a real diagonal matrix from a list
-
->>> diagl [1,2,3]
-(3><3)
- [ 1.0, 0.0, 0.0
- , 0.0, 2.0, 0.0
- , 0.0, 0.0, 3.0 ]
-
--}
-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 = vjoin [a,b]
-
-{- | horizontal concatenation of real matrices
-
- (unicode 0x00a6, broken bar)
-
->>> ident 3 ¦ konst 7 (3,4)
-(3><7)
- [ 1.0, 0.0, 0.0, 7.0, 7.0, 7.0, 7.0
- , 0.0, 1.0, 0.0, 7.0, 7.0, 7.0, 7.0
- , 0.0, 0.0, 1.0, 7.0, 7.0, 7.0, 7.0 ]
-
--}
-infixl 3 ¦
-(¦) :: Matrix Double -> Matrix Double -> Matrix Double
-a ¦ b = fromBlocks [[a,b]]
-
--- | vertical concatenation of real matrices
---
--- (unicode 0x2014, em dash)
-(——) :: Matrix Double -> Matrix Double -> Matrix Double
-infixl 2 ——
-a —— b = fromBlocks [[a],[b]]
-
-(#) :: 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
-
-{- | extract rows
-
->>> (20><4) [1..] ? [2,1,1]
-(3><4)
- [ 9.0, 10.0, 11.0, 12.0
- , 5.0,  6.0,  7.0,  8.0
- , 5.0,  6.0,  7.0,  8.0 ]
-
--}
-infixl 9 ?
-(?) :: Element t => Matrix t -> [Int] -> Matrix t
-(?) = flip extractRows
-
-{- | extract columns
-
-(unicode 0x00bf, inverted question mark, Alt-Gr ?)
-
->>> (3><4) [1..] ¿ [3,0]
-(3><2)
- [  4.0, 1.0
- ,  8.0, 5.0
- , 12.0, 9.0 ]
-
--}
-infixl 9 ¿
-(¿) :: Element t => Matrix t -> [Int] -> Matrix t
-(¿)= flip extractColumns
-
-
-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
-
---------------------------------------------------------------------------------
-
-{- | Compute mean vector and covariance matrix of the rows of a matrix.
-
->>> meanCov $ gaussianSample 666 1000 (fromList[4,5]) (diagl[2,3])
-(fromList [4.010341078059521,5.0197204699640405],
-(2><2)
- [     1.9862461923890056, -1.0127225830525157e-2
- , -1.0127225830525157e-2,     3.0373954915729318 ])
-
--}
-meanCov :: Matrix Double -> (Vector Double, Matrix Double)
-meanCov x = (med,cov) where
-    r    = rows x
-    k    = 1 / fromIntegral r
-    med  = konst k r `vXm` x
-    meds = konst 1 r `outer` med
-    xc   = x `sub` meds
-    cov  = scale (recip (fromIntegral (r-1))) (trans xc `mXm` xc)
-
---------------------------------------------------------------------------------
-
--- | Matrix of pairwise squared distances of row vectors
--- (using the matrix product trick in blog.smola.org)
-pairwiseD2 :: Matrix Double -> Matrix Double -> Matrix Double
-pairwiseD2 x y | ok = x2 `outer` oy + ox `outer` y2 - 2* x <> trans y
-               | otherwise = error $ "pairwiseD2 with different number of columns: "
-                                   ++ show (size x) ++ ", " ++ show (size y)
-  where
-    ox = one (rows x)
-    oy = one (rows y)
-    oc = one (cols x)
-    one k = constant 1 k
-    x2 = x * x <> oc
-    y2 = y * y <> oc
-    ok = cols x == cols y
-
---------------------------------------------------------------------------------
-
--- | outer products of rows
-rowOuters :: Matrix Double -> Matrix Double -> Matrix Double
-rowOuters a b = a' * b'
-  where
-    a' = kronecker a (ones 1 (cols b))
-    b' = kronecker (ones 1 (cols a)) b
-
---------------------------------------------------------------------------------
-
--- | solution of overconstrained homogeneous linear system
-null1 :: Matrix Double -> Vector Double
-null1 = last . toColumns . snd . rightSV
-
--- | solution of overconstrained homogeneous symmetric linear system
-null1sym :: Matrix Double -> Vector Double
-null1sym = last . toColumns . snd . eigSH'
-
---------------------------------------------------------------------------------
-
-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 = vjoin . 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
-