new module Numeric.LinearAlgebra.Real

1 files changed, 130 insertions, 0 deletions

diff --git a/lib/Numeric/LinearAlgebra/Real.hs b/lib/Numeric/LinearAlgebra/Real.hs
new file mode 100644
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+++ b/lib/Numeric/LinearAlgebra/Real.hs
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+-----------------------------------------------------------------------------
+{- |
+Module      :  Numeric.LinearAlgebra.Real
+Copyright   :  (c) Alberto Ruiz 2012
+License     :  GPL
+
+Maintainer  :  Alberto Ruiz (aruiz at um dot es)
+Stability   :  provisional
+
+Additional functions for real arrays.
+
+-}
+-----------------------------------------------------------------------------
+
+module Numeric.LinearAlgebra.Real(
+    (<>), (*>), (<*), (<\>), (\>),
+    vector,
+    linspace,
+    eye,
+    zeros, ones,
+    diagl,
+    row,
+    col,
+    (#),(&), (//), blocks,
+    rand, randn
+) where
+
+import Numeric.LinearAlgebra hiding ((<>), (<\>), linspace)
+import qualified Numeric.LinearAlgebra as LA
+import System.Random(randomIO)
+
+linspace :: Int -> (Double,Double) -> Vector Double
+linspace = LA.linspace
+
+
+infixl 7 <>
+-- | Matrix product ('multiply')
+(<>) :: Field t => Matrix t -> Matrix t -> Matrix t
+(<>) = multiply
+
+infixl 7 *>
+-- | matrix x vector
+(*>) :: Field t => Matrix t -> Vector t -> Vector t
+m *> v = flatten $ m <> (asColumn v)
+
+infixl 7 <*
+-- | vector x matrix
+(<*) :: Field t => Vector t -> Matrix t -> Vector t
+v <* m = flatten $ (asRow v) <> m
+
+
+-- | Least squares solution of a linear system for several right-hand sides, similar to the \\ operator of Matlab\/Octave. (\<\\\>) = 'linearSolveSVD'.
+(<\>) :: (Field a) => Matrix a -> Matrix a -> Matrix a
+infixl 7 <\>
+(<\>) = linearSolveSVD
+
+-- | Least squares solution of a linear system for a single right-hand side. See '(\<\\\>)'.
+(\>) :: (Field a) => Matrix a -> Vector a -> Vector a
+infixl 7 \>
+m \> v = flatten (m <\> reshape 1 v)
+
+-- | 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
+
+-- | Real identity matrix.
+eye :: Int -> Matrix Double
+eye = ident
+
+-- | Create a real vector from a list.
+vector :: [Double] -> Vector Double
+vector = fromList
+
+-- | Create a real diagonal matrix from a list.
+diagl :: [Double] -> Matrix Double
+diagl = diag . vector
+
+-- | Create a matrix or zeros.
+zeros :: Int -- ^ rows
+      -> Int -- ^ columns
+      -> Matrix Double
+zeros r c = konst 0 (r,c)
+
+-- | Create a matrix or ones.
+ones :: Int -- ^ rows
+     -> Int -- ^ columns
+     -> Matrix Double
+ones r c = konst 1 (r,c)
+
+-- | Concatenation of real vectors.
+infixl 9 #
+(#) :: Vector Double -> Vector Double -> Vector Double
+a # b = join [a,b]
+
+-- | Horizontal concatenation of real matrices.
+infixl 8 &
+(&) :: Matrix Double -> Matrix Double -> Matrix Double
+a & b = fromBlocks [[a,b]]
+
+-- | Vertical concatenation of real matrices.
+(//) :: Matrix Double -> Matrix Double -> Matrix Double
+infixl 7  //
+a // b = fromBlocks [[a],[b]]
+
+
+-- | Real block matrix from a rectangular list of lists.
+blocks :: [[Matrix Double]] -> Matrix Double
+blocks = fromBlocks
+
+-- | A real matrix with a single row, created from a list of elements.
+row :: [Double] -> Matrix Double
+row = asRow . vector
+
+-- | A real matrix with a single column, created from a list of elements.
+col :: [Double] -> Matrix Double
+col = asColumn . vector
+