-- Alternative interface and utilities for creation of real arrays, useful to work in interactive mode. module Real( module Numeric.LinearAlgebra, (<>), (*>), (<*), (<\>), (\>), vector, eye, zeros, ones, diagl, row, col, (#),(&), (//), blocks, rand ) where import Numeric.LinearAlgebra hiding ((<>), (<|>), (<->), (<\>), (.*), (*/)) import System.Random(randomIO) 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. rand :: Int -- ^ rows -> Int -- ^ columns -> IO (Matrix Double) rand r c = do seed <- randomIO return (reshape c \$ randomVector seed Uniform (r*c)) -- | 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. infixl 7 // (//) :: Matrix Double -> Matrix Double -> Matrix Double 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, create 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