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|
-----------------------------------------------------------------------------
{- |
Module : Numeric.LinearAlgebra
Copyright : (c) Alberto Ruiz 2006-14
License : BSD3
Maintainer : Alberto Ruiz
Stability : provisional
-}
-----------------------------------------------------------------------------
module Numeric.LinearAlgebra (
-- * Basic types and data processing
module Numeric.LinearAlgebra.Data,
-- * Arithmetic and numeric classes
-- |
-- The standard numeric classes are defined elementwise:
--
-- >>> fromList [1,2,3] * fromList [3,0,-2 :: Double]
-- fromList [3.0,0.0,-6.0]
--
-- >>> (3><3) [1..9] * ident 3 :: Matrix Double
-- (3><3)
-- [ 1.0, 0.0, 0.0
-- , 0.0, 5.0, 0.0
-- , 0.0, 0.0, 9.0 ]
--
-- In arithmetic operations single-element vectors and matrices
-- (created from numeric literals or using 'scalar') automatically
-- expand to match the dimensions of the other operand:
--
-- >>> 5 + 2*ident 3 :: Matrix Double
-- (3><3)
-- [ 7.0, 5.0, 5.0
-- , 5.0, 7.0, 5.0
-- , 5.0, 5.0, 7.0 ]
--
-- * Matrix product
(<.>),
-- | The overloaded multiplication operators may need type annotations to remove
-- ambiguity. In those cases we can also use the specific functions 'mXm', 'mXv', and 'dot'.
--
-- The matrix x matrix product is also implemented in the "Data.Monoid" instance, where
-- single-element matrices (created from numeric literals or using 'scalar')
-- are used for scaling.
--
-- >>> let m = (2><3)[1..] :: Matrix Double
-- >>> m <> 2 <> diagl[0.5,1,0]
-- (2><3)
-- [ 1.0, 4.0, 0.0
-- , 4.0, 10.0, 0.0 ]
--
-- 'mconcat' uses 'optimiseMult' to get the optimal association order.
-- * Other products
outer, kronecker, cross,
scale,
sumElements, prodElements, absSum,
-- * Linear Systems
(<\>),
linearSolve,
linearSolveLS,
linearSolveSVD,
luSolve,
cholSolve,
cgSolve,
-- * Inverse and pseudoinverse
inv, pinv, pinvTol,
-- * Determinant and rank
rcond, rank, ranksv,
det, invlndet,
-- * Singular value decomposition
svd,
fullSVD,
thinSVD,
compactSVD,
singularValues,
leftSV, rightSV,
-- * Eigensystems
eig, eigSH, eigSH',
eigenvalues, eigenvaluesSH, eigenvaluesSH',
geigSH',
-- * QR
qr, rq, qrRaw, qrgr,
-- * Cholesky
chol, cholSH, mbCholSH,
-- * Hessenberg
hess,
-- * Schur
schur,
-- * LU
lu, luPacked,
-- * Matrix functions
expm,
sqrtm,
matFunc,
-- * Nullspace
nullspacePrec,
nullVector,
nullspaceSVD,
null1, null1sym,
orth,
-- * Norms
norm1, norm2, normInf, pnorm, NormType(..),
-- * Correlation and convolution
corr, conv, corrMin, corr2, conv2,
-- * Random arrays
RandDist(..), randomVector, rand, randn, gaussianSample, uniformSample,
-- * Misc
meanCov, peps, relativeError, haussholder, optimiseMult, dot, udot, mXm, mXv, smXv, (<>), (◇), Seed, checkT,
-- * Auxiliary classes
Element, Container, Product, Contraction, LSDiv,
Complexable(), RealElement(),
RealOf, ComplexOf, SingleOf, DoubleOf,
IndexOf,
Field, Normed,
CGMat, Transposable
) where
import Numeric.LinearAlgebra.Data
import Numeric.Matrix()
import Numeric.Vector()
import Numeric.Container
import Numeric.LinearAlgebra.Algorithms
import Numeric.LinearAlgebra.Util
import Numeric.LinearAlgebra.Random
import Numeric.Sparse(smXv)
import Numeric.LinearAlgebra.Util.CG(cgSolve)
import Numeric.LinearAlgebra.Util.CG(CGMat)
|
