Matrix.QR.Householder

Documentation

leastSquares :: (Ix i, Enum i, Ix j, Enum j, RealFloat a) => Array (i, j) a -> Array i a -> Array j a

Solve an overconstrained linear problem, i.e. minimize ||Ax-b||. A must have dimensions m x n with m>=n and it must have full-rank. None of these conditions is checked.

decompose

Arguments

:: (Ix i, Enum i, Ix j, Enum j, RealFloat a)

=> Array (i, j) a

A

-> ([Reflection i a], Upper i j a)

QR(A)

solve :: (Ix i, Ix j, Fractional a) => ([Reflection i a], Upper i j a) -> Array i a -> Array j a

det :: (Ix i, Enum i, Ix j, Enum j, RealFloat a) => Array (i, j) a -> a

data Reflection i a

reflectMatrix :: (Ix i, Ix j, Num a) => Reflection i a -> Array (i, j) a -> Array (i, j) a

reflectVector :: (Ix i, Num a) => Reflection i a -> Array i a -> Array i a

data Upper i j a

matrixFromUpper :: (Ix i, Ix j, Num a) => Upper i j a -> Array (i, j) a

solveUpper :: (Ix i, Ix j, Fractional a) => Upper i j a -> Array i a -> Array j a

Assumes that Upper matrix is at least as high as wide and that it has full rank.

detUpper :: (Ix i, Ix j, Fractional a) => Upper i j a -> a