MatrixFactorizations.jl

A Julia package to contain non-standard matrix factorizations
Author JuliaLinearAlgebra
Popularity
16 Stars
Updated Last
5 Months Ago
Started In
March 2019

MatrixFactorizations.jl

Build Status

codecov

A Julia package to contain non-standard matrix factorizations. At the moment it implements the QL, RQ, and UL factorizations, a combined Cholesky factorization with inverse, and polar decompositions. In the future it may include other factorizations such as the LQ factorization.

QL Factorization

The QL Factorization is analogous to the QR factorization but with a lower-triangular matrix:

julia> using MatrixFactorizations

julia> A = randn(5,5);

julia> ql(A)
MatrixFactorizations.QL{Float64,Array{Float64,2}}
Q factor:
5×5 MatrixFactorizations.QLPackedQ{Float64,Array{Float64,2}}:
  0.155574  -0.112555   -0.686362   -0.701064   0.0233276
  0.363037  -0.0583277  -0.0329428   0.152682   0.916736 
 -0.670742   0.294355   -0.547867    0.347157   0.206843 
 -0.61094   -0.566041    0.324432   -0.353128   0.276396 
  0.144425  -0.759527   -0.349868    0.489877  -0.199681 
L factor:
5×5 Array{Float64,2}:
 -1.75734     0.0         0.0        0.0       0.0   
 -0.58336    -2.08515     0.0        0.0       0.0   
  0.0213518   0.0722477  -2.01325    0.0       0.0   
  0.930364   -0.46796    -0.322493  -2.9091    0.0   
  1.08725     0.746217    0.549688  -1.10194  -2.0581

julia> b = randn(5); ql(A) \ b  A \ b
true