GeneralizedSVD

A Julia program to compute the generalized singular value decomposition (GSVD).

Installation

To install GeneralizedSVD, from the Julia REPL, type ] to enter the Pkg REPL mode and run:

pkg> add GeneralizedSVD

or using the Pkg API:

julia> import Pkg; Pkg.add("GeneralizedSVD")

Example

julia> using GeneralizedSVD

julia> A = [1. 2 3 0; 5 4 2 1; 0 3 5 2; 2 1 3 3; 2 0 5 3];
julia> B = [1. 0 3 -1; -2 5 0 1; 4 2 -1 2];

julia> F = gsvd(A, B);

julia> F.C
5×4 SparseArrays.SparseMatrixCSC{Float64,Int64} with 4 stored entries:
  [1, 1]  =  1.0
  [2, 2]  =  0.894685
  [3, 3]  =  0.600408
  [4, 4]  =  0.27751

julia> F.S
3×4 SparseArrays.SparseMatrixCSC{Float64,Int64} with 3 stored entries:
  [1, 2]  =  0.446698
  [2, 3]  =  0.799694
  [3, 4]  =  0.960723

julia> F.R
4×4 Array{Float64,2}:
 5.74065  -7.07986   0.125979  -0.316232
 0.0      -7.96103  -2.11852   -2.98601
 0.0       0.0       5.72211   -0.43623
 0.0       0.0       0.0        5.66474

julia> [A; B] ≈ [F.U*F.C; F.V*F.S]*F.R*F.Q'
true

Documentation

• docs-url — documentation of the most recently tagged version.

Project Status

The package is tested against, and being developed for, Julia 1.3 on macOS and supports Float type.

Contact

• Ji Wang: jiiwang@ucdavis.edu
• Zhaojun Bai: zbai@ucdavis.edu