svdfact(A)

svdfact(A, [thin=true]) -> SVD

Compute the Singular Value Decomposition (SVD) of A and return an SVD object. U, S, V and Vt can be obtained from the factorization F with F[:U], F[:S], F[:V] and F[:Vt], such that A = U*diagm(S)*Vt. If thin is true, an economy mode decomposition is returned. The algorithm produces Vt and hence Vt is more efficient to extract than V. The default is to produce a thin decomposition.

Examples

julia> A = [1.0 2.0; 3.0 4.0];
julia> B = [5.0 6.0; 7.0 8.0];
julia> F = svdfact(A, B)
GeneralizedSVD{Float64,Float64,Array{Float64,2}}
U factor:
2×2 Array{Float64,2}:
 -0.404553  -0.914514
 -0.914514   0.404553
D1 factor:
2-element Array{Float64,1}:
 5.46499
 0.36597
V factor:
2×2 Array{Float64,2}:
 -0.576048  -0.817416
 -0.817416   0.576048
D2 factor:
2-element Array{Float64,1}:
 14.2697
 0.62637
R0 factor:
2×2 Array{Float64,2}:
 -0.404553  -0.914514
 -0.914514   0.404553
Q factor:
2×2 Array{Float64,2}:
 -0.576048  -0.817416
 -0.817416   0.576048

The svdfact() function computes the generalized singular value decomposition (SVD) of matrices A and B. It returns a GeneralizedSVD factorization object F, which contains the factors U, D1, V, D2, R0, and Q such that:

A = F[:U] * F[:D1] * F[:R0] * F[:Q]'
B = F[:V] * F[:D2] * F[:R0] * F[:Q]'

Here are some examples of how to use svdfact():

Compute the generalized SVD of two matrices:

julia> A = [1.0 2.0; 3.0 4.0];
julia> B = [5.0 6.0; 7.0 8.0];
julia> F = svdfact(A, B);

Access the factor matrices:

julia> U = F[:U];  # U factor matrix
julia> D1 = F[:D1];  # D1 factor vector
julia> V = F[:V];  # V factor matrix
julia> D2 = F[:D2];  # D2 factor vector
julia> R0 = F[:R0];  # R0 factor matrix
julia> Q = F[:Q];  # Q factor matrix

Note that the output may vary depending on the values and dimensions of the input matrices A and B.

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svdfact(A)

Examples

See Also

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