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svd

svd(A, [thin=true]) -> U, S, V

Wrapper around svdfact extracting all parts the factorization to a tuple. Direct use of svdfact is therefore generally more efficient. Computes the SVD of A, returning U, vector S, and V such that A == U*diagm(S)*V'. If thin is true, an economy mode decomposition is returned. The default is to produce a thin decomposition.

Examples

julia> A = [1 2; 3 4];
julia> B = [5 6; 7 8];
julia> U, V, Q, D1, D2, R0 = svd(A, B);

julia> U
2×2 Array{Float64,2}:
 -0.404553  -0.914514
 -0.914514   0.404553

julia> V
2×2 Array{Float64,2}:
 -0.404553  -0.914514
 -0.914514   0.404553

julia> Q
2×2 Array{Float64,2}:
 -0.576048  -0.817416
 -0.817416   0.576048

julia> D1
2-element Array{Float64,1}:
 5.46499
 0.365966

julia> D2
2-element Array{Float64,1}:
 14.2274
 0.332311

julia> R0
2×2 Array{Float64,2}:
 -0.576048  -0.817416
 -0.817416   0.576048

In this example, the svd function is used to compute the generalized Singular Value Decomposition (SVD) of matrices A and B. The resulting tuple contains U, V, Q, D1, D2, and R0 matrices.

• U represents the left singular vectors of A and B.
• V represents the right singular vectors of A and B.
• Q is the orthogonal matrix used to transform A and B.
• D1 and D2 are the diagonal matrices containing the singular values of A and B respectively.
• R0 is an auxiliary matrix used in the decomposition.

It is important to note that using svdfact directly is generally more efficient than using svd and extracting the individual parts.

See Also

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