CODEWITHSUNDEEP
matrixjulialinear-algebranumerical-methods
James Rider
James Rider

Reputation: 805

Rank r matrix approximation via SVD in Julia?

Suppose we have computed the svd of a matrix A in Julia via svd(A). How would we compute a rank r approximation of that matrix A in Julia, given we already have its singular value decomposition?

Upvotes: 0

Views: 688

Answers (1)

Picaud Vincent
Picaud Vincent

Reputation: 10982

I would suggest something as follows:

using LinearAlgebra

A=rand(10,20)

svd_fact = svd(A)

function r_rank_approx(svd::SVD,r::Int)
    @assert 1 ≤ r
    
    n,m = size(svd)
    u,s,v = svd

    r = min(r,min(n,m))

    # like u[:,1:r]*Diagonal(s[1:r])*v[:,1:r]'
    # but reduce number of memory allocs
    view(u,:,1:r)*Diagonal(view(s,1:r))*view(v,:,1:r)'
end

r_rank_approx(svd_fact,2)

The idea is to only use the first r-singular values from the complete SVD.

Note: if you have big matrices, there are dedicated algorithms that compute a truncated SVD directly, see TSVD.jl by example.

Upvotes: 1

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