Support complex matrices?

[ssfrr]

I'm not sure if the underyling algorithm is amenable to supporting complex matrices. If so do you think it's an easy add to the package? Currently it throws an error trying to get eps(::Complex)

MWE:

u = randn(ComplexF64, 100)
v = randn(ComplexF64, 20)
D = u*v' .+ randn.(ComplexF64) .* 0.1
A, E, s, sv = rpca(D)

[baggepinnen]

I have not considered complex matrices, but there is not reason not to allow them right away! I'll have a look and see what we can do

[baggepinnen]

The following now works on master v1.3.1

           u = randn(ComplexF64, 100)
            v = randn(ComplexF64, 20)
            E = randn(ComplexF64,100,20) .* 10 .* (rand.() .< 0.01)
            A = u*v'
            D = A .+ E
            Ah, Eh, s, sv = rpca(D)
            @test sum(abs2, Eh-E)/sum(abs2, E) < 1e-5
            @test sum(abs2, Ah-A)/sum(abs2, A) < 1e-5

I had to find a replacement for the soft thresholding operator for complex numbers, the following seems to work okay but not much thought has gotten into it

@inline function soft_th(x::Complex, ϵ)
    m,a = abs(x), angle(x)
    m = max(m-ϵ,zero(m)) + min(m+ϵ,zero(m))
    m*cis(a)
end

[ssfrr]

Great, thanks! I’ll try it out and see if this improves things over regular PCA for my problem.