Using GPU to accelerate the eigen decomposition in the psuedo-inverse calculation in nystrom.jl

[changhe3]

Here is my implementation:

using CuArrays, CUDAnative, LinearAlgebra, MLKernel

function make_symmetric(A::Mat, uplo::Char='U') where {T<:AbstractFloat, Vec<:AbstractVector{T}, Mat<:AbstractMatrix{T}}
    return LinearAlgebra.copytri!(A |> Matrix{T}, uplo)
end

function nystrom_inv_gpu!(A::Mat) where {T<:AbstractFloat, Vec<:AbstractVector{T}, Mat<:AbstractMatrix{T}}
    A = cu(A)
    vals, vectors = CuArrays.CUSOLVER.syevd!('V', 'U', A)
    tol = eps(T)*size(A,1)
    max_eig = maximum(vals)
    # for i in eachindex(vals)
    #     vals[i] = abs(vals[i]) <= max_eig * tol ? zero(T) : one(T) / sqrt(vals[i])
    # end
    predicate = one(T) .* (vals .>= max_eig * tol)
    vals .= predicate .* CUDAnative.rsqrt.(vals .^ predicate)
    QD = CuArrays.CUBLAS.dgmm!('R', vectors, vals, vectors)
    W = CuArrays.CUBLAS.syrk('U', 'N', QD)
    return make_symmetric(W)
end

[trthatcher]

Hi @changhe3

Unfortunately I'm not planning on maintaining this library anymore due to other commitments (it's been that way for a while) and I will be archiving the repo. There's another library that is the go-forward solution... I would open up an issue related to the Nystrom factorization over there:

https://github.com/theogf/KernelFunctions.jl

Great work though!