Matrix inversion for CuArray

[xukai92]

inv is not defined for CuArray

I attempted to use a wrap over CuArrays.CUBLAS.matinv_batched, i.e. Base.inv(x::CuArray{<:Real,2}) = CuArrays.CUBLAS.matinv_batched([x])[2][1]. But this only supports matrix smaller than 32x32.

Any idea how to support it formally?

[xukai92]

A related issue is :\ is not defined for CuArray but could be wrapped by several CUBALS functions:

const CuOrAdj = Union{CuArray, LinearAlgebra.Adjoint{T, CuArray{T, 2}}} where {T<:AbstractFloat}
function Base.:\(_A::AT1, _B::AT2) where {AT1<:CuOrAdj, AT2<:CuOrAdj}
    A, B = copy(_A), copy(_B)
    A, ipiv = CuArrays.CUSOLVER.getrf!(A)
    return CuArrays.CUSOLVER.getrs!('N', A, ipiv, B)
end

PS: this is related because some matrix inversion could be replaced by :\

[xukai92]

cc @mohamed82008 @MikeInnes

[MikeInnes]

Perhaps we should start with a patch that adds \ to CuArrays, and then think about building inv on top?

[xukai92]

Perhaps we should start with a patch that adds \ to CuArrays, and then think about building inv on top?

On it.

[aterenin]

I need inv for UpperTriangular types. I presume this is still something that's not been implemented? I can try to add and make a PR if so.