CUSOLVER: support eigendecomposition

[hayatoikoma]

I am currently trying to perform an eigendecomposition on GPU.
Is there any plan for CuArrays.jl to support it from CUSOLVER sometime soon?

[kshyatt]

With the merge of JuliaGPU/CuArrays.jl#170, we support these for sparse matrices - if you want the new dense solvers, I can try to add those?

[hayatoikoma]

Thank you for making it available for sparse matrices.

It is no longer required for me, but I guess the dense solver will be useful for somebody else?

[maleadt]

These seem implemented:

CUDA.jl/lib/cusolver/linalg.jl

Lines 113 to 134 in 2a3cec9

	# eigenvalues
	function LinearAlgebra.eigen(A::Symmetric{T,<:CuMatrix}) where {T<:BlasReal}
	A2 = copy(A.data)
	Eigen(syevd!('V', 'U', A2)...)
	end
	function LinearAlgebra.eigen(A::Hermitian{T,<:CuMatrix}) where {T<:BlasComplex}
	A2 = copy(A.data)
	Eigen(heevd!('V', 'U', A2)...)
	end
	function LinearAlgebra.eigen(A::Hermitian{T,<:CuMatrix}) where {T<:BlasReal}
	eigen(Symmetric(A))
	end
	function LinearAlgebra.eigen(A::CuMatrix{T}) where {T<:BlasReal}
	A2 = copy(A)
	issymmetric(A) ? Eigen(syevd!('V', 'U', A2)...) : error("GPU eigensolver supports only Hermitian or Symmetric matrices.")
	end
	function LinearAlgebra.eigen(A::CuMatrix{T}) where {T<:BlasComplex}
	A2 = copy(A)
	ishermitian(A) ? Eigen(heevd!('V', 'U', A2)...) : error("GPU eigensolver supports only Hermitian or Symmetric matrices.")
	end