inv or logdet for symmetric matrices

[theogf]

If you are looking like me to compute logdet on Symmetric matrices you need to go call some "low-level" functions in CUDA.CUSOLVER
This is connected to #116

Here is an unsafe gist for logdet :

function LinearAlgebra.logdet(A::CUDA.CuMatrix)
    d_A = copy(A) # Create a copy
    _, info = CUDA.CUSOLVER.potrfBatched!('L', [d_A]) # Update d_A in-place to be passed to a Cholesky constructor
    L = LinearAlgebra.Cholesky(d_A, 'L', first(info)).L # Create the corresponding lower-triangular matrix
    return 2 * sum(log, diag(L)) # Compute logdet by summing the elements of the diagonal
end

I suppose this could be improved and be more faithful to the implementation in LinearAlgebra but that's further work
For inv one can do a similar thing :

function LinearAlgebra.inv(A::CUDA.CuMatrix)
    d_A = copy(A)
    _, info = CUDA.CUSOLVER.potrfBatched!('L', [d_A])
    L = LinearAlgebra.Cholesky(d_A, 'L', first(info)).L
    return (I / L) / L'
end

If you'd rather use lu instead replace the second and third line of each algorithm by

    d_A, p_inv, info = CUDA.CUSOLVER.getrf!(d_A) # Update d_A in-place to be passed to be passed to a LU constructor
    fact = LinearAlgebra.LU(d_A, Int64.(collect(p_inv), zero()) # Create a LU object

and change the last line accordingly

[theogf]

I just noted that (I / L) / L' is definitely not good since it is calling the generic LinearAlgebra functions and are therefore using scalar indexing

[kshyatt]

inv at least works currently, though logdet does not. Would be a nice first issue!