[WIP] Compute the determinant of a matrix on the GPU #6193
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This PR adds a GpuLU op for computing the LU factorization of a square matrix on the GPU. The GpuLU op is used to define the gpu_det and gpu_slogdet helper functions. These functions are used to define lifter optimizations that replace the theano.tensor.nlinalg.Det op with a graph that computes the determinant from the LU factorization as explained here: https://en.wikipedia.org/wiki/LU_decomposition#Computing_the_determinant
For small matrices on a Titan Xp, moving the determinant operation to the GPU is slightly slower than on the CPU. However, moving the determinant operation to the GPU removes a memory transfer, which can result in a significant sppedup when calling the Det op inside a scan loop. For matrices bigger than 1000x1000, the GPU version is faster.
I've marked this as WIP since I believe a better job can be done by writing a GpuDet Op that implements the same algorithm in the Op c_code. I'm looking at how the Magma Ops do this, but I'm not sure how to call cusolver directly from C code.