Complex matrix inversion

[wqinc]

New to this framework and we are investigating if Halide could be extended to solving matrix-intensive computational physics problems. Thank you for this great piece of work.

A silly question if you don't mind, could we use Halide to experiment with scheduling complex matrix inversions and multiplications (in a CPU-GPU heterogeneous setting)? I would really appreciate it if anyone could point me to some references as I don't seem to find any in the code/tutorials.

[abadams]

Matrix multiplications should be good. Matrix inversions might be trickier, depending on what you're doing. E.g. you can write a good panel update routine for the inner loop of Cholesky, but it's much harder to write an entire Cholesky decomposition in Halide.

There's a GPU real-valued matrix multiply with a good schedule here: https://github.com/halide/Halide/tree/master/apps/cuda_mat_mul

and here's an example of some hand-rolled syntactic sugar for dealing with complex values (it wraps Halide's Tuple support): https://github.com/halide/Halide/blob/master/apps/fft/complex.h

[MDBrothers]

@wqinc What about using QR decomposition with Givens rotations for matrix "inversion"? The rotations can be computed on the rows in parallel.