A leaner gesv_rbt_async with improved execution speed and accuracy

[asenzz]

This pull request introduces two solver functions using GESV RBT:

magma_int_t
magma_zgesv_rbt_async(
        const magma_bool_t refine, const magma_int_t n, const magma_int_t nrhs,
        const magmaDoubleComplex *const dA_, const magma_int_t lda,
        magmaDoubleComplex *const dB_, const magma_int_t ldb,
        magma_int_t *const info,
        const magma_int_t iter_max, const double bwdmax,
        magma_queue_t queue)

magma_int_t
magma_zgesv_rbt_refine_async(
        const magma_int_t n, const magma_int_t nrhs,
        const magmaDoubleComplex *const dA_, const magma_int_t lda,
        magmaDoubleComplex *const dB_, const magma_int_t ldb,
        magma_int_t *info,
        const magma_int_t iter_max, const double bwdmax,
        magma_queue_t queue)

As you can see they introduce 3 new parameters

• iter_max - maximum number of refinement iterations, old behaviour is iter_max set to 30.
• bwdmax - refinement threshold, error above this threshold will cause more refinement iterations up until iter_max is reached, set to zero to make sure all iterations specified in iter_max are executed.
• queue - an already constructed MAGMA queue, that can be reused further in order to avoid spending cycles on initializing and uninitializing a new queue every time the function is called.

I wrote this function in order to speed up the tuning of support vector regression parameters where I find it perform better than the rest of solvers present in MAGMA. This version has a slightly better accuracy since it saves the best solution from all iterations, instead of using the last iteration solution. The fact that it uses async functions internally and an already initialized queue saved me about 30% of measure time when called over the process of tuning parameters, in the magnitude of 3000 to 10000 calls on a Dell R730 with 4xV100 Nvidia cards. It can use a specific CUDA stream created by the user since it take a magma_queue_t as an argument.
I haven't written unit tests for these methods but they should be similar to the old magma_zgesv_rbt function. I tested the accuracy of this implementation in my project, Tempus.

Use magma_zgesv_rbt_refine_async to refine an already present solution in dB_. I haven't tested this function.

[asenzz]

I must of closed this by mistake, apologies. The changes are in the gesv_rbt_async branch.

[nbeams]

Hi @asenzz, thanks for your interest in contributing to MAGMA! After some internal discussion, we feel adding an interface to the asynchronous memory management would be too big of a departure from MAGMA's usual interface at the moment. For routines where users have requested versions without memory allocation costs, we have the "expert" interfaces (see, e.g., magma_zgetrf_expert_gpu_work, magma_zgetri_expert_gpu_work, etc.). These routines can then be used by the standard interface routines, or used directly by expert users who wish to manage their own workspace memory.

If you want to try to change this PR to use that kind of interface, you would be welcome to do so, but of course we understand if you don't want to take the time to do this. Thanks again for your interest in MAGMA, and we hope it continues to be useful to you!

[asenzz]

Alright Natalie, I will try to update the _async methods to the _expert_gpu_work kind of format when time permits. Best regards