[oneMKL][Sparse BLAS] Add `oneapi::mkl::sparse::spsm()` API

[gajanan-choudhary]

This is a request tracker to add an API for sparse triangular solve with a dense matrix right-hand-side to the sparse BLAS domain in the oneMKL Specification.

• The operation performed is, $\text{op}(A)\cdot Y = \alpha\cdot\text{op}(X)$, where:
  • $A$ is a sparse matrix,
  • $X$ and $Y$ are dense matrices,
  • $\alpha$ is a scalar, and
  • $\text{op}(\cdot)$ is one non-transpose/transpose/conjugate-transpose.
• Going by the recent overhaul in [oneMKL][spblas] Update sparse blas API #522, in all likelihood, the APIs will look like:

  namespace oneapi::mkl::sparse {
  
      struct spsm_descr;
      using spsm_descr_t = spsm_descr*;
  
      void init_spsm_descr (sycl::queue                       &queue,
                            oneapi::mkl::sparse::spsm_descr_t *p_spsm_descr);
  
      sycl::event release_spsm_descr (sycl::queue                       &queue,
                                      oneapi::mkl::sparse::spsm_descr_t spsm_descr,
                                      const std::vector<sycl::event>    &dependencies = {});
  
      enum class spsm_alg {
          default_alg,
          no_optimize_alg,
      };
  
      void spsm_buffer_size(
          sycl::queue                                &queue,
          oneapi::mkl::transpose                     opA,
          oneapi::mkl::transpose                     opX,
          const void*                                alpha,
          oneapi::mkl::sparse::matrix_view           A_view,
          oneapi::mkl::sparse::matrix_handle_t       A_handle,
          oneapi::mkl::sparse::dense_matrix_handle_t X_handle,
          oneapi::mkl::sparse::dense_matrix_handle_t Y_handle,
          oneapi::mkl::sparse::spsm_alg              alg,
          oneapi::mkl::sparse::spsm_descr_t          spsm_descr,
          std::size_t                                &temp_buffer_size);
  
      void spsm_optimize(
          sycl::queue                                &queue,
          oneapi::mkl::transpose                     opA,
          oneapi::mkl::transpose                     opX,
          const void*                                alpha,
          oneapi::mkl::sparse::matrix_view           A_view,
          oneapi::mkl::sparse::matrix_handle_t       A_handle,
          oneapi::mkl::sparse::dense_matrix_handle_t X_handle,
          oneapi::mkl::sparse::dense_matrix_handle_t Y_handle,
          oneapi::mkl::sparse::spsm_alg              alg,
          oneapi::mkl::sparse::spsm_descr_t          spsm_descr,
          sycl::buffer<std::uint8_t, 1>              workspace);
  
      sycl::event spsm_optimize(
          sycl::queue                                &queue,
          oneapi::mkl::transpose                     opA,
          oneapi::mkl::transpose                     opX,
          const void*                                alpha,
          oneapi::mkl::sparse::matrix_view           A_view,
          oneapi::mkl::sparse::matrix_handle_t       A_handle,
          oneapi::mkl::sparse::dense_matrix_handle_t X_handle,
          oneapi::mkl::sparse::dense_matrix_handle_t Y_handle,
          oneapi::mkl::sparse::spsm_alg              alg,
          oneapi::mkl::sparse::spsm_descr_t          spsm_descr,
          void*                                      workspace,
          const std::vector<sycl::event>             &dependencies = {});
  
      sycl::event spsm(
          sycl::queue                                &queue,
          oneapi::mkl::transpose                     opA,
          oneapi::mkl::transpose                     opX,
          const void*                                alpha,
          oneapi::mkl::sparse::matrix_view           A_view,
          oneapi::mkl::sparse::matrix_handle_t       A_handle,
          oneapi::mkl::sparse::dense_matrix_handle_t X_handle,
          oneapi::mkl::sparse::dense_matrix_handle_t Y_handle,
          oneapi::mkl::sparse::spsm_alg              alg,
          oneapi::mkl::sparse::spsm_descr_t          spsm_descr,
          const std::vector<sycl::event>             &dependencies = {});
  
  }