Prior Art

Summary

These represent a range of features, including wrappers around or implementations of BLAS-like features and generic multidimensional array libraries.

Some of these projects are actively developed, some are relative static, while others are historical in nature.

C++ Universe

• Eigen
• Armadillo
• Boost.uBLAS
• Boost.MultiArray
• Blaze
• Elemental
• TBLIS
• Cyclops Tensor Framework (CTF)
• Kokkos View
• Kokkos Kernels
• Blitz++
• FreePOOMA
• LAPACK++
• Matrix Template Library (MTL4)
• GLAS: Generic Linear Algebra Software
• FLENS
• Seldon

Other Universes

• Numpy (Python)
• PETSc (C89-based, with Matlab, Fortran, and other language bindings)
• BLIS (C-based)
• libflame (C-based)
• LAPACK (legacy Fortran)
• ScaLAPACK (legacy Fortran)
• PLASMA
• MAGMA
• MIR-GLAS (D)
• Matlab
• Fortran 95+ (sorry, I couldn't find a better website)

If you believe Wikipedia, see this.

Existing C++ Linear Algebra Projects Synopsis

I'd like us to give just a short synopsis of capabilities in existing C++ based Linear Algebra Libraries which address issues we listed as important for this project. I am mostly interested in design principles not completeness of math functionality.

Kokkos-Kernels

Provides BLAS, Sparse and Graph kernels on node using Kokkos. As far as I know this may be the closest existing thing to what we want to do since it already incorporates a number of key concepts (such as that it is using multi dimensional arrays with layouts as input parameters and is valid for any scalar type combination).

• C++ based interface using Kokkos::View (i.e. what mdspan is mostly based off).

  • template<class AViewType,
         class XViewType,
         class YViewType>
    void gemv (const char trans[],
      typename AViewType::const_value_type& alpha, const AViewType& A,
      const XViewType& x, typename YViewType::const_value_type& beta, const YViewType& y);

• Can accept any Scalar type combination (i.e. AViewType, XViewType, YViewType can have different Scalar types)
• Can accept any layouts (e.g. XViewType can be a non-contigues subarray for example a row in a column major matrix)
• Is memory space aware. Kokkos::View has a memory space template parameter, which in mdspan could be incorporated via the accessor_property. Chooses execution mechanism (CUDA,OpenMP,etc.) based on memory space.
• Can call TPLs (MKL,CUBLAS etc.) if scalar type, data layout and memory space match the TPL capabilities.
• Starts to provide nested BLAS. e.g. calling BLAS with a CUDA-Block, or an OpenMP team of threads.

   gemv(team_handle, 'N', alpha, A, x, beta, y);