The Linear Algebra Mapping Problem. Current State of Linear Algebra Languages and Libraries

We observe a disconnect between the developers and end users of linear algebra libraries. On one hand, numerical high-performance communities invest significant effort in development optimization highly sophisticated kernels libraries, aiming at maximum exploitation both properties input matrices, architectural features target computing platform. other are progressively less likely to go through error-prone time consuming process directly using said libraries by writing their code C or Fortran; instead, languages such as Matlab, Julia, Eigen Armadillo, which offer higher level abstraction, becoming more popular. Users given opportunity matrix computations with syntax that closely resembles mathematical description; it is then compiler an interpreter internally maps program lower kernels, provided BLAS LAPACK. Unfortunately, our experience suggests terms performance, this translation typically vastly suboptimal. In paper, we first introduce Linear Algebra Mapping Problem, investigate how effectively benchmark test problems solved popular high-level programming languages. Specifically, consider Octave, R, Armadillo (C++), NumPy (Python); meant standard optimizations common subexpression elimination loop-invariant motion, well specific optimal parenthesization product kernel selection for matrices properties. The aim study give concrete guidelines support computations.