Prof. Paolo Bientinessi
Department of Computing Science, Umeå University
Matrix computations appear in virtually every domain of science and engineering, and due to the seemingly unstoppable growth of data science, are now as widespread as ever. In response to such a massive demand, the numerical linear algebra community puts tremendous effort in the identification, analysis, and optimization of a reasonably small set of simple operations---such as those included in the BLAS and LAPACK libraries---that serve as building blocks for most users' target computations. However, in a recent investigation, we observed a noticeable disconnect between the developers and the end users of numerical linear algebra libraries: Low-level languages such as C and Fortran and progressively less likely to be used, in favor of high-level programming languages such as Matlab, Julia, and R, make it possible to code matrix computations at the same level of abstraction at which experts reason about them. Unfortunately, our experience suggests that this increase in productivity often comes together with significantly suboptimal algorithms. Under the cover, all such languages face the problem of expressing a target matrix computation in terms of available building blocks; we refer to this problem as the "Linear Algebra Mapping Problem" (LAMP). In this talk, we define the problem, present the challenges it poses, and carefully survey how it is currently solved by the state-of-the-art languages.