Efficient algorithms to perform linear algebra operations on 3D arrays in vector languages

Francois Cuvelier (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

In a few number of applications, a need arises to do some usual linear algebra operations on a very large number of very small matrices of the same size, refered in this report by 3D-array. These operations could be as simple as sum or products, or more complex like computation of determinants, factorizing, solving, ... The aim of this report is to describe some vectorized algorithms for each one of these operations and to give eciency measures. For example, computing the LU decomposition with partial pivoting of one million of 8-by-8 matrices on our reference computer is performed in 3.1 seconds with Matlab, 5.6 seconds with Octave and 9.7 seconds with Python.

Domaines: Analyse numérique [math.NA]; Analyse numérique [cs.NA]

Francois Cuvelier. Efficient algorithms to perform linear algebra operations on 3D arrays in vector languages. 2018. ⟨hal-01809975⟩