arXiv subjects

Francisco López

Publications and source records attributed to Francisco López.

4 recordsLinked to original sources

arXiv2025

Compilation of Generalized Matrix Chains with Symbolic Sizes

Generalized Matrix Chains (GMCs) are products of matrices where each matrix carries features (e.g., general, symmetric, triangular, positive-definite) and is optionally transposed and/or inverted. GMCs are commonly evaluated via sequences of calls to BLAS and LAPACK kernels. When matrix sizes are known, one can craft a sequence of kernel calls to evaluate a GMC that minimizes some cost, e.g., the number of floating-point operations (FLOPs). Even in these circumstances, high-level languages and libraries, upon which users usually rely, typically perform a suboptimal mapping of the input GMC onto a sequence of kernels. In this work, we go one step beyond and consider matrix sizes to be symbolic (unknown); this changes the nature of the problem since no single sequence of kernel calls is optimal for all possible combinations of matrix sizes. We design and evaluate a code generator for GMCs with symbolic sizes that relies on multi-versioning. At compile-time, when the GMC is known but the sizes are not, code is generated for a few carefully selected sequences of kernel calls. At run-time, when sizes become known, the best generated variant for the matrix sizes at hand is selected and executed. The code generator uses new theoretical results that guarantee that the cost is within a constant factor from optimal for all matrix sizes and an empirical tuning component that further tightens the gap to optimality in practice. In experiments, we found that the increase above optimal in both FLOPs and execution time of the generated code was less than 15\% for 95\% of the tested chains.

cs.MS↗

arXiv2025

Track Component Failure Detection Using Data Analytics over existing STDS Track Circuit data

Track Circuits (TC) are the main signalling devices used to detect the presence of a train on a rail track. It has been used since the 19th century and nowadays there are many types depending on the technology. As a general classification, Track Circuits can be divided into 2 main groups, DC (Direct Current) and AC (Alternating Current) circuits. This work is focused on a particular AC track circuit, called "Smart Train Detection System" (STDS), designed with both high and low-frequency bands. This approach uses STDS current data applied to an SVM (support vector machine) classifier as a type of failure identifier. The main purpose of this work consists on determine automatically which is the component of the track that is failing to improve the maintenance action. Model was trained to classify 15 different failures that belong to 3 more general categories. The method was tested with field data from 10 different track circuits and validated by the STDS track circuit expert and maintainers. All use cases were correctly classified by the method.

eess.SP↗

arXiv2025

On the Parenthesisations of Matrix Chains: All are Useful, Few Are Essential

The product of a matrix chain consisting of $n$ matrices can be computed in $C_{n-1}$ (Catalan's number) different ways, each identified by a distinct parenthesisation of the chain. The best algorithm to select a parenthesisation that minimises the cost runs in $O(n \log n)$ time. Approximate algorithms run in $O(n)$ time and find solutions that are guaranteed to be within a certain factor from optimal; the best factor is currently $1.155$. In this article, we first prove two results that characterise different parenthesisations, and then use those results to improve on the best known approximation algorithms. Specifically, we show that (a) each parenthesisation is optimal somewhere in the problem domain, and (b) exactly $n + 1$ parenthesisations are essential in the sense that the removal of any one of them causes an unbounded penalty for an infinite number of problem instances. By focusing on essential parenthesisations, we improve on the best known approximation algorithm and show that the approximation factor is at most $1.143$.

cs.DM↗

arXiv2022

FLOPs as a Discriminant for Dense Linear Algebra Algorithms

Expressions that involve matrices and vectors, known as linear algebra expressions, are commonly evaluated through a sequence of invocations to highly optimised kernels provided in libraries such as BLAS and LAPACK. A sequence of kernels represents an algorithm, and in general, because of associativity, algebraic identities, and multiple kernels, one expression can be evaluated via many different algorithms. These algorithms are all mathematically equivalent (i.e., in exact arithmetic, they all compute the same result), but often differ noticeably in terms of execution time. When faced with a decision, high-level languages, libraries, and tools such as Julia, Armadillo, and Linnea choose by selecting the algorithm that minimises the FLOP count. In this paper, we test the validity of the FLOP count as a discriminant for dense linear algebra algorithms, analysing "anomalies": problem instances for which the fastest algorithm does not perform the least number of FLOPs. To do so, we focused on relatively simple expressions and analysed when and why anomalies occurred. We found that anomalies exist and tend to cluster into large contiguous regions. For one expression anomalies were rare, whereas for the other they were abundant. We conclude that FLOPs is not a sufficiently dependable discriminant even when building algorithms with highly optimised kernels. Plus, most of the anomalies remained as such even after filtering out the inter-kernel cache effects. We conjecture that combining FLOP counts with kernel performance models will significantly improve our ability to choose optimal algorithms.

cs.PF↗