arXiv subjects

Paolo Bientinesi

Publications and source records attributed to Paolo Bientinesi.

At least 19 recordsLinked to original sources

arXiv2026

Performance Reporting of Mathematical Library Installations with LAAB - An Overview

We present the Linear Algebra Aware Benchmarks (LAAB) framework for systematically assessing and reporting the performance of mathematical library installations on HPC systems. Mathematical libraries provide interfaces for operations that form the computational building blocks of scientific applications. Reporting their performance is important for assessing application efficiency, estimating compute-time requirements, and preparing resource-allocation requests. In this paper, we define four objectives for performance reporting: 1) traceability, linking each report to the exact library installation and execution settings; 2) compatibility, relating library-operation performance to higher-level scientific applications that use them; 3) reliability, supporting interpretation in the presence of measurement variability; and 4) accessibility, ensuring that reports, benchmark definitions, and relevant metadata are available for inspection and reproduction. We then present the design of LAAB and show how it addresses the challenges associated with these objectives.

cs.PF↗

arXiv2026

Performance Benchmarking: Software for the Density Matrix Renormalization Group

The performance of scientific software often determines the scale of problems that can be solved in practice. As multiple implementations of the same algorithm emerge, systematic evaluation is needed to compare their strengths and limitations. The density matrix renormalization group (DMRG) algorithm, widely used to study quantum systems, has over 50 software implementations. These implementations vary in multiple aspects that can strongly affect performance. However, despite the need, performance evaluations of these implementations are scarce and lack a consistent standard; many existing evaluations are either too incomplete to enable meaningful comparisons or focus on objectives other than direct performance comparisons, thereby limiting understanding of how the implementations compare. Here, we present a performance-oriented benchmarking framework to facilitate meaningful comparisons of DMRG implementations, and we apply it to quantify the performance of eight implementations, highlighting similarities and differences among them. Furthermore, we examine multiple parameter settings, optimization strategies, and implementation-specific features to demonstrate how parameter configuration can affect performance and how systematic evaluation can reveal non-obvious trade-offs. The results show significant performance differences, up to two orders of magnitude in some cases, not only between different implementations when aligning parameters, but also within the same implementation when comparing different parameter configurations. Hence, our results demonstrate the significant value and insight that can be gained from conducting rigorous performance evaluations. Using our results and framework as a starting point, more rigorous benchmarking will ultimately help users and developers make informed decisions and support future development efforts to build better, more efficient software.

physics.comp-ph↗

arXiv2026

Real-time, EDM-inspired sonification of the activity of a supercomputer

The project described in this paper explores the informative sonification of data received in real time from a supercomputer. These data capture the current activities in all the nodes of the computer, therefore, their sonification functions as a form of continuous monitoring of the nodes' behavior and, by extension, of the system as a whole. Because such monitoring is theoretically unending, the resulting sonification must be musically capable of conveying information through sound in a way that remains both intelligible and engaging over long durations. Rather than imposing a predefined musical style onto the data, we sought to identify one which the data themselves could plausibly support. From a small set of candidates, we selected EDM because it is a family of genres whose structural and temporal characteristics align well with continuous, data-driven processes and long-term listening. Through this style-based approach, this research builds on the long tradition of computer data sonification while uniquely combining three elements rarely addressed together: monitoring (rather than debugging) as the primary goal, real-time (rather than post-mortem) data interpretation, and generation of virtually infinite and stylistically coherent (rather than incongruous) music.

cs.SD↗

arXiv2026

Report on the second Toulouse Tensor Workshop

This report documents the program of the second Toulouse Tensor Workshop which took place at the University of Toulouse on September 17-19, 2025, and summarizes the main points of discussion. This workshop follows the first Workshop (CECAM workshop on Tensor Contraction Library Standardization), which took place in Toulouse one year earlier, on May 24-25, 2024 and led to the formation of a tensor standardization working group, which has since specified a low-level standard interface for tensor operations available freely on GitHub. The 2025 workshop brought together developers of applications which rely extensively on tensor computations such as quantum many-body simulations in chemistry and physics (material science and electronic structure calculations), as well as developers and experts of tensor software who have the know-how to provide the technical support for such applications. The workshop enabled the community to provide feedback on the specified low-level interface and how it can be further refined. It also initiated a discussion on how the standardization efforts should be oriented in the near feature, in particular on what should be higher-level interfaces and how to tackle other requirements of the community such as tensor decompositions, symmetric tensors and structured sparsity support.

cs.MS↗

arXiv2026

Tensor Algebra Processing Primitives (TAPP): Towards a Standard for Tensor Operations

To address the absence of a universal standard interface for tensor operations, we introduce the Tensor Algebra Processing Primitives (TAPP), a C-based interface designed to decouple the application layer from hardware-specific implementations. We provide a mathematical formulation of tensor contractions and a reference implementation to ensure correctness and facilitate the validation of optimized kernels. Developed through community consensus involving academic and industrial stakeholders, TAPP aims to enable performance portability and resolving dependency challenges. The viability of the standard is demonstrated through successful integrations with the TBLIS and cuTENSOR libraries, as well as the DIRAC quantum chemistry package.

cs.MS↗

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

The Software Landscape for the Density Matrix Renormalization Group

The density matrix renormalization group (DMRG) algorithm is a cornerstone computational method for studying quantum many-body systems, renowned for its accuracy and adaptability. Despite DMRG's broad applicability across fields such as materials science, quantum chemistry, and quantum computing, numerous independent implementations have been developed. This survey maps the rapidly expanding DMRG software landscape, providing a comprehensive comparison of features among 35 existing packages. We found significant overlap in features among the packages when comparing key aspects, such as parallelism strategies for high-performance computing and symmetry-adapted formulations that enhance efficiency. This overlap suggests opportunities for modularization of common operations, including tensor operations, symmetry representations, and eigensolvers, as the packages are mostly independent and share few third-party library dependencies where functionality is factored out. More widespread modularization and standardization would result in reduced duplication of efforts and improved interoperability. We believe that the proliferation of packages and the current lack of standard interfaces and modularity are more social than technical. We aim to raise awareness of existing packages, guide researchers in finding a suitable package for their needs, and help developers identify opportunities for collaboration, modularity standardization, and optimization. Ultimately, this work emphasizes the value of greater cohesion and modularity, which would benefit DMRG software, allowing these powerful algorithms to tackle more complex and ambitious problems.

physics.comp-ph↗

arXiv2025

Enabling mixed-precision in spectral element codes

Mixed-precision computing has the potential to significantly reduce the cost of exascale computations, but determining when and how to implement it in programs can be challenging. In this article, we propose a methodology for enabling mixed-precision with the help of computer arithmetic tools, roofline model, and computer arithmetic techniques. As case studies, we consider Nekbone, a mini-application for the Computational Fluid Dynamics (CFD) solver Nek5000, and a modern Neko CFD application. With the help of the Verificarlo tool and computer arithmetic techniques, we introduce a strategy to address stagnation issues in the preconditioned Conjugate Gradient method in Nekbone and apply these insights to implement a mixed-precision version of Neko. We evaluate the derived mixed-precision versions of these codes by combining metrics in three dimensions: accuracy, time-to-solution, and energy-to-solution. Notably, mixed-precision in Nekbone reduces time-to-solution by roughly 1.62x and energy-to-solution by 2.43x on MareNostrum 5, while in the real-world Neko application, the gain is up to 1.3x in both time and energy, with the accuracy that matches double-precision results.

cs.MS↗

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↗

arXiv2024

Inspection of I/O Operations from System Call Traces using Directly-Follows-Graph

We aim to identify the differences in Input/Output(I/O) behavior between multiple user programs through the inspection of system calls (i.e., requests made to the operating system). A typical program issues a large number of I/O requests to the operating system, thereby making the process of inspection challenging. In this paper, we address this challenge by presenting a methodology to synthesize I/O system call traces into a specific type of directed graph, known as the Directly-Follows-Graph (DFG). Based on the DFG, we present a technique to compare the traces from multiple programs or different configurations of the same program, such that it is possible to identify the differences in the I/O behavior. We apply our methodology to the IOR benchmark, and compare the contentions for file accesses when the benchmark is run with different options for file output and software interface.

cs.PF↗

arXiv2024

Analyzing and reducing the synthetic-to-real transfer gap in Music Information Retrieval: the task of automatic drum transcription

Automatic drum transcription is a critical tool in Music Information Retrieval for extracting and analyzing the rhythm of a music track, but it is limited by the size of the datasets available for training. A popular method used to increase the amount of data is by generating them synthetically from music scores rendered with virtual instruments. This method can produce a virtually infinite quantity of tracks, but empirical evidence shows that models trained on previously created synthetic datasets do not transfer well to real tracks. In this work, besides increasing the amount of data, we identify and evaluate three more strategies that practitioners can use to improve the realism of the generated data and, thus, narrow the synthetic-to-real transfer gap. To explore their efficacy, we used them to build a new synthetic dataset and then we measured how the performance of a model scales and, specifically, at what value it will stagnate when increasing the number of training tracks for different datasets. By doing this, we were able to prove that the aforementioned strategies contribute to make our dataset the one with the most realistic data distribution and the lowest synthetic-to-real transfer gap among the synthetic datasets we evaluated. We conclude by highlighting the limits of training with infinite data in drum transcription and we show how they can be overcome.

cs.SD↗

arXiv2024

Ranking with Ties based on Noisy Performance Data

We consider the problem of ranking a set of objects based on their performance when the measurement of said performance is subject to noise. In this scenario, the performance is measured repeatedly, resulting in a range of measurements for each object. If the ranges of two objects do not overlap, then we consider one object as 'better' than the other, and we expect it to receive a higher rank; if, however, the ranges overlap, then the objects are incomparable, and we wish them to be assigned the same rank. Unfortunately, the incomparability relation of ranges is in general not transitive; as a consequence, in general the two requirements cannot be satisfied simultaneously, i.e., it is not possible to guarantee both distinct ranks for objects with separated ranges, and same rank for objects with overlapping ranges. This conflict leads to more than one reasonable way to rank a set of objects. In this paper, we explore the ambiguities that arise when ranking with ties, and define a set of reasonable rankings, which we call partial rankings. We develop and analyse three different methodologies to compute a partial ranking. Finally, we show how performance differences among objects can be investigated with the help of partial ranking.

cs.PF↗

arXiv2024

Enabling mixed-precision with the help of tools: A Nekbone case study

Mixed-precision computing has the potential to significantly reduce the cost of exascale computations, but determining when and how to implement it in programs can be challenging. In this article, we consider Nekbone, a mini-application for the CFD solver Nek5000, as a case study, and propose a methodology for enabling mixed-precision with the help of computer arithmetic tools and roofline model. We evaluate the derived mixed-precision program by combining metrics in three dimensions: accuracy, time-to-solution, and energy-to-solution. Notably, the introduction of mixed-precision in Nekbone, reducing time-to-solution by 40.7% and energy-to-solution by 47% on 128 MPI ranks.

cs.MS↗

arXiv2022

A Test for FLOPs as a Discriminant for Linear Algebra Algorithms

Linear algebra expressions, which play a central role in countless scientific computations, are often computed via a sequence of calls to existing libraries of building blocks (such as those provided by BLAS and LAPACK). A sequence identifies a computing strategy, i.e., an algorithm, and normally for one linear algebra expression many alternative algorithms exist. Although mathematically equivalent, those algorithms might exhibit significant differences in terms of performance. Several high-level languages and tools for matrix computations such as Julia, Armadillo, Linnea, etc., make algorithmic choices by minimizing the number of Floating Point Operations (FLOPs). However, there can be several algorithms that share the same (or have nearly identical) number of FLOPs; in many cases, these algorithms exhibit execution times which are statistically equivalent and one could arbitrarily select one of them as the best algorithm. It is however not unlikely to find cases where the execution times are significantly different from one another (despite the FLOP count being almost the same). It is also possible that the algorithm that minimizes FLOPs is not the one that minimizes execution time. In this work, we develop a methodology to test the reliability of FLOPs as discriminant for linear algebra algorithms. Given a set of algorithms (for an instance of a linear algebra expression) as input, the methodology ranks them into performance classes; i.e., multiple algorithms are allowed to share the same rank. To this end, we measure the algorithms iteratively until the changes in the ranks converge to a value close to zero. FLOPs are a valid discriminant for an instance if all the algorithms with minimum FLOPs are assigned the best rank; otherwise, the instance is regarded as an anomaly, which can then be used in the investigation of the root cause of performance differences.

cs.PF↗

arXiv2022

MOM: Matrix Operations in MLIR

Modern research in code generators for dense linear algebra computations has shown the ability to produce optimized code with a performance which compares and often exceeds the one of state-of-the-art implementations by domain experts. However, the underlying infrastructure is often developed in isolation making the interconnection of logically combinable systems complicated if not impossible. In this paper, we propose to leverage MLIR as a unifying compiler infrastructure for the optimization of dense linear algebra operations. We propose a new MLIR dialect for expressing linear algebraic computations including matrix properties to enable high-level algorithmic transformations. The integration of this new dialect in MLIR enables end-to-end compilation of matrix computations via conversion to existing lower-level dialects already provided by the framework.

cs.PL↗

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↗

arXiv2022

The landscape of software for tensor computations

Tensors (also commonly seen as multi-linear operators or as multi-dimensional arrays) are ubiquitous in scientific computing and in data science, and so are the software efforts for tensor operations. Particularly in recent years, we have observed an explosion in libraries, compilers, packages, and toolboxes; unfortunately these efforts are very much scattered among the different scientific domains, and inevitably suffer from replication, suboptimal implementations, and in many cases, limited visibility. As a first step towards countering these inefficiencies, here we survey and loosely classify software packages related to tensor computations. Our aim is to assemble a comprehensive and up-to-date snapshot of the tensor software landscape, with the intention of helping both users and developers. Aware of the difficulties inherent in any multi-discipline survey, we very much welcome the reader's help in amending and expanding our software list, which currently features 80 projects.

cs.MS↗

arXiv2022

Algorithm 979: Recursive Algorithms for Dense Linear Algebra -- The ReLAPACK Collection

To exploit both memory locality and the full performance potential of highly tuned kernels, dense linear algebra libraries such as LAPACK commonly implement operations as blocked algorithms. However, to achieve next-to-optimal performance with such algorithms, significant tuning is required. On the other hand, recursive algorithms are virtually tuning free, and yet attain similar performance. In this paper, we first analyze and compare blocked and recursive algorithms in terms of performance, and then introduce ReLAPACK, an open-source library of recursive algorithms to seamlessly replace most of LAPACK's blocked algorithms. In many scenarios, ReLAPACK clearly outperforms reference LAPACK, and even improves upon the performance of optimizes libraries.

cs.MS↗