Mathematical Software
We describe a practical algorithm for computing the Stokes multipliers of a linear differential equation with polynomial coefficients at an irregular singular point of single level one. The algorithm follows a classical approach based on…
The Mersenne Twister MT19937 pseudorandom number generator, introduced by the last two authors in 1998, is still widely used. It passes all existing statistical tests, except for the linear complexity test, which measures the ratio of the…
We present f4ncgb, a new open-source C++ library for Gr\"obner basis computations in free algebras, which transfers recent advancements in commutative Gr\"obner basis software to the noncommutative setting. As our experiments show, f4ncgb…
Model-based approaches to imaging, like specialized image enhancements in astronomy, facilitate explanations of relationships between observed inputs and computed outputs. These models may be expressed with extended matrix-vector (EMV)…
A major challenge in the deployment of scientific software solutions is the adaptation of research prototypes to production-grade code. While high-level languages like MATLAB are useful for rapid prototyping, they lack the resource…
We present OGRe, a modern Mathematica package for tensor calculus, designed to be both powerful and user-friendly. The package can be used in a variety of contexts where tensor calculations are needed, in both mathematics and physics, but…
C++ leans towards a memory-inefficient storage of structs: The compiler inserts padding bits, while it is not able to exploit knowledge about the range of integers, enums or bitsets. Furthermore, the language provides no support for…
MIRGE is a computational approach for scientific computing based on NumPy-like array computation, but using lazy evaluation to recast computation as data-flow graphs, where nodes represent immutable, multi-dimensional arrays. Evaluation of…
Sparse tensor operations are increasingly important in diverse applications such as social networks, deep learning, diagnosis, crime, and review analysis. However, a major obstacle in sparse tensor research is the lack of large-scale sparse…
This paper presents tensorflow-riemopt, a Python library for geometric machine learning in TensorFlow. The library provides efficient implementations of neural network layers with manifold-constrained parameters, geometric operations on…
Sequential sampling models (SSMs) are a widely used framework describing decision-making as a stochastic, dynamic process of evidence accumulation. SSMs popularity across cognitive science has driven the development of various software…
We introduce a new abstraction for the representation and solution of multi-domain problems using finite element methods. This is an advance over previous work in that it achieves a single higher-level abstraction that represents…
We discuss a numerical package, named ORTHOCUB, for the computation of linear functionals of both integral and differential type on multivariate polynomial spaces. The weighted sums corresponding to such integral and differential cubatures…
Block-tridiagonal systems are prevalent in state estimation and optimal control, and solving these systems is often the computational bottleneck. Improving the underlying solvers therefore has a direct impact on the real-time performance of…
Solving and visualizing the potential roots of complex functions is essential in both theoretical and applied domains, yet often computationally intensive. We present a hardware-accelerated algorithm for complex function roots density graph…
In this paper, we introduce CDL, a software library designed for the analysis of permutations and linear orders subject to various structural restrictions. Prominent examples of these restrictions include pattern avoidance, a topic of…
Massively parallel molecular simulations require pseudorandom number streams that are provably non-overlapping and reproducible across thousands of compute units in parallel computing environments. In the widely used LAMMPS package, the…
We demonstrate a multiplication method based on numbers represented as set of polynomial radix 2 indices stored as an integer list. The 'polynomial integer index multiplication' method is a set of algorithms implemented in python code. We…
The exponentially convergent trapezoidal rule is applied to a suitable integral representation of the Faddeeva function to derive a simple formula for its evaluation. I describe its properties, strategies for maximising its efficiency, and…
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…