Mathematical Software
Stencil codes are performance-critical in many compute-intensive applications, but suffer from significant address calculation and irregular memory access overheads. This work presents SARIS, a general and highly flexible methodology for…
Floating-point arithmetic performance determines the overall performance of important applications, from graphics to AI. Meeting the IEEE-754 specification for floating-point requires that final results of addition, subtraction,…
An algebraic modeling system (AMS) is a type of mathematical software for optimization problems, which allows users to define symbolic mathematical models in a specific language, instantiate them with given source of data, and solve them…
We describe the ARKODE library of one-step time integration methods for ordinary differential equation (ODE) initial-value problems (IVPs). In addition to providing standard explicit and diagonally implicit Runge--Kutta methods, ARKODE also…
The fractal dimension of a surface allows its degree of roughness to be characterized quantitatively. However, limited effort is attempted to calculate the fractal dimension of surfaces computed from precisely known atomic coordinates from…
BlackJAX is a library implementing sampling and variational inference algorithms commonly used in Bayesian computation. It is designed for ease of use, speed, and modularity by taking a functional approach to the algorithms' implementation.…
Pseudo-Random Number Generators (PRNGs) have become ubiquitous in machine learning technologies because they are interesting for numerous methods. The field of machine learning holds the potential for substantial advancements across various…
We present Groebner.jl, a Julia package for computing Groebner bases with the F4 algorithm. Groebner.jl is an efficient, portable, and open-source software. Groebner.jl works over integers modulo a prime and over the rationals, supports…
We overview the ensmallen numerical optimization library, which provides a flexible C++ framework for mathematical optimization of user-supplied objective functions. Many types of objective functions are supported, including general,…
This report provides a comprehensive analysis of the performance of MindOpt Adapter for CPLEX 12.9 in benchmark testing. CPLEX, recognized as a robust Mixed Integer Programming (MIP) solver, has faced some scrutiny regarding its performance…
Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division.…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
LongMemory.jl is a package for time series long memory modelling in Julia. The package provides functions to generate long memory, estimate model parameters, and forecast. Generating methods include fractional differencing, stochastic error…
PyPartMC is a Pythonic interface to PartMC, a stochastic, particle-resolved aerosol model implemented in Fortran. Both PyPartMC and PartMC are free, libre, and open-source. PyPartMC reduces the number of steps and mitigates the effort…
This living paper reviews the present High Performance Computing (HPC) capabilities of the Tinker-HP molecular modeling package. We focus here on the reference, double precision, massively parallel molecular dynamics engine present in…
Hypergraphs, or generalization of graphs such that edges can contain more than two nodes, have become increasingly prominent in understanding complex network analysis. Unlike graphs, hypergraphs have relatively few supporting platforms, and…
In a topology optimization setting, design-dependent fluidic pressure loads pose several challenges as their direction, magnitude, and location alter with topology evolution. This paper offers a compact 100-line MATLAB code, TOPress, for…
Recently, reinforcement algorithms discovered new algorithms that really jump-started a wave of excitements and a flourishing of publications. However, there is little on implementations, applications, and, especially, no absolute…
This paper describes PyOED, a highly extensible scientific package that enables developing and testing model-constrained optimal experimental design (OED) for inverse problems. Specifically, PyOED aims to be a comprehensive Python toolkit…
We present a new approach for estimating parameters in rational ODE models from given (measured) time series data. In typical existing approaches, an initial guess for the parameter values is made from a given search interval. Then, in a…