Mathematical Software
Differential equations arise in mathematics, physics,medicine, pharmacology, communications, image processing and animation, etc. An Ordinary Differential Equation (ODE) is a differential equation if it involves derivatives with respect to…
This paper presents an implementation of the Schwerdtfeger-Fillmore-Springer-Cnops construction (SFSCc) along with illustrations of its usage. SFSCc linearises the linear-fraction action of the Moebius group in R^n. This has clear…
Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…
In this paper we introduce DiffSharp, an automatic differentiation (AD) library designed with machine learning in mind. AD is a family of techniques that evaluate derivatives at machine precision with only a small constant factor of…
The generic matrix-matrix multiplication (GEMM) is arguably the most popular computational kernel of the 20th century. Yet, surprisingly, no common methodology for evaluating GEMM performance has been established over the many decades of…
Quantifying simulation uncertainties is a critical component of rigorous predictive simulation. A key component of this is forward propagation of uncertainties in simulation input data to output quantities of interest. Typical approaches…
BOAT is a free cross-platform software for statistical data analysis and numerical computing. Thanks to its multiple-precision floating point engine, it allows arbitrary-precision calculations, whose digits of precision are only limited by…
Dense linear algebra libraries, such as BLAS and LAPACK, provide a relevant collection of numerical tools for many scientific and engineering applications. While there exist high performance implementations of the BLAS (and LAPACK)…
Matrix operations such as matrix inversion, eigenvalue decomposition, singular value decomposition are ubiquitous in real-world applications. Unfortunately, many of these matrix operations so time and memory expensive that they are…
Mathematica is a powerful application package for doing mathematics and is used almost in all branches of science. It has widespread applications ranging from quantum computation, statistical analysis, number theory, zoology, astronomy, and…
Starting from the basic level of mathematica here we illustrate how to use a mathematica notebook and write a program in the notebook. Next, we investigate elaborately the way of linking of external programs with mathematica, so-called the…
We are interested in the asymptotic behavior of orthogonal polynomials of the generalized Jacobi type as their degree $n$ goes to $\infty$. These are defined on the interval $[-1,1]$ with weight function…
Block operations during simulation in Scicos and VSS environments can naturally be described as Nsp functions. But the direct use of Nsp functions for simulation leads to poor performance since the Nsp language is interpreted, not compiled.…
We present Rust-Bio, the first general purpose bioinformatics library for the innovative Rust programming language. Rust-Bio leverages the unique combination of speed, memory safety and high-level syntax offered by Rust to provide a fast…
As computational challenges in optimization and statistical inference grow ever harder, algorithms that utilize derivatives are becoming increasingly more important. The implementation of the derivatives that make these algorithms so…
Sparse matrix-vector multiplication (SpMV) is a central building block for scientific software and graph applications. Recently, heterogeneous processors composed of different types of cores attracted much attention because of their…
General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method (AMG), breadth first search and shortest path problem. Compared to other sparse BLAS routines,…
This document describes an infra-structure provided by the R package performanceEstimation that allows to estimate the predictive performance of different approaches (workflows) to predictive tasks. The infra-structure is generic in the…
The speed of many one-line transformation methods for the production of, for example, Levy alpha-stable random numbers, which generalize Gaussian ones, and Mittag-Leffler random numbers, which generalize exponential ones, is very high and…
This article describes our experience developing and maintaining automated tests for scientific applications. The main idea evolves around building on already existing tests by cloning and grafting. The idea is demonstrated on a minimal…