NumPy is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. The predecessor of NumPy, Numeric, was originally created by Jim Hugunin with contributions from several other developers. In 2005, Travis Oliphant created NumPy by incorporating features of the competing Numarray into Numeric, with extensive modifications. NumPy is open-source software and has many contributors. NumPy is a NumFOCUS fiscally sponsored project.
Jack Joseph Dongarra is an American computer scientist and mathematician. He is the American University Distinguished Professor of Computer Science in the Electrical Engineering and Computer Science Department at the University of Tennessee. He holds the position of a Distinguished Research Staff member in the Computer Science and Mathematics Division at Oak Ridge National Laboratory, Turing Fellowship in the School of Mathematics at the University of Manchester, and is an adjunct professor and teacher in the Computer Science Department at Rice University. He served as a faculty fellow at the Texas A&M University Institute for Advanced Study (2014–2018). Dongarra is the founding director of the Innovative Computing Laboratory at the University of Tennessee. He was the recipient of the Turing Award in 2021.
LAPACK is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition. It also includes routines to implement the associated matrix factorizations such as LU, QR, Cholesky and Schur decomposition. LAPACK was originally written in FORTRAN 77, but moved to Fortran 90 in version 3.2 (2008). The routines handle both real and complex matrices in both single and double precision. LAPACK relies on an underlying BLAS implementation to provide efficient and portable computational building blocks for its routines.
Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication. They are the de facto standard low-level routines for linear algebra libraries; the routines have bindings for both C and Fortran. Although the BLAS specification is general, BLAS implementations are often optimized for speed on a particular machine, so using them can bring substantial performance benefits. BLAS implementations will take advantage of special floating point hardware such as vector registers or SIMD instructions.
Mathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data.
AMD Core Math Library (ACML) is an end-of-life software development library released by AMD, replaced by many open source libraries, including AMD libm 4.0. This library provides mathematical routines optimized for AMD processors.
IPOPT, short for "Interior Point OPTimizer, pronounced I-P-Opt", is a software library for large scale nonlinear optimization of continuous systems. It is written in Fortran and C and is released under the EPL. IPOPT implements a primal-dual interior point method, and uses line searches based on Filter methods. IPOPT can be called from various modeling environments and C.
Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization which may be considered a quasi-Newton method. SQP methods are used on mathematical problems for which the objective function and the constraints are twice continuously differentiable.
Computational Engineering is an emerging discipline that deals with the development and application of computational models for engineering, known as Computational Engineering Models or CEM. Computational engineering uses computers to solve engineering design problems important to a variety of industries. At this time, various different approaches are summarized under the term Computational Engineering, including using computational geometry and virtual design for engineering tasks, often coupled with a simulation-driven approach In Computational Engineering, algorithms solve mathematical and logical models that describe engineering challenges, sometimes coupled with some aspect of AI, specifically Reinforcement Learning.
Trilinos is a collection of open-source software libraries, called packages, intended to be used as building blocks for the development of scientific applications. The word "Trilinos" is Greek and conveys the idea of "a string of pearls", suggesting a number of software packages linked together by a common infrastructure. Trilinos was developed at Sandia National Laboratories from a core group of existing algorithms and utilizes the functionality of software interfaces such as the BLAS, LAPACK, and MPI . In 2004, Trilinos received an R&D100 Award.
ARPACK, the ARnoldi PACKage, is a numerical software library written in FORTRAN 77 for solving large scale eigenvalue problems in the matrix-free fashion.
Intel oneAPI Math Kernel Library is a library of optimized math routines for science, engineering, and financial applications. Core math functions include BLAS, LAPACK, ScaLAPACK, sparse solvers, fast Fourier transforms, and vector math.
LINDO is a software package for linear programming, integer programming, nonlinear programming, stochastic programming and global optimization.
ILNumerics is a mathematical class library for Common Language Infrastructure (CLI) developers and a domain specific language (DSL) for the implementation of numerical algorithms on the .NET platform. While algebra systems with graphical user interfaces focus on prototyping of algorithms, implementation of such algorithms into distribution-ready applications is done using development environments and general purpose programming languages (GPL). ILNumerics is an extension to Visual Studio and aims at supporting the creation of technical applications based on .NET.
Artelys Knitro is a commercial software package for solving large scale nonlinear mathematical optimization problems.
