|
Comparison Of Linear Algebra Libraries
The following tables provide a comparison of linear algebra software libraries, either specialized or general purpose libraries with significant linear algebra coverage. Dense linear algebra General information Matrix types and operations Matrix types (special types like bidiagonal/tridiagonal are not listed): * ''Real'' – general (nonsymmetric) real * ''Complex'' – general (nonsymmetric) complex * ''SPD'' – symmetric positive definite (real) * ''HPD'' – Hermitian positive definite (complex) * ''SY'' – symmetric (real) * ''HE'' – Hermitian (complex) * ''BND'' – band Operations: * ''TF'' – triangular factorizations (LU, Cholesky) * ''OF'' – orthogonal factorizations (QR, QL, generalized factorizations) * ''EVP'' – eigenvalue problems * ''SVD'' – singular value decomposition In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Algebra
Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions. Linear algebra is also used in most sciences and fields of engineering, because it allows modeling many natural phenomena, and computing efficiently with such models. For nonlinear systems, which cannot be modeled with linear algebra, it is often used for dealing with first-order approximations, using the fact that the differential of a multivariate function at a point is the linear ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GNU Scientific Library
The GNU Scientific Library (or GSL) is a software library for numerical computations in applied mathematics and science. The GSL is written in C; wrappers are available for other programming languages. The GSL is part of the GNU Project and is distributed under the GNU General Public License. Project history The GSL project was initiated in 1996 by physicists Mark Galassi and James Theiler of Los Alamos National Laboratory.GSL homepage They aimed at writing a modern replacement for widely used but somewhat outdated Fortran libraries such as . They carried out the overall design and wrote early modules; with that ready they recruited other scientists ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NET Framework
The .NET Framework (pronounced as "''dot net"'') is a proprietary software framework developed by Microsoft that runs primarily on Microsoft Windows. It was the predominant implementation of the Common Language Infrastructure (CLI) until being superseded by the cross-platform .NET project. It includes a large class library called Framework Class Library (FCL) and provides language interoperability (each language can use code written in other languages) across several programming languages. Programs written for .NET Framework execute in a software environment (in contrast to a computer hardware, hardware environment) named the Common Language Runtime (CLR). The CLR is an process virtual machine, application virtual machine that provides services such as security, memory management, and exception handling. As such, computer code written using .NET Framework is called "managed code". FCL and CLR together constitute the .NET Framework. FCL provides the user interface, data access, d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CenterSpace Software
CenterSpace Software, LLC. is a commercial software development company with headquarters in Corvallis, Oregon, USA, that produces numerical and statistical class libraries for the .NET Framework. CenterSpace also provides advanced software project consulting services. CenterSpace Software produced the first commercial .NET numerical class library in March, 2003. CenterSpace products include: * NMath - A $1,595. NET numerical analysis package Developers at CenterSpace Software wrote the book The Elements of C# Style. CenterSpace won the Willamette Angel Conference in 2009. CenterSpace accepts bitcoin Bitcoin (abbreviation: BTC; sign: ₿) is a decentralized digital currency that can be transferred on the peer-to-peer bitcoin network. Bitcoin transactions are verified by network nodes through cryptography and recorded in a public distr ... for software and maintenance. References External links CenterSpace web site {{DEFAULTSORT:Centerspace Software Software co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NMath
NMath is a numerical package for the Microsoft .NET Framework. It is developed by CenterSpace Software. Version 1.0 was released in March, 2003 as NMath Core. The current version is called NMath 7.1, released in December, 2019. NMath is built on Math Kernel Library, MKL, a numerical library from Intel Corporation, Intel. Features NMath contains vector and matrix classes, complex numbers, factorizations, decompositions, linear programming, minimization, root-finding, structured and sparse matrix, least squares, polynomials, simulated annealing, curve fitting, numerical integration and differentiationing. See also * Comparison of numerical-analysis software * List of numerical-analysis software References External links CenterSpace Software {{DEFAULTSORT:Nmath .NET programming tools C Sharp libraries C Sharp software Component-based software engineering Econometrics software Mathematical optimization software Numerical software Programming tools for Windows Windows-only soft ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Algorithms Group
The NAG Numerical Library is a software product developed and sold by The Numerical Algorithms Group Ltd. It is a software library of numerical analysis routines, containing more than 1,900 mathematical and statistical algorithms. Areas covered by the library include linear algebra, optimization, quadrature, the solution of ordinary and partial differential equations, regression analysis, and time series analysis. Users of the NAG Library call its routines from within their applications in order to incorporate its mathematical or statistical functionality and to solve numerical problems - for example, finding the minimum or maximum of a function, fitting a curve or surface to data, or solving a differential equation. The Library is available in the many forms, but namely the NAG C Library, the NAG Fortran Library, and the NAG Library for .NET. Its contents are accessible from several computing environments, including standard languages such as C, C++, Fortran, Visual Basic, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NAG Numerical Library
The NAG Numerical Library is a software product developed and sold by The Numerical Algorithms Group Ltd. It is a software library of numerical analysis routines, containing more than 1,900 mathematical and statistical algorithms. Areas covered by the library include linear algebra, optimization, quadrature, the solution of ordinary and partial differential equations, regression analysis, and time series analysis. Users of the NAG Library call its routines from within their applications in order to incorporate its mathematical or statistical functionality and to solve numerical problems - for example, finding the minimum or maximum of a function, fitting a curve or surface to data, or solving a differential equation. The Library is available in the many forms, but namely the NAG C Library, the NAG Fortran Library, and the NAG Library for .NET. Its contents are accessible from several computing environments, including standard languages such as C, C++, Fortran, Visual Basic, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generic Programming
Generic programming is a style of computer programming in which algorithms are written in terms of types ''to-be-specified-later'' that are then ''instantiated'' when needed for specific types provided as parameters. This approach, pioneered by the ML programming language in 1973, permits writing common functions or types that differ only in the set of types on which they operate when used, thus reducing duplication. Such software entities are known as ''generics'' in Ada, C#, Delphi, Eiffel, F#, Java, Nim, Python, Go, Rust, Swift, TypeScript and Visual Basic .NET. They are known as '' parametric polymorphism'' in ML, Scala, Julia, and Haskell (the Haskell community also uses the term "generic" for a related but somewhat different concept); ''templates'' in C++ and D; and ''parameterized types'' in the influential 1994 book ''Design Patterns''. The term "generic programming" was originally coined by David Musser and Alexander Stepanov in a more specific se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Template Library
The Matrix Template Library (MTL) is a linear algebra library for C++ programs. The MTL uses template programming, which considerably reduces the code length. All matrices and vectors are available in all classical numerical formats: float, double, complex or complex. Furthermore, generic programming allows the usage of arbitrary types as long as they provide the necessary operations. For instance one can use arbitrary integer formats (e.g. unsigned short), types for interval arithmetic (e.g. boost::interval) from the Boost C++ Libraries, quaternions (e.g. boost::quaternion), types of higher precision (e.g. GNU Multi-Precision Library) and appropriate user-defined types. The MTL supports several implementations of dense matrices and sparse matrices. MTL2 has been developed by Jeremy Siek and Andrew Lumsdaine. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Math
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Math Kernel Library
Intel oneAPI Math Kernel Library (Intel oneMKL; formerly Intel Math Kernel Library or Intel MKL) 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. The library supports Intel processors and is available for Windows, Linux and macOS operating systems. ''Intel oneAPI Math Kernel Library'' is not to be confused with ''oneAPI Math Kernel Library'' (oneMKL) Interfaces, a piece of open-source glue code that allows Intel MKL routines to be used from Data Parallel C++. History and licensing Intel launched the Math Kernel Library on May 9, 2003, and called it blas.lib. The project's development teams are located in Russia and the United States. The library was available in a standalone form, free of charge under the terms of Intel Simplified Software License which allow redistribution. Since April 2020, MKL has become part of oneAPI ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Librsb
librsb is an open-source parallel computing, parallel library for Sparse Matrix, sparse matrix computations using the ''Recursive Sparse Blocks'' (RSB) matrix format. librsb provides Cache (computing), cache efficient Thread (computing), multi-threaded Sparse BLAS operations via OpenMP, and is best suited to large Sparse Matrix, sparse matrices. Features librsb provides: *Conversion from/to COO, CSR, CSC sparse matrix formats. *Support for the four BLAS types. *Support for general, symmetric, hermitian matrices. *Parallel threaded, eventually strided: **Sparse matrix-vector multiplication. **Sparse matrix-dense matrix multiplication. **Sparse matrix-vector triangular solve. **Sparse matrix-dense matrix triangular solve. *Sparse matrix-sparse matrix multiplication. *Elemental sparse matrix operations (scaling, add, etc). *Row-wise or column-wise scaling. *Rows / colu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
