The NAG Numerical Library is a software product developed and sold by The Numerical Algorithms Group Ltd. It is a

software library In computer science, a library is a collection of non-volatile resources used by computer programs, often for software development. These may include configuration data, documentation, help data, message templates, pre-written code and sub ...

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods ...

routines, containing more than 1,900 mathematical and statistical algorithms. Areas covered by the library include

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 ...

optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

, quadrature, the solution of ordinary and

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

regression analysis In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one ...

, and

time series analysis In mathematics 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 m ...

. 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++ C++ (pronounced "C plus plus") is a high-level general-purpose programming language created by Danish computer scientist Bjarne Stroustrup as an extension of the C programming language, or "C with Classes". The language has expanded significan ...

, Fortran,

Visual Basic Visual Basic is a name for a family of programming languages from Microsoft. It may refer to: * Visual Basic .NET (now simply referred to as "Visual Basic"), the current version of Visual Basic launched in 2002 which runs on .NET * Visual Basic ( ...

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Python Python may refer to: Snakes * Pythonidae, a family of nonvenomous snakes found in Africa, Asia, and Australia ** ''Python'' (genus), a genus of Pythonidae found in Africa and Asia * Python (mythology), a mythical serpent Computing * Python (pro ...

and C#, as well as packages such as

MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementa ...

, R,

LabVIEW Laboratory Virtual Instrument Engineering Workbench (LabVIEW) is a system-design platform and development environment for a visual programming language from National Instruments. The graphical language is named "G"; not to be confused with G-c ...

Excel ExCeL London (an abbreviation for Exhibition Centre London) is an exhibition centre, international convention centre and former hospital in the Custom House area of Newham, East London. It is situated on a site on the northern quay of the ...

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and Ch. Supported operating systems include the 32 bit and 64 bit versions of

Windows Windows is a group of several proprietary graphical operating system families developed and marketed by Microsoft. Each family caters to a certain sector of the computing industry. For example, Windows NT for consumers, Windows Server for ser ...

Linux Linux ( or ) is a family of open-source Unix-like operating systems based on the Linux kernel, an operating system kernel first released on September 17, 1991, by Linus Torvalds. Linux is typically packaged as a Linux distribution, w ...

and

macOS macOS (; previously OS X and originally Mac OS X) is a Unix operating system developed and marketed by Apple Inc. since 2001. It is the primary operating system for Apple's Mac computers. Within the market of desktop and lapt ...

, as well as Solaris,

AIX Aix or AIX may refer to: Computing * AIX, a line of IBM computer operating systems *An Alternate Index, for a Virtual Storage Access Method Key Sequenced Data Set * Athens Internet Exchange, a European Internet exchange point Places Belgi ...

and HP-UX.

History

The original version of the NAG Library was written in Algol 60 and Fortran. It contained 98 user-callable routines, and was released for the ICL 1906A and 1906S machines on October 1, 1971. Three further Marks of the library appeared in the following five years; during this time the Algol version was ported to Algol 68, with the following platforms being supported:

CDC 7600 The CDC 7600 was the Seymour Cray-designed successor to the CDC 6600, extending Control Data's dominance of the supercomputer field into the 1970s. The 7600 ran at 36.4 MHz (27.5 ns clock cycle) and had a 65 Kword primary memory (with a 6 ...

/ CYBER (

CDC The Centers for Disease Control and Prevention (CDC) is the national public health agency of the United States. It is a United States federal agency, under the Department of Health and Human Services, and is headquartered in Atlanta, Georgi ...

ALGOL 68 ALGOL 68 (short for ''Algorithmic Language 1968'') is an imperative programming language that was conceived as a successor to the ALGOL 60 programming language, designed with the goal of a much wider scope of application and more rigorously d ...

IBM 360 The IBM System/360 (S/360) is a family of mainframe computer systems that was announced by IBM on April 7, 1964, and delivered between 1965 and 1978. It was the first family of computers designed to cover both commercial and scientific applica ...

/370/AMDAHL ( FLACC

), ICL 1900 (

ALGOL 68R ALGOL (; short for "Algorithmic Language") is a family of imperative computer programming languages originally developed in 1958. ALGOL heavily influenced many other languages and was the standard method for algorithm description used by the ...

), ICL 1906A/S (

), ICL 2900 (

ALGOL 68RS ALGOL 68RS is the second ALGOL 68 compiler written by I. F. Currie and J. D. Morrison, at the Royal Signals and Radar Establishment (RSRE). Unlike the earlier ALGOL 68-R, it was designed to be portable, and implemented the language of the Revise ...

) and

Telefunken Telefunken was a German radio and television apparatus company, founded in Berlin in 1903, as a joint venture of Siemens & Halske and the ''Allgemeine Elektrizitäts-Gesellschaft'' (AEG) ('General electricity company'). The name "Telefunken" ap ...

TR440 (

ALGOL 68C ALGOL 68C is an imperative computer programming language, a dialect of ALGOL 68, that was developed by Stephen R. Bourne and Michael Guy to program the Cambridge Algebra System (CAMAL). The initial compiler was written in the Princeton Syntax ...

). The first partially vectorized implementation of the NAG Fortran Library for the Cray-1 was released in 1983, while the first release of the NAG Parallel Library (which is specially designed for

distributed memory In computer science, distributed memory refers to a multiprocessor computer system in which each processor has its own private memory. Computational tasks can only operate on local data, and if remote data are required, the computational task mu ...

parallel computer architectures) was in the early 1990s. Mark 1 of the NAG C Library was released in 1990. In 1992, the Library incorporated

LAPACK LAPACK ("Linear Algebra Package") 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 als ...

routines for the first time; NAG had been a collaborator in the LAPACK project since 1987. The first release of the NAG Library for SMP & multicore,NAG Library for SMP & multicore
/ref> which takes advantage of the

shared memory In computer science, shared memory is memory that may be simultaneously accessed by multiple programs with an intent to provide communication among them or avoid redundant copies. Shared memory is an efficient means of passing data between progr ...

parallelism of Symmetric Multi-Processors (SMP) and multicore processors, appeared in 1997 for multiprocessor machines built using the

Dec Alpha Alpha (original name Alpha AXP) is a 64-bit reduced instruction set computer (RISC) instruction set architecture (ISA) developed by Digital Equipment Corporation (DEC). Alpha was designed to replace 32-bit VAX complex instruction set compute ...

and

SPARC SPARC (Scalable Processor Architecture) is a reduced instruction set computer (RISC) instruction set architecture originally developed by Sun Microsystems. Its design was strongly influenced by the experimental Berkeley RISC system develope ...

architectures. The NAG Library for .NET, which is a CLI DLL assembly containing methods and objects that give Common Language Infrastructure (CLI) users access to NAG algorithms, was first released in 2010.

Current version

Mark 27 of the NAG Library houses over 1,900 mathematical and statistical algorithms organised into chapters.

References

{{reflist

External links

NAG Numerical Libraries
History of computing in the United Kingdom Numerical libraries Science and technology in Oxfordshire

History

Current version

See also

References

External links