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NAG

NAG Fortran Library

Numerics and Statistics ...

Development

NAG^. has a worldwide reputation for the excellence of its Fortran Library which contains over 1000 user-callable routines.

NAG has released a library in the new standard, Fortran 90, and a library of parallel algorithms in Fortran for distributed-memory machines. This pioneering work ensures that NAG will continue to stay at the forefront of numerical software technology.

The Fortran Library is organized into chapters, each chapter devoted to a branch of numerical or statistical computation. A full list of the routines is available but some of the areas covered include:

Minimization

constrained or unconstrained
with or without derivatives
nonlinear least-squares
linear and quadratic programming (LP and QP)
mixed integer linear programming (ILP)
nonlinear programming

Ordinary Differential Equations

initial value problems
boundary value problems
differential alegbraic problems
Sturm-Liouville problems

Partial Differential Equations

elliptic equations
Helmholtz equations
systems of time-dependent PDEs in one space dimension using the method of lines, first and second order

Transforms

FFTs for single or multiple series of real, complex or Hermitian data
sine and cosine transforms
convolutions
inverse Laplace transforms

Quadrature

fully adaptive with specialised weight functions over finite and infinite intervals
multidimensional quadrature
Gaussian quadrature

Linear Algebra

linear systems, (real, complex, dense, banded, tridiagonal, Toeplitz, sparse)
linear least-squares (dense or sparse)
singular value decomposition
eigenvalue problems, real or complex, symmetric or nonsymmetric
generalized eigenvalue problems
iteratrive solvers and preconditioners for large sparse linear systems
high performance software derived from LAPACK
Basic Linear Algebra Subprograms (BLAS)

Nonlinear Equations

root of single equation
solution of general system
roots of polynomials

Integral Equations

Fredholm nonsingular, 2nd kind
Volterra convolution
weakly singular convolution Volterra-Abel

Curve and Surface Fitting

interpolation/approximation
one or two dimensions (regular or scattered data)
polynomials or splines
least-squares, l₁ or l fits

Special Functions

Bessel, Hankel and Airy functions, real and complex arguments
Kelvin functions
elliptic, exponential, trigonometric and Fresnel integrals
Gamma and related functions

Basic Statistics

data summaries and displays
distribution functions

Random Number Generation

wide range of distributions
time series
matrices
random sampling

Correlation and Regression

product-moment correlation
non-parametric correlation
simple linear regression
multiple linear regression (general linear model)
generalized linear models
robust techniques

Multivariate Methods

principal component analysis
canonical correlation analysis
factor analysis
cluster analysis
discriminant analysis
mutlidimensional scaling

Analysis of Variance

factorial designs
general block designs

Univariate Estimation

confidence intervals
maximum likelihood estimation
robust estimation

Nonparametric Statistics

many standard tests
goodness of fit tests
tests of randomness

Smoothing

smoothing splines
density estimation

Contingency Table Analysis

² statistics
multiway tables
latent variable model

Survival Analysis

Kaplin Meier estimates
Cox's regression model

Time Series Analysis

ARIMA model fitting and forecasting
multivariate model fitting and forecasting
spectral analysis
Kalman filters

Sorting

integer, real or character data

Utilities

machine and mathematical constants
printing procedures
date and time
CPU time

The Benefits

Accuracy and Reliability: The NAG Fortran Library has been developed in both single and double precision. On many systems both precisions are provided. On other systems the precision chosen is that which is considered most suitable in general for numerical computation (usually double).; The correctness of each Library routine is evaluated and verified by specially written test programs which are performed on each of the machine ranges for which the Library is available. Only when an implementation satisfies NAG's stringent accuracy standards is it released.
Cost Effective: The NAG Fortran Library, with over 1100 user-callable routines, gives easy access to complex and highly sophisticated algorithms. At less than the cost of employing a programmer for a month, it is the most cost effective way of solving your numerical and statistical problems.
Saves Development Time: Developing robust, reliable and accurate code to solve the problems that the NAG Fortran Library can tackle takes many years of effort. Solving your problems with the NAG Fortran Library saves development time and money. Why wait longer for your results?
Protects your Investment: You invest much time and money in your application programs. Once they are installed, you rely on their results. NAG routines are maintained on a regular basis, fully documented and supported and designed for portability. Whatever the future holds, you can rely on NAG for your continuing numerical and statistical software needs.

Software

For each target platform the software supplied includes the compiled library, example program material and documentation for all available routines. Each example program, together with a data file (if needed) and a results file, illustrates the use of a particular routine. It can also be used as a template for your own application.

To help your staff install NAG software on your hardware, a detailed Installers' Note is provided. A separate Users' Note gives implementation-specific details that may be required by the end-user.

NAG software is distributed on a range of media, to suit your requirements. Full details of these media options can be supplied on request.

To assist users who wish to call the Fortran Library from C programs, a complete set of C Header Files is available.

Documentation

When you purchase the NAG Fortran Library you are automatically sent one copy of the NAG Fortran Library Manual or , if you are a PC user, a form of the On-line Browser.

The Manual is the principal printed form of documentation for the Library. It has the same chapter structure as the Library: each chapter of routines in the Library has a corresponding chapter (of the same name) in the Manual. General introductory documents and indexes can be found at the beginning of the Manual.

Each Chapter begins with an Introduction, giving a general background to the types of problem that can be solved, and guidance on selecting the most suitable routines. This is followed by a list of Contents and then a routine document for each documented routine in the chapter.

The On-line Browser supplied instead of the printed manual for PC users, is based on the On-line Information Supplement, described later in this article. DOS users receive a simple mechanism for viewing the On-line Information Supplement files; for users of the 16 and 32 bit DLLs this capability is augmented by the facility to cut and paste appropriate Visual Basic Declare statements and C Header File information into user programs.

The library documentation is also available in hypertext-based form as one of our TextWare products. This is described more fully later in this article.

Support Service

Full product support is included in the annual licence fee and provides you with technical support (via NAG's Response Centre). You will also receive a news-sheet, called Network, and Maintenance Bulletins. New releases of the library are automatically sent to you as and when they become available. Clients who prefer to purchase a perpetual use licence can purchase full NAG support for 18% of the annual licence fee.

Technical Support: Technical Support is available via the NAG Response Centre, where details of your call will be taken and a log number (a unique reference to identify your query within NAG) will be given. Your details will be passed on to the relevant experts within NAG who can then fully investigate your problem or query before making a call back to you. You can be assured that the answers you receive will have been thoroughly researched ... usually by the very professionals involved in the development of the product. The NAG Response Centre can also be used just as a general enquiry service.
Network: Network is a periodical news-sheet which contains articles on new products and enhancements to existing products. Any events where you can meet NAG personnel and learn more about our products and services are listed in Network.; Your copy of Network also tells you about any special offers which may be available on NAG Products.
New Releases and Maintenance Bulletins: New releases are issued on a regular basis, primarily because of enhanced functionality, but also to include any necessary error corrections. Documentation updates are supplied with each new software release.; Maintenance Bulletins are issued periodically, if appropriate, between releases of the library. They notify users of any NAG Fortran Library routines with confirmed errors and give details of the necessary corrections.
The NAG WWW Service: The NAG website provides information about all of NAG's current products and services. In addition, it gives access to technical reports, summaries and code, as well as links to other sites of interest.; For the Fortran Library, a full contents list is available, with search facilities based either on keywords or the GAMS classification system. On-line documentation and example programs are also available for all the routines.; To fully explore these and other benefits view our whole website.
NAG Users Association: When you purchase your NAG Fortran Library you will, no doubt, want to become an active member of the NAG Users Association. As well as providing a valuable forum for the exchange of ideas, NAGUA hold regular meetings and seminars to help you get the most out of your NAG products.; Your membership of NAGUA ensures that NAG remains in touch with the changing requirements of its many users.

Specialist Libraries

Specialist numerical libraries in Fortran are available separately for users with more intensive requirements: the Data Approximation Subroutine Library (DASL), developed at the National Physical Laboratory, for data-fitting problems; and the Harwell Sparse Matrix Library (HSML), extracted from the renowned Harwell Subroutine Library, for problems involving sparse matrices (real and complex linear systems, eigenvalue problems, nonlinear equations, approximation of derivatives and optimisation).

Availability

The NAG Fortran Library is available on a very wide range of computer systems. For each distinct system, an implementation of the Library is specially prepared by NAG. This implementation is then distributed to clients as a fully tested and compiled library.

The library is also provided as a set of DLLs (Dynamic Link Libraries) for use on Windows systems. In this form it can be called from Visual Basic, Excel or Visual C++. Visual Basic Declare Statements and C Header Files are included.

For Fortran 90 programmers, the Library is provided alongside our new Fortran 90 Library, fl90, as part of our FL90plus product. Fortran 90 interface blocks are included for all routines, and routines from both libraries can be called from the same program. The new fl90 library offers a more attractive interface, taking advantage of new features of Fortran 90, but does not yet match the full functionality of the Fortran 77 Library.

For full details of the implementations available, please contact NAG.

Products to Supplement the Library

TextWare

Nag has recently launched a new range of electronic hypertext-based documentation called TextWare.

For the Fortran Library, TextWare is currently available for use on a range of Unix platforms. The product consists of an electronic book form of the full manual (apart from the indexes) together with a browser, and uses the DynaText electronic publishing system developed by Electronic Book Technologies Inc.

Its features include:

Typeset Mathematics

Pop-up windows

Table of Contents Navigation

Hypertext Navigation

Searching

Context searches

Boolean searches

Partial searches

Proximity searches

Copying and Exporting of text

Graphics

Alternative Views.

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Programs for Programmers

NAG