NAG Fortran Library - Latest Content

New at Mark 26 of the NAG Fortran Library

Now at its 26th major release, the NAG Fortran Library contains hundreds of routines which are powerful, reliable, flexible and ready for use from a wide range of operating systems, languages, environments and packages including Excel, Java, MATLAB®, .NET/C# and many more. We have selected key highlights from the NAG Library and show in more detail how a particular routine or set of routines can be used, and explain how they complement the existing capabilities of the NAG Library. A full comprehensive overview of what is new can be found in the NAG Fortran Library Manual.

To learn more about a specific area/routine click on the relevant link below.

New Functionality at Mark 26

At Mark 26 of the NAG Library new functionality has been introduced in addition to improvements in existing areas. The Library now contains 1855 user-callable routines, all of which are documented, of which 37 are new at this mark.

Chapter D01 (Quadrature) has two new routines to calculate weights and abscissae for use in Gaussian quadrature and a new routine to solve a specific Gaussian quadrature problem.

Chapter D02 (Ordinary Differential Equations) has reverse communication versions of the Runge–Kutta step and interpolation routines. The interpolation routine has extended the functionality to include the high-order method.

Chapter E04 (Minimizing or Maximizing a Function) has a new suite of routines, NAG Modelling Optimization Suite for quadratic programming (QP), linear semidefinite programming (SDP), semidefinite programming with bilinear matrix inequalities (BMI-SDP), and general nonlinear programming (NLP). This suite can, for example, solve the nearest correlation matrix problem with individually weighted elements or minimize the maximum eigenvalue of a matrix. The suite introduces a novel interface, allowing the gradual build up of a problem definition and avoiding the long parameter lists of earlier interfaces. The SDP solver is based upon a generalized augmented Lagrangian method and as such complements existing solvers in the optimization chapters. The QP/NLP solver of this suite is based upon IPOPT, an interior-point method optimization package, suitable for large-scale problems, that complements the active-set sequential quadratic programming (SQP) solvers already present.

Chapter F08 (Least Squares and Eigenvalue Problems (LAPACK)) has additional blocked (BLAS-3) variants of routines for computing the generalized SVD, or generalized eigenvalues of real or complex matrix pairs.

Chapter G02 (Correlation and Regression Analysis) has a new nearest correlation routine that, using a shrinking method, allows the fixing of arbitrary elements in the input matrix.

Chapter X06 (OpenMP Utilities has a new routine to identify, at runtime, whether you are using a threaded Library or not.

At this release we have made changes to the introductory documentation supporting the Library. The document previously called the 'Essential Introduction' has been revised so that relevant information and advice on how to use the Library and its documentation can be found quickly. The document has been renamed to How to Use the NAG Library and its Documentation.

We have also provided clarification of the term 'Direct and Reverse Communication Routines', see Section 3.3.3 in How to Use the NAG Library and its Documentation, and taken the decision to document a number of error conditions, i.e., Dynamic Memory Allocation, License Management and Unexpected Errors (see Sections 3.7, 3.8 and 3.9 in How to Use the NAG Library and its Documentation).

You will also notice that on every HTML page there is now a Keyword Search box.

The new functionality added at Mark 26 further enhances the comprehensive collection of numerical and statistical techniques offered by the library:

Numerical Facilities

  • Optimization, including linear, quadratic, integer and nonlinear
    programming and least squares problems
  • Ordinary and partial differential equations, and mesh generation
  • Numerical integration and integral equations
  • Roots of nonlinear equations (including polynomials)
  • Solution of dense, banded and sparse linear equations and eigenvalue
  • Solution of linear and nonlinear least squares problems
  • Special functions
  • Curve and surface fitting and interpolation

Statistical Facilities

  • Random number generation
  • Simple calculations on statistical data
  • Correlation and regression analysis
  • Multivariate methods
  • Analysis of variance and contingency table analysis
  • Time series analysis
  • Nonparametric statistics