The NAG Fortran Library - Included in Mark 24

Now at its 24th major release, the NAG Fortran Library contains over 1,700 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've 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's new can be found in the user manual.

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

New functionality at Mark 24

There have also been extensions in functionality included in the areas of quadrature, statistics, wavelet and Fast Fourier Transforms, ordinary differential equations, interpolation, surface fitting, optimization, matrix operations, linear algebra, operations research, and special functions. A new Chapter X07 (IEEE Arithmetic) has also been introduced, providing routines relating to IEEE arithmetic.

  • Fast Fourier Transforms (FFTs) for two-dimensional and three dimensional real data. (NAG Library Chapter C06 - Summation of Series)
  • Three-dimensional discrete wavelet transforms. (NAG Library Chapter C09 - Wavelet Transforms)
  • Comprehensive one-dimensional adaptive quadrature routine and a variant for badly behaved integrands. (NAG Library Chapter D01 - Quadrature)
  • Threadsafe versions of the suite implementing Runge-Kutta methods. (NAG Library Chapter D02 - Ordinary Differential Equations)
  • The modified Shepard's method for interpolating in dimensions greater than 5. (NAG Library Chapter E01 Interpolation)
  • A two-stage approximation method for two-dimensional scattered data. (NAG Library Chapter E02 - Curve and Surface Fitting)
  • Non-negative least squares and improved MPS data reader. (NAG Library Chapter E04 - Minimizing or Maximizing a Function)
  • Multi-start versions of general nonlinear programming and least squares routines. (NAG Library Chapter E05 - Global Optimization of a Function)
  • Greatly extended range of matrix function routines including the calculation of condition numbers and the action on another matrix. (NAG Library Chapter F01 - Matrix Operations, Including Inversion)
  • Driver routine for calculating selected eigenvalues/vectors of general sparse matrices. (NAG Library Chapter F02 - Eigenvalues and Eigenvectors)
  • Norm estimators for rectangular matrices. (NAG Library Chapter F04 - Simultaneous Linear Equations)
  • Block diagonal (possibly overlapping) preconditioner and associated solver for real and complex nonsymmetric sparse matrices. (NAG Library Chapter F11 - Large Scale Linear Systems)
  • A driver for selected eigenvalues/vectors of general banded complex eigenproblems. (NAG Library Chapter F12 - Large Scale Eigenproblems)
  • Routines for combining summary statistics from blocks of data, probabilities from a multivariate Student's t-distribution, and a large set of vectorized versions of routines for probabilities and density functions. (NAG Library Chapter G01 - Simple Calculations on Statistical Data)
  • Routines for weighted nearest correlation matrix and combining two sums of squares. (NAG Library Chapter G02 - Correlation and Regression Analysis)
  • Gaussian mixture model routine. (NAG Library Chapter G03 - Multivariate Methods)
  • Brownian bridge and random field routines. (NAG Library Chapter G05 - Random Number Generators)
  • Moving averages for inhomogeneous time series. (NAG Library Chapter G13 - Time Series Analysis)
  • Routines for computing best subsets. (NAG Library Chapter H - Operations Research)
  • Confluent hypergeometric, log beta and incomplete beta; and a large set of vectorized versions of existing special functions. (NAG Library Chapter S - Approximations of Special Functions)
  • Testing and setting Infs and NaNs. (NAG Library Chapter X07 - IEEE Arithmetic)

The new functionality added at Mark 24 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 problems
  • 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