NAG Fortran Library - Latest Content

New at Mark 25 of the NAG Fortran Library

Now at its 25th 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.

Mini Articles

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 user manual.

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

New Functionality at Mark 25

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.

  • Routines for real symmetric discrete Fourier transforms with simplified interface. (NAG Library Chapter C06 Summation of Series)
  • Routines for inserting coefficients to make working with the DWT functions easier. Also routines for the maximal overlap discrete wavelet transform (MODWT) and its inverse in one dimension, for time series analysis. (NAG Library Chapter C09 Wavelet Transforms)
  • New routine for high dimensional quadrature using sparse grids. (NAG Library Chapter D01 Quadrature)
  • Replacement for the general nonlinear boundary value problem solver using collocation. (NAG Library Chapter D02 Ordinary Differential Equations)
  • Routine for the triangulation of a two-dimensional scattered grid, and routine for the barycentric interpolation on function values on a triangulated scattered grid. (NAG Library Chapter E01 Interpolation)
  • Routine for minimax polynomial fitting of a set of data points. (NAG Library Chapter E02 Curve and Surface Fitting)
  • New and improved algorithms are available for the matrix logarithm, the matrix square root, the matrix exponential and general matrix powers. Also routines for computing Fréchet derivatives. (NAG Library Chapter F01 Matrix Operations, Including Inversion)
  • Routines for the solution of the real and complex quadratic eigenvalue problem, and a driver routine for calculating selected eigenvalues/vectors of symmetric sparse matrices. (NAG Library Chapter F02 Eigenvalues and Eigenvectors)
  • Routines for recursive, explicitly blocked factorization and applying for general matrices and for triangular-pentagonal matrices, and routines for the complete CS decomposition of an orthogonal or unitary matrix. (NAG Library Chapter F08 Least Squares and Eigenvalue Problems (LAPACK))
  • Routine for the bandwidth reduction of a sparse symmetric matrix by reverse Cuthill-McKee reordering. (NAG Library Chapter F11 Large Scale Linear Systems)
  • Routine for scaled accumulated dot product (BLAS_DDOT). (NAG Library Chapter F16 Further Linear Algebra Support Routines)
  • Routine for computing probabilities for the Dickey-Fuller unit root test. (NAG Library Chapter G01 Simple Calculations on Statistical Data)
  • Additional nearest correlation matrix routine that allows the leading principal submatrix to be preserved. Also routines for performing Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) and forward stagewise regression. (NAG Library Chapter G02 Correlation and Regression Analysis)
  • Routines for generating training and validation datasets suitable for use in cross-validation. (NAG Library Chapter G05 Random Number Generators)
  • Kernel density estimation using a Gaussian kernel. (NAG Library Chapter G10 Smoothing in Statistics)
  • Routines for computing: the Dickey-Fuller unit root test statistic; applying the unscented Kalman filter to a nonlinear state-space model with additive noise; and change point analysis using the PELT algorithm or using binary segmentation. (NAG Library Chapter G13 Time Series Analysis)
  • Routine for solving mixed integer nonlinear programming problems; optional settings via two option routines. Also routine for approximating solutions to the classical travelling salesman problem via simulated annealing. (NAG Library Chapter H Operations Research)
  • Routines for evaluating the Gauss hypergeometric function for real arguments and for computing the European option price from Heston's stochastic volatility model with term structure. (NAG Library Chapter S Approximations of Special Functions)
  • A chapter of routines for controlling the OpenMP environment. (NAG Library Chapter X06 OpenMP Utilities)

The new functionality added at Mark 25 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