The NAG Toolbox for MATLAB® - New functions

The NAG Toolbox for MATLAB® contains over 1,500 algorithms - providing a wide range of powerful, reliable and flexible functions in a single Toolbox.

We've selected key highlights from Mark 24 and shown in more detail how a particular function or set of functions can be used and how they link into the existing capabilities of the NAG Toolbox for MATLAB.

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

Enhanced Chapters 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 Toolbox:

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

Enhancements at previous Mark

At Mark 23 a number of improvements were included to the way that the Toolbox can be used:

  • Function Handles - Users can provide function handles instead of an M-File to evaluate a function. For more details see Using Function Handles instead of M-Files. (The M-File approach is also still supported.)
  • Exceptions - For people who use try ... catch ... end blocks to handle exceptions. Mark 23 only uses warnings in cases where the output values may be of use. In all other cases an exception is thrown. For more details see nag_issue_warnings.
  • Integer Types - Some Integer Utility functions have been introduced to help write programs that are portable between 32 and 64-bit platforms.
  • New format for examples - All examples are now provided as single functions.
  • Long names - Mark 23 offers descriptive names for all NAG Toolbox functions in addition to 5 character function names. Users can use either scheme.

The new functionality added at Mark 23 further enhances the comprehensive collection of numerical and statistical techniques offered by the Toolbox.

For more information about the NAG Toolbox for MATLAB, select any of the links in the top right box, or contact us to discuss your needs.