# NAG Toolbox for MATLABĀ® - New at Mark 22

Three new chapters have been introduced into the NAG Toolbox for MATLAB at Mark 22, Wavelets Transforms, Global Optimization and Further Linear Algebra Routines, and a further new sub-chapter, Option Pricing Formulae. Extensions have been included in other areas namely statistics, optimization, linear algebra, ordinary differential equations, regression, random numbers, searching, and special functions.

We've selected key highlights from Mark 22 and shown in more detail how a particular routine or set of routines can be used and how they link into the existing capabilities of the NAG Toolbox for MATLAB.

Enhanced Chapters at Mark 22

• Ridge Regression (NAG Toolbox for MATLAB Chapter G02 - Correlation and Regression Analysis)
• Optimization (NAG Toolbox for MATLAB Chapter E04 - Minimizing and Maximising a Function)
• Partial-least squares (NAG Toolbox for MATLAB Chapter G02 - Correlation and Regression Analysis)
• Nearest Correlation Matrix (NAG Toolbox for MATLAB Chapter G02 - Correlation and Regression Analysis)
• Index-2 differential algebraic equations (NAG Toolbox for MATLAB Chapter D02 - Ordinary Differential Equations)
• New base generators for pseudo-random sequences, including the Mersenne Twister, a new Wichmann-Hill generator and the ACORN generator (NAG Toolbox for MATLAB Chapter G05 - Random Number Generators)
• Sobol quasi-random generator now allows for up to 50,000 dimensions (NAG Toolbox for MATLAB Chapter G05 - Random Number Generators)
• Scrambled quasi-random sequences (NAG Toolbox for MATLAB Chapter G05 - Random Number Generators)
• Multiple independent pseudo-random sequences via both skip-ahead and leap-frog algorithms (NAG Toolbox for MATLAB Chapter G05 - Random Number Generators)
• Matrix exponential (NAG Toolbox for MATLAB Chapter F01 - Matrix Operations, Including Inversion)
• ProMax rotations (NAG Toolbox for MATLAB Chapter G03 - Multivariate Methods)
• Searching arrays of real-valued, integer or character data (NAG Toolbox for MATLAB Chapter M01 - Sorting and Searching)
• Lambert's W function (NAG Toolbox for MATLAB Chapter C05 - Roots of One or More Transcendental Equations)
• Fast quantile routine (NAG Toolbox for MATLAB Chapter G01 - Simple Calculations on Statistical Data)
• Exponential smoothing of a univariate times series (NAG Toolbox for MATLAB Chapter G13 - Time Series Analysis)
• Obtaining leading terms in the singular value decomposition of a real general matrix (NAG Toolbox for MATLAB Chapter F02 - Eigenvalues and Eigenvectors)

## The new functionality added at Mark 22 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

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