# The NAG Toolbox for MATLABĀ® - 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 23 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.

- Multi-start Optimization (Mark 23)
- Bound Optimization BY Quadratic Approximation (Mark 23)
- Quantile Linear Regression (Mark 23)
- Sampling with Unequal Weights (Mark 23)
- Copulas (Mark 23)
- Global Optimization
- Nearest Correlation Matrix
- Additions to Nearest Correlation Matrix (Mark 23)
- Quantiles
- Search routines

## Enhanced Chapters at Mark 23

- Roots of One or More Transcendental Equations (Chapter C05) has a new function for solving sparse nonlinear systems and a new function for determining values of the complex Lambert-W function. Additionally, some functions have been added to replace existing functions, making it easier to pass information through to user-supplied functions.
- Summation of Series (Chapter C06) has a function for summing a Chebyshev series at a vector of points.
- Wavelet Transforms (Chapter C09) has added one-dimensional continuous and two-dimensional discrete wavelet transform functions.
- Ordinary Differential Equations (Chapter D02) has a new suite of functions for solving boundary-value problems by an implementation of the Chebyshev pseudospectral method.
- Numerical Differentiation (Chapter D04) has added an alternative interface to its numerical differentiation function.
- Interpolation (Chapter E01) has added functions for interpolation of four- and five-dimensional data.
- Curve and Surface Fitting (Chapter E02) has an additional function for evaluating derivatives of a bicubic spline fit.
- Minimizing or Maximizing a Function (Chapter E04) has a new minimization by quadratic approximation function.
- Global Optimization of a Function (Chapter E05) has new functions implementing Particle Swarm Optimization and new Multistart Optimization functions. The existing function for multi-level coordinate search now allows equality bound constraints.
- Matrix Operations, Including Inversion (Chapter F01) has new functions for matrix exponentials and functions of symmetric/Hermitian matrices; there is also a suite of functions for converting storage formats of triangular and symmetric matrices.
- Chapter F03 (Determinants) has new functions to evaluate the determinant of matrices factorized by functions from Chapter F07.
- Linear Equations (Chapter F07) has LAPACK mixed-precision Cholesky solvers, pivoted Cholesky factorizations, and functions that perform operations on matrices in Rectangular Full Packed format.
- Least Squares and Eigenvalue Problems (Chapter F08 ) has LAPACK functions for computing the singular value decomposition by the fast Jacobi method.
- Further Linear Algebra Support Routines (Chapter F16) has new functions for evaluating norms of banded matrices.
- Simple Calculations on Statistical Data (Chapter G01) has new functions for quantiles of streamed data, bivariate Student's t-distribution and two probability density functions.
- Correlation and Regression Analysis (Chapter G02) has new functions for nearest correlation matrices, hierarchical mixed effects regression, and quantile regression.
- Random Number Generators (Chapter G05) has a new function for skip-ahead by powers of 2 and weighted sampling without replacement. In addition, the suite of base generators has been extended to include the L'Ecuyer MRG32k3a generator. Skip-ahead for the Mersenne Twister base generator is also now available.
- Univariate Estimation (Chapter G07) has new functions for Pareto distribution parameter estimation and outlier detection by the method of Peirce.
- Nonparametric Statistics (Chapter G08) has functions for the Anderson-Darling goodness-of-fit test.
- Survival Analysis (Chapter G12) has a new function for computing rank statistics when comparing survival curves.
- Approximations of Special Functions (Chapter S) has new beta and incomplete beta functions and the S30 sub-chapter has a new function for computing Greeks for Heston's model option pricing formula.

## Other enhancements at Mark 23

At Mark 23 a number of improvements have been 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:

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

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.