NAG updates Toolbox for MATLAB
The Numerical Algorithms Group (NAG) has added 149 new numerical functions to its NAG Toolbox for MATLAB, the software used by quantitative investors to develop algorithms and perform data analysis.
The Toolbox is intended to boost the capability of the standard MATLAB setup.
Among the new functions are:
• Matrix Operations – As a result of a project with Professor Nick Higham at the University of Manchester the following matrix functions are now included in the NAG Toolbox – matrix exponential and functions of symmetric/Hermitian matrices.
• Nearest Correlation Matrix – The Nearest Correlation Matrix functionality has been extended to include functions for k-factor structure and weights and bounds on the matrix elements.
• Skip ahead for the Mersenne Twister random number generator – The Mersenne Twister is a fast generator with extremely long period. Skipping ahead within the generator is not widely available elsewhere and consequently is a useful enhancement for many NAG Toolbox users.
• L’Ecuyer random number generator – Combines two multiple recursive generators to provide a sequence with good statistical properties in high dimensions and a long period.
• Vectorised Simple Functions – Unlike their scalar counterparts, which take a single set of parameters and perform a single function evaluation, these functions take vectors of parameters and perform multiple function evaluations in a single callthus speeding up the calculations.
• Interpolation – New functions have been added for the interpolation of four- and five-dimensional data.
• Two-dimensional Wavelets – Functions for two dimensional discrete wavelet transforms have been introduced; these important tools often used for image processing.
• New Optimization Techniques:
1. Multi-start Optimization – Two new functions further expand NAG’s global optimization coverage.
2. Minimization by Quadratic Approximation (BOBYQA) – of particular use with noisy functions.
3. Stochastic Global Optimization using Particle Swarm Optimization – Particle Swarm Optimization (PSO) is one of the most well-established of the stochastic approaches applied to global optimization. This NAG implementation is probably the most robust available since it can also utilize a local optimization algorithm.
• Quantile Regression – One advantage of quantile regression versus the more usual least squares regression (also in the NAG Toolbox) is that it is more robust if outliers are present in the response measurement.
• Sparse Nonlinear functions – Can now be solved using a new function in our ‘Roots of One or More Transcendental Equations’ Chapter.
The Toolbox has also been adjusted to enable these new functions to work on multiple core processors (computer chips with more than one core central processing unit) as well as systems that are multi-processor driven.