October 7, 2013. The Numerical Algorithms Group has announced the latest release of its NAG Toolbox for MATLAB to Mark 24. Over 130 new functions have been integrated into the Toolbox at Mark 24, bringing the total of math and statistics functions to 1,500. NAG Toolbox for MATLAB complements MathWorks' MATLAB by allowing the easy use of NAG and MATLAB functions concurrently giving increased algorithmic choice.
The new NAG Toolbox includes the following math and stats functionality:
- Multistart (Multiglobal) optimization. A new global optimization function for nonlinear sum-of-squares problems with nonlinear constraints uses a method that can be configured to return the best few minimum points found, and is designed to complement the general nonlinear global optimization multistart function introduced at Mark 23.
- Non-negative least squares (local optimization). NAG has added a bounded variable linear least squares solver into the local optimization chapter. Often the requirement is for the less general non-negative least squares problem that this function also addresses. It is designed for dense problems of moderate size, though no practical size limit is enforced by the function itself. Optionally the user may ask for a solution of minimal length to enforce uniqueness whenever the matrix is not of full rank.
- Nearest Correlation Matrix. Adding to the existing nearest correlation matrix functionality in the NAG Library is the “individually weighted elements” nearest correlation matrix function. This function allows the user to weight individual elements in their approximate correlation matrix. It can also force the computed correlation matrix to be positive definite, required by some applications to improve the condition of the matrix.
- Inhomogeneous Time Series. A suite of three new functions for processing inhomogeneous time series has been added to the time series analysis chapter. An inhomogeneous time series is one that has been sampled at irregular time intervals.
- Gaussian Mixture Model. A new statistical clustering function is a useful tool for summarizing groups in a multivariate dataset.
- Confluent Hypergeometric Function (1F1). Functions to evaluate the confluent hypergeometric function, commonly found in many applications including option pricing, have been included. These functions have been designed to provide high accuracy solutions over a large range of input parameters. Furthermore, they may be used to determine scaled solutions for when the value of the function is not explicitly representable.
- Brownian Bridge and Random Fields. Functions for simulating a Brownian bridge and from a family of random fields have been added to the random number generators chapter.
- Best Subsets. A general-purpose branch and bound algorithm for selecting the best subset of features from a larger population of features has been added to the operations research chapter.
- Real Sparse Eigenproblems. A new function that computes selected eigenvalues and eigenvectors of a real sparse general matrix has been included. It combines flexible algorithms from the sparse linear algebra chapters under a simple interface. The function has proven to be extremely efficient at solving user-supplied large sparse eigenproblems.
- Matrix Functions. Further additions have been made in the area of matrix functions resulting from NAG’s Knowledge Transfer Partnership with the University of Manchester. New functions compute the matrix logarithm, exponential, sine, cosine, sinh, or cosh of real and complex matrices (Schur-Parlett algorithm), function of real and complex matrices (using numerical differentiation) and function of real and complex matrices (using user-supplied derivatives).
- Two Stage Spline Approximation. Mark 24 features the first part of collaborative work with the University of Strathclyde. The new functionality sits in the curve and surface fitting chapter; it may be used to compute a spline approximation to a set of scattered data, which it does using a two stage approximation method.
Speaking of Mark 24, a senior developer at one of NAG’s partners said “I was particularly pleased to see the addition of the Log Matrix and Exponential Matrix functions and the fact that these solvers worked with general matrices as well as symmetric is particularly useful for me. The further additions to the suite of Nearest Correlation Matrix functions as well as new additions to the Eigenvalues Chapter are of course very valuable too. I am also interested to experiment with the Real Confluent Hypergeometric function as this may have several uses in future projects”
In addition, the new toolbox is HPC enabled; over a third of the functions are parallelized to take advantage of manycore/multicore systems. Highly detailed documentation is accessible from MATLAB’s help system, giving background information and function specification. In addition it guides users to a suitable function for their particular problem via decision trees. If users need help, NAG’s development team are on hand to offer assistance with problems. NAG offers a range of tailored training courses either at its offices or on site.
The NAG Toolbox for MATLAB is available for 32-bit and 64-bit Microsoft Windows and 64-bit Linux systems; it will also be made available for Mac OS X.