News (NAG Toolbox Mark 25)

At Mark 25 of the NAG Toolbox new functionality has been introduced in addition to improvements in existing areas. The Toolbox now contains 1625 user-callable functions, all of which are documented, of which 76 are new at this mark.

Chapter C06 (summation of series) has replacement functions for real symmetric discrete Fourier transforms with simplified interface.

Chapter C09 (wavelet transforms) has new functions for inserting coefficients into and extracting coefficients from the compact form used in the multilevel two-dimensional functions and all three-dimensional functions, which make working with the DWT functions easier as demonstrated in the examples. There are also functions for the maximal overlap discrete wavelet transform (MODWT) and its inverse in one dimension, which are useful in time series analysis.

Chapter D01 (quadrature) has a function for high dimensional quadrature using sparse grids.

Chapter D02 (ordinary differential equations) has a threadsafe replacement for the the general nonlinear boundary value problem solver using collocation.

Chapter E01 (interpolation) has a function for the triangulation of a two-dimensional scattered grid, and a function for the barycentric interpolation on function values on a triangulated scattered grid.

Chapter E02 (curve and surface fitting) has a replacement function for minimax polynomial fitting of a set of data points.

Chapter F01 (matrix operations, including inversion) has greatly extended its range of matrix functions. New and improved algorithms are available for the matrix logarithm, the matrix square root, the matrix exponential and general matrix powers. We also now have functions for computing Fréchet derivatives.

Chapter F02 (eigenvalues and eigenvectors) has functions for the solution of the real and complex quadratic eigenvalue problem, and a driver function for calculating selected eigenvalues/vectors of symmetric sparse matrices.

Chapter F08 (least squares and eigenvalue problems (lapack)) has functions for recursive, explicitly blocked $QR$ factorization and applying $Q$ for general matrices and for triangular-pentagonal matrices, and has functions for the complete CS decomposition of an orthogonal or unitary matrix.

Chapter F11 (large scale linear systems) has a function for the bandwidth reduction of a sparse symmetric matrix by reverse Cuthill–McKee reordering.

Chapter F16 (further linear algebra support routines) has a function for scaled accumulated dot product (BLAS_DDOT).

Chapter G01 (simple calculations on statistical data) has a function for computing probabilities for the Dickey–Fuller unit root test.

Chapter G02 (correlation and regression analysis) has functions for performing Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) and forward stagewise regression. There is also an additional nearest correlation matrix function that allows the leading principal submatrix to be preserved.

Chapter G05 (random number generators) has functions for generating training and validation datasets suitable for use in cross-validation.

Chapter G10 (smoothing in statistics) has a thread safe replacement for kernel density estimation using a Gaussian kernel.

Chapter G13 (time series analysis) has functions for computing: the Dickey–Fuller unit root test statistic; applying the unscented Kalman filter to a nonlinear state-space model with additive noise; and change point analysis using the PELT algorithm or using binary segmentation.

Chapter H (operations research) has a function for solving mixed integer nonlinear programming problems; optional settings for this are supplied and interrogated via two new option functions. Additionally, there is a function for approximating solutions to the classical travelling salesman problem.

Chapter S (approximations of special functions) has functions for evaluating the Gauss hypergeometric function for real arguments and for computing the European option price from Heston's stochastic volatility model with term structure.

Chapter X06 (Multi-threading Utilities) is a new chapter of functions that provide utilities for controlling the OpenMP environment for your program.