NAG C Library News, Mark 25 (PDF version)
NAG Library Manual

# NAG LibraryNAG C Library News, Mark 25

## 1  Introduction

At Mark 25 of the NAG C Library new functionality has been introduced in addition to improvements in existing areas. The Library now contains 1551 user-callable functions, all of which are documented, of which 58 are new at this mark.
Chapter d01 (Quadrature) has a function for high dimensional quadrature using sparse grids.
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 f01 (Matrix Operations, Including Inversion) has functions for converting between full, packed and rectangular full packed (RFP) matrix storage formats.
Chapter f02 (Eigenvalues and Eigenvectors) has a driver function for calculating selected eigenvalues/vectors of symmetric sparse matrices.
Chapter f07 (Linear Equations (LAPACK)) has functions for pivoted Cholesky factorization of positive semidefinite matrices and functions for the factorization, solution and inverse of positive definite matrices stored in rectangular full packed format.
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 (NAG Interface to BLAS) has linear algebra support functions for symmetric, Hermitian and triangular matrices stored in rectangular full packed format.
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 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 x06 (OpenMP Utilities) is a new chapter of functions that provide utilities for controlling the OpenMP environment for your program.

## 2  New Functions

The 58 new user-callable functions included in the NAG C Library at Mark 25 are as follows.
 FunctionName Purpose d01esc Multi-dimensional quadrature using sparse grids e01eac Triangulation of two-dimensional scattered grid, method of Renka and Cline e01ebc Barycentric interpolation on function values provided on a two-dimensional scattered grid f01vac Copies a real triangular matrix from full format to packed format f01vbc Copies a complex triangular matrix from full format to packed format f01vcc Copies a real triangular matrix from packed format to full format f01vdc Copies a complex triangular matrix from packed format to full format f01vec Copies a real triangular matrix from full format to Rectangular Full Packed format f01vfc Copies a complex triangular matrix from full format to Rectangular Full Packed format f01vgc Copies a real triangular matrix from Rectangular Full Packed format to full format f01vhc Copies a complex triangular matrix from Rectangular Full Packed format to full format f01vjc Copies a real triangular matrix from packed format to Rectangular Full Packed format f01vkc Copies a complex triangular matrix from packed format to Rectangular Full Packed format f01vlc Copies a real triangular matrix from Rectangular Full Packed format to packed format f01vmc Copies a complex triangular matrix from Rectangular Full Packed format to packed format f02fkc Selected eigenvalues and eigenvectors of a real symmetric sparse matrix f07kdc Cholesky factorization, with complete pivoting, of a real, symmetric, positive semidefinite matrix f07krc Cholesky factorization of complex Hermitian positive semidefinite matrix f07wdc Cholesky factorization of real symmetric positive definite matrix, Rectangular Full Packed format f07wec Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by nag_dpftrf (f07wdc), Rectangular Full Packed format f07wjc Inverse of real symmetric positive definite matrix, matrix already factorized by nag_dpftrf (f07wdc), Rectangular Full Packed format f07wkc Inverse of real triangular matrix, Rectangular Full Packed format f07wrc Cholesky factorization of complex Hermitian positive definite matrix, Rectangular Full Packed format f07wsc Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by nag_zpftrf (f07wrc), Rectangular Full Packed format f07wwc Inverse of complex Hermitian positive definite matrix, matrix already factorized by nag_zpftrf (f07wrc), Rectangular Full Packed format f07wxc Inverse of complex triangular matrix, Rectangular Full Packed format f11yec Reverse Cuthill–McKee reordering of a sparse symmetric matrix in CCS format f16rkc 1-norm, $\infty$-norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format f16ukc 1-norm, $\infty$-norm, Frobenius norm, largest absolute element, complex Hermitian matrix, Rectangular Full Packed format f16ylc Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix, Rectangular Full Packed format f16yqc Rank-$k$ update of a real symmetric matrix, Rectangular Full Packed format f16zlc Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix, Rectangular Full Packed format f16zqc Rank-$k$ update of a complex Hermitian matrix, Rectangular Full Packed format g01ewc Computes probabilities for the Dickey–Fuller unit root test g02anc Computes a correlation matrix from an approximate matrix with fixed submatrix g02mac Least angle regression (LARS), least absolute shrinkage and selection operator (LASSO) and forward stagewise regression g02mbc Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) and forward stagewise regression using the cross-products matrix g02mcc Additional parameter calculate following Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) or forward stagewise regression g05pvc Permutes a matrix, vector, vector triplet into a form suitable for $K$-fold cross validation g05pwc Permutes a matrix, vector, vector triplet into a form suitable for random sub-sampling validation g13awc Computes (augmented) Dickey–Fuller unit root test statistic g13ejc Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise (reverse communication) g13ekc Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise g13nac Change point detection, using the PELT algorithm g13nbc Change points detection using the PELT algorithm, user supplied cost function g13ndc Change point detection, using binary segmentation g13nec Change point detection, using binary segmentation, user supplied cost function h02dac Mixed integer nonlinear programming h02zkc Option setting routine for nag_mip_sqp (h02dac) h02zlc Option getting routine for nag_mip_sqp (h02dac) h03bbc Travelling Salesman Problem, simulated annealing x06aac Sets the number of threads for OpenMP parallel regions x06abc The number of OpenMP threads in the current team x06acc An upper bound on the number of threads in the next parallel region x06adc The OpenMP thread number of the calling thread x06afc Tests for an active OpenMP parallel region x06agc Enables or disables nested OpenMP parallelism x06ahc Tests the status of nested OpenMP parallelism

## 3  Internal Changes Affecting Users

The following function has been significantly updated or enhanced at this mark.
nag_running_median_smoother (g10cac)
nag_running_median_smoother (g10cac) is a smoothing function with two possible smoothing methods. The function was previously using the incorrect method (i.e., if you asked for method A you would get method B, and vice versa).

## 4  Withdrawn Functions

The following functions have been withdrawn from the NAG C Library at Mark 25. Warning of their withdrawal was included in the NAG C Library Manual at Mark 24, together with advice on which functions to use instead. See the document ‘Advice on Replacement Calls for Withdrawn/Superseded Functions’ for more detailed guidance.

## 5  Functions Scheduled for Withdrawal

The functions listed below are scheduled for withdrawal from the NAG C Library, because improved functions have now been included in the Library. You are advised to stop using functions which are scheduled for withdrawal and to use recommended replacement functions instead. See the document ‘Advice on Replacement Calls for Withdrawn/Superseded Functions’ for more detailed guidance, including advice on how to change a call to the old function into a call to its recommended replacement.
The following functions will be withdrawn at Mark 26.
The following functions have been superseded, but will not be withdrawn from the Library until Mark 27 at the earliest.
 SupersededFunction Replacement Function(s) d01tac nag_quad_1d_gauss_vec (d01uac)

NAG C Library News, Mark 25 (PDF version)
NAG Library Manual