NAG C Library News, Mark 25

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.

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 |

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).

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.

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) |