Mark 23 NAG Fortran Library News (PDF version)
NAG Library Manual

NAG Library

Mark 23 NAG Fortran Library News

+ Contents

1  Introduction

At Mark 23 of the NAG Library new functionality has been introduced in addition to improvements in existing areas. The Library now contains 1704 user-callable routines, all of which are documented, of which 116 are new at this mark.
No new chapters or sub-chapters have been introduced; however there have been extensions in functionality included in the areas of statistics, nonlinear equations, wavelets, ordinary differential equations, interpolation, surface fitting, optimization, matrix operations, linear algebra, and special functions.
Chapter C05 (Roots of One or More Transcendental Equations) has a new routine for solving sparse nonlinear systems and a new routine for determining values of the complex Lambert–W function. Additionally, some routines have beed added to replace existing routines, making it easier to pass information through to user-supplied functions.
Chapter C06 (Summation of Series) has a routine for summing a Chebyshev series at a vector of points.
Chapter C09 (Wavelet Transforms) has added one-dimensional continuous and two-dimensional discrete wavelet transform routines.
Chapter D02 (Ordinary Differential Equations) has a new suite of routines for solving boundary-value problems by an implementation of the Chebyshev pseudospectral method.
Chapter D04 (Numerical Differentiation) has added an alternative interface to its numerical differentiation routine.
Chapter E01 (Interpolation) has added routines for interpolation of four- and five-dimensional data.
Chapter E02 (Curve and Surface Fitting) has an additional routine for evaluating derivatives of a bicubic spline fit.
Chapter E04 (Minimizing or Maximizing a Function) has a new minimization by quadratic approximation routine.
Chapter E05 (Global Optimization of a Function) has new routines implementing Particle Swarm Optimization. The existing routine for multi-level coordinate search now allows equality bound constraints.
Chapter F01 (Matrix Operations, Including Inversion) has new routines for matrix exponentials and functions of symmetric/Hermitian matrices; there is also a suite of routines for converting storage formats of triangular and symmetric matrices.
Chapter F03 (Determinants) has been overhauled to use factorizations by routines from Chapter F07.
Chapter F06 (Linear Algebra Support Routines) has new support routines for matrices stored in Rectangular Full Packed format.
Chapter F07 (Linear Equations (LAPACK)) has LAPACK 3.2 mixed-precision Cholesky solvers, pivoted Cholesky factorizations, and routines that perform operations on matrices in Rectangular Full Packed format.
Chapter F08 (Least Squares and Eigenvalue Problems (LAPACK)) has LAPACK 3.2 routines for computing the singular value decomposition by the fast Jacobi method.
Chapter F16 (Further Linear Algebra Support Routines) has new routines for evaluating norms of banded matrices.
Chapter G01 (Simple Calculations on Statistical Data) has new routines for quantiles of streamed data, bivariate Student's t-distribution and two probability density functions.
Chapter G02 (Correlation and Regression Analysis) has new routines for nearest correlation matrices, hierarchical mixed effects regression, and quantile regression.
Chapter G05 (Random Number Generators) has new generators of bivariate and multivariate copulas, skip-ahead for the Mersenne Twister base generator, skip-ahead by powers of 2 and weighted sampling without replacement. In addition, the suite of base generators has been extended with the inclusion of the L'Ecuyer MRG32K3a generator.
Chapter G07 (Univariate Estimation) has new routines for Pareto distribution parameter estimation and outlier detection by the method of Peirce.
Chapter G08 (Nonparametric Statistics) has routines for the Anderson–Darling goodness-of-fit test.
Chapter G12 (Survival Analysis) has a new routine for computing rank statistics when comparing survival curves.
Chapter S (Approximations of Special Functions) has a new routine for the scaled log gamma function and the S30 sub-chapter has a new routine for computing Greeks for Heston's model option pricing formula.

2  New Routines

The 116 new user-callable routines included in the NAG Library at Mark 23 are as follows.
Routine
Name

Purpose
C05AUF Zero of continuous function, Brent algorithm, from a given starting value, binary search for interval
C05AWF Zero of continuous function, continuation method, from a given starting value
C05AYF Zero of continuous function in a given interval, Brent algorithm
C05BBF Values of Lambert's W function, W(z)
C05QBF Solution of a system of nonlinear equations using function values only (easy-to-use)
C05QCF Solution of a system of nonlinear equations using function values only (comprehensive)
C05QDF Solution of a system of nonlinear equations using function values only (reverse communication)
C05QSF Solution of a sparse system of nonlinear equations using function values only (easy-to-use)
C05RBF Solution of a system of nonlinear equations using first derivatives (easy-to-use)
C05RCF Solution of a system of nonlinear equations using first derivatives (comprehensive)
C05RDF Solution of a system of nonlinear equations using first derivatives (reverse communication)
C05ZDF Check user's routine for calculating first derivatives of a set of nonlinear functions of several variables
C06DCF Sum of a Chebyshev series at a set of points
C09ABF Two-dimensional wavelet filter initialization
C09BAF One-dimensional real continuous wavelet transform
C09EAF Two-dimensional discrete wavelet transform
C09EBF Two-dimensional inverse discrete wavelet transform
C09ECF Two-dimensional multi-level discrete wavelet transform
C09EDF Two-dimensional inverse multi-level discrete wavelet transform
D02UAF Coefficients of Chebyshev interpolating polynomial from function values on Chebyshev grid
D02UBF Function or low-order-derivative values on Chebyshev grid from coefficients of Chebyshev interpolating polynomial
D02UCF Chebyshev Gauss–Lobatto grid generation
D02UDF Differentiate a function by the FFT using function values on Chebyshev grid
D02UEF Solve linear constant coefficient boundary value problem on Chebyshev grid, Integral formulation
D02UWF Interpolate a function from Chebyshev grid to uniform grid using barycentric Lagrange interpolation
D02UYF Clenshaw–Curtis quadrature weights for integration using computed Chebyshev coefficients
D02UZF Chebyshev polynomial evaluation, Tk(x)
D04BAF Numerical differentiation, user-supplied function values, derivatives up to order 14, derivatives with respect to one real variable
D04BBF Generates sample points for function evaluations by D04BAF
E01TKF Interpolating functions, modified Shepard's method, four variables
E01TLF Interpolated values, evaluate interpolant computed by E01TKF, function and first derivatives, four variables
E01TMF Interpolating functions, modified Shepard's method, five variables
E01TNF Interpolated values, evaluate interpolant computed by E01TMF, function and first derivatives, five variables
E02DHF Evaluation of spline surface at mesh of points with derivatives
E04JCF Minimum by quadratic approximation, function of several variables, simple bounds, using function values only
E05SAF Global optimization using particle swarm algorithm (PSO), bound constraints only
E05SBF Global optimization using particle swarm algorithm (PSO), comprehensive
E05ZKF Option setting routine for E05SAF and E05SBF
E05ZLF Option getting routine for E05SAF and E05SBF
F01EDF Real symmetric matrix exponential
F01EFF Function of a real symmetric matrix
F01FCF Complex matrix exponential
F01FDF Complex Hermitian matrix exponential
F01FFF Function of a complex Hermitian matrix
F01VAF Copies a real triangular matrix from full format to packed format scheme
F01VBF Copies a complex triangular matrix from full format to packed format scheme
F01VCF Copies a real triangular matrix from packed format to full format scheme
F01VDF Copies a complex triangular matrix from packed format to full format scheme
F01VEF Copies a real triangular matrix from full format to Rectangular Full Packed format scheme
F01VFF Copies a complex triangular matrix from full format to Rectangular Full Packed format scheme
F01VGF Copies a real triangular matrix from Rectangular Full Packed format to full format scheme
F01VHF Copies a complex triangular matrix from Rectangular Full Packed format to full format scheme
F01VJF Copies a real triangular matrix from packed format to Rectangular Full Packed format scheme
F01VKF Copies a complex triangular matrix from packed format to Rectangular Full Packed format scheme
F01VLF Copies a real triangular matrix from Rectangular Full Packed format to packed format scheme
F01VMF Copies a complex triangular matrix from Rectangular Full Packed format to packed format scheme
F03BAF Determinant of real matrix, matrix already factorized by F07ADF (DGETRF)
F03BFF Determinant of real symmetric positive definite matrix
F03BHF Determinant of real symmetric positive definite banded matrix
F03BNF Determinant of complex matrix
F06ABF Constructs a modified Givens transformation matrix
F06EQF Applies a modified givens transformation to two row vectors
F06WAF 1-norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format
F06WBF Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix, Rectangular Full Packed format
F06WCF Rank-k update of a real symmetric matrix, Rectangular Full Packed format
F06WNF 1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, Rectangular Full Packed format
F06WPF Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix, Rectangular Full Packed format
F06WQF Rank-k update of a complex Hermitian matrix, Rectangular Full Packed format
F07FCF Uses the Cholesky factorization to compute the solution for a real symmetric positive definite system of linear equations
F07FQF Uses the Cholesky factorization to compute the solution for a complex Hermitian positive definite system of linear equations
F07KDF Cholesky factorization of real symmetric positive semidefinite matrix
F07KRF Cholesky factorization of complex Hermitian positive semidefinite matrix
F07WDF Cholesky factorization of real symmetric positive definite matrix, Rectangular Full Packed format
F07WEF Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by F07WDF (DPFTRF), Rectangular Full Packed format
F07WJF Inverse of real symmetric positive definite matrix, matrix already factorized by F07WDF (DPFTRF), Rectangular Full Packed format
F07WKF Inverse of real triangular matrix, Rectangular Full Packed format, expert driver
F07WRF Cholesky factorization of complex Hermitian positive definite matrix, Rectangular Full Packed format
F07WSF Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by F07WRF (ZPFTRF), Rectangular Full Packed format
F07WWF Inverse of complex Hermitian positive definite matrix, matrix already factorized by F07WRF (ZPFTRF), Rectangular Full Packed format
F07WXF Inverse of complex triangular matrix, Rectangular Full Packed format
F08KHF Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
F08KJF Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
F16RBF 1-norm, -norm, Frobenius norm, largest absolute element, real band matrix
F16UBF 1-norm, -norm, Frobenius norm, largest absolute element, complex band matrix
G01ANF Calculates approximate quantiles from a data stream of known size
G01APF Calculates approximate quantiles from a data stream of unknown size
G01HCF Computes probabilities for the bivariate Student's t-distribution
G01KAF Calculates the value for the probability density function of the Normal distribution at a chosen point
G01KFF Calculates the value for the probability density function of the gamma distribution at a chosen point
G02ABF Computes the nearest correlation matrix to a real square matrix, augmented G02AAF to incorporate weights and bounds
G02AEF Computes the nearest correlation matrix with k-factor structure to a real square matrix
G02JCF Hierarchical mixed effects regression, initialization routine for G02JDF and G02JEF
G02JDF Hierarchical mixed effects regression using Restricted Maximum Likelihood (REML)
G02JEF Hierarchical mixed effects regression using Maximum Likelihood (ML)
G02QFF Quantile linear regression, simple interface, independent, identically distributed (IID) errors
G02QGF Quantile linear regression, comprehensive interface
G02ZKF Option setting routine for G02QGF
G02ZLF Option getting routine for G02QGF
G05KKF Primes a pseudorandom number generator for generating multiple streams using skip-ahead, skipping ahead a power of 2
G05NEF Pseudorandom sample, without replacement, unequal weights
G05REF Generates a matrix of pseudorandom numbers from a bivariate Clayton/Cook–Johnson copula
G05RFF Generates a matrix of pseudorandom numbers from a bivariate Frank copula
G05RGF Generates a matrix of pseudorandom numbers from a bivariate Plackett copula
G05RHF Generates a matrix of pseudorandom numbers from a multivariate Clayton/Cook–Johnson copula
G05RJF Generates a matrix of pseudorandom numbers from a multivariate Frank copula
G05RKF Generates a matrix of pseudorandom numbers from a Gumbel–Hougaard copula
G07BFF Estimates parameter values of the generalized Pareto distribution
G07GAF Outlier detection using method of Peirce, raw data or single variance supplied
G07GBF Outlier detection using method of Peirce, two variances supplied
G08CHF Calculates the Anderson–Darling goodness-of-fit test statistic
G08CJF Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of uniformly distributed data
G08CKF Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of a fully-unspecified Normal distribution
G08CLF Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of an unspecified exponential distribution
G12ABF Computes rank statistics for comparing survival curves
S14AHF Scaled log gamma function
S30NBF Heston's model option pricing formula with Greeks

3  Withdrawn Routines

The following routines have been withdrawn from the NAG Library at Mark 23. Warning of their withdrawal was included in the NAG Library Manual at Mark 22, together with advice on which routines to use instead. See the document ‘Advice on Replacement Calls for Withdrawn/Superseded Routines’ for more detailed guidance.
Withdrawn
Routine

Replacement Routine(s)
F02BJF F08WAF (DGGEV)
F02EAF F08PAF (DGEES)
F02EBF F08NAF (DGEEV)
F02FAF F08FAF (DSYEV)
F02FCF F08FBF (DSYEVX)
F02FDF F08SAF (DSYGV)
F02FHF F08UAF (DSBGV)
F02GAF F08PNF (ZGEES)
F02GBF F08NNF (ZGEEV)
F02GJF F08WNF (ZGGEV)
F02HAF F08FNF (ZHEEV)
F02HCF F08FPF (ZHEEVX)
F02HDF F08SNF (ZHEGV)
F02WEF F08KBF (DGESVD)
F02XEF F08KPF (ZGESVD)
F04AAF F07AAF (DGESV)
F04ACF F07HAF (DPBSV)
F04ADF F07ANF (ZGESV)
F04ARF F07AAF (DGESV)
F04EAF F07CAF (DGTSV)
F04FAF F07JAF (DPTSV), or F07JDF (DPTTRF) and F07JEF (DPTTRS)
F04JAF F08KAF (DGELSS)
F04JDF F08KAF (DGELSS)
F04JLF F08ZBF (DGGGLM)
F04JMF F08ZAF (DGGLSE)
F04KLF F08ZPF (ZGGGLM)
F04KMF F08ZNF (ZGGLSE)
G05YAF G05YLF and G05YMF
G05YBF G05YLF and either G05YJF or G05YKF

4  Routines Scheduled for Withdrawal

The routines listed below are scheduled for withdrawal from the NAG Library, because improved routines have now been included in the Library. You are advised to stop using routines which are scheduled for withdrawal and to use recommended replacement routines instead. See the document ‘Advice on Replacement Calls for Withdrawn/Superseded Routines’ for more detailed guidance, including advice on how to change a call to the old routine into a call to its recommended replacement.
The following routines will be withdrawn at Mark 24.
Routines Scheduled
for Withdrawal

Replacement Routine(s)
E04CCF E04CBF
E04ZCF No longer required
G05HKF G05PDF
G05HLF G05PEF
G05HMF G05PFF
G05HNF G05PGF
G05KAF G05SAF
G05KBF G05KFF
G05KCF G05KGF
G05KEF G05TBF
G05LAF G05SKF
G05LBF G05SNF
G05LCF G05SDF
G05LDF G05SHF
G05LEF G05SBF
G05LFF G05SJF
G05LGF G05SQF
G05LHF G05SPF
G05LJF G05SFF
G05LKF G05SMF
G05LLF G05SJF
G05LMF G05SSF
G05LNF G05SLF
G05LPF G05SRF
G05LQF G05SGF
G05LXF G05RYF
G05LYF G05RZF
G05LZF G05RZF
G05MAF G05TLF
G05MBF G05TCF
G05MCF G05THF
G05MDF G05TFF
G05MEF G05TKF
G05MJF G05TAF
G05MKF G05TJF
G05MLF G05TEF
G05MRF G05TGF
G05MZF G05TDF
G05NAF G05NCF
G05NBF G05NDF
G05PAF G05PHF
G05PCF G05PJF
G05QAF G05PXF
G05QBF G05PYF
G05QDF G05PZF
G05RAF G05RDF
G05RBF G05RCF
G05YCF G05YLF
G05YDF G05YMF
G05YEF G05YLF
G05YFF G05YMF
G05YGF G05YLF
G05YHF G05YMF
G13DCF G13DDF
P01ABF No longer required
X02DAF No longer required
X02DJF No longer required
The following routines have been superseded, but will not be withdrawn from the Library until Mark 25 at the earliest.
Superseded
Routine

Replacement Routine(s)
C05ADF C05AYF
C05AGF C05AUF
C05AJF C05AWF
C05NBF C05QBF
C05NCF C05QCF
C05NDF C05QDF
C05PBF C05RBF
C05PCF C05RCF
C05PDF C05RDF
C05ZAF C05ZDF
C06DBF C06DCF
F03AAF F07ADF (DGETRF) and F03BAF
F03ABF F07FDF (DPOTRF) and F03BFF
F03ACF F07HDF (DPBTRF) and F03BHF
F03ADF F07ARF (ZGETRF) and F03BNF
F03AEF F07FDF (DPOTRF) and F03BFF
F03AFF F07ADF (DGETRF) and F03BAF
F04AFF No replacement.
F04AGF No replacement.
F04AHF No replacement.
F04AJF No replacement.

Mark 23 NAG Fortran Library News (PDF version)
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2011