Mark 22 NAG Library for SMP & Multicore News (PDF version)
NAG Library Manual

NAG Library

Mark 22 NAG Library for SMP & Multicore News

+− Contents

+− 1  Introduction
    2  New Routines
    3  Tuned Routines
    4  Enhanced Routines
    5  Withdrawn Routines
    6  Routines Scheduled for Withdrawal
    7  Withdrawn Tuned Routines

1  Introduction

1.1  New Functionality

At Mark 22 of the NAG Library for SMP & Multicore new functionality has been introduced in addition to improvements in existing areas. The Library now contains 1617 user-callable routines of which 129 are new at this mark.
Three new chapters have been introduced on wavelet transforms, global optimization, further linear algebra support routines; a new sub-chapter has also been introduced on option pricing; and extensions have been included in the areas of statistics, optimization, linear algebra, ordinary differential equations, regression, random numbers, searching, and special functions.
The new Chapter C09 (Wavelet Transforms) has routines for performing one-dimensional discrete, single-level and multi-level, wavelet transforms and their inverses.
The new Chapter E05 (Global Optimization of a Function) has a routine for performing global optimization on a problem with simple bounds using a multi-level coordinate search, which is complemented by a number of support routines for initializing the data and setting optional parameters.
The new Chapter F16 (Further Linear Algebra Support Routines) contains various useful level-1 routines from the BLAS Technical Forum (BLAST).
Chapter C05 (Roots of One or More Transcendental Equations) has a new routine to evaluate real values of Lambert's W function.
Chapter D02 (Ordinary Differential Equations) has extended its functionality to include routines that use the integration method of DASSL; thus, implicit differential algebraic equations of index 2 can now be solved.
Chapter E04 (Minimizing or Maximizing a Function) has added a replacement routine for applying the simplex algorithm which should perform significantly faster than the original.
Chapter F01 (Matrix Operations, Including Inversion) contains a new routine for computing the matrix exponential of a real-valued matrix.
Chapter F02 (Eigenvalues and Eigenvectors) contains a new routine for obtaining leading terms in the singular value decomposition of a real general matrix.
Chapter F07 (Linear Equations (LAPACK)) contains two new routines for solving systems of linear equations using mixed single and double precision arithmetic. For well conditioned problems, these can produce results accurate to double precision while taking advantage of the higher performance of single precision routines on many computer architectures.
Chapter G01 (Simple Calculations on Statistical Data) contains a new routine for finding quantiles of an unordered vector.
Chapter G02 (Correlation and Regression Analysis) contains new routines for: computing the nearest correlation matrix to a real square matrix; computing predicted value and error from a generalized linear model; ridge regression; and partial least squares.
Chapter G03 (Multivariate Methods) contains a new routine for performing ProMax rotations.
Chapter G05 (Random Number Generators) has been overhauled to provide a consistent set of routines for: initializing pseudorandom, quasi-random and scrambled quasi-random base generators; generating vectors from distributions; generating matrices from Copula and multivariate distributions; and generating realizations from (V)ARMA models and GARCH processes. The base generators now include the Mersenne Twister and ACORN generators.
Chapter G13 (Time Series Analysis) contains new routines for exponential smoothing of a univariate time series, and fitting a VARMA model to a multivariate time series.
Chapter M01 (Sorting and Searching) is renamed from ‘Sorting’ and contains routines for searching arrays of real-valued, integer or character data.
Chapter S (Approximations of Special Functions) now includes a suite of routines for evaluating various option pricing formulae. This chapter also contains new routines for computing the scaled complement of the error function (erfcx), and computing elliptic integrals in the classical Legendre form.
Plots of example program results have been added to many routine documents. In some cases the example program has been modified slightly to produce a larger set of results giving a more representative plot of the solution profile produced.

1.2  New SMP parallelism and other optimizations

The focus in this release has been to implement SMP parallelism in a broader range of chapters than in previous Marks, which focussed on dense and sparse linear algebra and FFTs.

2  New Routines

The 129 new user-callable routines included in the NAG Library at Mark 22 are as follows.
Routine
Name
Purpose
A00ADFLibrary identification, details of implementation, major and minor marks
C05BAFReal values of Lambert's W function, Wx
C09AAFWavelet filter initialization
C09CAFone-dimensional discrete wavelet transform
C09CBFone-dimensional inverse discrete wavelet transform
C09CCFone-dimensional multi-level discrete wavelet transform
C09CDFone-dimensional inverse multi-level discrete wavelet transform
D02MCFImplicit ordinary differential equations/DAEs, initial value problem, DASSL method continuation for D02NEF
D02MWFImplicit ordinary differential equations/DAEs, initial value problem, setup for D02NEF
D02NEFImplicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator
D02NPFImplicit ordinary differential equations/DAEs, initial value problem linear algebra setup routine for D02NEF
E04CBFUnconstrained minimization using simplex algorithm, function of several variables using function values only
E05JAFInitialization routine for E05JBF
E05JBFGlobal optimization by multi-level coordinate search, simple bounds, using function values only
E05JCFSupply optional parameter values for E05JBF from external file
E05JDFSet a single optional parameter for E05JBF from a character string
E05JEFSet a single optional parameter for E05JBF from an ‘ON’/‘OFF’-valued character argument
E05JFFSet a single optional parameter for E05JBF from an integer argument
E05JGFSet a single optional parameter for E05JBF from a real argument
E05JHFDetermine whether an optional parameter for E05JBF has been set by you or not
E05JJFGet the setting of an ‘ON’/‘OFF’-valued character optional parameter of E05JBF
E05JKFGet the setting of an Integer valued optional parameter of E05JBF
E05JLFGet the setting of a real valued optional parameter of E05JBF
F01ECFReal matrix exponential
F02WGFComputes leading terms in the singular value decomposition of a real general matrix; also computes corresponding left and right singular vectors
F07ACFMixed precision real system solver
F07AQFMixed precision complex system solver
F16DLFSum elements of integer vector
F16DNFMaximum value and location, integer vector
F16DPFMinimum value and location, integer vector
F16DQFMaximum absolute value and location, integer vector
F16DRFMinimum absolute value and location, integer vector
F16EHFReal scaled vector addition preserving input
F16ELFSum elements of real vector
F16GHFComplex scaled vector addition preserving input
F16GLFSum elements of complex vector
F16JNFMaximum value and location, real vector
F16JPFMinimum value and location, real vector
F16JQFMaximum absolute value and location, real vector
F16JRFMinimum absolute value and location, real vector
F16JSFMaximum absolute value and location, complex vector
F16JTFMinimum absolute value and location, complex vector
G01AMFFind quantiles of an unordered vector, real numbers
G02AAFComputes the nearest correlation matrix to a real square matrix, using the method of Qi and Sun
G02GPFComputes a predicted value and its associated standard error based on a previously fitted generalized linear model.
G02KAFRidge regression, optimizing a ridge regression parameter
G02KBFRidge regression using a number of supplied ridge regression parameters
G02LAFPartial least-squares (PLS) regression using singular value decomposition
G02LBFPartial least-squares (PLS) regression using Wold's iterative method
G02LCFPLS parameter estimates following partial least-squares regression by G02LAF or G02LBF
G02LDFPLS predictions based on parameter estimates from G02LCF
G03BDFProMax rotations
G05KFFInitializes a pseudorandom number generator to give a repeatable sequence
G05KGFInitializes a pseudorandom number generator to give a non-repeatable sequence
G05KHFPrimes a pseudorandom number generator for generating multiple streams using leap-frog
G05KJFPrimes a pseudorandom number generator for generating multiple streams using skip-ahead
G05NCFPseudorandom permutation of an integer vector
G05NDFPseudorandom sample from an integer vector
G05PDFGenerates a realization of a time series from a GARCH process with asymmetry of the form εt-1+γ2
G05PEFGenerates a realization of a time series from a GARCH process with asymmetry of the form εt-1+γεt-12
G05PFFGenerates a realization of a time series from an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
G05PGFGenerates a realization of a time series from an exponential GARCH (EGARCH) process
G05PHFGenerates a realization of a time series from an ARMA model
G05PJFGenerates a realization of a multivariate time series from a VARMA model
G05PMFGenerates a realization of a time series from an exponential smoothing model
G05PXFGenerates a random orthogonal matrix
G05PYFGenerates a random correlation matrix
G05PZFGenerates a random two-way table
G05RCFGenerates a matrix of pseudorandom numbers from a Student's t-copula
G05RDFGenerates a matrix of pseudorandom numbers from a Gaussian copula
G05RYFGenerates a matrix of pseudorandom numbers from a multivariate Student's t-distribution
G05RZFGenerates a matrix of pseudorandom numbers from a multivariate Normal distribution
G05SAFGenerates a vector of pseudorandom numbers from a uniform distribution over 0,1
G05SBFGenerates a vector of pseudorandom numbers from a beta distribution
G05SCFGenerates a vector of pseudorandom numbers from a Cauchy distribution
G05SDFGenerates a vector of pseudorandom numbers from a χ2 distribution
G05SEFGenerates a vector of pseudorandom numbers from a Dirichlet distribution
G05SFFGenerates a vector of pseudorandom numbers from an exponential distribution
G05SGFGenerates a vector of pseudorandom numbers from an exponential mix distribution
G05SHFGenerates a vector of pseudorandom numbers from an F-distribution
G05SJFGenerates a vector of pseudorandom numbers from a gamma distribution
G05SKFGenerates a vector of pseudorandom numbers from a Normal distribution
G05SLFGenerates a vector of pseudorandom numbers from a logistic distribution
G05SMFGenerates a vector of pseudorandom numbers from a log-normal distribution
G05SNFGenerates a vector of pseudorandom numbers from a Student's t-distribution
G05SPFGenerates a vector of pseudorandom numbers from a triangular distribution
G05SQFGenerates a vector of pseudorandom numbers from a uniform distribution over a,b
G05SRFGenerates a vector of pseudorandom numbers from a von Mises distribution
G05SSFGenerates a vector of pseudorandom numbers from a Weibull distribution
G05TAFGenerates a vector of pseudorandom integers from a binomial distribution
G05TBFGenerates a vector of pseudorandom logical values
G05TCFGenerates a vector of pseudorandom integers from a geometric distribution
G05TDFGenerates a vector of pseudorandom integers from a general discrete distribution
G05TEFGenerates a vector of pseudorandom integers from a hypergeometric distribution
G05TFFGenerates a vector of pseudorandom integers from a logarithmic distribution
G05TGFGenerates a vector of pseudorandom integers from a multinomial distribution
G05THFGenerates a vector of pseudorandom integers from a negative binomial distribution
G05TJFGenerates a vector of pseudorandom integers from a Poisson distribution
G05TKFGenerates a vector of pseudorandom integers from a Poisson distribution with varying mean
G05TLFGenerates a vector of pseudorandom integers from a uniform distribution
G05YLFInitializes a quasi-random number generator
G05YMFGenerates a uniform quasi-random number sequence
G05YNFInitializes a scrambled quasi-random number generator
G13AMFUnivariate time series, exponential smoothing
G13DDFMultivariate time series, estimation of VARMA model
M01NAFBinary search in set of real numbers
M01NBFBinary search in set of integer numbers
M01NCFBinary search in set of character data
S15AGFScaled complement of error function, erfcxx
S21BEFElliptic integral of 1st kind, Legendre form, Fϕ|m
S21BFFElliptic integral of 2nd kind, Legendre form, Eϕ|m
S21BGFElliptic integral of 3rd kind, Legendre form, Πn;ϕ|m
S21BHFComplete elliptic integral of 1st kind, Legendre form, Km
S21BJFComplete elliptic integral of 2nd kind, Legendre form, Em
S30AAFBlack–Scholes–Merton option pricing formula
S30ABFBlack–Scholes–Merton option pricing formula with Greeks
S30BAFFloating-strike lookback option pricing formula
S30BBFFloating-strike lookback option pricing formula with Greeks
S30CAFBinary option: cash-or-nothing pricing formula
S30CBFBinary option: cash-or-nothing pricing formula with Greeks
S30CCFBinary option: asset-or-nothing pricing formula
S30CDFBinary option: asset-or-nothing pricing formula with Greeks
S30FAFStandard barrier option pricing formula
S30JAFJump-diffusion, Merton's model, option pricing formula
S30JBFJump-diffusion, Merton's model, option pricing formula with Greeks
S30NAFHeston's model option pricing formula
S30QCFAmerican option: Bjerksund and Stensland pricing formula
S30SAFAsian option: geometric continuous average rate pricing formula
S30SBFAsian option: geometric continuous average rate pricing formula with Greeks

3  Tuned Routines

The following is a list of user-callable routines that have been parallelized, or otherwise optimized, since the last release. There are 50 of these routines at this release in the areas of quadrature, partial differential equations (PDEs), interpolation, curve and surface fitting, linear algebra, correlation and regression analysis, multivariate methods, random number generators (RNGs), time series analysis, sorting and option pricing. See the document ‘Tuned and Enhanced Routines in the NAG Library for SMP & Multicore’ for a full list of tuned routines.
Note: on some implementations, the equivalent vendor library routines may be substituted for some of the following list – consult the Users' Note for your implementation for further information.
Routine
Name
Purpose
D01DAFTwo-dimensional quadrature, finite region
D01FCFMulti-dimensional adaptive quadrature over hyper-rectangle
D01GAFOne-dimensional quadrature, integration of function defined by data values, Gill–Miller method
D03RAFGeneral system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectangular region
D03RBFGeneral system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectilinear region
E01SGFInterpolating functions, modified Shepard's method, two variables
E01SHFInterpolated values, evaluate interpolant computed by E01SGF, function and first derivatives, two variables
E01TGFInterpolating functions, modified Shepard's method, three variables
E01THFInterpolated values, evaluate interpolant computed by E01TGF, function and first derivatives, three variables
E02CAFLeast-squares surface fit by polynomials, data on lines parallel to one independent coordinate axis
E02CBFEvaluation of fitted polynomial in two variables
E02DFFEvaluation of fitted bicubic spline at a mesh of points
F01CTFSum or difference of two real matrices, optional scaling and transposition
F01CWFSum or difference of two complex matrices, optional scaling and transposition
F05AAFGram–Schmidt orthogonalisation of n vectors of order m
G02AAFComputes the nearest correlation matrix to a real square matrix, using the method of Qi and Sun
G02BAFPearson product-moment correlation coefficients, all variables, no missing values
G02BDFCorrelation-like coefficients (about zero), all variables, no missing values
G02BNFKendall/Spearman non-parametric rank correlation coefficients, no missing values, overwriting input data
G02BPFKendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, overwriting input data
G02BQFKendall/Spearman non-parametric rank correlation coefficients, no missing values, preserving input data
G02BRFKendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, preserving input data
G03CAFComputes maximum likelihood estimates of the parameters of a factor analysis model, factor loadings, communalities and residual correlations
G03EAFComputes distance matrix
G03ECFHierarchical cluster analysis
G05RCFGenerates a matrix of pseudorandom numbers from a Student's t-copula
G05RDFGenerates a matrix of pseudorandom numbers from a Gaussian copula
G05YJFGenerates a Normal quasi-random number sequence
G05YKFGenerates a log-normal quasi-random number sequence
G05YMFGenerates a uniform quasi-random number sequence
G13EAFCombined measurement and time update, one iteration of Kalman filter, time-varying, square root covariance filter
G13EBFCombined measurement and time update, one iteration of Kalman filter, time-invariant, square root covariance filter
M01CAFSort a vector, real numbers
M01CBFSort a vector, integer numbers
M01CCFSort a vector, character data
S30AAFBlack–Scholes–Merton option pricing formula
S30ABFBlack–Scholes–Merton option pricing formula with Greeks
S30BAFFloating-strike lookback option pricing formula
S30BBFFloating-strike lookback option pricing formula with Greeks
S30CAFBinary option: cash-or-nothing pricing formula
S30CBFBinary option: cash-or-nothing pricing formula with Greeks
S30CCFBinary option: asset-or-nothing pricing formula
S30CDFBinary option: asset-or-nothing pricing formula with Greeks
S30FAFStandard barrier option pricing formula
S30JAFJump-diffusion, Merton's model, option pricing formula
S30JBFJump-diffusion, Merton's model, option pricing formula with Greeks
S30NAFHeston's model option pricing formula
S30QCFAmerican option: Bjerksund and Stensland pricing formula
S30SAFAsian option: geometric continuous average rate pricing formula
S30SBFAsian option: geometric continuous average rate pricing formula with Greeks

4  Enhanced Routines

These routines call one or more of the tuned routines as part of their core operations and may thereby exhibit improved performance and scalability. There are 49 newly enhanced routines at this Mark; these include the areas of roots of equations, ordinary differential equations (ODEs), integral equations, mesh generation, optimization, linear algebra, calculation on statistical data, correlation and regression analysis, multivariate methods, analysis of variance, random number generators (RNGs), univariate estimation, nonparametric statistics and time series analysis. See the document ‘Tuned and Enhanced Routines in the NAG Library for SMP & Multicore’ for a full list of enhanced routines.
Routine
Name
Purpose
C05NBFSolution of system of nonlinear equations using function values only (easy-to-use)
C05NCFSolution of system of nonlinear equations using function values only (comprehensive)
C05NDFSolution of system of nonlinear equations using function values only (reverse communication)
C05PBFSolution of system of nonlinear equations using first derivatives (easy-to-use)
C05PCFSolution of system of nonlinear equations using first derivatives (comprehensive)
C05PDFSolution of system of nonlinear equations using first derivatives (reverse communication)
D02NEFImplicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator
D05BDFNonlinear convolution Volterra–Abel equation, second kind, weakly singular
D05BEFNonlinear convolution Volterra–Abel equation, first kind, weakly singular
D06CBFGenerates a sparsity pattern of a Finite Element matrix associated with a given mesh
D06CCFRenumbers a given mesh using Gibbs method
E05JBFGlobal optimization by multi-level coordinate search, simple bounds, using function values only
F01ECFReal matrix exponential
F02WGFComputes leading terms in the singular value decomposition of a real general matrix; also computes corresponding left and right singular vectors
F07ACFMixed precision real system solver
F07AQFMixed precision complex system solver
F08PEFComputes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
F08PSFComputes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
F11MDFReal sparse nonsymmetric linear systems, setup for F11MEF
G01AGFLineprinter scatterplot of two variables
G01AHFLineprinter scatterplot of one variable against Normal scores
G01ARFConstructs a stem and leaf plot
G01EMFComputes probability for the Studentized range statistic
G01JDFComputes lower tail probability for a linear combination of (central) χ2 variables
G02HKFCalculates a robust estimation of a correlation matrix, Huber's weight function
G02JBFLinear mixed effects regression using Maximum Likelihood (ML)
G02KAFRidge regression, optimizing a ridge regression parameter
G02KBFRidge regression using a number of supplied ridge regression parameters
G02LAFPartial least-squares (PLS) regression using singular value decomposition
G02LCFPLS parameter estimates following partial least-squares regression by G02LAF or G02LBF
G03BDFProMax rotations
G04EAFComputes orthogonal polynomials or dummy variables for factor/classification variable
G05PJFGenerates a realization of a multivariate time series from a VARMA model
G05PYFGenerates a random correlation matrix
G07BEFComputes maximum likelihood estimates for parameters of the Weibull distribution
G07DAFRobust estimation, median, median absolute deviation, robust standard deviation
G07DBFRobust estimation, M-estimates for location and scale parameters, standard weight functions
G07DCFRobust estimation, M-estimates for location and scale parameters, user-defined weight functions
G07DDFComputes a trimmed and winsorized mean of a single sample with estimates of their variance
G07EAFRobust confidence intervals, one-sample
G07EBFRobust confidence intervals, two-sample
G08AGFPerforms the Wilcoxon one-sample (matched pairs) signed rank test
G08AKFComputes the exact probabilities for the Mann–Whitney U statistic, ties in pooled sample
G08CBFPerforms the one-sample Kolmogorov–Smirnov test for standard distributions
G08CCFPerforms the one-sample Kolmogorov–Smirnov test for a user-supplied distribution
G08CDFPerforms the two-sample Kolmogorov–Smirnov test
G11BBFComputes multiway table from set of classification factors using given percentile/quantile
G11BCFComputes marginal tables for multiway table computed by G11BAF or G11BBF
G13DDFMultivariate time series, estimation of VARMA model

5  Withdrawn Routines

The following routines have been withdrawn from the NAG Library at Mark 22. Warning of their withdrawal was included in the NAG Library Manual at Mark 21, 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)
E04UNFE04USF/E04USA
F11GAFF11GDF
F11GBFF11GEF
F11GCFF11GFF
G05CAFG05SAF
G05CBFG05KFF
G05CCFG05KGF
G05CFFF06DFF
G05CGFF06DFF
G05DAFG05SQF
G05DBFG05SFF
G05DCFG05SLF
G05DDFG05SKF
G05DEFG05SMF
G05DFFG05SCF
G05DHFG05SDF
G05DJFG05SNF
G05DKFG05SHF
G05DPFG05SSF
G05DRFG05TKF
G05DYFG05TLF
G05DZFG05TBF
G05EAFG05RZF
G05EBFG05TLF
G05ECFG05TJF
G05EDFG05TAF
G05EEFG05THF
G05EFFG05TEF
G05EGFG05PHF
G05EHFG05NCF
G05EJFG05NDF
G05EWFG05PHF
G05EXFG05TDF
G05EYFG05TDF
G05EZFG05RZF
G05FAFG05SQF
G05FBFG05SFF
G05FDFG05SKF
G05FEFG05SBF
G05FFFG05SJF
G05FSFG05SRF
G05GAFG05PXF
G05GBFG05PYF
G05HDFG05PJF
G05ZAFNo replacement routine required

6  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 immediately 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 23.
Routines Scheduled
for Withdrawal
Replacement Routine(s)
F02BJFF08WAF (DGGEV)
F02EAFF08PAF (DGEES)
F02EBFF08NAF (DGEEV)
F02FAFF08FAF (DSYEV)
F02FCFF08FBF (DSYEVX)
F02FDFF08SAF (DSYGV)
F02FHFF08UAF (DSBGV)
F02GAFF08PNF (ZGEES)
F02GBFF08NNF (ZGEEV)
F02GJFF08WNF (ZGGEV)
F02HAFF08FNF (ZHEEV)
F02HCFF08FPF (ZHEEVX)
F02HDFF08SNF (ZHEGV)
F02WEFF08KBF (DGESVD)
F02XEFF08KPF (ZGESVD)
F04AAFF07AAF (DGESV)
F04ACFF07HAF (DPBSV)
F04ADFF07ANF (ZGESV)
F04ARFF07AAF (DGESV)
F04EAFF07CAF (DGTSV)
F04FAFF07JAF (DPTSV), F07JDF (DPTTRF) and F07JEF (DPTTRS)
F04JAFF08KAF (DGELSS)
F04JDFF08KAF (DGELSS)
F04JLFF08ZBF (DGGGLM)
F04JMFF08ZAF (DGGLSE)
F04KLFF08ZPF (ZGGGLM)
F04KMFF08ZNF (ZGGLSE)
G05YAFG05YLF and G05YMF
G05YBFG05YLF and either G05YJF or G05YKF
The following routines have been superseded, but will not be withdrawn from the Library until Mark 24 at the earliest.
Superseded
Routine
Replacement Routine(s)
E04CCFE04CBF
G05HKFG05PDF
G05HLFG05PEF
G05HMFG05PFF
G05HNFG05PGF
G05KAFG05SAF
G05KBFG05KFF
G05KCFG05KGF
G05KEFG05TBF
G05LAFG05SKF
G05LBFG05SNF
G05LCFG05SDF
G05LDFG05SHF
G05LEFG05SBF
G05LFFG05SJF
G05LGFG05SQF
G05LHFG05SPF
G05LJFG05SFF
G05LKFG05SMF
G05LLFG05SJF
G05LMFG05SSF
G05LNFG05SLF
G05LPFG05SRF
G05LQFG05SGF
G05LXFG05RYF
G05LYFG05RZF
G05LZFG05RZF
G05MAFG05TLF
G05MBFG05TCF
G05MCFG05THF
G05MDFG05TFF
G05MEFG05TKF
G05MJFG05TAF
G05MKFG05TJF
G05MLFG05TEF
G05MRFG05TGF
G05MZFG05TDF
G05NAFG05NCF
G05NBFG05NDF
G05PAFG05PHF
G05PCFG05PJF
G05QAFG05PXF
G05QBFG05PYF
G05QDFG05PZF
G05RAFG05RDF
G05RBFG05RCF
G05YCFG05YLF
G05YDFG05YMF
G05YEFG05YLF
G05YFFG05YMF
G05YGFG05YLF
G05YHFG05YMF
G13DCFG13DDF
P01ABFNo longer required
X02DAFNo longer required
X02DJFNo longer required

7  Withdrawn Tuned Routines

Mark 21 of the Library contained tuned versions of the LAPACK 3.0 versions of F08PEF (DHSEQR) and F08PSF (ZHSEQR). NAG Library for SMP & Multicore, Mark 22 replaces these with the much improved algorithm introduced in LAPACK 3.1. This should perform much better on single and multiple processors, but as we have not made any significant modifications to the original source, we have removed these routines from the list of tuned routines. They may, however, benefit from optimizations we have made to other LAPACK routines, hence they are included in Section 4.
Mark 22 NAG Library for SMP & Multicore News (PDF version)
NAG Library Manual
© The Numerical Algorithms Group Ltd, Oxford, UK. 2009