NAG Library Contents Overview
A00 – Library Identification
The routines in this chapter provide information about the NAG Library.
Information about the precise implementation of the NAG Library in use will be needed when communicating with the NAG Technical Support Service (see NAG Library Manual Introductory document 'Support from NAG').
A02 – Complex Arithmetic
This chapter provides facilities for arithmetic operations involving complex numbers.
C02 – Zeros of Polynomials
This chapter is concerned with computing the zeros of a polynomial with real or complex coefficients.
C05 – Roots of One or More Transcendental Equations
This chapter is concerned with the calculation of zeros of continuous functions of one or more variables. The majority of problems considered are for realvalued functions of real variables, in which case complex equations must be expressed in terms of the equivalent larger system of real equations.
C06 – Summation of Series
This chapter is concerned with the following tasks.

 Calculating the discrete Fourier transform of a sequence of real or complex data values.
 Calculating the discrete convolution or the discrete correlation of two sequences of real or complex data values using discrete Fourier transforms.
 Calculating the inverse Laplace transform of a usersupplied routine.
 Direct summation of orthogonal series.
 Acceleration of convergence of a seuqnce of real values.
C09 – Wavelet Transforms
This chapter is concerned with the analysis of datasets (or functions or operators) in terms of frequency and scale components using wavelet transforms. Wavelet transforms have been applied in many fields from time series analysis to image processing and the localization in either frequency or scale that they provide is useful for data compression or denoising. In general the standard wavelet transform uses dilation and scaling of a chosen function, ψ(t), (called the mother wavelet) such that ψ_{a,b}(t)=1/(sqrt(a))ψ((tb)/a) where a gives the scaling and b determines the translation. Wavelet methods can be divided into continuous transforms and discrete transforms. In the continuous case, the pair a and b are real numbers with a>0. For the discrete transform, a and b can be chosen as a=2^{j}, b=k2^{j} for integers j, k ψ_{j,k}(t)=2^{j/2}ψ(2^{j}tk).
The continuous real valued, onedimensional wavelet transform (CWT) is included in this chapter. The discrete wavelet transform (DWT) at a single level together with its inverse and the multilevel DWT with inverse are also provided for one, two and three dimensions. The Maximal Overlap DWT (MODWT) together with its inverse and the multilevel MODWT with inverse are provided for one dimension. The choice of wavelet for CWT includes the Morlet wavelet and derivatives of a Gaussian while the DWT and MODWT offer the orthogonal wavelets of Daubechies and a selection of biorthogonal wavelets.
D01 – Quadrature
This chapter provides routines for the numerical evaluation of definite integrals in one or more dimensions and for evaluating weights and abscissae of integration rules.
D02 – Ordinary Differential Equations
This chapter is concerned with the numerical solution of ordinary differential equations. There are two main types of problem: those in which all boundary conditions are specified at one point (initial value problems), and those in which the boundary conditions are distributed between two or more points (boundary value problems and eigenvalue problems). Routines are available for initial value problems, twopoint boundary value problems and Sturm–Liouville eigenvalue problems.
D03 – Partial Differential Equations
This chapter is concerned with the numerical solution of partial differential equations.
D04 – Numerical Differentiation
This chapter is concerned with calculating approximations to derivatives of a function f.
D05 – Integral Equations
This chapter is concerned with the numerical solution of integral equations. Provision will be made for most of the standard types of equation (see the Chapter Introduction). The following are, however, specifically excluded:

 Equations arising in the solution of partial differential equations by integral equation methods. In cases where the prime purpose of an algorithm is the solution of a partial differential equation it will normally be included in Chapter D03.
 Calculation of inverse integral transforms. This problem falls within the scope of Chapter C06.
D06 – Mesh Generation
This chapter is concerned with automatic mesh generation

 with line segments, over the boundary of a closed twodimensional connected polygonal domain;
 with triangles, over a given twodimensional region using only its boundary mesh.
E01 – Interpolation
This chapter is concerned with the interpolation of a function of one or more variables. When provided with the value of the function (and possibly one or more of its lowestorder derivatives) at each of a number of values of the variable(s), the NAG Library routines provide either an interpolating function or an interpolated value. For some of the interpolating functions, there are supporting NAG Library routines to evaluate, differentiate or integrate them.
E02 – Curve and Surface Fitting
The main aim of this chapter is to assist you in finding a function which approximates a set of data points. Typically the data contain random errors, as of experimental measurement, which need to be smoothed out. To seek an approximation to the data, it is first necessary to specify for the approximating function a mathematical form (a polynomial, for example) which contains a number of unspecified coefficients: the appropriate fitting routine then derives for the coefficients the values which provide the best fit of that particular form. The chapter deals mainly with curve and surface fitting (i.e., fitting with functions of one and of two variables) when a polynomial or a cubic spline is used as the fitting function, since these cover the most common needs. However, fitting with other functions and/or more variables can be undertaken by means of general linear or nonlinear routines (some of which are contained in other chapters) depending on whether the coefficients in the function occur linearly or nonlinearly. Cases where a graph rather than a set of data points is given can be treated simply by first reading a suitable set of points from the graph.
The chapter also contains routines for evaluating, differentiating and integrating polynomial and spline curves and surfaces, once the numerical values of their coefficients have been determined.
There is also a routine for computing a Padé approximant of a mathematical function (see the Chapter Introduction).
E04 – Minimizing or Maximizing a Function
This chapter provides routines for solving various mathematical optimization problems by solvers based on local stopping criteria. The main classes of problems covered in this chapter are:
For a full overview of the functionality offered in this chapter, see the Chapter Introduction or the Chapter Contents (Chapter E04).
See also other chapters in the Library relevant to optimization:
This introduction is only a brief guide to the subject of optimization designed for the casual user. It discusses a classification of the optimization problems and presents an overview of the algorithms and their stopping criteria to assist choosing the right solver for a particular problem. Anyone with a difficult or protracted problem to solve will find it beneficial to consult a more detailed text, see the References section in the Chapter Introduction. If you are unfamiliar with the mathematics of the subject you may find the Chapter Introduction a useful starting point.

 Linear Programming (LP) – dense and sparse;
 Quadratic Programming (QP) – convex and nonconvex, dense and sparse;
 Nonlinear Programming (NLP) – dense and sparse, based on activeset SQP methods and interior point method (IPM);
 Semidefinite Programming (SDP) – both linear matrix inequalities (LMI) and bilinear matrix inequalities (BMI);
 Derivativefree Optimization (DFO);
 Least Squares (LSQ), data fitting – linear and nonlinear, constrained and unconstrained.
 Chapter E05 contains routines to solve global optimization problems;
 Chapter H addresses problems arising in operational research and focuses on Mixed Integer Programming (MIP);
 Chapters F07 and F08 include routines for linear algebra and in particular unconstrained linear least squares;
 Chapter E02 focuses on curve and surface fitting, in which linear data fitting in l_{1} norm might be of interest.
E05 – Global Optimization of a Function
Global optimization involves finding the absolute maximum or minimum value of a function (the objective function) of several variables, possibly subject to restrictions (defined by a set of bounds or constraint functions) on the values of the variables. Such problems can be much harder to solve than local optimization problems (which are discussed in Chapter E04) because it is difficult to determine whether a potential optimum found is global, and because of the nonlocal methods required to avoid becoming trapped near local optima. Most optimization routines in the NAG Library are concerned with function minimization only, since the problem of maximizing a given objective function F is equivalent to minimizing F. In E05JB, E05SA and E05SB, you may specify whether you are solving a minimization or maximization problem; in the latter case, the required transformation of the objective function will be carried out automatically. In what follows we refer exclusively to minimization problems.
This introduction is a brief guide to the subject of global optimization, designed for the casual user. For further details you may find it beneficial to consult a more detailed text, see the References section in the Chapter Introduction. Furthermore, much of the material in the E04 Chapter Introduction is also relevant in this context and it is strongly recommended that you read the E04 Chapter Introduction.
F01 – Matrix Operations, Including Inversion
This chapter provides facilities for four types of problem:
See the Chapter Introduction where these problems are discussed.

 Matrix Inversion
 Matrix Factorizations
 Matrix Arithmetic and Manipulation
 Matrix Functions
F02 – Eigenvalues and Eigenvectors
This chapter provides routines for various types of matrix eigenvalue problem:
Routines are provided for both real and complex data.
The majority of routines for these problems can be found in Chapter F08 which contains software derived from LAPACK (see Anderson et al. (1999) LAPACK Users' Guide). However, you should read the the F02 Chapter Introduction before turning to Chapter F08, especially if you are a new user. Chapter F12 contains routines for large sparse eigenvalue problems, although one such routine is also available in this chapter.
Chapters F02 and F08 contain Black Box (or Driver) routines that enable many problems to be solved by a call to a single routine, and the decision trees in the Chapter Introduction direct you to the most appropriate routines in Chapters F02 and F08. The Chapter F02 routines call routines in Chapters F07 and F08 wherever possible to perform the computations, and there are pointers in the Chapter Introduction to the relevant decision trees in Chapter F08.

 standard eigenvalue problems (finding eigenvalues and eigenvectors of a square matrix A);
 singular value problems (finding singular values and singular vectors of a rectangular matrix A);
 generalized eigenvalue problems (finding eigenvalues and eigenvectors of a matrix pencil AλB).
 quadratic eigenvalue problems (finding eigenvalues and eigenvectors of the quadratic λ^{2}A+λB+C).
F03 – Determinants
This chapter is concerned with the calculation of determinants of square matrices.
F04 – Simultaneous Linear Equations
This chapter is concerned with the solution of the matrix equation AX=B, where B may be a single vector or a matrix of multiple righthand sides. The matrix A may be real, complex, symmetric, Hermitian, positive definite, positive definite Toeplitz or banded. It may also be rectangular, in which case a least squares solution is obtained.
Much of the functionality of this chapter has been superseded by routines from Chapters F07 and F08 (LAPACK routines) as those chapters have grown and have included driver and expert driver routines.
For a general introduction to sparse systems of equations, see the F11 Chapter Introduction, which provides routines for large sparse systems. Some routines for sparse problems are also included in this chapter; they are described in the Chapter Introduction.
F05 – Orthogonalization
This chapter is concerned with the orthogonalization of vectors in a finite dimensional space.
F06 – Linear Algebra Support Routines
This chapter is concerned with basic linear algebra routines which perform elementary algebraic operations involving scalars, vectors and matrices. It includes routines which conform to the specifications of the BLAS (Basic Linear Algebra Subprograms).
F07 – Linear Equations (LAPACK)
This chapter provides routines for the solution of systems of simultaneous linear equations, and associated computations. It provides routines for
Routines are provided for both real and complex data.
For a general introduction to the solution of systems of linear equations, you should turn first to the F04 Chapter Introduction. The decision trees, in the F04 Chapter Introduction, direct you to the most appropriate routines in Chapters F04 and F07 for solving your particular problem. In particular, Chapters F04 and F07 contain Black Box (or driver) routines which enable some standard types of problem to be solved by a call to a single routine. Where possible, routines in Chapter F04 call Chapter F07 routines to perform the necessary computational tasks.
There are two types of driver routines in this chapter: simple drivers which just return the solution to the linear equations; and expert drivers which also return condition and error estimates and, in many cases, also allow equilibration. The simple drivers for real matrices have names of the form F07_AF (D__SV) and for complex matrices have names of the form F07_NF (Z__SV). The expert drivers for real matrices have names of the form F07_BF (D__SVX) and for complex matrices have names of the form F07_PF (Z__SVX).
The routines in this chapter (Chapter F07) handle only dense and band matrices (not matrices with more specialised structures, or general sparse matrices).
The routines in this chapter have all been derived from the LAPACK project (see Anderson et al. (1999) LAPACK Users' Guide). They have been designed to be efficient on a wide range of highperformance computers, without compromising efficiency on conventional serial machines.

 matrix factorizations;
 solution of linear equations;
 estimating matrix condition numbers;
 computing error bounds for the solution of linear equations;
 matrix inversion;
 computing scaling factors to equilibrate a matrix.
F08 – Least Squares and Eigenvalue Problems (LAPACK)
This chapter provides routines for the solution of linear least squares problems, eigenvalue problems and singular value problems, as well as associated computations. It provides routines for:
Routines are provided for both real and complex data.
For a general introduction to the solution of linear least squares problems, you should turn first to Chapter F04. The decision trees, at the end of Chapter F04, direct you to the most appropriate routines in Chapters F04 and F08. Chapters F04 and F08 contain Black Box (or driver) routines which enable standard linear least squares problems to be solved by a call to a single routine.
For a general introduction to eigenvalue and singular value problems, you should turn first to Chapter F02. The decision trees, at the end of Chapter F02, direct you to the most appropriate routines in Chapters F02 and F08. Chapters F02 and F08 contain Black Box (or driver) routines which enable standard types of problem to be solved by a call to a single routine. Often routines in Chapter F02 call Chapter F08 routines to perform the necessary computational tasks.
The routines in this chapter (Chapter F08) handle only dense, band, tridiagonal and Hessenberg matrices (not matrices with more specialised structures, or general sparse matrices). The tables in the Chapter Introduction and the decision trees in the Chapter Introduction direct you to the most appropriate routines in Chapter F08.
The routines in this chapter have all been derived from the LAPACK project (see Anderson et al. (1999) LAPACK Users' Guide). They have been designed to be efficient on a wide range of highperformance computers, without compromising efficiency on conventional serial machines.

 solution of linear least squares problems
 solution of symmetric eigenvalue problems
 solution of nonsymmetric eigenvalue problems
 solution of singular value problems
 solution of generalized linear least squares problems
 solution of generalized symmetricdefinite eigenvalue problems
 solution of generalized nonsymmetric eigenvalue problems
 solution of generalized singular value problems
 matrix factorizations associated with the above problems
 estimating condition numbers of eigenvalue and eigenvector problems
 estimating the numerical rank of a matrix
 solution of the Sylvester matrix equation
F11 – Large Scale Linear Systems
This chapter provides routines for the solution of large sparse systems of simultaneous linear equations. These include iterative methods for real nonsymmetric and symmetric, complex nonHermitian and Hermitian linear systems and direct methods for general real linear systems. Further direct methods are currently available in Chapters F01 and F04.
F12 – Large Scale Eigenproblems
This chapter provides routines for computing some eigenvalues and eigenvectors of largescale (sparse) standard and generalized eigenvalue problems. It provides routines for:
Routines are provided for both real and complex data.
The routines in this chapter have all been derived from the ARPACK software suite (see Lehoucq et al. (1998) ARPACK Users' Guide: Solution of Largescale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods), a collection of Fortran 77 subroutines designed to solve large scale eigenvalue problems. The interfaces provided in this chapter have been chosen to combine ease of use with the flexibility of the original ARPACK software. The underlying iterative methods and algorithms remain essentially the same as those in ARPACK and are described fully in Lehoucq et al. (1998) ARPACK Users' Guide: Solution of Largescale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods.
The algorithms used are based upon an algorithmic variant of the Arnoldi process called the Implicitly Restarted Arnoldi Method. For symmetric matrices, this reduces to a variant of the Lanczos process called the Implicitly Restarted Lanczos Method. These variants may be viewed as a synthesis of the Arnoldi/Lanczos process with the Implicitly Shifted QR technique that is suitable for large scale problems. For many standard problems, a matrix factorization is not required. Only the action of the matrix on a vector is needed.

 solution of symmetric eigenvalue problems;
 solution of nonsymmetric eigenvalue problems;
 solution of generalized symmetricdefinite eigenvalue problems;
 solution of generalized nonsymmetric eigenvalue problems;
 partial singular value decomposition.
F16 – Further Linear Algebra Support Routines
This chapter is concerned with basic linear algebra routines which perform elementary algebraic operations involving scalars, vectors and matrices. Most routines for such operations conform either to the specifications of the BLAS (Basic Linear Algebra Subprograms) or to the specifications of the BLAST (Basic Linear Algebra Subprograms Technical) Forum. This chapter includes routines from the BLAST specifications. Most (BLAS) routines for such operations are available in Chapter F06.
G01 – Simple Calculations on Statistical Data
This chapter covers three topics:

 plots, descriptive statistics, and exploratory data analysis;
 statistical distribution functions and their inverses;
 testing for Normality and other distributions.
G02 – Correlation and Regression Analysis
This chapter is concerned with two techniques

 correlation analysis and
 regression modelling,
 both of which are concerned with determining the interrelationships among two or more variables.
Other chapters of the NAG Library which cover similar problems are Chapters E02 and E04. Chapter E02 routines may be used to fit linear models by criteria other than least squares, and also for polynomial regression; Chapter E04 routines may be used to fit nonlinear models and linearly constrained linear models.
G03 – Multivariate Methods
This chapter is concerned with methods for studying multivariate data. A multivariate dataset consists of several variables recorded on a number of objects or individuals. Multivariate methods can be classified as those that seek to examine the relationships between the variables (e.g., principal components), known as variabledirected methods, and those that seek to examine the relationships between the objects (e.g., cluster analysis), known as individualdirected methods.
Multiple regression is not included in this chapter as it involves the relationship of a single variable, known as the response variable, to the other variables in the dataset, the explanatory variables. Routines for multiple regression are provided in Chapter G02.
G04 – Analysis of Variance
This chapter is concerned with methods for analysing the results of designed experiments. The range of experiments covered include:
Further designs may be analysed by combining the analyses provided by multiple calls to routines or by using general linear model routines provided in Chapter G02.

 single factor designs with equal sized blocks such as randomized complete block and balanced incomplete block designs,
 row and column designs such as Latin squares, and
 complete factorial designs.
G05 – Random Number Generators
This chapter is concerned with the generation of sequences of independent pseudorandom and quasirandom numbers from various distributions, and models.
G07 – Univariate Estimation
This chapter deals with the estimation of unknown parameters of a univariate distribution. It includes both point and interval estimation using maximum likelihood and robust methods.
G08 – Nonparametric Statistics
The routines in this chapter perform nonparametric statistical tests which are based on distributionfree methods of analysis. For convenience, the chapter contents are divided into five types of test: tests of location, tests of dispersion, tests of distribution, tests of association and correlation, and tests of randomness. There are also routines to fit linear regression models using the ranks of the observations.
The emphasis in this chapter is on testing; if you wish to compute nonparametric correlations you are referred to Chapter G02, which contains several routines for that purpose.
There are a large number of nonparametric tests available. A selection of some of the more commonly used tests are included in this chapter.
G10 – Smoothing in Statistics
This chapter is concerned with methods for smoothing data. Included are methods for density estimation, smoothing time series data, and statistical applications of splines. These methods may also be viewed as nonparametric modelling.
G11 – Contingency Table Analysis
The routines in this chapter are for the analysis of discrete multivariate data. One suite of routines computes tables while other routines are for the analysis of twoway contingency tables, conditional logistic models and onefactor analysis of binary data.
Routines in Chapter G02 may be used to fit generalized linear models to discrete data including binary data and contingency tables.
G12 – Survival Analysis
This chapter is concerned with statistical techniques used in the analysis of survival/reliability/failure time data.
Other chapters contain routines which are also used to analyse this type of data. Chapter G02 contains generalized linear models, Chapter G07 contains routines to fit distribution models, and Chapter G08 contains rank based methods.
G13 – Time Series Analysis
This chapter provides facilities for investigating and modelling the statistical structure of series of observations collected at points in time. The models may then be used to forecast the series.
The chapter covers the following models and approaches.

 Univariate time series analysis, including autocorrelation functions and autoregressive moving average (ARMA) models.
 Univariate spectral analysis.
 Transfer function (multiinput) modelling, in which one time series is dependent on other time series.
 Bivariate spectral methods including coherency, gain and input response functions.
 Vector ARMA models for multivariate time series.
 Kalman filter models (linear and nonlinear).
 GARCH models for volatility.
 Inhomogeneous Time Series.
H – Operations Research
This chapter provides routines to solve certain integer programming, transportation and shortest path problems. Additionally 'best subset' routines are included.
M01 – Sorting and Searching
This chapter is concerned with sorting and searching numeric or character data. It handles only the simplest types of data structure and it is concerned only with internal sorting and searching – that is, sorting and searching a set of data which can all be stored within the program.
If you have large files of data or complicated data structures to be sorted or searched you should use a comprehensive sorting or searching program or package.
S – Approximations of Special Functions
This chapter is concerned with the provision of some commonly occurring physical and mathematical functions.
X01 – Mathematical Constants
This chapter is concerned with the provision of mathematical constants required by other routines within the Library.
X02 – Machine Constants
This chapter is concerned with parameters which characterise certain aspects of the computing environment in which the NAG Library is implemented. They relate primarily to floatingpoint arithmetic, but also to integer arithmetic, the elementary functions and exception handling. The values of the parameters vary from one implementation of the Library to another, but within the context of a single implementation they are constants.
The parameters are intended for use primarily by other routines in the Library, but users of the Library may sometimes need to refer to them directly.
X03 – Inner Products
This chapter is concerned with the calculation of innerproducts required by other routines within the Library.
X04 – Input/Output Utilities
This chapter contains utility routines concerned with input and output to or from an external file.
X05 – Date and Time Utilities
This chapter provides routines to obtain the current real time, and the amount of processor time used.
X06 – OpenMP Utilities
This chapter contains utilities for controlling the OpenMP environment for your program. They are based on OpenMP runtime library routines, although their functionality varies slightly.
X07 – IEEE Arithmetic
This chapter provides routines to handle various aspects of IEEE floatingpoint arithmetic behaviour.
Routine Summaries
A00 – Library Identification
Examples of routines and methods in this chapter.
A00AA  nagf_info_impl_details Library identification, details of implementation and mark 
A00AC  nagf_info_licence Check availability of a valid licence key 
A00AD  nagf_info_impl_details_separate Library identification, details of implementation, major and minor marks 
A02 – Complex Arithmetic
Examples of routines and methods in this chapter.
A02AA  nagf_complex_sqrt Square root of complex number 
A02AB  nagf_complex_abs Modulus of complex number 
A02AC  nagf_complex_divide Quotient of two complex numbers 
C02 – Zeros of Polynomials
Examples of routines and methods in this chapter.
C02AF  nagf_zeros_poly_complex All zeros of complex polynomial, modified Laguerre's method 
C02AG  nagf_zeros_poly_real All zeros of real polynomial, modified Laguerre's method 
C02AH  nagf_zeros_quadratic_complex All zeros of complex quadratic equation 
C02AJ  nagf_zeros_quadratic_real All zeros of real quadratic equation 
C02AK  nagf_zeros_cubic_real All zeros of real cubic equation 
C02AL  nagf_zeros_quartic_real All zeros of real quartic equation 
C02AM  nagf_zeros_cubic_complex All zeros of complex cubic equation 
C02AN  nagf_zeros_quartic_complex All zeros of complex quartic equation 
C05 – Roots of One or More Transcendental Equations
Examples of routines and methods in this chapter.
C05AU  nagf_roots_contfn_brent_interval Zero of continuous function, Brent algorithm, from a given starting value, binary search for interval 
C05AV  nagf_roots_contfn_interval_rcomm Binary search for interval containing zero of continuous function (reverse communication) 
C05AW  nagf_roots_contfn_cntin Zero of continuous function, continuation method, from a given starting value 
C05AX  nagf_roots_contfn_cntin_rcomm Zero of continuous function, continuation method, from a given starting value (reverse communication) 
C05AY  nagf_roots_contfn_brent Zero of continuous function in a given interval, Brent algorithm 
C05AZ  nagf_roots_contfn_brent_rcomm Zero of continuous function in a given interval, Brent algorithm (reverse communication) 
C05BA  nagf_roots_lambertw_real Real values of Lambert's W function, W(x) 
C05BB  nagf_roots_lambertw_complex Values of Lambert's W function, W(z) 
C05QB  nagf_roots_sys_func_easy Solution of a system of nonlinear equations using function values only (easytouse) 
C05QC  nagf_roots_sys_func_expert Solution of a system of nonlinear equations using function values only (comprehensive) 
C05QD  nagf_roots_sys_func_rcomm Solution of a system of nonlinear equations using function values only (reverse communication) 
C05QS  nagf_roots_sparsys_func_easy Solution of a sparse system of nonlinear equations using function values only (easytouse) 
C05RB  nagf_roots_sys_deriv_easy Solution of a system of nonlinear equations using first derivatives (easytouse) 
C05RC  nagf_roots_sys_deriv_expert Solution of a system of nonlinear equations using first derivatives (comprehensive) 
C05RD  nagf_roots_sys_deriv_rcomm Solution of a system of nonlinear equations using first derivatives (reverse communication) 
C05ZD  nagf_roots_sys_deriv_check Check user's routine for calculating first derivatives of a set of nonlinear functions of several variables 
C06 – Summation of Series
Examples of routines and methods in this chapter.
C06BA  nagf_sum_accelerate Acceleration of convergence of sequence, Shanks' transformation and epsilon algorithm 
C06DC  nagf_sum_chebyshev Sum of a Chebyshev series at a set of points 
C06FA  nagf_sum_fft_real_1d_rfmt Single onedimensional real discrete Fourier transform, extra workspace for greater speed 
C06FB  nagf_sum_fft_hermitian_1d_rfmt Single onedimensional Hermitian discrete Fourier transform, extra workspace for greater speed 
C06FC  nagf_sum_fft_complex_1d_sep Single onedimensional complex discrete Fourier transform, extra workspace for greater speed 
C06FF  nagf_sum_fft_complex_multid_1d_sep Onedimensional complex discrete Fourier transform of multidimensional data 
C06FJ  nagf_sum_fft_complex_multid_sep Multidimensional complex discrete Fourier transform of multidimensional data 
C06FK  nagf_sum_convcorr_real Circular convolution or correlation of two real vectors, no restrictions on n 
C06FX  nagf_sum_fft_complex_3d_sep Threedimensional complex discrete Fourier transform 
C06LA  nagf_sum_invlaplace_crump Inverse Laplace transform, Crump's method 
C06LB  nagf_sum_invlaplace_weeks Inverse Laplace transform, modified Weeks' method 
C06LC  nagf_sum_invlaplace_weeks_eval Evaluate inverse Laplace transform as computed by C06LB 
C06PA  nagf_sum_fft_realherm_1d Single onedimensional real and Hermitian complex discrete Fourier transform, using complex storage format for Hermitian sequences 
C06PC  nagf_sum_fft_complex_1d Single onedimensional complex discrete Fourier transform, complex data type 
C06PF  nagf_sum_fft_complex_multid_1d Onedimensional complex discrete Fourier transform of multidimensional data (using complex data type) 
C06PJ  nagf_sum_fft_complex_multid Multidimensional complex discrete Fourier transform of multidimensional data (using complex data type) 
C06PK  nagf_sum_convcorr_complex Circular convolution or correlation of two complex vectors 
C06PP  nagf_sum_fft_realherm_1d_multi_row Multiple onedimensional real and Hermitian complex discrete Fourier transforms, using row ordered complex storage format for Hermitian sequences 
C06PQ  nagf_sum_fft_realherm_1d_multi_col Multiple onedimensional real and Hermitian complex discrete Fourier transforms, using column ordered complex storage format for Hermitian sequences 
C06PR  nagf_sum_fft_complex_1d_multi_row Multiple onedimensional complex discrete Fourier transforms using complex data type 
C06PS  nagf_sum_fft_complex_1d_multi_col Multiple onedimensional complex discrete Fourier transforms, complex data type 
C06PU  nagf_sum_fft_complex_2d Twodimensional complex discrete Fourier transform, complex data type 
C06PV  nagf_sum_fft_real_2d Twodimensional realtocomplex discrete Fourier transform 
C06PW  nagf_sum_fft_hermitian_2d Twodimensional complextoreal discrete Fourier transform 
C06PX  nagf_sum_fft_complex_3d Threedimensional complex discrete Fourier transform, complex data type 
C06PY  nagf_sum_fft_real_3d Threedimensional realtocomplex discrete Fourier transform 
C06PZ  nagf_sum_fft_hermitian_3d Threedimensional complextoreal discrete Fourier transform 
C06RA  nagf_sum_fft_real_sine_simple Discrete sine transform (easytouse) 
C06RB  nagf_sum_fft_real_cosine_simple Discrete cosine transform (easytouse) 
C06RC  nagf_sum_fft_real_qtrsine_simple Discrete quarterwave sine transform (easytouse) 
C06RD  nagf_sum_fft_real_qtrcosine_simple Discrete quarterwave cosine transform (easytouse) 
C06RE  nagf_sum_fft_sine Multiple discrete sine transforms, simple 
C06RF  nagf_sum_fft_cosine Multiple discrete cosine transforms, simple 
C06RG  nagf_sum_fft_qtrsine Multiple discrete quarterwave sine transforms, simple 
C06RH  nagf_sum_fft_qtrcosine Multiple discrete quarterwave cosine transforms, simple 
C09 – Wavelet Transforms
Examples of routines and methods in this chapter.
C09AA  nagf_wav_1d_init Onedimensional wavelet filter initialization 
C09AB  nagf_wav_2d_init Twodimensional wavelet filter initialization 
C09AC  nagf_wav_3d_init Threedimensional wavelet filter initialization 
C09BA  nagf_wav_1d_cont Onedimensional real continuous wavelet transform 
C09CA  nagf_wav_1d_sngl_fwd Onedimensional discrete wavelet transform 
C09CB  nagf_wav_1d_sngl_inv Onedimensional inverse discrete wavelet transform 
C09CC  nagf_wav_1d_multi_fwd Onedimensional multilevel discrete wavelet transform 
C09CD  nagf_wav_1d_multi_inv Onedimensional inverse multilevel discrete wavelet transform 
C09DA  nagf_wav_1d_mxolap_fwd Onedimensional maximal overlap discrete wavelet transform (MODWT) 
C09DB  nagf_wav_1d_mxolap_inv Onedimensional inverse maximal overlap discrete wavelet transform (IMODWT) 
C09DC  nagf_wav_1d_mxolap_multi_fwd Onedimensional multilevel maximal overlap discrete wavelet transform (MODWT) 
C09DD  nagf_wav_1d_mxolap_multi_inv Onedimensional inverse multilevel maximal overlap discrete wavelet transform (IMODWT) 
C09EA  nagf_wav_2d_sngl_fwd Twodimensional discrete wavelet transform 
C09EB  nagf_wav_2d_sngl_inv Twodimensional inverse discrete wavelet transform 
C09EC  nagf_wav_2d_multi_fwd Twodimensional multilevel discrete wavelet transform 
C09ED  nagf_wav_2d_multi_inv Twodimensional inverse multilevel discrete wavelet transform 
C09EY  nagf_wav_2d_coeff_ext Twodimensional discrete wavelet transform coefficient extraction 
C09EZ  nagf_wav_2d_coeff_ins Twodimensional discrete wavelet transform coefficient insertion 
C09FA  nagf_wav_3d_sngl_fwd Threedimensional discrete wavelet transform 
C09FB  nagf_wav_3d_sngl_inv Threedimensional inverse discrete wavelet transform 
C09FC  nagf_wav_3d_multi_fwd Threedimensional multilevel discrete wavelet transform 
C09FD  nagf_wav_3d_mxolap_multi_inv Threedimensional inverse multilevel discrete wavelet transform 
C09FY  nagf_wav_3d_coeff_ext Threedimensional discrete wavelet transform coefficient extraction 
C09FZ  nagf_wav_3d_coeff_ins Threedimensional discrete wavelet transform coefficient insertion 
D01 – Quadrature
Examples of routines and methods in this chapter.
D01AH  nagf_quad_1d_fin_well Onedimensional quadrature, adaptive, finite interval, strategy due to Patterson, suitable for wellbehaved integrands 
D01AJ  nagf_quad_1d_fin_bad Onedimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands 
D01AK  nagf_quad_1d_fin_osc Onedimensional quadrature, adaptive, finite interval, method suitable for oscillating functions 
D01AL  nagf_quad_1d_fin_sing Onedimensional quadrature, adaptive, finite interval, allowing for singularities at userspecified breakpoints 
D01AM  nagf_quad_1d_inf Onedimensional quadrature, adaptive, infinite or semiinfinite interval 
D01AN  nagf_quad_1d_fin_wtrig Onedimensional quadrature, adaptive, finite interval, weight function cos (ωx) or sin (ωx) 
D01AP  nagf_quad_1d_fin_wsing Onedimensional quadrature, adaptive, finite interval, weight function with endpoint singularities of algebraicologarithmic type 
D01AQ  nagf_quad_1d_fin_wcauchy Onedimensional quadrature, adaptive, finite interval, weight function 1/(xc), Cauchy principal value (Hilbert transform) 
D01AR  nagf_quad_1d_indef Onedimensional quadrature, nonadaptive, finite interval with provision for indefinite integrals 
D01AS  nagf_quad_1d_inf_wtrig Onedimensional quadrature, adaptive, semiinfinite interval, weight function cos (ωx) or sin (ωx) 
D01AT  nagf_quad_1d_fin_bad_vec Onedimensional quadrature, adaptive, finite interval, variant of D01AJ efficient on vector machines 
D01AU  nagf_quad_1d_fin_osc_vec Onedimensional quadrature, adaptive, finite interval, variant of D01AK efficient on vector machines 
D01BC  nagf_quad_1d_gauss_wgen Calculation of weights and abscissae for Gaussian quadrature rules, general choice of rule 
D01BD  nagf_quad_1d_fin_smooth Onedimensional quadrature, nonadaptive, finite interval 
D01DA  nagf_quad_2d_fin Twodimensional quadrature, finite region 
D01EA  nagf_quad_md_adapt_multi Multidimensional adaptive quadrature over hyperrectangle, multiple integrands 
D01ES  nagf_quad_md_sgq_multi_vec Multidimensional quadrature using sparse grids 
D01FB  nagf_quad_md_gauss Multidimensional Gaussian quadrature over hyperrectangle 
D01FC  nagf_quad_md_adapt Multidimensional adaptive quadrature over hyperrectangle 
D01FD  nagf_quad_md_sphere Multidimensional quadrature, Sag–Szekeres method, general product region or nsphere 
D01FD  nagf_quad_md_sphere_dummy_region dummy 
D01GA  nagf_quad_1d_data Onedimensional quadrature, integration of function defined by data values, Gill–Miller method 
D01GB  nagf_quad_md_mcarlo Multidimensional quadrature over hyperrectangle, Monte–Carlo method 
D01GC  nagf_quad_md_numth Multidimensional quadrature, general product region, numbertheoretic method 
D01GD  nagf_quad_md_numth_vec Multidimensional quadrature, general product region, numbertheoretic method, variant of D01GC efficient on vector machines 
D01GY  nagf_quad_md_numth_coeff_prime Korobov optimal coefficients for use in D01GC or D01GD, when number of points is prime 
D01GZ  nagf_quad_md_numth_coeff_2prime Korobov optimal coefficients for use in D01GC or D01GD, when number of points is product of two primes 
D01JA  nagf_quad_md_sphere_bad Multidimensional quadrature over an nsphere, allowing for badly behaved integrands 
D01PA  nagf_quad_md_simplex Multidimensional quadrature over an nsimplex 
D01RA  nagf_quad_1d_gen_vec_multi_rcomm Onedimensional quadrature, adaptive, finite interval, multiple integrands, vectorized abscissae, reverse communication 
D01RB  nagf_quad_d01rb_dummy 
D01RC  nagf_quad_1d_gen_vec_multi_dimreq Determine required array dimensions for D01RA 
D01RG  nagf_quad_1d_fin_gonnet_vec Onedimensional quadrature, adaptive, finite interval, strategy due to Gonnet, allowing for badly behaved integrands 
D01TB  nagf_quad_1d_gauss_wres Precomputed weights and abscissae for Gaussian quadrature rules, restricted choice of rule 
D01TD  nagf_quad_1d_gauss_wrec Calculation of weights and abscissae for Gaussian quadrature rules, method of Golub and Welsch 
D01TE  nagf_quad_1d_gauss_recm Generates recursion coefficients needed by D01TD to calculate a Gaussian quadrature rule 
D01UA  nagf_quad_1d_gauss_vec Onedimensional Gaussian quadrature, choice of weight functions (vectorized) 
D01UB  nagf_quad_1d_inf_exp_wt Nonautomatic routine to evaluate ∫_{0}^{∞}exp (x^{2})f(x) dx 
D01ZK  nagf_quad_opt_set Option setting routine 
D01ZL  nagf_quad_opt_get Option getting routine 
D02 D02M–N – Ordinary Differential Equations Integrators for Stiff Ordinary Differential Systems
Examples of routines and methods in this chapter.
D02AG  nagf_ode_bvp_shoot_genpar_intern Ordinary differential equations, boundary value problem, shooting and matching technique, allowing interior matching point, general parameters to be determined 
D02BG  nagf_ode_ivp_rkm_val_simple Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until a component attains given value (simple driver) 
D02BH  nagf_ode_ivp_rkm_zero_simple Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until function of solution is zero (simple driver) 
D02BJ  nagf_ode_ivp_rk_zero_simple Ordinary differential equations, initial value problem, Runge–Kutta method, until function of solution is zero, integration over range with intermediate output (simple driver) 
D02CJ  nagf_ode_ivp_adams_zero_simple Ordinary differential equations, initial value problem, Adams' method, until function of solution is zero, intermediate output (simple driver) 
D02EJ  nagf_ode_ivp_bdf_zero_simple Ordinary differential equations, stiff initial value problem, backward differentiation formulae method, until function of solution is zero, intermediate output (simple driver) 
D02GA  nagf_ode_bvp_fd_nonlin_fixedbc Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem 
D02GA  nagf_ode_bvp_fd_nonlin_gen_dummy_jacobf dummy 
D02GA  nagf_ode_bvp_fd_nonlin_gen_dummy_jacobg dummy 
D02GA  nagf_ode_bvp_fd_nonlin_gen_dummy_jaceps dummy 
D02GA  nagf_ode_bvp_fd_nonlin_gen_dummy_jacgep dummy 
D02GB  nagf_ode_bvp_fd_lin_gen Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, general linear problem 
D02HA  nagf_ode_bvp_shoot_bval Ordinary differential equations, boundary value problem, shooting and matching, boundary values to be determined 
D02HB  nagf_ode_bvp_shoot_genpar Ordinary differential equations, boundary value problem, shooting and matching, general parameters to be determined 
D02HB  nagf_ode_bvp_shoot_genpar_algeq_dummy_prsol dummy 
D02HB  nagf_ode_bvp_shoot_genpar_algeq_dummy_eqn dummy 
D02JA  nagf_ode_bvp_coll_nth Ordinary differential equations, boundary value problem, collocation and least squares, single nthorder linear equation 
D02JB  nagf_ode_bvp_coll_sys Ordinary differential equations, boundary value problem, collocation and least squares, system of firstorder linear equations 
D02KA  nagf_ode_sl2_reg_finite Secondorder Sturm–Liouville problem, regular system, finite range, eigenvalue only 
D02KA  nagf_ode_sl2_reg_finite_dummy_monit dummy 
D02KD  nagf_ode_sl2_breaks_vals Secondorder Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, userspecified breakpoints 
D02KE  nagf_ode_sl2_breaks_funs Secondorder Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, userspecified breakpoints 
D02LA  nagf_ode_ivp_2nd_rkn Secondorder ordinary differential equations, initial value problem, Runge–Kutta–Nystrom method 
D02LX  nagf_ode_ivp_2nd_rkn_setup Secondorder ordinary differential equations, initial value problem, setup for D02LA 
D02LY  nagf_ode_ivp_2nd_rkn_diag Secondorder ordinary differential equations, initial value problem, diagnostics for D02LA 
D02LZ  nagf_ode_ivp_2nd_rkn_interp Secondorder ordinary differential equations, initial value problem, interpolation for D02LA 
D02MC  nagf_ode_dae_dassl_cont Implicit ordinary differential equations/DAEs, initial value problem, DASSL method continuation for D02NE 
D02MV  nagf_ode_ivp_stiff_dassl Ordinary differential equations, initial value problem, DASSL method, setup for D02M–N routines 
D02MW  nagf_ode_dae_dassl_setup Implicit ordinary differential equations/DAEs, initial value problem, setup for D02NE 
D02MZ  nagf_ode_ivp_stiff_interp Ordinary differential equations, initial value problem, interpolation for D02M–N routines (all integration methods), natural interpolant 
D02NB  nagf_ode_ivp_stiff_exp_fulljac Explicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive) 
D02NB  nagf_ode_ivp_stiff_exp_fulljac_dummy_monit dummy 
D02NB  nagf_ode_ivp_stiff_exp_fulljac_dummy_jac dummy 
D02NC  nagf_ode_ivp_stiff_exp_bandjac Explicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive) 
D02NC  nagf_ode_ivp_stiff_exp_bandjac_dummy_jac dummy 
D02ND  nagf_ode_ivp_stiff_exp_sparjac Explicit ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive) 
D02ND  nagf_ode_ivp_stiff_exp_sparjac_dummy_jac dummy 
D02NE  nagf_ode_dae_dassl_gen Implicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator 
D02NE  nagf_ode_dae_dassl_gen_dummy_jac dummy 
D02NG  nagf_ode_ivp_stiff_imp_fulljac Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive) 
D02NG  nagf_ode_ivp_stiff_imp_fulljac_dummy_jac dummy 
D02NH  nagf_ode_ivp_stiff_imp_bandjac Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive) 
D02NH  nagf_ode_ivp_stiff_imp_bandjac_dummy_jac dummy 
D02NJ  nagf_ode_ivp_stiff_imp_sparjac Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive) 
D02NJ  nagf_ode_ivp_stiff_imp_sparjac_dummy_jac dummy 
D02NM  nagf_ode_ivp_stiff_exp_revcom Explicit ordinary differential equations, stiff initial value problem (reverse communication, comprehensive) 
D02NN  nagf_ode_ivp_stiff_imp_revcom Implicit/algebraic ordinary differential equations, stiff initial value problem (reverse communication, comprehensive) 
D02NP  nagf_ode_dae_dassl_linalg Implicit ordinary differential equations/DAEs, initial value problem linear algebra setup routine for D02NE 
D02NR  nagf_ode_ivp_stiff_sparjac_enq Ordinary differential equations, initial value problem, for use with D02M–N routines, sparse Jacobian, enquiry routine 
D02NS  nagf_ode_ivp_stiff_fulljac_setup Ordinary differential equations, initial value problem, for use with D02M–N routines, full Jacobian, linear algebra set up 
D02NT  nagf_ode_ivp_stiff_bandjac_setup Ordinary differential equations, initial value problem, for use with D02M–N routines, banded Jacobian, linear algebra set up 
D02NU  nagf_ode_ivp_stiff_sparjac_setup Ordinary differential equations, initial value problem, for use with D02M–N routines, sparse Jacobian, linear algebra set up 
D02NV  nagf_ode_ivp_stiff_bdf Ordinary differential equations, initial value problem, backward differentiation formulae method, setup for D02M–N routines 
D02NW  nagf_ode_ivp_stiff_blend Ordinary differential equations, initial value problem, Blend method, setup for D02M–N routines 
D02NX  nagf_ode_ivp_stiff_sparjac_diag Ordinary differential equations, initial value problem, sparse Jacobian, linear algebra diagnostics, for use with D02M–N routines 
D02NY  nagf_ode_ivp_stiff_integ_diag Ordinary differential equations, initial value problem, integrator diagnostics, for use with D02M–N routines 
D02NZ  nagf_ode_ivp_stiff_contin Ordinary differential equations, initial value problem, setup for continuation calls to integrator, for use with D02M–N routines 
D02PE  nagf_ode_ivp_rkts_range Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output 
D02PF  nagf_ode_ivp_rkts_onestep Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step 
D02PG  nagf_ode_ivp_rk_step_revcomm Ordinary differential equations, initial value problem, Runge–Kutta method, integration by reverse communication 
D02PH  nagf_ode_ivp_rk_interp_setup Set up interpolant by reverse communication for solution and derivative evaluations at points within the range of the last integration step taken by D02PG 
D02PJ  nagf_ode_ivp_rk_interp_eval Evaluate interpolant, set up using D02PQ, to approximate solution and/or solution derivatives at a point within the range of the last integration step taken by D02PG 
D02PQ  nagf_ode_ivp_rkts_setup Ordinary differential equations, initial value problem, setup for D02PE and D02PF 
D02PR  nagf_ode_ivp_rkts_reset_tend Ordinary differential equations, initial value problem, resets end of range for D02PF 
D02PS  nagf_ode_ivp_rkts_interp Ordinary differential equations, initial value problem, interpolation for D02PF 
D02PT  nagf_ode_ivp_rkts_diag Ordinary differential equations, initial value problem, integration diagnostics for D02PE and D02PF 
D02PU  nagf_ode_ivp_rkts_errass Ordinary differential equations, initial value problem, error assessment diagnostics for D02PE and D02PF 
D02QF  nagf_ode_ivp_adams_roots Ordinary differential equations, initial value problem, Adams' method with rootfinding (direct communication, comprehensive) 
D02QG  nagf_ode_ivp_adams_roots_revcom Ordinary differential equations, initial value problem, Adams' method with rootfinding (reverse communication, comprehensive) 
D02QW  nagf_ode_ivp_adams_setup Ordinary differential equations, initial value problem, setup for D02QF and D02QG 
D02QX  nagf_ode_ivp_adams_diag Ordinary differential equations, initial value problem, diagnostics for D02QF and D02QG 
D02QY  nagf_ode_ivp_adams_rootdiag Ordinary differential equations, initial value problem, rootfinding diagnostics for D02QF and D02QG 
D02QZ  nagf_ode_ivp_adams_interp Ordinary differential equations, initial value problem, interpolation for D02QF or D02QG 
D02RA  nagf_ode_bvp_fd_nonlin_gen Ordinary differential equations, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility 
D02SA  nagf_ode_bvp_shoot_genpar_algeq Ordinary differential equations, boundary value problem, shooting and matching technique, subject to extra algebraic equations, general parameters to be determined 
D02SA  nagf_ode_bvp_shoot_genpar_algeq_dummy_monit dummy 
D02TG  nagf_ode_bvp_coll_nth_comp nthorder linear ordinary differential equations, boundary value problem, collocation and least squares 
D02TL  nagf_ode_bvp_coll_nlin_solve Ordinary differential equations, general nonlinear boundary value problem, collocation technique (thread safe) 
D02TV  nagf_ode_bvp_coll_nlin_setup Ordinary differential equations, general nonlinear boundary value problem, setup for D02TL 
D02TX  nagf_ode_bvp_coll_nlin_contin Ordinary differential equations, general nonlinear boundary value problem, continuation facility for D02TL 
D02TY  nagf_ode_bvp_coll_nlin_interp Ordinary differential equations, general nonlinear boundary value problem, interpolation for D02TL 
D02TZ  nagf_ode_bvp_coll_nlin_diag Ordinary differential equations, general nonlinear boundary value problem, diagnostics for D02TL 
D02UA  nagf_ode_bvp_ps_lin_coeffs Coefficients of Chebyshev interpolating polynomial from function values on Chebyshev grid 
D02UB  nagf_ode_bvp_ps_lin_cgl_vals Function or loworderderivative values on Chebyshev grid from coefficients of Chebyshev interpolating polynomial 
D02UC  nagf_ode_bvp_ps_lin_cgl_grid Chebyshev Gauss–Lobatto grid generation 
D02UD  nagf_ode_bvp_ps_lin_cgl_deriv Differentiate a function by the FFT using function values on Chebyshev grid 
D02UE  nagf_ode_bvp_ps_lin_solve Solve linear constant coefficient boundary value problem on Chebyshev grid, Integral formulation 
D02UW  nagf_ode_bvp_ps_lin_grid_vals Interpolate a function from Chebyshev grid to uniform grid using barycentric Lagrange interpolation 
D02UY  nagf_ode_bvp_ps_lin_quad_weights Clenshaw–Curtis quadrature weights for integration using computed Chebyshev coefficients 
D02UZ  nagf_ode_bvp_ps_lin_cheb_eval Chebyshev polynomial evaluation, T_{k}(x) 
D02XJ  nagf_ode_ivp_stiff_nat_interp Ordinary differential equations, initial value problem, interpolation for D02M–N routines (BLEND and BDF methods only), natural interpolant 
D02XK  nagf_ode_ivp_stiff_c1_interp Ordinary differential equations, initial value problem, interpolation for D02M–N routines, C^{1} interpolant 
D02ZA  nagf_ode_ivp_stiff_errest Ordinary differential equations, initial value problem, weighted norm of local error estimate for D02M–N routines 
D03 – Partial Differential Equations
Examples of routines and methods in this chapter.
D03EA  nagf_pde_2d_laplace Elliptic PDE, Laplace's equation, twodimensional arbitrary domain 
D03EB  nagf_pde_2d_ellip_fd Elliptic PDE, solution of finite difference equations by SIP, fivepoint twodimensional molecule, iterate to convergence 
D03EC  nagf_pde_3d_ellip_fd Elliptic PDE, solution of finite difference equations by SIP for sevenpoint threedimensional molecule, iterate to convergence 
D03ED  nagf_pde_2d_ellip_mgrid Elliptic PDE, solution of finite difference equations by a multigrid technique 
D03EE  nagf_pde_2d_ellip_discret Discretize a secondorder elliptic PDE on a rectangle 
D03FA  nagf_pde_3d_ellip_helmholtz Elliptic PDE, Helmholtz equation, threedimensional Cartesian coordinates 
D03MA  nagf_pde_2d_triangulate Triangulation of plane region 
D03NC  nagf_pde_1d_blackscholes_fd Finite difference solution of the Black–Scholes equations 
D03ND  nagf_pde_1d_blackscholes_closed Analytic solution of the Black–Scholes equations 
D03NE  nagf_pde_1d_blackscholes_means Compute average values for D03ND 
D03PC  nagf_pde_1d_parab_fd_old General system of parabolic PDEs, method of lines, finite differences, one space variable 
D03PC  nagf_pde_1d_parab_remesh_fd_dummy_odedef_old dummy 
D03PC  nagf_pde_1d_parab_remesh_fd_dummy_monitf_old dummy 
D03PD  nagf_pde_1d_parab_coll_old General system of parabolic PDEs, method of lines, Chebyshev C^{0} collocation, one space variable 
D03PE  nagf_pde_1d_parab_keller General system of firstorder PDEs, method of lines, Keller box discretization, one space variable 
D03PE  nagf_pde_1d_parab_dae_keller_remesh_fd_dummy_odedef dummy 
D03PE  nagf_pde_1d_parab_dae_keller_remesh_fd_dummy_monitf dummy 
D03PF  nagf_pde_1d_parab_convdiff General system of convectiondiffusion PDEs with source terms in conservative form, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable 
D03PH  nagf_pde_1d_parab_dae_fd_old General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable 
D03PJ  nagf_pde_1d_parab_dae_coll_old General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C^{0} collocation, one space variable 
D03PK  nagf_pde_1d_parab_dae_keller General system of firstorder PDEs, coupled DAEs, method of lines, Keller box discretization, one space variable 
D03PL  nagf_pde_1d_parab_convdiff_dae General system of convectiondiffusion PDEs with source terms in conservative form, coupled DAEs, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable 
D03PP  nagf_pde_1d_parab_remesh_fd_old General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable 
D03PR  nagf_pde_1d_parab_remesh_keller General system of firstorder PDEs, coupled DAEs, method of lines, Keller box discretization, remeshing, one space variable 
D03PS  nagf_pde_1d_parab_convdiff_remesh General system of convectiondiffusion PDEs, coupled DAEs, method of lines, upwind scheme, remeshing, one space variable 
D03PU  nagf_pde_1d_parab_euler_roe Roe's approximate Riemann solver for Euler equations in conservative form, for use with D03PF, D03PL and D03PS 
D03PV  nagf_pde_1d_parab_euler_osher Osher's approximate Riemann solver for Euler equations in conservative form, for use with D03PF, D03PL and D03PS 
D03PW  nagf_pde_1d_parab_euler_hll Modified HLL Riemann solver for Euler equations in conservative form, for use with D03PF, D03PL and D03PS 
D03PX  nagf_pde_1d_parab_euler_exact Exact Riemann solver for Euler equations in conservative form, for use with D03PF, D03PL and D03PS 
D03PY  nagf_pde_1d_parab_coll_interp PDEs, spatial interpolation with D03PD or D03PJ 
D03PZ  nagf_pde_1d_parab_fd_interp PDEs, spatial interpolation with D03PC, D03PE, D03PF, D03PH, D03PK, D03PL, D03PP, D03PR or D03PS 
D03RA  nagf_pde_2d_gen_order2_rectangle General system of secondorder PDEs, method of lines, finite differences, remeshing, two space variables, rectangular region 
D03RB  nagf_pde_2d_gen_order2_rectilinear General system of secondorder PDEs, method of lines, finite differences, remeshing, two space variables, rectilinear region 
D03RZ  nagf_pde_2d_gen_order2_rectilinear_extractgrid Extract grid data from D03RB 
D03UA  nagf_pde_2d_ellip_fd_iter Elliptic PDE, solution of finite difference equations by SIP, fivepoint twodimensional molecule, one iteration 
D03UB  nagf_pde_3d_ellip_fd_iter Elliptic PDE, solution of finite difference equations by SIP, sevenpoint threedimensional molecule, one iteration 
D04 – Numerical Differentiation
Examples of routines and methods in this chapter.
D04AA  nagf_numdiff Numerical differentiation, derivatives up to order 14, function of one real variable 
D04BA  nagf_numdiff_rcomm Numerical differentiation, usersupplied function values, derivatives up to order 14, derivatives with respect to one real variable 
D04BB  nagf_numdiff_sample Generates sample points for function evaluations by D04BA 
D05 – Integral Equations
Examples of routines and methods in this chapter.
D05AA  nagf_inteq_fredholm2_split Linear nonsingular Fredholm integral equation, second kind, split kernel 
D05AB  nagf_inteq_fredholm2_smooth Linear nonsingular Fredholm integral equation, second kind, smooth kernel 
D05BA  nagf_inteq_volterra2 Nonlinear Volterra convolution equation, second kind 
D05BD  nagf_inteq_abel2_weak Nonlinear convolution Volterra–Abel equation, second kind, weakly singular 
D05BE  nagf_inteq_abel1_weak Nonlinear convolution Volterra–Abel equation, first kind, weakly singular 
D05BW  nagf_inteq_volterra_weights Generate weights for use in solving Volterra equations 
D05BY  nagf_inteq_abel_weak_weights Generate weights for use in solving weakly singular Abeltype equations 
D06 – Mesh Generation
Examples of routines and methods in this chapter.
D06AA  nagf_mesh_2d_gen_inc Generates a twodimensional mesh using a simple incremental method 
D06AB  nagf_mesh_2d_gen_delaunay Generates a twodimensional mesh using a Delaunay–Voronoi process 
D06AC  nagf_mesh_2d_gen_front Generates a twodimensional mesh using an Advancingfront method 
D06BA  nagf_mesh_2d_gen_boundary Generates a boundary mesh 
D06CA  nagf_mesh_2d_smooth_bary Uses a barycentering technique to smooth a given mesh 
D06CB  nagf_mesh_2d_sparsity Generates a sparsity pattern of a Finite Element matrix associated with a given mesh 
D06CC  nagf_mesh_2d_renumber Renumbers a given mesh using Gibbs method 
D06DA  nagf_mesh_2d_transform_affine Generates a mesh resulting from an affine transformation of a given mesh 
D06DB  nagf_mesh_2d_join Joins together two given adjacent (possibly overlapping) meshes 
E01 – Interpolation
Examples of routines and methods in this chapter.
E01AA  nagf_interp_1d_aitken Interpolated values, Aitken's technique, unequally spaced data, one variable 
E01AB  nagf_interp_1d_everett Interpolated values, Everett's formula, equally spaced data, one variable 
E01AE  nagf_interp_1d_cheb Interpolating functions, polynomial interpolant, data may include derivative values, one variable 
E01BA  nagf_interp_1d_spline Interpolating functions, cubic spline interpolant, one variable 
E01BE  nagf_interp_1d_monotonic Interpolating functions, monotonicitypreserving, piecewise cubic Hermite, one variable 
E01BF  nagf_interp_1d_monotonic_eval Interpolated values, interpolant computed by E01BE, function only, one variable 
E01BG  nagf_interp_1d_monotonic_deriv Interpolated values, interpolant computed by E01BE, function and first derivative, one variable 
E01BH  nagf_interp_1d_monotonic_intg Interpolated values, interpolant computed by E01BE, definite integral, one variable 
E01DA  nagf_interp_2d_spline_grid Interpolating functions, fitting bicubic spline, data on rectangular grid 
E01EA  nagf_interp_2d_triangulate Triangulation of twodimensional scattered grid, method of Renka and Cline 
E01EB  nagf_interp_2d_triang_bary_eval Barycentric interpolation on function values provided on a twodimensional scattered grid 
E01RA  nagf_interp_1d_ratnl Interpolating functions, rational interpolant, one variable 
E01RB  nagf_interp_1d_ratnl_eval Interpolated values, evaluate rational interpolant computed by E01RA, one variable 
E01SA  nagf_interp_2d_scat Interpolating functions, method of Renka and Cline, two variables 
E01SB  nagf_interp_2d_scat_eval Interpolated values, evaluate interpolant computed by E01SA, two variables 
E01SG  nagf_interp_2d_scat_shep Interpolating functions, modified Shepard's method, two variables 
E01SH  nagf_interp_2d_scat_shep_eval Interpolated values, evaluate interpolant computed by E01SG, function and first derivatives, two variables 
E01TG  nagf_interp_3d_scat_shep Interpolating functions, modified Shepard's method, three variables 
E01TH  nagf_interp_3d_scat_shep_eval Interpolated values, evaluate interpolant computed by E01TG, function and first derivatives, three variables 
E01TK  nagf_interp_4d_scat_shep Interpolating functions, modified Shepard's method, four variables 
E01TL  nagf_interp_4d_scat_shep_eval Interpolated values, evaluate interpolant computed by E01TK, function and first derivatives, four variables 
E01TM  nagf_interp_5d_scat_shep Interpolating functions, modified Shepard's method, five variables 
E01TN  nagf_interp_5d_scat_shep_eval Interpolated values, evaluate interpolant computed by E01TM, function and first derivatives, five variables 
E01ZM  nagf_interp_nd_scat_shep Interpolating function, modified Shepard's method, d dimensions 
E01ZN  nagf_interp_nd_scat_shep_eval Interpolated values, evaluate interpolant computed by E01ZM, function and first derivatives, d dimensions 
E02 – Curve and Surface Fitting
Examples of routines and methods in this chapter.
E02AD  nagf_fit_1dcheb_arb Least squares curve fit, by polynomials, arbitrary data points 
E02AE  nagf_fit_1dcheb_eval Evaluation of fitted polynomial in one variable from Chebyshev series form (simplified parameter list) 
E02AF  nagf_fit_1dcheb_glp Least squares polynomial fit, special data points (including interpolation) 
E02AG  nagf_fit_1dcheb_con Least squares polynomial fit, values and derivatives may be constrained, arbitrary data points 
E02AH  nagf_fit_1dcheb_deriv Derivative of fitted polynomial in Chebyshev series form 
E02AJ  nagf_fit_1dcheb_integ Integral of fitted polynomial in Chebyshev series form 
E02AK  nagf_fit_1dcheb_eval2 Evaluation of fitted polynomial in one variable from Chebyshev series form 
E02AL  nagf_1d_minimax_polynomial Minimax curve fit by polynomials 
E02BA  nagf_fit_1dspline_knots Least squares curve cubic spline fit (including interpolation) 
E02BB  nagf_fit_1dspline_eval Evaluation of fitted cubic spline, function only 
E02BC  nagf_fit_1dspline_deriv Evaluation of fitted cubic spline, function and derivatives 
E02BD  nagf_fit_1dspline_integ Evaluation of fitted cubic spline, definite integral 
E02BE  nagf_fit_1dspline_auto Least squares cubic spline curve fit, automatic knot placement 
E02BF  nagf_fit_1dspline_deriv_vector Evaluation of fitted cubic spline, function and optionally derivatives at a vector of points 
E02CA  nagf_fit_2dcheb_lines Least squares surface fit by polynomials, data on lines parallel to one independent coordinate axis 
E02CB  nagf_fit_2dcheb_eval Evaluation of fitted polynomial in two variables 
E02DA  nagf_fit_2dspline_panel Least squares surface fit, bicubic splines 
E02DC  nagf_fit_2dspline_grid Least squares surface fit by bicubic splines with automatic knot placement, data on rectangular grid 
E02DD  nagf_fit_2dspline_sctr Least squares surface fit by bicubic splines with automatic knot placement, scattered data 
E02DE  nagf_fit_2dspline_evalv Evaluation of fitted bicubic spline at a vector of points 
E02DF  nagf_fit_2dspline_evalm Evaluation of fitted bicubic spline at a mesh of points 
E02DH  nagf_fit_2dspline_derivm Evaluation of spline surface at mesh of points with derivatives 
E02GA  nagf_fit_glin_l1sol L_{1}approximation by general linear function 
E02GB  nagf_fit_glinc_l1sol L_{1}approximation by general linear function subject to linear inequality constraints 
E02GC  nagf_fit_glin_linf L_{∞}approximation by general linear function 
E02JD  nagf_fit_2dspline_ts_sctr Spline approximation to a set of scattered data using a twostage approximation method 
E02JE  nagf_fit_2dspline_ts_evalv Evaluation at a vector of points of a spline computed by E02JD 
E02JF  nagf_fit_2dspline_ts_evalm Evaluation at a mesh of points of a spline computed by E02JD 
E02RA  nagf_fit_pade_app Padé approximants 
E02RB  nagf_fit_pade_eval Evaluation of fitted rational function as computed by E02RA 
E02ZA  nagf_fit_2dspline_sort Sort twodimensional data into panels for fitting bicubic splines 
E02ZK  nagf_fit_opt_set Option setting routine 
E02ZL  nagf_fit_opt_get Option getting routine 
E04 – Minimizing or Maximizing a Function
Examples of routines and methods in this chapter.
E04AB  nagf_opt_one_var_func_old Minimum, function of one variable, using function values only 
E04BB  nagf_opt_one_var_deriv_old Minimum, function of one variable, using first derivative 
E04CB  nagf_opt_uncon_simplex Unconstrained minimum, Nelder–Mead simplex algorithm, using function values only 
E04CB  nagf_opt_uncon_simplex_dummy_monit 
E04DG  nagf_opt_uncon_conjgrd_comp_old Unconstrained minimum, preconditioned conjugate gradient algorithm, using first derivatives (comprehensive) 
E04DJ  nagf_opt_uncon_conjgrd_option_file_old Supply optional parameter values for E04DG from external file 
E04DK  nagf_opt_uncon_conjgrd_option_string_old Supply optional parameter values to E04DG from a character string 
E04FC  nagf_opt_lsq_uncon_mod_func_comp Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (comprehensive) 
E04FD  nagf_opt_lsq_dummy_lsqmon dummy 
E04FY  nagf_opt_lsq_uncon_mod_func_easy Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (easytouse) 
E04GB  nagf_opt_lsq_uncon_quasi_deriv_comp Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasiNewton algorithm, using first derivatives (comprehensive) 
E04GD  nagf_opt_lsq_uncon_mod_deriv_comp Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (comprehensive) 
E04GY  nagf_opt_lsq_uncon_quasi_deriv_easy Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasiNewton algorithm, using first derivatives (easytouse) 
E04GZ  nagf_opt_lsq_uncon_mod_deriv_easy Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (easytouse) 
E04HC  nagf_opt_check_deriv Check user's routine for calculating first derivatives of function 
E04HD  nagf_opt_check_deriv2 Check user's routine for calculating second derivatives of function 
E04HE  nagf_opt_lsq_uncon_mod_deriv2_comp Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (comprehensive) 
E04HY  nagf_opt_lsq_uncon_mod_deriv2_easy Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (easytouse) 
E04JC  nagf_opt_bounds_bobyqa_func Bound constrained minimum, modelbased algorithm, using function values only 
E04JY  nagf_opt_bounds_quasi_func_easy Bound constrained minimum, quasiNewton algorithm, using function values only (easytouse) 
E04KD  nagf_opt_bounds_mod_deriv_comp Bound constrained minimum, modified Newton algorithm, using first derivatives (comprehensive) 
E04KY  nagf_opt_bounds_quasi_deriv_easy Bound constrained minimum, quasiNewton algorithm, using first derivatives (easytouse) 
E04KZ  nagf_opt_bounds_mod_deriv_easy Bound constrained minimum, modified Newton algorithm, using first derivatives (easytouse) 
E04LB  nagf_opt_bounds_mod_deriv2_comp Bound constrained minimum, modified Newton algorithm, using first and second derivatives (comprehensive) 
E04LY  nagf_opt_bounds_mod_deriv2_easy Bound constrained minimum, modified Newton algorithm, using first and second derivatives (easytouse) 
E04MF  nagf_opt_lp_solve_old Linear programming (LP), dense, activeset method 
E04MG  nagf_opt_lp_option_file_old Supply optional parameter values for E04MF from external file 
E04MH  nagf_opt_lp_option_string_old Supply optional parameter values to E04MF from a character string 
E04MW  nagf_opt_miqp_mps_write Write MPS data file defining LP, QP, MILP or MIQP problem 
E04MX  nagf_opt_miqp_mps_read Read MPS data file defining LP, QP, MILP or MIQP problem 
E04MZ  nagf_opt_qpconvex1_sparse_mps Read MPS data file defining LP or QP problem, deprecated 
E04NC  nagf_opt_lsq_lincon_solve_old Linear programming (LP) convex quadratic programming (QP) or linearlyconstrained linear least squares problem, dense 
E04ND  nagf_opt_lsq_lincon_option_file_old Supply optional parameter values for E04NC from external file 
E04NE  nagf_opt_lsq_lincon_option_string_old Supply optional parameter values to E04NC from a character string 
E04NF  nagf_opt_qp_dense_solve_old General (possibly nonconvex) quadratic programming (QP) , dense, activeset method 
E04NG  nagf_opt_qp_dense_option_file_old Supply optional parameter values for E04NF from external file 
E04NH  nagf_opt_qp_dense_option_string_old Supply optional parameter values to E04NF from a character string 
E04NK  nagf_opt_qpconvex1_sparse_solve_old Linear programming (LP) or convex quadratic programming (QP), sparse, activeset method 
E04NK  nagf_opt_qpconvex1_sparse_dummy_qphx_old dummy 
E04NL  nagf_opt_qpconvex1_sparse_option_file_old Supply optional parameter values for E04NK from external file 
E04NM  nagf_opt_qpconvex1_sparse_option_string_old Supply optional parameter values to E04NK from a character string 
E04NP  nagf_opt_qpconvex2_sparse_init Initialization routine for E04NQ 
E04NQ  nagf_opt_qpconvex2_sparse_solve Linear programming (LP) or convex quadratic programming (QP), sparse, activeset method, recommended 
E04NR  nagf_opt_qpconvex2_sparse_option_file Supply optional parameter values for E04NQ from external file 
E04NS  nagf_opt_qpconvex2_sparse_option_string Set a single option for E04NQ from a character string 
E04NS  nagf_opt_qpconvex2_sparse_dummy_qphx dummy 
E04NT  nagf_opt_qpconvex2_sparse_option_integer_set Set a single option for E04NQ from an integer argument 
E04NU  nagf_opt_qpconvex2_sparse_option_double_set Set a single option for E04NQ from a real argument 
E04NX  nagf_opt_qpconvex2_sparse_option_integer_get Get the setting of an integer valued option of E04NQ 
E04NY  nagf_opt_qpconvex2_sparse_option_double_get Get the setting of a real valued option of E04NQ 
E04PC  nagf_opt_bnd_lin_lsq Computes the least squares solution to a set of linear equations subject to fixed upper and lower bounds on the variables. An option is provided to return a minimal length solution if a solution is not unique 
E04RA  nagf_opt_handle_init Initialization of a handle for the NAG optimization modelling suite for problems, such as, quadratic programming (QP), nonlinear programming (NLP), linear semidefinite programming (SDP) or SDP with bilinear matrix inequalities (BMISDP) 
E04RD  nagf_opt_sdp_read_sdpa A reader of sparse SDPA data files for linear SDP problems 
E04RE  nagf_opt_handle_set_linobj Define a linear objective function to a problem initialized by E04RA 
E04RF  nagf_opt_handle_set_quadobj Define a linear or a quadratic objective function to a problem initialized by E04RA 
E04RG  nagf_opt_handle_set_nlnobj Define a nonlinear objective function to a problem initialized by E04RA 
E04RH  nagf_opt_handle_set_simplebounds Define bounds of variables of a problem initialized by E04RA 
E04RJ  nagf_opt_handle_set_linconstr Define a block of linear constraints to a problem initialized by E04RA 
E04RK  nagf_opt_handle_set_nlnconstr Define a block of nonlinear constraints to a problem initialized by E04RA 
E04RL  nagf_opt_handle_set_nlnhess Define a structure of Hessian of the objective, constraints or the Lagrangian to a problem initialized by E04RA 
E04RN  nagf_opt_handle_set_linmatineq Add one or more linear matrix inequality constraints to a problem initialized by E04RA 
E04RP  nagf_opt_handle_set_quadmatineq Define bilinear matrix terms to a problem initialized by E04RA 
E04RY  nagf_opt_handle_print Print information about a problem handle initialized by E04RA 
E04RZ  nagf_opt_handle_free Destroy the problem handle initialized by E04RA and deallocate all the memory used 
E04ST  nagf_opt_handle_solve_ipopt Run an interior point solver on a sparse nonlinear programming problem (NLP) initialized by E04RA and defined by other routines from the suite 
E04ST  nagf_opt_ipopt_dummy_mon dummy 
E04ST  nagf_opt_ipopt_dummy_objfun dummy 
E04ST  nagf_opt_ipopt_dummy_objgrd dummy 
E04ST  nagf_opt_ipopt_dummy_confun dummy 
E04ST  nagf_opt_ipopt_dummy_congrd dummy 
E04ST  nagf_opt_ipopt_dummy_hess dummy 
E04SV  nagf_opt_handle_solve_pennon Run the Pennon solver on a compatible problem initialized by E04RA and defined by other routines from the suite, such as, semidefinite programming (SDP) and SDP with bilinear matrix inequalities (BMI) 
E04UC  nagf_opt_nlp1_solve_old Nonlinear programming (NLP), dense, activeset SQP method, using function values and optionally first derivatives, recommended 
E04UD  nagf_opt_nlp1_option_file_old Supply optional parameter values for E04UC or E04UF from external file 
E04UD  nagf_opt_nlp1_dummy_confun dummy 
E04UE  nagf_opt_nlp1_option_string_old Supply optional parameter values to E04UC or E04UF from a character string 
E04UF  nagf_opt_nlp1_rcomm_old Nonlinear programming (NLP), dense, activeset, SQP method, using function values and optionally first derivatives (reverse communication, comprehensive) 
E04UG  nagf_opt_nlp1_sparse_solve_old Nonlinear programming (NLP), sparse, activeset SQP method, using function values and optionally first derivatives 
E04UG  nagf_opt_nlp1_sparse_dummy_confun dummy 
E04UG  nagf_opt_nlp1_sparse_dummy_objfun dummy 
E04UH  nagf_opt_nlp1_sparse_option_file_old Supply optional parameter values for E04UG from external file 
E04UJ  nagf_opt_nlp1_sparse_option_string_old Supply optional parameter values to E04UG from a character string 
E04UQ  nagf_opt_lsq_gencon_deriv_option_file_old Supply optional parameter values for E04US from external file 
E04UR  nagf_opt_lsq_gencon_deriv_option_string_old Supply optional parameter values to E04US from a character string 
E04US  nagf_opt_lsq_gencon_deriv_old Minimum of a sum of squares, nonlinear constraints, dense, activeset SQP method, using function values and optionally first derivatives 
E04VG  nagf_opt_nlp2_sparse_init Initialization routine for E04VH 
E04VH  nagf_opt_nlp2_sparse_solve Nonlinear programming (NLP), sparse, activeset SQP method, using function values and optionally first derivatives, recommended 
E04VJ  nagf_opt_nlp2_sparse_jacobian Determine the pattern of nonzeros in the Jacobian matrix for E04VH 
E04VK  nagf_opt_nlp2_sparse_option_file Supply optional parameter values for E04VH from external file 
E04VL  nagf_opt_nlp2_sparse_option_string Set a single option for E04VH from a character string 
E04VM  nagf_opt_nlp2_sparse_option_integer_set Set a single option for E04VH from an integer argument 
E04VN  nagf_opt_nlp2_sparse_option_double_set Set a single option for E04VH from a real argument 
E04VR  nagf_opt_nlp2_sparse_option_integer_get Get the setting of an integer valued option of E04VH 
E04VS  nagf_opt_nlp2_sparse_option_double_get Get the setting of a real valued option of E04VH 
E04WB  nagf_opt_init Initialization routine for E04DG, E04MF, E04NC, E04NF, E04NK, E04UC, E04UF, E04UG and E04US 
E04WC  nagf_opt_nlp2_init Initialization routine for E04WD 
E04WD  nagf_opt_nlp2_solve Nonlinear programming (NLP), dense, activeset SQP method, using function values and optionally first derivatives 
E04WD  nagf_opt_nlp2_dummy_confun dummy 
E04WE  nagf_opt_nlp2_option_file Supply optional parameter values for E04WD from external file 
E04WF  nagf_opt_nlp2_option_string Set a single option for E04WD from a character string 
E04WG  nagf_opt_nlp2_option_integer_set Set a single option for E04WD from an integer argument 
E04WH  nagf_opt_nlp2_option_double_set Set a single option for E04WD from a real argument 
E04WK  nagf_opt_nlp2_option_integer_get Get the setting of an integer valued option of E04WD 
E04WL  nagf_opt_nlp2_option_double_get Get the setting of a real valued option of E04WD 
E04XA  nagf_opt_estimate_deriv_old Estimate (using numerical differentiation) gradient and/or Hessian of a function 
E04YA  nagf_opt_lsq_check_deriv Check user's routine for calculating Jacobian of first derivatives 
E04YB  nagf_opt_lsq_check_hessian Check user's routine for calculating Hessian of a sum of squares 
E04YC  nagf_opt_lsq_uncon_covariance Covariance matrix for nonlinear least squares problem (unconstrained) 
E04ZM  nagf_opt_handle_opt_set Option setting routine for the solvers from the NAG optimization modelling suite 
E04ZN  nagf_opt_handle_opt_get Option getting routine for the solvers from the NAG optimization modelling suite 
E04ZP  nagf_opt_handle_opt_set_file Option setting routine for the solvers from the NAG optimization modelling suite from external file 
E05 – Global Optimization of a Function
Examples of routines and methods in this chapter.
E05JA  nagf_glopt_bnd_mcs_init Initialization routine for E05JB 
E05JB  nagf_glopt_bnd_mcs_solve Global optimization by multilevel coordinate search, simple bounds, using function values only 
E05JC  nagf_glopt_bnd_mcs_optset_file Supply optional parameter values for E05JB from external file 
E05JD  nagf_glopt_bnd_mcs_optset_string Set a single optional parameter for E05JB from a character string 
E05JE  nagf_glopt_bnd_mcs_optset_char Set a single optional parameter for E05JB from an 'ON'/'OFF'valued character argument 
E05JF  nagf_glopt_bnd_mcs_optset_int Set a single optional parameter for E05JB from an integer argument 
E05JG  nagf_glopt_bnd_mcs_optset_real Set a single optional parameter for E05JB from a real argument 
E05JH  nagf_glopt_bnd_mcs_option_check Determine whether an optional parameter for E05JB has been set by you or not 
E05JJ  nagf_glopt_bnd_mcs_optget_char Get the setting of an 'ON'/'OFF'valued character optional parameter of E05JB 
E05JK  nagf_glopt_bnd_mcs_optget_int Get the setting of an integer valued optional parameter of E05JB 
E05JL  nagf_glopt_bnd_mcs_optget_real Get the setting of a real valued optional parameter of E05JB 
E05SA  nagf_glopt_bnd_pso Global optimization using particle swarm algorithm (PSO), bound constraints only 
E05SB  nagf_glopt_nlp_pso Global optimization using particle swarm algorithm (PSO), comprehensive 
E05SX  nagf_glopt_bnd_pso_dummy_monmod dummy 
E05SY  nagf_glopt_nlp_pso_dummy_monmod dummy 
E05UC  nagf_glopt_nlp_multistart_sqp Global optimization using multistart, nonlinear constraints 
E05UD  nagf_glopt_nlp_multistart_dcf dummy 
E05US  nagf_glopt_nlp_multistart_sqp_lsq Global optimization of a sum of squares problem using multistart, nonlinear constraints 
E05ZK  nagf_glopt_optset Option setting routine for E05SA, E05SB, E05UC and E05US 
E05ZL  nagf_glopt_optget Option getting routine for E05SA, E05SB, E05UC and E05US 
F01 – Matrix Operations, Including Inversion
Examples of routines and methods in this chapter.
F01AB  nagf_matop_real_symm_posdef_inv Inverse of real symmetric positive definite matrix using iterative refinement 
F01AD  nagf_matop_real_symm_posdef_inv_noref Inverse of real symmetric positive definite matrix 
F01BL  nagf_matop_real_gen_pseudinv Pseudoinverse and rank of real m by n matrix (m≥n) 
F01BR  nagf_matop_real_gen_sparse_lu LU factorization of real sparse matrix 
F01BS  nagf_matop_real_gen_sparse_lu_reuse LU factorization of real sparse matrix with known sparsity pattern 
F01BU  nagf_matop_real_symm_posdef_fac ULDL^{T}U^{T} factorization of real symmetric positive definite band matrix 
F01BV  nagf_matop_real_symm_posdef_geneig Reduction to standard form, generalized real symmetricdefinite banded eigenproblem 
F01CK  nagf_matop_real_gen_matmul Multiplication of real matrices 
F01CR  nagf_matop_real_gen_trans_inplace Transposition of a real matrix 
F01CT  nagf_matop_real_addsub Sum or difference of two real matrices, optional scaling and transposition 
F01CW  nagf_matop_complex_addsub Sum or difference of two complex matrices, optional scaling and transposition 
F01EC  nagf_matop_real_gen_matrix_exp Real matrix exponential 
F01ED  nagf_matop_real_symm_matrix_exp Real symmetric matrix exponential 
F01EF  nagf_matop_real_symm_matrix_fun Function of a real symmetric matrix 
F01EJ  nagf_matop_real_gen_matrix_log Real matrix logarithm 
F01EK  nagf_matop_real_gen_matrix_fun_std Exponential, sine, cosine, sinh or cosh of a real matrix (Schur–Parlett algorithm) 
F01EL  nagf_matop_real_gen_matrix_fun_num Function of a real matrix (using numerical differentiation) 
F01EM  nagf_matop_real_gen_matrix_fun_usd Function of a real matrix (using usersupplied derivatives) 
F01EN  nagf_matop_real_gen_matrix_sqrt Real matrix square root 
F01EP  nagf_matop_real_tri_matrix_sqrt Real upper quasitriangular matrix square root 
F01EQ  nagf_matop_real_gen_matrix_pow General power of a real matrix 
F01FC  nagf_matop_complex_gen_matrix_exp Complex matrix exponential 
F01FD  nagf_matop_complex_herm_matrix_exp Complex Hermitian matrix exponential 
F01FF  nagf_matop_complex_herm_matrix_fun Function of a complex Hermitian matrix 
F01FJ  nagf_matop_complex_gen_matrix_log Complex matrix logarithm 
F01FK  nagf_matop_complex_gen_matrix_fun_std Exponential, sine, cosine, sinh or cosh of a complex matrix (Schur–Parlett algorithm) 
F01FL  nagf_matop_complex_gen_matrix_fun_num Function of a complex matrix (using numerical differentiation) 
F01FM  nagf_matop_complex_gen_matrix_fun_usd Function of a complex matrix (using usersupplied derivatives) 
F01FN  nagf_matop_complex_gen_matrix_sqrt Complex matrix square root 
F01FP  nagf_matop_complex_tri_matrix_sqrt Complex upper triangular matrix square root 
F01FQ  nagf_matop_complex_gen_matrix_pow General power of a complex matrix 
F01GA  nagf_matop_real_gen_matrix_actexp Action of a real matrix exponential on a real matrix 
F01GB  nagf_matop_real_gen_matrix_actexp_rcomm Action of a real matrix exponential on a real matrix (reverse communication) 
F01HA  nagf_matop_complex_gen_matrix_actexp Action of a complex matrix exponential on a complex matrix 
F01HB  nagf_matop_complex_gen_matrix_actexp_rcomm Action of a complex matrix exponential on a complex matrix (reverse communication) 
F01JA  nagf_matop_real_gen_matrix_cond_std Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a real matrix 
F01JB  nagf_matop_real_gen_matrix_cond_num Condition number for a function of a real matrix (using numerical differentiation) 
F01JC  nagf_matop_real_gen_matrix_cond_usd Condition number for a function of a real matrix (using usersupplied derivatives) 
F01JD  nagf_matop_real_gen_matrix_cond_sqrt Condition number for square root of real matrix 
F01JE  nagf_matop_real_gen_matrix_cond_pow Condition number for real matrix power 
F01JF  nagf_matop_real_gen_matrix_frcht_pow Fréchet derivative of real matrix power 
F01JG  nagf_matop_real_gen_matrix_cond_exp Condition number for real matrix exponential 
F01JH  nagf_matop_real_gen_matrix_frcht_exp Fréchet derivative of real matrix exponential 
F01JJ  nagf_matop_real_gen_matrix_cond_log Condition number for real matrix logarithm 
F01JK  nagf_matop_real_gen_matrix_frcht_log Fréchet derivative of real matrix logarithm 
F01KA  nagf_matop_complex_gen_matrix_cond_std Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a complex matrix 
F01KB  nagf_matop_complex_gen_matrix_cond_num Condition number for a function of a complex matrix (using numerical differentiation) 
F01KC  nagf_matop_complex_gen_matrix_cond_usd Condition number for a function of a complex matrix (using usersupplied derivatives) 
F01KD  nagf_matop_complex_gen_matrix_cond_sqrt Condition number for square root of complex matrix 
F01KE  nagf_matop_complex_gen_matrix_cond_pow Condition number for complex matrix power 
F01KF  nagf_matop_complex_gen_matrix_frcht_pow Fréchet derivative of complex matrix power 
F01KG  nagf_matop_complex_gen_matrix_cond_exp Condition number for complex matrix exponential 
F01KH  nagf_matop_complex_gen_matrix_frcht_exp Fréchet derivative of complex matrix exponential 
F01KJ  nagf_matop_complex_gen_matrix_cond_log Condition number for complex matrix logarithm 
F01KK  nagf_matop_complex_gen_matrix_frcht_log Fréchet derivative of complex matrix logarithm 
F01LE  nagf_matop_real_gen_tridiag_lu LU factorization of real tridiagonal matrix 
F01LH  nagf_matop_real_gen_blkdiag_lu LU factorization of real almost block diagonal matrix 
F01MC  nagf_matop_real_vband_posdef_fac LDL^{T} factorization of real symmetric positive definite variablebandwidth matrix 
F01QG  nagf_matop_real_trapez_rq RQ factorization of real m by n upper trapezoidal matrix (m≤n) 
F01QJ  nagf_matop_real_gen_rq RQ factorization of real m by n matrix (m≤n) 
F01QK  nagf_matop_real_gen_rq_formq Operations with orthogonal matrices, form rows of Q, after RQ factorization by F01QJ 
F01RG  nagf_matop_complex_trapez_rq RQ factorization of complex m by n upper trapezoidal matrix (m≤n) 
F01RJ  nagf_matop_complex_gen_rq RQ factorization of complex m by n matrix (m≤n) 
F01RK  nagf_matop_complex_gen_rq_formq Operations with unitary matrices, form rows of Q, after RQ factorization by F01RJ 
F01VA  nagf_matop_dtrttp Copies a real triangular matrix from full format to packed format 
F01VB  nagf_matop_ztrttp Copies a complex triangular matrix from full format to packed format 
F01VC  nagf_matop_dtpttr Copies a real triangular matrix from packed format to full format 
F01VD  nagf_matop_ztpttr Copies a complex triangular matrix from packed format to full format 
F01VE  nagf_matop_dtrttf Copies a real triangular matrix from full format to Rectangular Full Packed format 
F01VF  nagf_matop_ztrttf Copies a complex triangular matrix from full format to Rectangular Full Packed format 
F01VG  nagf_matop_dtfttr Copies a real triangular matrix from Rectangular Full Packed format to full format 
F01VH  nagf_matop_ztfttr Copies a complex triangular matrix from Rectangular Full Packed format to full format 
F01VJ  nagf_matop_dtpttf Copies a real triangular matrix from packed format to Rectangular Full Packed format 
F01VK  nagf_matop_ztpttf Copies a complex triangular matrix from packed format to Rectangular Full Packed format 
F01VL  nagf_matop_dtfttp Copies a real triangular matrix from Rectangular Full Packed format to packed format 
F01VM  nagf_matop_ztfttp Copies a complex triangular matrix from Rectangular Full Packed format to packed format 
F01ZA  nagf_matop_real_tri_pack Convert real matrix between packed triangular and square storage formats 
F01ZB  nagf_matop_complex_tri_pack Convert complex matrix between packed triangular and square storage formats 
F01ZC  nagf_matop_real_band_pack Convert real matrix between packed banded and rectangular storage formats 
F01ZD  nagf_matop_complex_band_pack Convert complex matrix between packed banded and rectangular storage formats 
F02 – Eigenvalues and Eigenvectors
Examples of routines and methods in this chapter.
F02EC  nagf_eigen_real_gen_eigsys Selected eigenvalues and eigenvectors of real nonsymmetric matrix (Black Box) 
F02EK  nagf_eigen_real_gen_sparse_arnoldi Selected eigenvalues and eigenvectors of a real sparse general matrix 
F02EK  nagf_eigen_arnoldi_option dummy 
F02EK  nagf_eigen_arnoldi_monit_gen dummy 
F02FJ  nagf_eigen_real_symm_sparse_eigsys Selected eigenvalues and eigenvectors of sparse symmetric eigenproblem (Black Box) 
F02FJ  nagf_eigen_monit dummy 
F02FK  nagf_eigen_real_symm_sparse_arnoldi Selected eigenvalues and eigenvectors of a real symmetric sparse matrix 
F02FK  nagf_eigen_arnoldi_monit_symm dummy 
F02GC  nagf_eigen_complex_gen_eigsys Selected eigenvalues and eigenvectors of complex nonsymmetric matrix (Black Box) 
F02JC  nagf_eigen_real_gen_quad Solves the quadratic eigenvalue problem for real matrices 
F02JQ  nagf_eigen_complex_gen_quad Solves the quadratic eigenvalue problem for complex matrices 
F02WG  nagf_eigen_real_gen_partialsvd Computes leading terms in the singular value decomposition of a real general matrix; also computes corresponding left and right singular vectors 
F02WU  nagf_eigen_real_triang_svd SVD of real upper triangular matrix (Black Box) 
F02XU  nagf_eigen_complex_triang_svd SVD of complex upper triangular matrix (Black Box) 
F03 – Determinants
Examples of routines and methods in this chapter.
F03BA  nagf_det_real_gen Determinant of real matrix, matrix already factorized by F07AD 
F03BF  nagf_det_real_sym Determinant of real symmetric positive definite matrix 
F03BH  nagf_det_real_band_sym Determinant of real symmetric positive definite banded matrix previously factorized by F07HD 
F03BN  nagf_det_complex_gen Determinant of complex matrix previously LU factorized 
F04 – Simultaneous Linear Equations
Examples of routines and methods in this chapter.
F04AM  nagf_linsys_real_gen_lsqsol Least squares solution of m real equations in n unknowns, rank =n, m≥n using iterative refinement (Black Box) 
F04AX  nagf_linsys_real_sparse_fac_solve Solution of real sparse simultaneous linear equations (coefficient matrix already factorized) 
F04BA  nagf_linsys_real_square_solve Computes the solution, estimated condition number and errorbound to a real system of linear equations 
F04BB  nagf_linsys_real_band_solve Computes the solution, estimated condition number and errorbound to a real banded system of linear equations 
F04BC  nagf_linsys_real_tridiag_solve Computes the solution, estimated condition number and errorbound to a real tridiagonal system of linear equations 
F04BD  nagf_linsys_real_posdef_solve Computes the solution, estimated condition number and errorbound to a real symmetric positive definite system of linear equations 
F04BE  nagf_linsys_real_posdef_packed_solve Computes the solution, estimated condition number and errorbound to a real symmetric positive definite system of linear equations, packed storage 
F04BF  nagf_linsys_real_posdef_band_solve Computes the solution, estimated condition number and errorbound to a real symmetric positive definite banded system of linear equations 
F04BG  nagf_linsys_real_posdef_tridiag_solve Computes the solution, estimated condition number and errorbound to a real symmetric positive definite tridiagonal system of linear equations 
F04BH  nagf_linsys_real_symm_solve Computes the solution, estimated condition number and errorbound to a real symmetric system of linear equations 
F04BJ  nagf_linsys_real_symm_packed_solve Computes the solution, estimated condition number and errorbound to a real symmetric system of linear equations, packed storage 
F04CA  nagf_linsys_complex_square_solve Computes the solution, estimated condition number and errorbound to a complex system of linear equations 
F04CB  nagf_linsys_complex_band_solve Computes the solution, estimated condition number and errorbound to a complex banded system of linear equations 
F04CC  nagf_linsys_complex_tridiag_solve Computes the solution, estimated condition number and errorbound to a complex tridiagonal system of linear equations 
F04CD  nagf_linsys_complex_posdef_solve Computes the solution, estimated condition number and errorbound to a complex Hermitian positive definite system of linear equations 
F04CE  nagf_linsys_complex_posdef_packed_solve Computes the solution, estimated condition number and errorbound to a complex Hermitian positive definite system of linear equations, packed storage 
F04CF  nagf_linsys_complex_posdef_band_solve Computes the solution, estimated condition number and errorbound to a complex Hermitian positive definite banded system of linear equations 
F04CG  nagf_linsys_complex_posdef_tridiag_solve Computes the solution, estimated condition number and errorbound to a complex Hermitian positive definite tridiagonal system of linear equations 
F04CH  nagf_linsys_complex_herm_solve Computes the solution and errorbound to a complex Hermitian system of linear equations 
F04CJ  nagf_linsys_complex_herm_packed_solve Computes the solution, estimated condition number and errorbound to a complex Hermitian system of linear equations, packed storage 
F04DH  nagf_linsys_complex_symm_solve Computes the solution, estimated condition number and errorbound to a complex symmetric system of linear equations 
F04DJ  nagf_linsys_complex_symm_packed_solve Computes the solution, estimated condition number and errorbound to a complex symmetric system of linear equations, packed storage 
F04FE  nagf_linsys_real_toeplitz_yule Solution of the Yule–Walker equations for real symmetric positive definite Toeplitz matrix, one righthand side 
F04FF  nagf_linsys_real_toeplitz_solve Solution of real symmetric positive definite Toeplitz system, one righthand side 
F04JG  nagf_linsys_real_gen_solve Least squares (if rank =n) or minimal least squares (if rank <n) solution of m real equations in n unknowns, m≥n 
F04LE  nagf_linsys_real_tridiag_fac_solve Solution of real tridiagonal simultaneous linear equations (coefficient matrix already factorized by F01LE) 
F04LH  nagf_linsys_real_blkdiag_fac_solve Solution of real almost block diagonal simultaneous linear equations (coefficient matrix already factorized by F01LH) 
F04MC  nagf_linsys_real_posdef_vband_solve Solution of real symmetric positive definite variablebandwidth simultaneous linear equations (coefficient matrix already factorized by F01MC) 
F04ME  nagf_linsys_real_toeplitz_yule_update Update solution of the Yule–Walker equations for real symmetric positive definite Toeplitz matrix 
F04MF  nagf_linsys_real_toeplitz_update Update solution of real symmetric positive definite Toeplitz system 
F04QA  nagf_linsys_real_gen_sparse_lsqsol Sparse linear least squares problem, m real equations in n unknowns 
F04YA  nagf_linsys_real_gen_lsq_covmat Covariance matrix for linear least squares problems, m real equations in n unknowns 
F04YD  nagf_linsys_real_gen_norm_rcomm Norm estimation (for use in condition estimation), real rectangular matrix 
F04ZD  nagf_linsys_complex_gen_norm_rcomm Norm estimation (for use in condition estimation), complex rectangular matrix 
F05 – Orthogonalization
Examples of routines and methods in this chapter.
F05AA  nagf_orthog_real_gram_schmidt Gram–Schmidt orthogonalization of n vectors of order m 
F06 – Linear Algebra Support Routines
Examples of routines and methods in this chapter.
F06AA  nagf_blas_drotg Generate real plane rotation 
F06BA  nagf_blas_drotgc Generate real plane rotation, storing tangent 
F06BC  nagf_blas_dcsg Recover cosine and sine from given real tangent 
F06BE  nagf_blas_drotj Generate real Jacobi plane rotation 
F06BH  nagf_blas_drot2 Apply real similarity rotation to 2 by 2 symmetric matrix 
F06BL  nagf_blas_ddiv Compute quotient of two real scalars, with overflow flag 
F06BM  nagf_blas_dnorm Compute Euclidean norm from scaled form 
F06BN  nagf_blas_dpyth Compute square root of (a^{2}+b^{2}), real a and b 
F06BP  nagf_blas_deig2 Compute eigenvalue of 2 by 2 real symmetric matrix 
F06CA  nagf_blas_zrotgc Generate complex plane rotation, storing tangent, real cosine 
F06CB  nagf_blas_zrotgs Generate complex plane rotation, storing tangent, real sine 
F06CC  nagf_blas_zcsg Recover cosine and sine from given complex tangent, real cosine 
F06CD  nagf_blas_zcsgs Recover cosine and sine from given complex tangent, real sine 
F06CH  nagf_blas_zrot2 Apply complex similarity rotation to 2 by 2 Hermitian matrix 
F06CL  nagf_blas_zdiv Compute quotient of two complex scalars, with overflow flag 
F06DB  nagf_blas_iload Broadcast scalar into integer vector 
F06DF  nagf_blas_icopy Copy integer vector 
F06EA  nagf_blas_ddot Dot product of two real vectors 
F06EC  nagf_blas_daxpy Add scalar times real vector to real vector 
F06ED  nagf_blas_dscal Multiply real vector by scalar 
F06EF  nagf_blas_dcopy Copy real vector 
F06EG  nagf_blas_dswap Swap two real vectors 
F06EJ  nagf_blas_dnrm2 Compute Euclidean norm of real vector 
F06EK  nagf_blas_dasum Sum absolute values of real vector elements 
F06EP  nagf_blas_drot Apply real plane rotation 
F06ER  nagf_blas_ddoti Dot product of a real sparse and a full vector 
F06ET  nagf_blas_daxpyi Add scalar times real sparse vector to a full vector 
F06EU  nagf_blas_dgthr Gather real sparse vector 
F06EV  nagf_blas_dgthrz Gather and set to zero real sparse vector 
F06EW  nagf_blas_dsctr Scatter real sparse vector 
F06EX  nagf_blas_droti Apply plane rotation to a real sparse and a full vector 
F06FA  nagf_blas_dvcos Compute cosine of angle between two real vectors 
F06FB  nagf_blas_dload Broadcast scalar into real vector 
F06FC  nagf_blas_ddscl Multiply real vector by diagonal matrix 
F06FD  nagf_blas_axpzy Multiply real vector by scalar, preserving input vector 
F06FE  nagf_blas_drscl Multiply real vector by reciprocal of scalar 
F06FG  nagf_blas_dnegv Negate real vector 
F06FJ  nagf_blas_dssq Update Euclidean norm of real vector in scaled form 
F06FK  nagf_blas_dnrm2w Compute weighted Euclidean norm of real vector 
F06FL  nagf_blas_darang Elements of real vector with largest and smallest absolute value 
F06FP  nagf_blas_drots Apply real symmetric plane rotation to two vectors 
F06FQ  nagf_blas_dsrotg Generate sequence of real plane rotations 
F06FR  nagf_blas_dnhousg Generate real elementary reflection, NAG style 
F06FS  nagf_blas_dlhousg Generate real elementary reflection, LINPACK style 
F06FT  nagf_blas_dnhous Apply real elementary reflection, NAG style 
F06FU  nagf_blas_dlhous Apply real elementary reflection, LINPACK style 
F06GA  nagf_blas_zdotu Dot product of two complex vectors, unconjugated 
F06GB  nagf_blas_zdotc Dot product of two complex vectors, conjugated 
F06GC  nagf_blas_zaxpy Add scalar times complex vector to complex vector 
F06GD  nagf_blas_zscal Multiply complex vector by complex scalar 
F06GF  nagf_blas_zcopy Copy complex vector 
F06GG  nagf_blas_zswap Swap two complex vectors 
F06GR  nagf_blas_zdotui Dot product of a complex sparse and a full vector, unconjugated 
F06GS  nagf_blas_zdotci Dot product of a complex sparse and a full vector, conjugated 
F06GT  nagf_blas_zaxpyi Add scalar times complex sparse vector to a full vector 
F06GU  nagf_blas_zgthr Gather complex sparse vector 
F06GV  nagf_blas_zgthrz Gather and set to zero complex sparse vector 
F06GW  nagf_blas_zsctr Scatter complex sparse vector 
F06HB  nagf_blas_zload Broadcast scalar into complex vector 
F06HC  nagf_blas_zdscl Multiply complex vector by complex diagonal matrix 
F06HD  nagf_blas_zaxpzy Multiply complex vector by complex scalar, preserving input vector 
F06HG  nagf_blas_znegv Negate complex vector 
F06HM  nagf_blas_zrot Apply plane rotation with real cosine and complex sine 
F06HP  nagf_blas_zcrot Apply complex plane rotation 
F06HQ  nagf_blas_zsrotg Generate sequence of complex plane rotations 
F06HR  nagf_blas_zhousg Generate complex elementary reflection 
F06HT  nagf_blas_zhous Apply complex elementary reflection 
F06JD  nagf_blas_zdscal Multiply complex vector by real scalar 
F06JJ  nagf_blas_dznrm2 Compute Euclidean norm of complex vector 
F06JK  nagf_blas_dzasum Sum absolute values of complex vector elements 
F06JL  nagf_blas_idamax Index, real vector element with largest absolute value 
F06JM  nagf_blas_izamax Index, complex vector element with largest absolute value 
F06KC  nagf_blas_zddscl Multiply complex vector by real diagonal matrix 
F06KD  nagf_blas_zdaxpzy Multiply complex vector by real scalar, preserving input vector 
F06KE  nagf_blas_zdrscl Multiply complex vector by reciprocal of real scalar 
F06KF  nagf_blas_zdcopy Copy real vector to complex vector 
F06KJ  nagf_blas_dzssq Update Euclidean norm of complex vector in scaled form 
F06KL  nagf_blas_idrank Last nonnegligible element of real vector 
F06KP  nagf_blas_zdrot Apply real plane rotation to two complex vectors 
F06PA  nagf_blas_dgemv Matrixvector product, real rectangular matrix 
F06PB  nagf_blas_dgbmv Matrixvector product, real rectangular band matrix 
F06PC  nagf_blas_dsymv Matrixvector product, real symmetric matrix 
F06PD  nagf_blas_dsbmv Matrixvector product, real symmetric band matrix 
F06PE  nagf_blas_dspmv Matrixvector product, real symmetric packed matrix 
F06PF  nagf_blas_dtrmv Matrixvector product, real triangular matrix 
F06PG  nagf_blas_dtbmv Matrixvector product, real triangular band matrix 
F06PH  nagf_blas_dtpmv Matrixvector product, real triangular packed matrix 
F06PJ  nagf_blas_dtrsv System of equations, real triangular matrix 
F06PK  nagf_blas_dtbsv System of equations, real triangular band matrix 
F06PL  nagf_blas_dtpsv System of equations, real triangular packed matrix 
F06PM  nagf_blas_dger Rank1 update, real rectangular matrix 
F06PP  nagf_blas_dsyr Rank1 update, real symmetric matrix 
F06PQ  nagf_blas_dspr Rank1 update, real symmetric packed matrix 
F06PR  nagf_blas_dsyr2 Rank2 update, real symmetric matrix 
F06PS  nagf_blas_dspr2 Rank2 update, real symmetric packed matrix 
F06QF  nagf_blas_dmcopy Matrix copy, real rectangular or trapezoidal matrix 
F06QH  nagf_blas_dmload Matrix initialization, real rectangular matrix 
F06QJ  nagf_blas_dgeap Permute rows or columns, real rectangular matrix, permutations represented by an integer array 
F06QK  nagf_blas_dgeapr Permute rows or columns, real rectangular matrix, permutations represented by a real array 
F06QM  nagf_blas_dsysrc Orthogonal similarity transformation of real symmetric matrix as a sequence of plane rotations 
F06QP  nagf_blas_dutr1 QR factorization by sequence of plane rotations, rank1 update of real upper triangular matrix 
F06QQ  nagf_blas_dutupd QR factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row 
F06QR  nagf_blas_duhqr QR or RQ factorization by sequence of plane rotations, real upper Hessenberg matrix 
F06QS  nagf_blas_dusqr QR or RQ factorization by sequence of plane rotations, real upper spiked matrix 
F06QT  nagf_blas_dutsqr QR factorization of UP or RQ factorization of PU, U real upper triangular, P a sequence of plane rotations 
F06QV  nagf_blas_dutsrh Compute upper Hessenberg matrix by sequence of plane rotations, real upper triangular matrix 
F06QW  nagf_blas_dutsrs Compute upper spiked matrix by sequence of plane rotations, real upper triangular matrix 
F06QX  nagf_blas_dgesrc Apply sequence of plane rotations, real rectangular matrix 
F06RA  nagf_blas_dlange 1norm, ∞norm, Frobenius norm, largest absolute element, real general matrix 
F06RB  nagf_blas_dlangb 1norm, ∞norm, Frobenius norm, largest absolute element, real band matrix 
F06RC  nagf_blas_dlansy 1norm, ∞norm, Frobenius norm, largest absolute element, real symmetric matrix 
F06RD  nagf_blas_dlansp 1norm, ∞norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage 
F06RE  nagf_blas_dlansb 1norm, ∞norm, Frobenius norm, largest absolute element, real symmetric band matrix 
F06RJ  nagf_blas_dlantr 1norm, ∞norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix 
F06RK  nagf_blas_dlantp 1norm, ∞norm, Frobenius norm, largest absolute element, real triangular matrix, packed storage 
F06RL  nagf_blas_dlantb 1norm, ∞norm, Frobenius norm, largest absolute element, real triangular band matrix 
F06RM  nagf_blas_dlanhs 1norm, ∞norm, Frobenius norm, largest absolute element, real upper Hessenberg matrix 
F06RN  nagf_blas_dlangt 1norm, ∞norm, Frobenius norm, largest absolute element, real tridiagonal matrix 
F06RP  nagf_blas_dlanst 1norm, ∞norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix 
F06SA  nagf_blas_zgemv Matrixvector product, complex rectangular matrix 
F06SB  nagf_blas_zgbmv Matrixvector product, complex rectangular band matrix 
F06SC  nagf_blas_zhemv Matrixvector product, complex Hermitian matrix 
F06SD  nagf_blas_zhbmv Matrixvector product, complex Hermitian band matrix 
F06SE  nagf_blas_zhpmv Matrixvector product, complex Hermitian packed matrix 
F06SF  nagf_blas_ztrmv Matrixvector product, complex triangular matrix 
F06SG  nagf_blas_ztbmv Matrixvector product, complex triangular band matrix 
F06SH  nagf_blas_ztpmv Matrixvector product, complex triangular packed matrix 
F06SJ  nagf_blas_ztrsv System of equations, complex triangular matrix 
F06SK  nagf_blas_ztbsv System of equations, complex triangular band matrix 
F06SL  nagf_blas_ztpsv System of equations, complex triangular packed matrix 
F06SM  nagf_blas_zgeru Rank1 update, complex rectangular matrix, unconjugated vector 
F06SN  nagf_blas_zgerc Rank1 update, complex rectangular matrix, conjugated vector 
F06SP  nagf_blas_zher Rank1 update, complex Hermitian matrix 
F06SQ  nagf_blas_zhpr Rank1 update, complex Hermitian packed matrix 
F06SR  nagf_blas_zher2 Rank2 update, complex Hermitian matrix 
F06SS  nagf_blas_zhpr2 Rank2 update, complex Hermitian packed matrix 
F06TA  nagf_blas_zsymv Matrixvector product, complex symmetric matrix 
F06TB  nagf_blas_zsyr Rank1 update, complex symmetric matrix 
F06TC  nagf_blas_zspmv Matrixvector product, complex symmetric packed matrix 
F06TD  nagf_blas_zspr Rank1 update, complex symmetric packed matrix 
F06TF  nagf_blas_zmcopy Matrix copy, complex rectangular or trapezoidal matrix 
F06TH  nagf_blas_zmload Matrix initialization, complex rectangular matrix 
F06TM  nagf_blas_zhesrc Unitary similarity transformation of Hermitian matrix as a sequence of plane rotations 
F06TP  nagf_blas_zutr1 QR factorization by sequence of plane rotations, rank1 update of complex upper triangular matrix 
F06TQ  nagf_blas_zutupd QR factorization by sequence of plane rotations, complex upper triangular matrix augmented by a full row 
F06TR  nagf_blas_zuhqr QR or RQ factorization by sequence of plane rotations, complex upper Hessenberg matrix 
F06TS  nagf_blas_zusqr QR or RQ factorization by sequence of plane rotations, complex upper spiked matrix 
F06TT  nagf_blas_zutsqr QR factorization of UP or RQ factorization of PU, U complex upper triangular, P a sequence of plane rotations 
F06TV  nagf_blas_zutsrh Compute upper Hessenberg matrix by sequence of plane rotations, complex upper triangular matrix 
F06TW  nagf_blas_zutsrs Compute upper spiked matrix by sequence of plane rotations, complex upper triangular matrix 
F06TX  nagf_blas_zgesrc Apply sequence of plane rotations, complex rectangular matrix, real cosine and complex sine 
F06TY  nagf_blas_zgesrs Apply sequence of plane rotations, complex rectangular matrix, complex cosine and real sine 
F06UA  nagf_blas_zlange 1norm, ∞norm, Frobenius norm, largest absolute element, complex general matrix 
F06UB  nagf_blas_zlangb 1norm, ∞norm, Frobenius norm, largest absolute element, complex band matrix 
F06UC  nagf_blas_zlanhe 1norm, ∞norm, Frobenius norm, largest absolute element, complex Hermitian matrix 
F06UD  nagf_blas_zlanhp 1norm, ∞norm, Frobenius norm, largest absolute element, complex Hermitian matrix, packed storage 
F06UE  nagf_blas_zlanhb 1norm, ∞norm, Frobenius norm, largest absolute element, complex Hermitian band matrix 
F06UF  nagf_blas_zlansy 1norm, ∞norm, Frobenius norm, largest absolute element, complex symmetric matrix 
F06UG  nagf_blas_zlansp 1norm, ∞norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage 
F06UH  nagf_blas_zlansb 1norm, ∞norm, Frobenius norm, largest absolute element, complex symmetric band matrix 
F06UJ  nagf_blas_zlantr 1norm, ∞norm, Frobenius norm, largest absolute element, complex trapezoidal/triangular matrix 
F06UK  nagf_blas_zlantp 1norm, ∞norm, Frobenius norm, largest absolute element, complex triangular matrix, packed storage 
F06UL  nagf_blas_zlantb 1norm, ∞norm, Frobenius norm, largest absolute element, complex triangular band matrix 
F06UM  nagf_blas_zlanhs 1norm, ∞norm, Frobenius norm, largest absolute element, complex Hessenberg matrix 
F06UN  nagf_blas_zlangt 1norm, ∞norm, Frobenius norm, largest absolute element, complex tridiagonal matrix 
F06UP  nagf_blas_zlanht 1norm, ∞norm, Frobenius norm, largest absolute element, complex Hermitian tridiagonal matrix 
F06VJ  nagf_blas_zgeap Permute rows or columns, complex rectangular matrix, permutations represented by an integer array 
F06VK  nagf_blas_zgeapr Permute rows or columns, complex rectangular matrix, permutations represented by a real array 
F06VX  nagf_blas_zsgesr Apply sequence of plane rotations, complex rectangular matrix, real cosine and sine 
F06WA  nagf_blas_dlansf 1norm, ∞norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format 
F06WB  nagf_blas_dtfsm Solves a system of equations with multiple righthand sides, real triangular coefficient matrix, Rectangular Full Packed format 
F06WC  nagf_blas_dsfrk Rankk update of a real symmetric matrix, Rectangular Full Packed format 
F06WN  nagf_blas_zlanhf 1norm, ∞norm, Frobenius norm, largest absolute element, complex Hermitian matrix, Rectangular Full Packed format 
F06WP  nagf_blas_ztfsm Solves system of equations with multiple righthand sides, complex triangular coefficient matrix, Rectangular Full Packed format 
F06WQ  nagf_blas_zhfrk Rankk update of a complex Hermitian matrix, Rectangular Full Packed format 
F06YA  nagf_blas_dgemm Matrixmatrix product, two real rectangular matrices 
F06YC  nagf_blas_dsymm Matrixmatrix product, one real symmetric matrix, one real rectangular matrix 
F06YF  nagf_blas_dtrmm Matrixmatrix product, one real triangular matrix, one real rectangular matrix 
F06YJ  nagf_blas_dtrsm Solves a system of equations with multiple righthand sides, real triangular coefficient matrix 
F06YP  nagf_blas_dsyrk Rankk update of a real symmetric matrix 
F06YR  nagf_blas_dsyr2k Rank2k update of a real symmetric matrix 
F06ZA  nagf_blas_zgemm Matrixmatrix product, two complex rectangular matrices 
F06ZC  nagf_blas_zhemm Matrixmatrix product, one complex Hermitian matrix, one complex rectangular matrix 
F06ZF  nagf_blas_ztrmm Matrixmatrix product, one complex triangular matrix, one complex rectangular matrix 
F06ZJ  nagf_blas_ztrsm Solves system of equations with multiple righthand sides, complex triangular coefficient matrix 
F06ZP  nagf_blas_zherk Rankk update of a complex Hermitian matrix 
F06ZR  nagf_blas_zher2k Rank2k update of a complex Hermitian matrix 
F06ZT  nagf_blas_zsymm Matrixmatrix product, one complex symmetric matrix, one complex rectangular matrix 
F06ZU  nagf_blas_zsyrk Rankk update of a complex symmetric matrix 
F06ZW  nagf_blas_zsyr2k Rank2k update of a complex symmetric matrix 
F07 – Linear Equations (LAPACK)
Examples of routines and methods in this chapter.
F07AA  nagf_lapack_dgesv Computes the solution to a real system of linear equations 
F07AB  nagf_lapack_dgesvx Uses the LU factorization to compute the solution, errorbound and condition estimate for a real system of linear equations 
F07AC  nagf_lapack_dsgesv Computes the solution to a real system of linear equations using mixed precision arithmetic 
F07AD  nagf_lapack_dgetrf LU factorization of real m by n matrix 
F07AE  nagf_lapack_dgetrs Solution of real system of linear equations, multiple righthand sides, matrix already factorized by F07AD 
F07AF  nagf_lapack_dgeequ Computes row and column scalings intended to equilibrate a general real matrix and reduce its condition number 
F07AG  nagf_lapack_dgecon Estimate condition number of real matrix, matrix already factorized by F07AD 
F07AH  nagf_lapack_dgerfs Refined solution with error bounds of real system of linear equations, multiple righthand sides 
F07AJ  nagf_lapack_dgetri Inverse of real matrix, matrix already factorized by F07AD 
F07AN  nagf_lapack_zgesv Computes the solution to a complex system of linear equations 
F07AP  nagf_lapack_zgesvx Uses the LU factorization to compute the solution, errorbound and condition estimate for a complex system of linear equations 
F07AQ  nagf_lapack_zcgesv Computes the solution to a complex system of linear equations using mixed precision arithmetic 
F07AR  nagf_lapack_zgetrf LU factorization of complex m by n matrix 
F07AS  nagf_lapack_zgetrs Solution of complex system of linear equations, multiple righthand sides, matrix already factorized by F07AR 
F07AT  nagf_lapack_zgeequ Computes row and column scalings intended to equilibrate a general complex matrix and reduce its condition number 
F07AU  nagf_lapack_zgecon Estimate condition number of complex matrix, matrix already factorized by F07AR 
F07AV  nagf_lapack_zgerfs Refined solution with error bounds of complex system of linear equations, multiple righthand sides 
F07AW  nagf_lapack_zgetri Inverse of complex matrix, matrix already factorized by F07AR 
F07BA  nagf_lapack_dgbsv Computes the solution to a real banded system of linear equations 
F07BB  nagf_lapack_dgbsvx Uses the LU factorization to compute the solution, errorbound and condition estimate for a real banded system of linear equations 
F07BD  nagf_lapack_dgbtrf LU factorization of real m by n band matrix 
F07BE  nagf_lapack_dgbtrs Solution of real band system of linear equations, multiple righthand sides, matrix already factorized by F07BD 
F07BF  nagf_lapack_dgbequ Computes row and column scalings intended to equilibrate a real banded matrix and reduce its condition number 
F07BG  nagf_lapack_dgbcon Estimate condition number of real band matrix, matrix already factorized by F07BD 
F07BH  nagf_lapack_dgbrfs Refined solution with error bounds of real band system of linear equations, multiple righthand sides 
F07BN  nagf_lapack_zgbsv Computes the solution to a complex banded system of linear equations 
F07BP  nagf_lapack_zgbsvx Uses the LU factorization to compute the solution, errorbound and condition estimate for a complex banded system of linear equations 
F07BR  nagf_lapack_zgbtrf LU factorization of complex m by n band matrix 
F07BS  nagf_lapack_zgbtrs Solution of complex band system of linear equations, multiple righthand sides, matrix already factorized by F07BR 
F07BT  nagf_lapack_zgbequ Computes row and column scalings intended to equilibrate a complex banded matrix and reduce its condition number 
F07BU  nagf_lapack_zgbcon Estimate condition number of complex band matrix, matrix already factorized by F07BR 
F07BV  nagf_lapack_zgbrfs Refined solution with error bounds of complex band system of linear equations, multiple righthand sides 
F07CA  nagf_lapack_dgtsv Computes the solution to a real tridiagonal system of linear equations 
F07CB  nagf_lapack_dgtsvx Uses the LU factorization to compute the solution, errorbound and condition estimate for a real tridiagonal system of linear equations 
F07CD  nagf_lapack_dgttrf LU factorization of real tridiagonal matrix 
F07CE  nagf_lapack_dgttrs Solves a real tridiagonal system of linear equations using the LU factorization computed by F07CD 
F07CG  nagf_lapack_dgtcon Estimates the reciprocal of the condition number of a real tridiagonal matrix using the LU factorization computed by F07CD 
F07CH  nagf_lapack_dgtrfs Refined solution with error bounds of real tridiagonal system of linear equations, multiple righthand sides 
F07CN  nagf_lapack_zgtsv Computes the solution to a complex tridiagonal system of linear equations 
F07CP  nagf_lapack_zgtsvx Uses the LU factorization to compute the solution, errorbound and condition estimate for a complex tridiagonal system of linear equations 
F07CR  nagf_lapack_zgttrf LU factorization of complex tridiagonal matrix 
F07CS  nagf_lapack_zgttrs Solves a complex tridiagonal system of linear equations using the LU factorization computed by F07CD 
F07CU  nagf_lapack_zgtcon Estimates the reciprocal of the condition number of a complex tridiagonal matrix using the LU factorization computed by F07CD 
F07CV  nagf_lapack_zgtrfs Refined solution with error bounds of complex tridiagonal system of linear equations, multiple righthand sides 
F07FA  nagf_lapack_dposv Computes the solution to a real symmetric positive definite system of linear equations 
F07FB  nagf_lapack_dposvx Uses the Cholesky factorization to compute the solution, errorbound and condition estimate for a real symmetric positive definite system of linear equations 
F07FC  nagf_lapack_dsposv Computes the solution to a real symmetric positive definite system of linear equations using mixed precision arithmetic 
F07FD  nagf_lapack_dpotrf Cholesky factorization of real symmetric positive definite matrix 
F07FE  nagf_lapack_dpotrs Solution of real symmetric positive definite system of linear equations, multiple righthand sides, matrix already factorized by F07FD 
F07FF  nagf_lapack_dpoequ Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number 
F07FG  nagf_lapack_dpocon Estimate condition number of real symmetric positive definite matrix, matrix already factorized by F07FD 
F07FH  nagf_lapack_dporfs Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple righthand sides 
F07FJ  nagf_lapack_dpotri Inverse of real symmetric positive definite matrix, matrix already factorized by F07FD 
F07FN  nagf_lapack_zposv Computes the solution to a complex Hermitian positive definite system of linear equations 
F07FP  nagf_lapack_zposvx Uses the Cholesky factorization to compute the solution, errorbound and condition estimate for a complex Hermitian positive definite system of linear equations 
F07FQ  nagf_lapack_zcposv Computes the solution to a complex Hermitian positive definite system of linear equations using mixed precision arithmetic 
F07FR  nagf_lapack_zpotrf Cholesky factorization of complex Hermitian positive definite matrix 
F07FS  nagf_lapack_zpotrs Solution of complex Hermitian positive definite system of linear equations, multiple righthand sides, matrix already factorized by F07FR 
F07FT  nagf_lapack_zpoequ Computes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number 
F07FU  nagf_lapack_zpocon Estimate condition number of complex Hermitian positive definite matrix, matrix already factorized by F07FR 
F07FV  nagf_lapack_zporfs Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple righthand sides 
F07FW  nagf_lapack_zpotri Inverse of complex Hermitian positive definite matrix, matrix already factorized by F07FR 
F07GA  nagf_lapack_dppsv Computes the solution to a real symmetric positive definite system of linear equations, packed storage 
F07GB  nagf_lapack_dppsvx Uses the Cholesky factorization to compute the solution, errorbound and condition estimate for a real symmetric positive definite system of linear equations, packed storage 
F07GD  nagf_lapack_dpptrf Cholesky factorization of real symmetric positive definite matrix, packed storage 
F07GE  nagf_lapack_dpptrs Solution of real symmetric positive definite system of linear equations, multiple righthand sides, matrix already factorized by F07GD, packed storage 
F07GF  nagf_lapack_dppequ Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number, packed storage 
F07GG  nagf_lapack_dppcon Estimate condition number of real symmetric positive definite matrix, matrix already factorized by F07GD, packed storage 
F07GH  nagf_lapack_dpprfs Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple righthand sides, packed storage 
F07GJ  nagf_lapack_dpptri Inverse of real symmetric positive definite matrix, matrix already factorized by F07GD, packed storage 
F07GN  nagf_lapack_zppsv Computes the solution to a complex Hermitian positive definite system of linear equations, packed storage 
F07GP  nagf_lapack_zppsvx Uses the Cholesky factorization to compute the solution, errorbound and condition estimate for a complex Hermitian positive definite system of linear equations, packed storage 
F07GR  nagf_lapack_zpptrf Cholesky factorization of complex Hermitian positive definite matrix, packed storage 
F07GS  nagf_lapack_zpptrs Solution of complex Hermitian positive definite system of linear equations, multiple righthand sides, matrix already factorized by F07GR, packed storage 
F07GT  nagf_lapack_zppequ Computes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number, packed storage 
F07GU  nagf_lapack_zppcon Estimate condition number of complex Hermitian positive definite matrix, matrix already factorized by F07GR, packed storage 
F07GV  nagf_lapack_zpprfs Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple righthand sides, packed storage 
F07GW  nagf_lapack_zpptri Inverse of complex Hermitian positive definite matrix, matrix already factorized by F07GR, packed storage 
F07HA  nagf_lapack_dpbsv Computes the solution to a real symmetric positive definite banded system of linear equations 
F07HB  nagf_lapack_dpbsvx Uses the Cholesky factorization to compute the solution, errorbound and condition estimate for a real symmetric positive definite banded system of linear equations 
F07HD  nagf_lapack_dpbtrf Cholesky factorization of real symmetric positive definite band matrix 
F07HE  nagf_lapack_dpbtrs Solution of real symmetric positive definite band system of linear equations, multiple righthand sides, matrix already factorized by F07HD 
F07HF  nagf_lapack_dpbequ Computes row and column scalings intended to equilibrate a real symmetric positive definite banded matrix and reduce its condition number 
F07HG  nagf_lapack_dpbcon Estimate condition number of real symmetric positive definite band matrix, matrix already factorized by F07HD 
F07HH  nagf_lapack_dpbrfs Refined solution with error bounds of real symmetric positive definite band system of linear equations, multiple righthand sides 
F07HN  nagf_lapack_zpbsv Computes the solution to a complex Hermitian positive definite banded system of linear equations 
F07HP  nagf_lapack_zpbsvx Uses the Cholesky factorization to compute the solution, errorbound and condition estimate for a complex Hermitian positive definite banded system of linear equations 
F07HR  nagf_lapack_zpbtrf Cholesky factorization of complex Hermitian positive definite band matrix 
F07HS  nagf_lapack_zpbtrs Solution of complex Hermitian positive definite band system of linear equations, multiple righthand sides, matrix already factorized by F07HR 
F07HT  nagf_lapack_zpbequ Computes row and column scalings intended to equilibrate a complex Hermitian positive definite banded matrix and reduce its condition number 
F07HU  nagf_lapack_zpbcon Estimate condition number of complex Hermitian positive definite band matrix, matrix already factorized by F07HR 
F07HV  nagf_lapack_zpbrfs Refined solution with error bounds of complex Hermitian positive definite band system of linear equations, multiple righthand sides 
F07JA  nagf_lapack_dptsv Computes the solution to a real symmetric positive definite tridiagonal system of linear equations 
F07JB  nagf_lapack_dptsvx Uses the LDL^{T} factorization to compute the solution, errorbound and condition estimate for a real symmetric positive definite tridiagonal system of linear equations 
F07JD  nagf_lapack_dpttrf Computes the LDL^{T} factorization of a real symmetric positive definite tridiagonal matrix 
F07JE  nagf_lapack_dpttrs Solves a real symmetric positive definite tridiagonal system using the LDL^{T} factorization computed by F07JD 
F07JG  nagf_lapack_dptcon Computes the reciprocal of the condition number of a real symmetric positive definite tridiagonal system using the LDL^{T} factorization computed by F07JD 
F07JH  nagf_lapack_dptrfs Refined solution with error bounds of real symmetric positive definite tridiagonal system of linear equations, multiple righthand sides 
F07JN  nagf_lapack_zptsv Computes the solution to a complex Hermitian positive definite tridiagonal system of linear equations 
F07JP  nagf_lapack_zptsvx Uses the LDL^{T} factorization to compute the solution, errorbound and condition estimate for a complex Hermitian positive definite tridiagonal system of linear equations 
F07JR  nagf_lapack_zpttrf Computes the LDL^{H} factorization of a complex Hermitian positive definite tridiagonal matrix 
F07JS  nagf_lapack_zpttrs Solves a complex Hermitian positive definite tridiagonal system using the LDL^{H} factorization computed by F07JR 
F07JU  nagf_lapack_zptcon Computes the reciprocal of the condition number of a complex Hermitian positive definite tridiagonal system using the LDL^{H} factorization computed by F07JR 
F07JV  nagf_lapack_zptrfs Refined solution with error bounds of complex Hermitian positive definite tridiagonal system of linear equations, multiple righthand sides 
F07KD  nagf_lapack_dpstrf Cholesky factorization, with complete pivoting, of a real, symmetric, positive semidefinite matrix 
F07KR  nagf_lapack_zpstrf Cholesky factorization of complex Hermitian positive semidefinite matrix 
F07MA  nagf_lapack_dsysv Computes the solution to a real symmetric system of linear equations 
F07MB  nagf_lapack_dsysvx Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations 
F07MD  nagf_lapack_dsytrf Bunch–Kaufman factorization of real symmetric indefinite matrix 
F07ME  nagf_lapack_dsytrs Solution of real symmetric indefinite system of linear equations, multiple righthand sides, matrix already factorized by F07MD 
F07MG  nagf_lapack_dsycon Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07MD 
F07MH  nagf_lapack_dsyrfs Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple righthand sides 
F07MJ  nagf_lapack_dsytri Inverse of real symmetric indefinite matrix, matrix already factorized by F07MD 
F07MN  nagf_lapack_zhesv Computes the solution to a complex Hermitian system of linear equations 
F07MP  nagf_lapack_zhesvx Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations 
F07MR  nagf_lapack_zhetrf Bunch–Kaufman factorization of complex Hermitian indefinite matrix 
F07MS  nagf_lapack_zhetrs Solution of complex Hermitian indefinite system of linear equations, multiple righthand sides, matrix already factorized by F07MR 
F07MU  nagf_lapack_zhecon Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07MR 
F07MV  nagf_lapack_zherfs Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple righthand sides 
F07MW  nagf_lapack_zhetri Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07MR 
F07NN  nagf_lapack_zsysv Computes the solution to a complex symmetric system of linear equations 
F07NP  nagf_lapack_zsysvx Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations 
F07NR  nagf_lapack_zsytrf Bunch–Kaufman factorization of complex symmetric matrix 
F07NS  nagf_lapack_zsytrs Solution of complex symmetric system of linear equations, multiple righthand sides, matrix already factorized by F07NR 
F07NU  nagf_lapack_zsycon Estimate condition number of complex symmetric matrix, matrix already factorized by F07NR 
F07NV  nagf_lapack_zsyrfs Refined solution with error bounds of complex symmetric system of linear equations, multiple righthand sides 
F07NW  nagf_lapack_zsytri Inverse of complex symmetric matrix, matrix already factorized by F07NR 
F07PA  nagf_lapack_dspsv Computes the solution to a real symmetric system of linear equations, packed storage 
F07PB  nagf_lapack_dspsvx Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage. Error bounds and a condition estimate are also computed 
F07PD  nagf_lapack_dsptrf Bunch–Kaufman factorization of real symmetric indefinite matrix, packed storage 
F07PE  nagf_lapack_dsptrs Solution of real symmetric indefinite system of linear equations, multiple righthand sides, matrix already factorized by F07PD, packed storage 
F07PG  nagf_lapack_dspcon Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07PD, packed storage 
F07PH  nagf_lapack_dsprfs Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple righthand sides, packed storage 
F07PJ  nagf_lapack_dsptri Inverse of real symmetric indefinite matrix, matrix already factorized by F07PD, packed storage 
F07PN  nagf_lapack_zhpsv Computes the solution to a complex Hermitian system of linear equations, packed storage 
F07PP  nagf_lapack_zhpsvx Uses the diagonal pivoting factorization to compute the solution to a complex, Hermitian, system of linear equations, error bounds and condition estimates. Packed storage 
F07PR  nagf_lapack_zhptrf Bunch–Kaufman factorization of complex Hermitian indefinite matrix, packed storage 
F07PS  nagf_lapack_zhptrs Solution of complex Hermitian indefinite system of linear equations, multiple righthand sides, matrix already factorized by F07PR, packed storage 
F07PU  nagf_lapack_zhpcon Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07PR, packed storage 
F07PV  nagf_lapack_zhprfs Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple righthand sides, packed storage 
F07PW  nagf_lapack_zhptri Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07PR, packed storage 
F07QN  nagf_lapack_zspsv Computes the solution to a complex symmetric system of linear equations, packed storage 
F07QP  nagf_lapack_zspsvx Uses the diagonal pivoting factorization to compute the solution to a complex, symmetric, system of linear equations, error bounds and condition estimates. Packed storage 
F07QR  nagf_lapack_zsptrf Bunch–Kaufman factorization of complex symmetric matrix, packed storage 
F07QS  nagf_lapack_zsptrs Solution of complex symmetric system of linear equations, multiple righthand sides, matrix already factorized by F07QR, packed storage 
F07QU  nagf_lapack_zspcon Estimate condition number of complex symmetric matrix, matrix already factorized by F07QR, packed storage 
F07QV  nagf_lapack_zsprfs Refined solution with error bounds of complex symmetric system of linear equations, multiple righthand sides, packed storage 
F07QW  nagf_lapack_zsptri Inverse of complex symmetric matrix, matrix already factorized by F07QR, packed storage 
F07TE  nagf_lapack_dtrtrs Solution of real triangular system of linear equations, multiple righthand sides 
F07TG  nagf_lapack_dtrcon Estimate condition number of real triangular matrix 
F07TH  nagf_lapack_dtrrfs Error bounds for solution of real triangular system of linear equations, multiple righthand sides 
F07TJ  nagf_lapack_dtrtri Inverse of real triangular matrix 
F07TS  nagf_lapack_ztrtrs Solution of complex triangular system of linear equations, multiple righthand sides 
F07TU  nagf_lapack_ztrcon Estimate condition number of complex triangular matrix 
F07TV  nagf_lapack_ztrrfs Error bounds for solution of complex triangular system of linear equations, multiple righthand sides 
F07TW  nagf_lapack_ztrtri Inverse of complex triangular matrix 
F07UE  nagf_lapack_dtptrs Solution of real triangular system of linear equations, multiple righthand sides, packed storage 
F07UG  nagf_lapack_dtpcon Estimate condition number of real triangular matrix, packed storage 
F07UH  nagf_lapack_dtprfs Error bounds for solution of real triangular system of linear equations, multiple righthand sides, packed storage 
F07UJ  nagf_lapack_dtptri Inverse of real triangular matrix, packed storage 
F07US  nagf_lapack_ztptrs Solution of complex triangular system of linear equations, multiple righthand sides, packed storage 
F07UU  nagf_lapack_ztpcon Estimate condition number of complex triangular matrix, packed storage 
F07UV  nagf_lapack_ztprfs Error bounds for solution of complex triangular system of linear equations, multiple righthand sides, packed storage 
F07UW  nagf_lapack_ztptri Inverse of complex triangular matrix, packed storage 
F07VE  nagf_lapack_dtbtrs Solution of real band triangular system of linear equations, multiple righthand sides 
F07VG  nagf_lapack_dtbcon Estimate condition number of real band triangular matrix 
F07VH  nagf_lapack_dtbrfs Error bounds for solution of real band triangular system of linear equations, multiple righthand sides 
F07VS  nagf_lapack_ztbtrs Solution of complex band triangular system of linear equations, multiple righthand sides 
F07VU  nagf_lapack_ztbcon Estimate condition number of complex band triangular matrix 
F07VV  nagf_lapack_ztbrfs Error bounds for solution of complex band triangular system of linear equations, multiple righthand sides 
F07WD  nagf_lapack_dpftrf Cholesky factorization of real symmetric positive definite matrix, Rectangular Full Packed format 
F07WE  nagf_lapack_dpftrs Solution of real symmetric positive definite system of linear equations, multiple righthand sides, coefficient matrix already factorized by F07WD, Rectangular Full Packed format 
F07WJ  nagf_lapack_dpftri Inverse of real symmetric positive definite matrix, matrix already factorized by F07WD, Rectangular Full Packed format 
F07WK  nagf_lapack_dtftri Inverse of real triangular matrix, Rectangular Full Packed format 
F07WR  nagf_lapack_zpftrf Cholesky factorization of complex Hermitian positive definite matrix, Rectangular Full Packed format 
F07WS  nagf_lapack_zpftrs Solution of complex Hermitian positive definite system of linear equations, multiple righthand sides, coefficient matrix already factorized by F07WR, Rectangular Full Packed format 
F07WW  nagf_lapack_zpftri Inverse of complex Hermitian positive definite matrix, matrix already factorized by F07WR, Rectangular Full Packed format 
F07WX  nagf_lapack_ztftri Inverse of complex triangular matrix, Rectangular Full Packed format 
F08 – Least Squares and Eigenvalue Problems (LAPACK)
Examples of routines and methods in this chapter.
F08AA  nagf_lapack_dgels Solves a real linear least squares problem of full rank 
F08AB  nagf_lapack_dgeqrt Performs a QR factorization of real general rectangular matrix, with explicit blocking 
F08AC  nagf_lapack_dgemqrt Applies the orthogonal transformation determined by F08AB 
F08AE  nagf_lapack_dgeqrf Performs a QR factorization of real general rectangular matrix 
F08AF  nagf_lapack_dorgqr Forms all or part of orthogonal Q from QR factorization determined by F08AE, F08BE and F08BF 
F08AG  nagf_lapack_dormqr Applies an orthogonal transformation determined by F08AE, F08BE and F08BF 
F08AH  nagf_lapack_dgelqf Performs a LQ factorization of real general rectangular matrix 
F08AJ  nagf_lapack_dorglq Forms all or part of orthogonal Q from LQ factorization determined by F08AH 
F08AK  nagf_lapack_dormlq Applies the orthogonal transformation determined by F08AH 
F08AN  nagf_lapack_zgels Solves a complex linear least problem of full rank 
F08AP  nagf_lapack_zgeqrt Performs a QR factorization of complex general rectangular matrix using recursive algorithm 
F08AQ  nagf_lapack_zgemqrt Applies the unitary transformation determined by F08AP 
F08AS  nagf_lapack_zgeqrf Performs a QR factorization of complex general rectangular matrix 
F08AT  nagf_lapack_zungqr Forms all or part of unitary Q from QR factorization determined by F08AS, F08BS and F08BT 
F08AU  nagf_lapack_zunmqr Applies a unitary transformation determined by F08AS, F08BS and F08BT 
F08AV  nagf_lapack_zgelqf Performs a LQ factorization of complex general rectangular matrix 
F08AW  nagf_lapack_zunglq Forms all or part of unitary Q from LQ factorization determined by F08AV 
F08AX  nagf_lapack_zunmlq Applies the unitary transformation determined by F08AV 
F08BA  nagf_lapack_dgelsy Computes the minimumnorm solution to a real linear least squares problem 
F08BB  nagf_lapack_dtpqrt QR factorization of real general triangularpentagonal matrix 
F08BC  nagf_lapack_dtpmqrt Applies the orthogonal transformation determined by F08BB 
F08BE  nagf_lapack_dgeqpf QR factorization, with column pivoting, of real general rectangular matrix 
F08BF  nagf_lapack_dgeqp3 QR factorization, with column pivoting, using BLAS3, of real general rectangular matrix 
F08BH  nagf_lapack_dtzrzf Reduces a real upper trapezoidal matrix to upper triangular form 
F08BK  nagf_lapack_dormrz Applies the orthogonal transformation determined by F08BH 
F08BN  nagf_lapack_zgelsy Computes the minimumnorm solution to a complex linear least squares problem 
F08BP  nagf_lapack_ztpqrt QR factorization of complex triangularpentagonal matrix 
F08BQ  nagf_lapack_ztpmqrt Applies the unitary transformation determined by F08BP 
F08BS  nagf_lapack_zgeqpf QR factorization, with column pivoting, of complex general rectangular matrix 
F08BT  nagf_lapack_zgeqp3 QR factorization, with column pivoting, using BLAS3, of complex general rectangular matrix 
F08BV  nagf_lapack_ztzrzf Reduces a complex upper trapezoidal matrix to upper triangular form 
F08BX  nagf_lapack_zunmrz Applies the unitary transformation determined by F08BV 
F08CE  nagf_lapack_dgeqlf QL factorization of real general rectangular matrix 
F08CF  nagf_lapack_dorgql Form all or part of orthogonal Q from QL factorization determined by F08CE 
F08CG  nagf_lapack_dormql Applies the orthogonal transformation determined by F08CE 
F08CH  nagf_lapack_dgerqf RQ factorization of real general rectangular matrix 
F08CJ  nagf_lapack_dorgrq Form all or part of orthogonal Q from RQ factorization determined by F08CH 
F08CK  nagf_lapack_dormrq Applies the orthogonal transformation determined by F08CH 
F08CS  nagf_lapack_zgeqlf QL factorization of complex general rectangular matrix 
F08CT  nagf_lapack_zungql Form all or part of unitary Q from QL factorization determined by F08CS 
F08CU  nagf_lapack_zunmql Applies the unitary transformation determined by F08CS 
F08CV  nagf_lapack_zgerqf RQ factorization of complex general rectangular matrix 
F08CW  nagf_lapack_zungrq Form all or part of unitary Q from RQ factorization determined by F08CV 
F08CX  nagf_lapack_zunmrq Applies the unitary transformation determined by F08CV 
F08FA  nagf_lapack_dsyev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix 
F08FB  nagf_lapack_dsyevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix 
F08FC  nagf_lapack_dsyevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divideandconquer) 
F08FD  nagf_lapack_dsyevr Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations) 
F08FE  nagf_lapack_dsytrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form 
F08FF  nagf_lapack_dorgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FE 
F08FG  nagf_lapack_dormtr Applies the orthogonal transformation determined by F08FE 
F08FL  nagf_lapack_ddisna Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix 
F08FN  nagf_lapack_zheev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix 
F08FP  nagf_lapack_zheevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix 
F08FQ  nagf_lapack_zheevd Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divideandconquer) 
F08FR  nagf_lapack_zheevr Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations) 
F08FS  nagf_lapack_zhetrd Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form 
F08FT  nagf_lapack_zungtr Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FS 
F08FU  nagf_lapack_zunmtr Applies the unitary transformation matrix determined by F08FS 
F08GA  nagf_lapack_dspev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage 
F08GB  nagf_lapack_dspevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage 
F08GC  nagf_lapack_dspevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divideandconquer or Pal–Walker–Kahan variant of the QL or QR algorithm) 
F08GE  nagf_lapack_dsptrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage 
F08GF  nagf_lapack_dopgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GE 
F08GG  nagf_lapack_dopmtr Applies the orthogonal transformation determined by F08GE 
F08GN  nagf_lapack_zhpev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage 
F08GP  nagf_lapack_zhpevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage 
F08GQ  nagf_lapack_zhpevd Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divideandconquer or Pal–Walker–Kahan variant of the QL or QR algorithm) 
F08GS  nagf_lapack_zhptrd Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage 
F08GT  nagf_lapack_zupgtr Generates a unitary transformation matrix from reduction to tridiagonal form determined by F08GS 
F08GU  nagf_lapack_zupmtr Applies the unitary transformation matrix determined by F08GS 
F08HA  nagf_lapack_dsbev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix 
F08HB  nagf_lapack_dsbevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix 
F08HC  nagf_lapack_dsbevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divideandconquer or Pal–Walker–Kahan variant of the QL or QR algorithm) 
F08HE  nagf_lapack_dsbtrd Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form 
F08HN  nagf_lapack_zhbev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix 
F08HP  nagf_lapack_zhbevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix 
F08HQ  nagf_lapack_zhbevd Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divideandconquer) 
F08HS  nagf_lapack_zhbtrd Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form 
F08JA  nagf_lapack_dstev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix 
F08JB  nagf_lapack_dstevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix 
F08JC  nagf_lapack_dstevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divideandconquer) 
F08JD  nagf_lapack_dstevr Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations) 
F08JE  nagf_lapack_dsteqr Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit QL or QR algorithm 
F08JF  nagf_lapack_dsterf Computes all eigenvalues of real symmetric tridiagonal matrix, rootfree variant of the QL or QR algorithm 
F08JG  nagf_lapack_dpteqr Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix 
F08JH  nagf_lapack_dstedc Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divideandconquer) 
F08JJ  nagf_lapack_dstebz Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection 
F08JK  nagf_lapack_dstein Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array 
F08JL  nagf_lapack_dstegr Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations) 
F08JS  nagf_lapack_zsteqr Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit QL or QR algorithm 
F08JU  nagf_lapack_zpteqr Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix 
F08JV  nagf_lapack_zstedc Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divideandconquer) 
F08JX  nagf_lapack_zstein Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array 
F08JY  nagf_lapack_zstegr Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations) 
F08KA  nagf_lapack_dgelss Computes the minimumnorm solution to a real linear least squares problem using singular value decomposition 
F08KB  nagf_lapack_dgesvd Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors 
F08KC  nagf_lapack_dgelsd Computes the minimumnorm solution to a real linear least squares problem using singular value decomposition (divideandconquer) 
F08KD  nagf_lapack_dgesdd Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divideandconquer) 
F08KE  nagf_lapack_dgebrd Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form 
F08KF  nagf_lapack_dorgbr Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by F08KE 
F08KG  nagf_lapack_dormbr Applies the orthogonal transformations from reduction to bidiagonal form determined by F08KE 
F08KH  nagf_lapack_dgejsv Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi) 
F08KJ  nagf_lapack_dgesvj Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi) 
F08KN  nagf_lapack_zgelss Computes the minimumnorm solution to a complex linear least squares problem using singular value decomposition 
F08KP  nagf_lapack_zgesvd Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors 
F08KQ  nagf_lapack_zgelsd Computes the minimumnorm solution to a complex linear least squares problem using singular value decomposition (divideandconquer) 
F08KR  nagf_lapack_zgesdd Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divideandconquer) 
F08KS  nagf_lapack_zgebrd Performs a unitary reduction of complex general rectangular matrix to bidiagonal form 
F08KT  nagf_lapack_zungbr Generates unitary transformation matrices from the reduction to bidiagonal form determined by F08KS 
F08KU  nagf_lapack_zunmbr Applies the unitary transformations from reduction to bidiagonal form determined by F08KS 
F08LE  nagf_lapack_dgbbrd Performs a reduction of real rectangular band matrix to upper bidiagonal form 
F08LS  nagf_lapack_zgbbrd Reduction of complex rectangular band matrix to upper bidiagonal form 
F08MD  nagf_lapack_dbdsdc Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divideandconquer) 
F08ME  nagf_lapack_dbdsqr Performs an SVD of real bidiagonal matrix reduced from real general matrix 
F08MS  nagf_lapack_zbdsqr Performs an SVD of real bidiagonal matrix reduced from complex general matrix 
F08NA  nagf_lapack_dgeev Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix 
F08NB  nagf_lapack_dgeevx Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors 
F08NE  nagf_lapack_dgehrd Performs an orthogonal reduction of real general matrix to upper Hessenberg form 
F08NF  nagf_lapack_dorghr Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by F08NE 
F08NG  nagf_lapack_dormhr Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by F08NE 
F08NH  nagf_lapack_dgebal Balances a real general matrix 
F08NJ  nagf_lapack_dgebak Transforms eigenvectors of real balanced matrix to those of original matrix supplied to F08NH 
F08NN  nagf_lapack_zgeev Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix 
F08NP  nagf_lapack_zgeevx Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors 
F08NS  nagf_lapack_zgehrd Performs a unitary reduction of complex general matrix to upper Hessenberg form 
F08NT  nagf_lapack_zunghr Generates a unitary transformation matrix from reduction to Hessenberg form determined by F08NS 
F08NU  nagf_lapack_zunmhr Applies the unitary transformation matrix from reduction to Hessenberg form determined by F08NS 
F08NV  nagf_lapack_zgebal Balances a complex general matrix 
F08NW  nagf_lapack_zgebak Transforms eigenvectors of complex balanced matrix to those of original matrix supplied to F08NV 
F08PA  nagf_lapack_dgees Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors 
F08PB  nagf_lapack_dgeesx Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues 
F08PE  nagf_lapack_dhseqr Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix 
F08PK  nagf_lapack_dhsein Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration 
F08PN  nagf_lapack_zgees Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors 
F08PP  nagf_lapack_zgeesx Computes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors; also computes a reciprocal condition number for the average of the selected eigenvalues and for the right invariant subspace corresponding to these eigenvalues 
F08PS  nagf_lapack_zhseqr Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix 
F08PX  nagf_lapack_zhsein Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration 
F08QF  nagf_lapack_dtrexc Reorders a Schur factorization of real matrix using orthogonal similarity transformation 
F08QG  nagf_lapack_dtrsen Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities 
F08QH  nagf_lapack_dtrsyl Solves the real Sylvester matrix equation AX+XB=C, A and B are upper quasitriangular or transposes 
F08QK  nagf_lapack_dtrevc Computes left and right eigenvectors of real upper quasitriangular matrix 
F08QL  nagf_lapack_dtrsna Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasitriangular matrix 
F08QT  nagf_lapack_ztrexc Reorders a Schur factorization of complex matrix using unitary similarity transformation 
F08QU  nagf_lapack_ztrsen Reorders a Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities 
F08QV  nagf_lapack_ztrsyl Solves the complex Sylvester matrix equation AX+XB=C, A and B are upper triangular or conjugatetransposes 
F08QX  nagf_lapack_ztrevc Computes left and right eigenvectors of complex upper triangular matrix 
F08QY  nagf_lapack_ztrsna Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix 
F08RA  nagf_lapack_dorcsd Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices 
F08RN  nagf_lapack_zuncsd Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices 
F08SA  nagf_lapack_dsygv Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite eigenproblem 
F08SB  nagf_lapack_dsygvx Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite eigenproblem 
F08SC  nagf_lapack_dsygvd Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite eigenproblem (divideandconquer) 
F08SE  nagf_lapack_dsygst Performs a reduction to standard form of real symmetricdefinite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by F07FD 
F08SN  nagf_lapack_zhegv Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitiandefinite eigenproblem 
F08SP  nagf_lapack_zhegvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitiandefinite eigenproblem 
F08SQ  nagf_lapack_zhegvd Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitiandefinite eigenproblem (divideandconquer) 
F08SS  nagf_lapack_zhegst Performs a reduction to standard form of complex Hermitiandefinite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by F07FR 
F08TA  nagf_lapack_dspgv Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite eigenproblem, packed storage 
F08TB  nagf_lapack_dspgvx Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite eigenproblem, packed storage 
F08TC  nagf_lapack_dspgvd Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite eigenproblem, packed storage (divideandconquer) 
F08TE  nagf_lapack_dspgst Performs a reduction to standard form of real symmetricdefinite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, packed storage, B factorized by F07GD 
F08TN  nagf_lapack_zhpgv Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitiandefinite eigenproblem, packed storage 
F08TP  nagf_lapack_zhpgvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitiandefinite eigenproblem, packed storage 
F08TQ  nagf_lapack_zhpgvd Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitiandefinite eigenproblem, packed storage (divideandconquer) 
F08TS  nagf_lapack_zhpgst Performs a reduction to standard form of complex Hermitiandefinite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, packed storage, B factorized by F07GR 
F08UA  nagf_lapack_dsbgv Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetricdefinite eigenproblem 
F08UB  nagf_lapack_dsbgvx Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetricdefinite eigenproblem 
F08UC  nagf_lapack_dsbgvd Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetricdefinite eigenproblem (divideandconquer) 
F08UE  nagf_lapack_dsbgst Performs a reduction of real symmetricdefinite banded generalized eigenproblem Ax=λBx to standard form Cy=λy, such that C has the same bandwidth as A 
F08UF  nagf_lapack_dpbstf Computes a split Cholesky factorization of real symmetric positive definite band matrix A 
F08UN  nagf_lapack_zhbgv Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitiandefinite eigenproblem 
F08UP  nagf_lapack_zhbgvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitiandefinite eigenproblem 
F08UQ  nagf_lapack_zhbgvd Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitiandefinite eigenproblem (divideandconquer) 
F08US  nagf_lapack_zhbgst Performs a reduction of complex Hermitiandefinite banded generalized eigenproblem Ax=λBx to standard form Cy=λy, such that C has the same bandwidth as A 
F08UT  nagf_lapack_zpbstf Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A 
F08VA  nagf_lapack_dggsvd Computes the generalized singular value decomposition of a real matrix pair 
F08VC  nagf_lapack_dggsvd3 Computes, using BLAS3, the generalized singular value decomposition of a real matrix pair 
F08VE  nagf_lapack_dggsvp Produces orthogonal matrices that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form 
F08VG  nagf_lapack_dggsvp3 Produces orthogonal matrices, using BLAS3, that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form 
F08VN  nagf_lapack_zggsvd Computes the generalized singular value decomposition of a complex matrix pair 
F08VQ  nagf_lapack_zggsvd3 Computes, using BLAS3, the generalized singular value decomposition of a complex matrix pair 
F08VS  nagf_lapack_zggsvp Produces unitary matrices that simultaneously reduce the complex, m by n, matrix A and the complex, p by n, matrix B to upper triangular form 
F08VU  nagf_lapack_zggsvp3 Produces unitary matrices, using BLAS3, that simultaneously reduce the complex, m by n, matrix A and the complex, p by n, matrix B to upper triangular form 
F08WA  nagf_lapack_dggev Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors 
F08WB  nagf_lapack_dggevx Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors 
F08WC  nagf_lapack_dggev3 Computes, for a real nonsymmetric matrix pair, using BLAS3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors 
F08WE  nagf_lapack_dgghrd Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form 
F08WF  nagf_lapack_dgghd3 Performs, using BLAS3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form 
F08WH  nagf_lapack_dggbal Balances a pair of real, square, matrices 
F08WJ  nagf_lapack_dggbak Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WH 
F08WN  nagf_lapack_zggev Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors 
F08WP  nagf_lapack_zggevx Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors 
F08WQ  nagf_lapack_zggev3 Computes, for a complex nonsymmetric matrix pair, using BLAS3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors 
F08WS  nagf_lapack_zgghrd Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form 
F08WT  nagf_lapack_zgghd3 Performs, using BLAS3, a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form 
F08WV  nagf_lapack_zggbal Balances a pair of complex, square, matrices 
F08WW  nagf_lapack_zggbak Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WV 
F08XA  nagf_lapack_dgges Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors 
F08XB  nagf_lapack_dggesx Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues 
F08XC  nagf_lapack_dgges3 Computes, for a real nonsymmetric matrix pair, using BLAS3, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors 
F08XE  nagf_lapack_dhgeqz Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices 
F08XN  nagf_lapack_zgges Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors 
F08XP  nagf_lapack_zggesx Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues 
F08XQ  nagf_lapack_zgges3 Computes, for a complex nonsymmetric matrix pair, using BLAS3, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors 
F08XS  nagf_lapack_zhgeqz Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices 
F08YE  nagf_lapack_dtgsja Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair 
F08YF  nagf_lapack_dtgexc Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation 
F08YG  nagf_lapack_dtgsen Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces 
F08YH  nagf_lapack_dtgsyl Solves the realvalued, generalized, quasitrangular, Sylvester equation 
F08YK  nagf_lapack_dtgevc Computes right and left generalized eigenvectors of the matrix pair (A,B) which is assumed to be in generalized upper Schur form 
F08YL  nagf_lapack_dtgsna Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form 
F08YS  nagf_lapack_ztgsja Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair 
F08YT  nagf_lapack_ztgexc Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation 
F08YU  nagf_lapack_ztgsen Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces 
F08YV  nagf_lapack_ztgsyl Solves the complex generalized Sylvester equation 
F08YX  nagf_lapack_ztgevc Computes left and right eigenvectors of a pair of complex upper triangular matrices 
F08YY  nagf_lapack_ztgsna Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form 
F08ZA  nagf_lapack_dgglse Solves the real linear equalityconstrained least squares (LSE) problem 
F08ZB  nagf_lapack_dggglm Solves a real general Gauss–Markov linear model (GLM) problem 
F08ZE  nagf_lapack_dggqrf Computes a generalized QR factorization of a real matrix pair 
F08ZF  nagf_lapack_dggrqf Computes a generalized RQ factorization of a real matrix pair 
F08ZN  nagf_lapack_zgglse Solves the complex linear equalityconstrained least squares (LSE) problem 
F08ZP  nagf_lapack_zggglm Solves a complex general Gauss–Markov linear model (GLM) problem 
F08ZS  nagf_lapack_zggqrf Computes a generalized QR factorization of a complex matrix pair 
F08ZT  nagf_lapack_zggrqf Computes a generalized RQ factorization of a complex matrix pair 
F11 – Large Scale Linear Systems
Examples of routines and methods in this chapter.
F11BD  nagf_sparse_real_gen_basic_setup Real sparse nonsymmetric linear systems, setup for F11BE 
F11BE  nagf_sparse_real_gen_basic_solver Real sparse nonsymmetric linear systems, preconditioned RGMRES, CGS, BiCGSTAB or TFQMR method 
F11BF  nagf_sparse_real_gen_basic_diag Real sparse nonsymmetric linear systems, diagnostic for F11BE 
F11BR  nagf_sparse_complex_gen_basic_setup Complex sparse nonHermitian linear systems, setup for F11BS 
F11BS  nagf_sparse_complex_gen_basic_solver Complex sparse nonHermitian linear systems, preconditioned RGMRES, CGS, BiCGSTAB or TFQMR method 
F11BT  nagf_sparse_complex_gen_basic_diag Complex sparse nonHermitian linear systems, diagnostic for F11BS 
F11DA  nagf_sparse_real_gen_precon_ilu Real sparse nonsymmetric linear systems, incomplete LU factorization 
F11DB  nagf_sparse_real_gen_precon_ilu_solve Solution of linear system involving incomplete LU preconditioning matrix generated by F11DA 
F11DC  nagf_sparse_real_gen_solve_ilu Solution of real sparse nonsymmetric linear system, RGMRES, CGS, BiCGSTAB or TFQMR method, preconditioner computed by F11DA 
F11DD  nagf_sparse_real_gen_precon_ssor_solve Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse nonsymmetric matrix 
F11DE  nagf_sparse_real_gen_solve_jacssor Solution of real sparse nonsymmetric linear system, RGMRES, CGS, BiCGSTAB, or TFQMR method, Jacobi or SSOR preconditioner (Black Box) 
F11DF  nagf_sparse_real_gen_precon_bdilu Real sparse nonsymmetric linear system, incomplete LU factorization of local or overlapping diagonal blocks 
F11DG  nagf_sparse_real_gen_solve_bdilu Solution of real sparse nonsymmetric linear system, RGMRES, CGS, BiCGSTAB or TFQMR method, incomplete LU block diagonal preconditioner computed by F11DF 
F11DK  nagf_sparse_real_gen_precon_jacobi Real, sparse, symmetric or nonsymmetric, linear systems, line Jacobi preconditioner 
F11DN  nagf_sparse_complex_gen_precon_ilu Complex sparse nonHermitian linear systems, incomplete LU factorization 
F11DP  nagf_sparse_complex_gen_precon_ilu_solve Solution of complex linear system involving incomplete LU preconditioning matrix generated by F11DN 
F11DQ  nagf_sparse_complex_gen_solve_ilu Solution of complex sparse nonHermitian linear system, RGMRES, CGS, BiCGSTAB or TFQMR method, preconditioner computed by F11DN (Black Box) 
F11DR  nagf_sparse_complex_gen_precon_ssor_solve Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse nonHermitian matrix 
F11DS  nagf_sparse_complex_gen_solve_jacssor Solution of complex sparse nonHermitian linear system, RGMRES, CGS, BiCGSTAB or TFQMR method, Jacobi or SSOR preconditioner Black Box 
F11DT  nagf_sparse_complex_gen_precon_bdilu Complex, sparse, nonHermitian linear system, incomplete LU factorization of local or overlapping diagonal blocks 
F11DU  nagf_sparse_complex_gen_solve_bdilu Solution of complex, sparse, nonHermitian linear system, RGMRES, CGS, BiCGSTAB or TFQMR method, incomplete LU block diagonal preconditioner computed by F11DT 
F11DX  nagf_sparse_complex_gen_precon_jacobi Complex, sparse, Hermitian or nonHermitian, linear systems, line Jacobi preconditioner 
F11GD  nagf_sparse_real_symm_basic_setup Real sparse symmetric linear systems, setup for F11GE 
F11GE  nagf_sparse_real_symm_basic_solver Real sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos method or the MINRES algorithm 
F11GF  nagf_sparse_real_symm_basic_diag Real sparse symmetric linear systems, diagnostic for F11GE 
F11GR  nagf_sparse_complex_herm_basic_setup Complex sparse Hermitian linear systems, setup for F11GS 
F11GS  nagf_sparse_complex_herm_basic_solver Complex sparse Hermitian linear systems, preconditioned conjugate gradient or Lanczos 
F11GT  nagf_sparse_complex_herm_basic_diag Complex sparse Hermitian linear systems, diagnostic for F11GS 
F11JA  nagf_sparse_real_symm_precon_ichol Real sparse symmetric matrix, incomplete Cholesky factorization 
F11JB  nagf_sparse_real_symm_precon_ichol_solve Solution of linear system involving incomplete Cholesky preconditioning matrix generated by F11JA 
F11JC  nagf_sparse_real_symm_solve_ichol Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JA (Black Box) 
F11JD  nagf_sparse_real_symm_precon_ssor_solve Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse symmetric matrix 
F11JE  nagf_sparse_real_symm_solve_jacssor Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box) 
F11JN  nagf_sparse_complex_herm_precon_ilu Complex sparse Hermitian matrix, incomplete Cholesky factorization 
F11JP  nagf_sparse_complex_herm_precon_ilu_solve Solution of complex linear system involving incomplete Cholesky preconditioning matrix generated by F11JN 
F11JQ  nagf_sparse_complex_herm_solve_ilu Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JN (Black Box) 
F11JR  nagf_sparse_complex_herm_precon_ssor_solve Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse Hermitian matrix 
F11JS  nagf_sparse_complex_herm_solve_jacssor Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box) 
F11MD  nagf_sparse_direct_real_gen_setup Real sparse nonsymmetric linear systems, setup for F11ME 
F11ME  nagf_sparse_direct_real_gen_lu LU factorization of real sparse matrix 
F11MF  nagf_sparse_direct_real_gen_solve Solution of real sparse simultaneous linear equations (coefficient matrix already factorized) 
F11MG  nagf_sparse_direct_real_gen_cond Estimate condition number of real matrix, matrix already factorized by F11ME 
F11MH  nagf_sparse_direct_real_gen_refine Refined solution with error bounds of real system of linear equations, multiple righthand sides 
F11MK  nagf_sparse_direct_real_gen_matmul Real sparse nonsymmetric matrixmatrix multiply, compressed column storage 
F11ML  nagf_sparse_direct_real_gen_norm 1norm, ∞norm, largest absolute element, real, square, sparse matrix 
F11MM  nagf_sparse_direct_real_gen_diag Real sparse nonsymmetric linear systems, diagnostic for F11ME 
F11XA  nagf_sparse_real_gen_matvec Real, sparse, nonsymmetric matrixvector multiply 
F11XE  nagf_sparse_real_symm_matvec Real sparse symmetric matrixvector multiply 
F11XN  nagf_sparse_complex_gen_matvec Complex sparse nonHermitian matrixvector multiply 
F11XS  nagf_sparse_complex_herm_matvec Complex sparse Hermitian matrixvector multiply 
F11YE  nagf_sparse_sym_rcm Reverse Cuthill–McKee reordering of a sparse symmetric matrix in CCS format 
F11ZA  nagf_sparse_real_gen_sort Real sparse nonsymmetric matrix reorder routine 
F11ZB  nagf_sparse_real_symm_sort Real sparse symmetric matrix reorder routine 
F11ZN  nagf_sparse_complex_gen_sort Complex sparse nonHermitian matrix reorder routine 
F11ZP  nagf_sparse_complex_herm_sort Complex sparse Hermitian matrix reorder routine 
F12 – Large Scale Eigenproblems
Examples of routines and methods in this chapter.
F12AA  nagf_sparseig_real_init Initialization routine for (F12AB) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse (standard or generalized) eigenproblem 
F12AB  nagf_sparseig_real_iter Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, reverse communication 
F12AC  nagf_sparseig_real_proc Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, postprocessing for F12AB 
F12AD  nagf_sparseig_real_option Set a single option from a string (F12AB/F12AC/F12AG) 
F12AE  nagf_sparseig_real_monit Provides monitoring information for F12AB 
F12AF  nagf_sparseig_real_band_init Initialization routine for (F12AG) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded (standard or generalized) eigenproblem 
F12AG  nagf_sparseig_real_band_solve Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded eigenproblem, driver 
F12AN  nagf_sparseig_complex_init Initialization routine for (F12AP) computing selected eigenvalues and, optionally, eigenvectors of a complex sparse (standard or generalized) eigenproblem 
F12AP  nagf_sparseig_complex_iter Selected eigenvalues and, optionally, eigenvectors of a complex sparse eigenproblem, reverse communication 
F12AQ  nagf_sparseig_complex_proc Selected eigenvalues and, optionally, eigenvectors of a complex sparse eigenproblem, postprocessing for F12AP 
F12AR  nagf_sparseig_complex_option Set a single option from a string (F12AP/F12AQ) 
F12AS  nagf_sparseig_complex_monit Provides monitoring information for F12AP 
F12AT  nagf_sparseig_complex_band_init Initialization routine for F12AU computing selected eigenvalues and, optionally, eigenvectors of a complex banded (standard or generalized) eigenproblem 
F12AU  nagf_sparseig_complex_band_solve Selected eigenvalues and, optionally, eigenvectors of complex nonHermitian banded eigenproblem, driver 
F12FA  nagf_sparseig_real_symm_init Initialization routine for (F12FB) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse (standard or generalized) eigenproblem 
F12FB  nagf_sparseig_real_symm_iter Selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, reverse communication 
F12FC  nagf_sparseig_real_symm_proc Selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, postprocessing for F12FB 
F12FD  nagf_sparseig_real_symm_option Set a single option from a string (F12FB/F12FC/F12FG) 
F12FE  nagf_sparseig_real_symm_monit Provides monitoring information for F12FB 
F12FF  nagf_sparseig_real_symm_band_init Initialization routine for (F12FG) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric banded (standard or generalized) eigenproblem 
F12FG  nagf_sparseig_real_symm_band_solve Selected eigenvalues and, optionally, eigenvectors of a real symmetric banded eigenproblem, driver 
F16 – Further Linear Algebra Support Routines
Examples of routines and methods in this chapter.
F16DL  nagf_blast_isum Sum elements of integer vector 
F16DN  nagf_blast_imax_val Maximum value and location, integer vector 
F16DP  nagf_blast_imin_val Minimum value and location, integer vector 
F16DQ  nagf_blast_iamax_val Maximum absolute value and location, integer vector 
F16DR  nagf_blast_iamin_val Minimum absolute value and location, integer vector 
F16EA  nagf_blast_ddot Dot product of two vectors, allows scaling and accumulation 
F16EC  nagf_blast_daxpby Real weighted vector addition 
F16EH  nagf_blast_dwaxpby Real weighted vector addition preserving input 
F16EL  nagf_blast_dsum Sum elements of real vector 
F16GC  nagf_blast_zaxpby Complex weighted vector addition 
F16GH  nagf_blast_zwaxpby Complex weighted vector addition preserving input 
F16GL  nagf_blast_zsum Sum elements of complex vector 
F16JN  nagf_blast_dmax_val Maximum value and location, real vector 
F16JP  nagf_blast_dmin_val Minimum value and location, real vector 
F16JQ  nagf_blast_damax_val Maximum absolute value and location, real vector 
F16JR  nagf_blast_damin_val Minimum absolute value and location, real vector 
F16JS  nagf_blast_zamax_val Maximum absolute value and location, complex vector 
F16JT  nagf_blast_zamin_val Minimum absolute value and location, complex vector 
F16RB  nagf_blast_dgb_norm 1norm, ∞norm, Frobenius norm, largest absolute element, real band matrix 
F16UB  nagf_blast_zgb_norm 1norm, ∞norm, Frobenius norm, largest absolute element, complex band matrix 
G01 – Simple Calculations on Statistical Data
Examples of routines and methods in this chapter.
G01AB  nagf_stat_summary_2var Means, corrected sums of squares and crossproducts, etc., two variables, from raw data 
G01AD  nagf_stat_summary_freq Mean, variance, skewness, kurtosis, etc., one variable, from frequency table 
G01AE  nagf_stat_frequency_table Frequency table from raw data 
G01AF  nagf_stat_contingency_table Twoway contingency table analysis, with χ^{2}/Fisher's exact test 
G01AL  nagf_stat_5pt_summary Computes a fivepoint summary (median, hinges and extremes) 
G01AM  nagf_stat_quantiles Find quantiles of an unordered vector, real numbers 
G01AN  nagf_stat_quantiles_stream_fixed Calculates approximate quantiles from a data stream of known size 
G01AP  nagf_stat_quantiles_stream_arbitrary Calculates approximate quantiles from a data stream of unknown size 
G01AR  nagf_stat_plot_stem_leaf Constructs a stem and leaf plot 
G01AS  nagf_stat_plot_box_whisker Constructs a box and whisker plot 
G01AT  nagf_stat_summary_onevar Computes univariate summary information: mean, variance, skewness, kurtosis 
G01AU  nagf_stat_summary_onevar_combine Combines multiple sets of summary information, for use after G01AT 
G01BJ  nagf_stat_prob_binomial Binomial distribution function 
G01BK  nagf_stat_prob_poisson Poisson distribution function 
G01BL  nagf_stat_prob_hypergeom Hypergeometric distribution function 
G01DA  nagf_stat_normal_scores_exact Normal scores, accurate values 
G01DB  nagf_stat_normal_scores_approx Normal scores, approximate values 
G01DC  nagf_stat_normal_scores_var Normal scores, approximate variancecovariance matrix 
G01DD  nagf_stat_test_shapiro_wilk Shapiro and Wilk's W test for Normality 
G01DH  nagf_stat_ranks_and_scores Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores 
G01EA  nagf_stat_prob_normal Computes probabilities for the standard Normal distribution 
G01EB  nagf_stat_prob_students_t Computes probabilities for Student's tdistribution 
G01EC  nagf_stat_prob_chisq Computes probabilities for χ^{2} distribution 
G01ED  nagf_stat_prob_f Computes probabilities for Fdistribution 
G01EE  nagf_stat_prob_beta Computes upper and lower tail probabilities and probability density function for the beta distribution 
G01EF  nagf_stat_prob_gamma Computes probabilities for the gamma distribution 
G01EM  nagf_stat_prob_studentized_range Computes probability for the Studentized range statistic 
G01EP  nagf_stat_prob_durbin_watson Computes bounds for the significance of a Durbin–Watson statistic 
G01ER  nagf_stat_prob_vonmises Computes probability for von Mises distribution 
G01ET  nagf_stat_prob_landau Landau distribution function 
G01EU  nagf_stat_prob_vavilov Vavilov distribution function 
G01EW  nagf_stat_prob_dickey_fuller_unit Computes probabilities for the Dickey–Fuller unit root test 
G01EY  nagf_stat_prob_kolmogorov1 Computes probabilities for the onesample Kolmogorov–Smirnov distribution 
G01EZ  nagf_stat_prob_kolmogorov2 Computes probabilities for the twosample Kolmogorov–Smirnov distribution 
G01FA  nagf_stat_inv_cdf_normal Computes deviates for the standard Normal distribution 
G01FB  nagf_stat_inv_cdf_students_t Computes deviates for Student's tdistribution 
G01FC  nagf_stat_inv_cdf_chisq Computes deviates for the χ^{2} distribution 
G01FD  nagf_stat_inv_cdf_f Computes deviates for the Fdistribution 
G01FE  nagf_stat_inv_cdf_beta Computes deviates for the beta distribution 
G01FF  nagf_stat_inv_cdf_gamma Computes deviates for the gamma distribution 
G01FM  nagf_stat_inv_cdf_studentized_range Computes deviates for the Studentized range statistic 
G01FT  nagf_stat_inv_cdf_landau Landau inverse function Ψ(x) 
G01GB  nagf_stat_prob_students_t_noncentral Computes probabilities for the noncentral Student's tdistribution 
G01GC  nagf_stat_prob_chisq_noncentral Computes probabilities for the noncentral χ^{2} distribution 
G01GD  nagf_stat_prob_f_noncentral Computes probabilities for the noncentral Fdistribution 
G01GE  nagf_stat_prob_beta_noncentral Computes probabilities for the noncentral beta distribution 
G01HA  nagf_stat_prob_bivariate_normal Computes probability for the bivariate Normal distribution 
G01HB  nagf_stat_prob_multi_normal Computes probabilities for the multivariate Normal distribution 
G01HC  nagf_stat_prob_bivariate_students_t Computes probabilities for the bivariate Student's tdistribution 
G01HD  nagf_stat_prob_multi_students_t Computes the probability for the multivariate Student's tdistribution 
G01JC  nagf_stat_prob_chisq_noncentral_lincomb Computes probability for a positive linear combination of χ^{2} variables 
G01JD  nagf_stat_prob_chisq_lincomb Computes lower tail probability for a linear combination of (central) χ^{2} variables 
G01KA  nagf_stat_pdf_normal Calculates the value for the probability density function of the Normal distribution at a chosen point 
G01KF  nagf_stat_pdf_gamma Calculates the value for the probability density function of the gamma distribution at a chosen point 
G01KK  nagf_stat_pdf_gamma_vector Computes a vector of values for the probability density function of the gamma distribution 
G01KQ  nagf_stat_pdf_normal_vector Computes a vector of values for the probability density function of the Normal distribution 
G01LB  nagf_stat_pdf_multi_normal_vector Computes a vector of values for the probability density function of the multivariate Normal distribution 
G01MB  nagf_stat_mills_ratio Computes reciprocal of Mills' Ratio 
G01MT  nagf_stat_pdf_landau Landau density function ϕ(λ) 
G01MU  nagf_stat_pdf_vavilov Vavilov density function ϕ_{V}(λ;κ,β^{2}) 
G01NA  nagf_stat_moments_quad_form Cumulants and moments of quadratic forms in Normal variables 
G01NB  nagf_stat_moments_ratio_quad_forms Moments of ratios of quadratic forms in Normal variables, and related statistics 
G01PT  nagf_stat_pdf_landau_moment1 Landau first moment function Φ_{1}(x) 
G01QT  nagf_stat_pdf_landau_moment2 Landau second moment function Φ_{2}(x) 
G01RT  nagf_stat_pdf_landau_deriv Landau derivative function ϕ^{′}(λ) 
G01SA  nagf_stat_prob_normal_vector Computes a vector of probabilities for the standard Normal distribution 
G01SB  nagf_stat_prob_students_t_vector Computes a vector of probabilities for the Student's tdistribution 
G01SC  nagf_stat_prob_chisq_vector Computes a vector of probabilities for χ^{2} distribution 
G01SD  nagf_stat_prob_f_vector Computes a vector of probabilities for Fdistribution 
G01SE  nagf_stat_prob_beta_vector Computes a vector of probabilities for the beta distribution 
G01SF  nagf_stat_prob_gamma_vector Computes a vector of probabilities for the gamma distribution 
G01SJ  nagf_stat_prob_binomial_vector Computes a vector of probabilities for the binomial distribution 
G01SK  nagf_stat_prob_poisson_vector Computes a vector of probabilities for the Poisson distribution 
G01SL  nagf_stat_prob_hypergeom_vector Computes a vector of probabilities for the hypergeometric distribution 
G01TA  nagf_stat_inv_cdf_normal_vector Computes a vector of deviates for the standard Normal distribution 
G01TB  nagf_stat_inv_cdf_students_t_vector Computes a vector of deviates for Student's tdistribution 
G01TC  nagf_stat_inv_cdf_chisq_vector Computes a vector of deviates for χ^{2} distribution 
G01TD  nagf_stat_inv_cdf_f_vector Computes a vector of deviates for Fdistribution 
G01TE  nagf_stat_inv_cdf_beta_vector Computes a vector of deviates for the beta distribution 
G01TF  nagf_stat_inv_cdf_gamma_vector Computes a vector of deviates for the gamma distribution 
G01WA  nagf_stat_moving_average Computes the mean and standard deviation using a rolling window 
G01ZU  nagf_stat_init_vavilov Initialization routine for G01MU and G01EU 
G02 – Correlation and Regression Analysis
Examples of routines and methods in this chapter.
G02AA  nagf_correg_corrmat_nearest Computes the nearest correlation matrix to a real square matrix, using the method of Qi and Sun 
G02AB  nagf_correg_corrmat_nearest_bounded Computes the nearest correlation matrix to a real square matrix, augmented G02AA to incorporate weights and bounds 
G02AE  nagf_correg_corrmat_nearest_kfactor Computes the nearest correlation matrix with kfactor structure to a real square matrix 
G02AJ  nagf_nearest_correlation_h_weight Computes the nearest correlation matrix to a real square matrix, using elementwise weighting 
G02AN  nagf_nearest_correlation_shrinking Computes a correlation matrix from an approximate matrix with fixed submatrix 
G02AP  nagf_nearest_correlation_target Computes a correlation matrix from an approximate one using a specified target matrix 
G02BA  nagf_correg_coeffs_pearson Pearson productmoment correlation coefficients, all variables, no missing values 
G02BB  nagf_correg_coeffs_pearson_miss_case Pearson productmoment correlation coefficients, all variables, casewise treatment of missing values 
G02BC  nagf_correg_coeffs_pearson_miss_pair Pearson productmoment correlation coefficients, all variables, pairwise treatment of missing values 
G02BD  nagf_correg_coeffs_zero Correlationlike coefficients (about zero), all variables, no missing values 
G02BE  nagf_correg_coeffs_zero_miss_case Correlationlike coefficients (about zero), all variables, casewise treatment of missing values 
G02BF  nagf_correg_coeffs_zero_miss_pair Correlationlike coefficients (about zero), all variables, pairwise treatment of missing values 
G02BG  nagf_correg_coeffs_pearson_subset Pearson productmoment correlation coefficients, subset of variables, no missing values 
G02BH  nagf_correg_coeffs_pearson_subset_miss_case Pearson productmoment correlation coefficients, subset of variables, casewise treatment of missing values 
G02BJ  nagf_correg_coeffs_pearson_subset_miss_pair Pearson productmoment correlation coefficients, subset of variables, pairwise treatment of missing values 
G02BK  nagf_correg_coeffs_zero_subset Correlationlike coefficients (about zero), subset of variables, no missing values 
G02BL  nagf_correg_coeffs_zero_subset_miss_case Correlationlike coefficients (about zero), subset of variables, casewise treatment of missing values 
G02BM  nagf_correg_coeffs_zero_subset_miss_pair Correlationlike coefficients (about zero), subset of variables, pairwise treatment of missing values 
G02BN  nagf_correg_coeffs_kspearman_overwrite Kendall/Spearman nonparametric rank correlation coefficients, no missing values, overwriting input data 
G02BP  nagf_correg_coeffs_kspearman_miss_case_overwrite Kendall/Spearman nonparametric rank correlation coefficients, casewise treatment of missing values, overwriting input data 
G02BQ  nagf_correg_coeffs_kspearman Kendall/Spearman nonparametric rank correlation coefficients, no missing values, preserving input data 
G02BR  nagf_correg_coeffs_kspearman_miss_case Kendall/Spearman nonparametric rank correlation coefficients, casewise treatment of missing values, preserving input data 
G02BS  nagf_correg_coeffs_kspearman_miss_pair Kendall/Spearman nonparametric rank correlation coefficients, pairwise treatment of missing values 
G02BT  nagf_correg_ssqmat_update Update a weighted sum of squares matrix with a new observation 
G02BU  nagf_correg_ssqmat Computes a weighted sum of squares matrix 
G02BW  nagf_correg_ssqmat_to_corrmat Computes a correlation matrix from a sum of squares matrix 
G02BX  nagf_correg_corrmat Computes (optionally weighted) correlation and covariance matrices 
G02BY  nagf_correg_corrmat_partial Computes partial correlation/variancecovariance matrix from correlation/variancecovariance matrix computed by G02BX 
G02BZ  nagf_correg_ssqmat_combine Combines two sums of squares matrices, for use after G02BU 
G02CA  nagf_correg_linregs_const Simple linear regression with constant term, no missing values 
G02CB  nagf_correg_linregs_noconst Simple linear regression without constant term, no missing values 
G02CC  nagf_correg_linregs_const_miss Simple linear regression with constant term, missing values 
G02CD  nagf_correg_linregs_noconst_miss Simple linear regression without constant term, missing values 
G02CE  nagf_correg_linregm_service_select Service routine for multiple linear regression, select elements from vectors and matrices 
G02CF  nagf_correg_linregm_service_reorder Service routine for multiple linear regression, reorder elements of vectors and matrices 
G02CG  nagf_correg_linregm_coeffs_const Multiple linear regression, from correlation coefficients, with constant term 
G02CH  nagf_correg_linregm_coeffs_noconst Multiple linear regression, from correlationlike coefficients, without constant term 
G02DA  nagf_correg_linregm_fit Fits a general (multiple) linear regression model 
G02DC  nagf_correg_linregm_obs_edit Add/delete an observation to/from a general linear regression model 
G02DD  nagf_correg_linregm_update Estimates of linear parameters and general linear regression model from updated model 
G02DE  nagf_correg_linregm_var_add Add a new independent variable to a general linear regression model 
G02DF  nagf_correg_linregm_var_del Delete an independent variable from a general linear regression model 
G02DG  nagf_correg_linregm_fit_newvar Fits a general linear regression model to new dependent variable 
G02DK  nagf_correg_linregm_constrain Estimates and standard errors of parameters of a general linear regression model for given constraints 
G02DN  nagf_correg_linregm_estfunc Computes estimable function of a general linear regression model and its standard error 
G02EA  nagf_correg_linregm_rssq Computes residual sums of squares for all possible linear regressions for a set of independent variables 
G02EC  nagf_correg_linregm_rssq_stat Calculates R^{2} and C_{P} values from residual sums of squares 
G02EE  nagf_correg_linregm_fit_onestep Fits a linear regression model by forward selection 
G02EF  nagf_correg_linregm_fit_stepwise Stepwise linear regression 
G02FA  nagf_correg_linregm_stat_resinf Calculates standardized residuals and influence statistics 
G02FC  nagf_correg_linregm_stat_durbwat Computes Durbin–Watson test statistic 
G02GA  nagf_correg_glm_normal Fits a generalized linear model with Normal errors 
G02GB  nagf_correg_glm_binomial Fits a generalized linear model with binomial errors 
G02GC  nagf_correg_glm_poisson Fits a generalized linear model with Poisson errors 
G02GD  nagf_correg_glm_gamma Fits a generalized linear model with gamma errors 
G02GK  nagf_correg_glm_constrain Estimates and standard errors of parameters of a general linear model for given constraints 
G02GN  nagf_correg_glm_estfunc Computes estimable function of a generalized linear model and its standard error 
G02GP  nagf_correg_glm_predict Computes a predicted value and its associated standard error based on a previously fitted generalized linear model 
G02HA  nagf_correg_robustm Robust regression, standard Mestimates 
G02HB  nagf_correg_robustm_wts Robust regression, compute weights for use with G02HD 
G02HD  nagf_correg_robustm_user Robust regression, compute regression with usersupplied functions and weights 
G02HF  nagf_correg_robustm_user_varmat Robust regression, variancecovariance matrix following G02HD 
G02HK  nagf_correg_robustm_corr_huber Calculates a robust estimation of a covariance matrix, Huber's weight function 
G02HL  nagf_correg_robustm_corr_user_deriv Calculates a robust estimation of a covariance matrix, usersupplied weight function plus derivatives 
G02HM  nagf_correg_robustm_corr_user Calculates a robust estimation of a covariance matrix, usersupplied weight function 
G02JA  nagf_correg_mixeff_reml Linear mixed effects regression using Restricted Maximum Likelihood (REML) 
G02JB  nagf_correg_mixeff_ml Linear mixed effects regression using Maximum Likelihood (ML) 
G02JC  nagf_correg_mixeff_hier_init Hierarchical mixed effects regression, initialization routine for G02JD and G02JE 
G02JD  nagf_correg_mixeff_hier_reml Hierarchical mixed effects regression using Restricted Maximum Likelihood (REML) 
G02JE  nagf_correg_mixeff_hier_ml Hierarchical mixed effects regression using Maximum Likelihood (ML) 
G02KA  nagf_correg_ridge_opt Ridge regression, optimizing a ridge regression parameter 
G02KB  nagf_correg_ridge Ridge regression using a number of supplied ridge regression parameters 
G02LA  nagf_correg_pls_svd Partial least squares (PLS) regression using singular value decomposition 
G02LB  nagf_correg_pls_wold Partial least squares (PLS) regression using Wold's iterative method 
G02LC  nagf_correg_pls_fit PLS parameter estimates following partial least squares regression by G02LA and G02LB 
G02LD  nagf_correg_pls_pred PLS predictions based on parameter estimates from G02LC 
G02MA  nagf_correg_lars Least angle regression (LARS), least absolute shrinkage and selection operator (LASSO) and forward stagewise regression 
G02MB  nagf_correg_lars_xtx Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) and forward stagewise regression using the crossproducts matrix 
G02MC  nagf_correg_lars_param Calculates additional parameter estimates following Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) or forward stagewise regression 
G02QF  nagf_correg_quantile_linreg_easy Linear quantile regression, simple interface, independent, identically distributed (IID) errors 
G02QG  nagf_correg_quantile_linreg Linear quantile regression, comprehensive interface 
G02ZK  nagf_correg_optset Option setting routine for G02QG 
G02ZL  nagf_correg_optget Option getting routine for G02QG 
G03 – Multivariate Methods
Examples of routines and methods in this chapter.
G03AA  nagf_mv_prin_comp Performs principal component analysis 
G03AC  nagf_mv_canon_var Performs canonical variate analysis 
G03AD  nagf_mv_canon_corr Performs canonical correlation analysis 
G03BA  nagf_mv_rot_orthomax Computes orthogonal rotations for loading matrix, generalized orthomax criterion 
G03BC  nagf_mv_rot_procrustes Computes Procrustes rotations 
G03BD  nagf_mv_rot_promax ProMax rotations 
G03CA  nagf_mv_factor Computes maximum likelihood estimates of the parameters of a factor analysis model, factor loadings, communalities and residual correlations 
G03CC  nagf_mv_factor_score Computes factor score coefficients (for use after G03CA) 
G03DA  nagf_mv_discrim Computes test statistic for equality of withingroup covariance matrices and matrices for discriminant analysis 
G03DB  nagf_mv_discrim_mahal Computes Mahalanobis squared distances for group or pooled variancecovariance matrices (for use after G03DA) 
G03DC  nagf_mv_discrim_group Allocates observations to groups according to selected rules (for use after G03DA) 
G03EA  nagf_mv_distance_mat Computes distance matrix 
G03EC  nagf_mv_cluster_hier Hierarchical cluster analysis 
G03EF  nagf_mv_cluster_kmeans Kmeans cluster analysis 
G03EH  nagf_mv_cluster_hier_dendrogram Constructs dendrogram (for use after G03EC) 
G03EJ  nagf_mv_cluster_hier_indicator Computes cluster indicator variable (for use after G03EC) 
G03FA  nagf_mv_multidimscal_metric Performs principal coordinate analysis, classical metric scaling 
G03FC  nagf_mv_multidimscal_ordinal Performs nonmetric (ordinal) multidimensional scaling 
G03GA  nagf_mv_gaussian_mixture Fits a Gaussian mixture model 
G03ZA  nagf_mv_z_scores Produces standardized values (zscores) for a data matrix 
G04 – Analysis of Variance
Examples of routines and methods in this chapter.
G04AG  nagf_anova_hier2 Twoway analysis of variance, hierarchical classification, subgroups of unequal size 
G04BB  nagf_anova_random Analysis of variance, randomized block or completely randomized design, treatment means and standard errors 
G04BC  nagf_anova_rowcol Analysis of variance, general row and column design, treatment means and standard errors 
G04CA  nagf_anova_factorial Analysis of variance, complete factorial design, treatment means and standard errors 
G04DA  nagf_anova_contrasts Computes sum of squares for contrast between means 
G04DB  nagf_anova_confidence Computes confidence intervals for differences between means computed by G04BB or G04BC 
G04EA  nagf_anova_dummyvars Computes orthogonal polynomials or dummy variables for factor/classification variable 
G05 – Random Number Generators
Examples of routines and methods in this chapter.
G05KF  nagf_rand_init_repeat Initializes a pseudorandom number generator to give a repeatable sequence 
G05KG  nagf_rand_init_nonrepeat Initializes a pseudorandom number generator to give a nonrepeatable sequence 
G05KH  nagf_rand_init_leapfrog Primes a pseudorandom number generator for generating multiple streams using leapfrog 
G05KJ  nagf_rand_init_skipahead Primes a pseudorandom number generator for generating multiple streams using skipahead 
G05KK  nagf_rand_init_skipahead_power2 Primes a pseudorandom number generator for generating multiple streams using skipahead, skipping ahead a power of 2 
G05NC  nagf_rand_permute Pseudorandom permutation of an integer vector 
G05ND  nagf_rand_sample Pseudorandom sample from an integer vector 
G05NE  nagf_rand_sample_wgt Pseudorandom sample, without replacement, unequal weights 
G05PD  nagf_rand_times_garch_asym1 Generates a realization of a time series from a GARCH process with asymmetry of the form (ε_{t1}+γ)^{2} 
G05PE  nagf_rand_times_garch_asym2 Generates a realization of a time series from a GARCH process with asymmetry of the form (ε_{t1}+γε_{t1})^{2} 
G05PF  nagf_rand_times_garch_GJR Generates a realization of a time series from an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process 
G05PG  nagf_rand_times_garch_exp Generates a realization of a time series from an exponential GARCH (EGARCH) process 
G05PH  nagf_rand_times_arma Generates a realization of a time series from an ARMA model 
G05PJ  nagf_rand_times_mv_varma Generates a realization of a multivariate time series from a VARMA model 
G05PM  nagf_rand_times_smooth_exp Generates a realization of a time series from an exponential smoothing model 
G05PV  nagf_rand_kfold_xyw Permutes a matrix, vector, vector triplet into a form suitable for Kfold cross validation 
G05PW  nagf_rand_subsamp_xyw Permutes a matrix, vector, vector triplet into a form suitable for random subsampling validation 
G05PX  nagf_rand_matrix_orthog Generates a random orthogonal matrix 
G05PY  nagf_rand_matrix_corr Generates a random correlation matrix 
G05PZ  nagf_rand_matrix_2waytable Generates a random twoway table 
G05RC  nagf_rand_copula_students_t Generates a matrix of pseudorandom numbers from a Student's tcopula 
G05RD  nagf_rand_copula_normal Generates a matrix of pseudorandom numbers from a Gaussian copula 
G05RE  nagf_rand_copula_clayton_bivar Generates a matrix of pseudorandom numbers from a bivariate Clayton/Cook–Johnson copula 
G05RF  nagf_rand_copula_frank_bivar Generates a matrix of pseudorandom numbers from a bivariate Frank copula 
G05RG  nagf_rand_copula_plackett_bivar Generates a matrix of pseudorandom numbers from a bivariate Plackett copula 
G05RH  nagf_rand_copula_clayton Generates a matrix of pseudorandom numbers from a multivariate Clayton/Cook–Johnson copula 
G05RJ  nagf_rand_copula_frank Generates a matrix of pseudorandom numbers from a multivariate Frank copula 
G05RK  nagf_rand_copula_gumbel Generates a matrix of pseudorandom numbers from a Gumbel–Hougaard copula 
G05RY  nagf_rand_multivar_students_t Generates a matrix of pseudorandom numbers from a multivariate Student's tdistribution 
G05RZ  nagf_rand_multivar_normal Generates a matrix of pseudorandom numbers from a multivariate Normal distribution 
G05SA  nagf_rand_dist_uniform01 Generates a vector of pseudorandom numbers from a uniform distribution over (0,1] 
G05SB  nagf_rand_dist_beta Generates a vector of pseudorandom numbers from a beta distribution 
G05SC  nagf_rand_dist_cauchy Generates a vector of pseudorandom numbers from a Cauchy distribution 
G05SD  nagf_rand_dist_chisq Generates a vector of pseudorandom numbers from a χ^{2} distribution 
G05SE  nagf_rand_dist_dirichlet Generates a vector of pseudorandom numbers from a Dirichlet distribution 
G05SF  nagf_rand_dist_exp Generates a vector of pseudorandom numbers from an exponential distribution 
G05SG  nagf_rand_dist_expmix Generates a vector of pseudorandom numbers from an exponential mix distribution 
G05SH  nagf_rand_dist_f Generates a vector of pseudorandom numbers from an Fdistribution 
G05SJ  nagf_rand_dist_gamma Generates a vector of pseudorandom numbers from a gamma distribution 
G05SK  nagf_rand_dist_normal Generates a vector of pseudorandom numbers from a Normal distribution 
G05SL  nagf_rand_dist_logistic Generates a vector of pseudorandom numbers from a logistic distribution 
G05SM  nagf_rand_dist_lognormal Generates a vector of pseudorandom numbers from a lognormal distribution 
G05SN  nagf_rand_dist_students_t Generates a vector of pseudorandom numbers from a Student's tdistribution 
G05SP  nagf_rand_dist_triangular Generates a vector of pseudorandom numbers from a triangular distribution 
G05SQ  nagf_rand_dist_uniform Generates a vector of pseudorandom numbers from a uniform distribution over [a,b] 
G05SR  nagf_rand_dist_vonmises Generates a vector of pseudorandom numbers from a von Mises distribution 
G05SS  nagf_rand_dist_weibull Generates a vector of pseudorandom numbers from a Weibull distribution 
G05TA  nagf_rand_int_binomial Generates a vector of pseudorandom integers from a binomial distribution 
G05TB  nagf_rand_logical Generates a vector of pseudorandom logical values 
G05TC  nagf_rand_int_geom Generates a vector of pseudorandom integers from a geometric distribution 
G05TD  nagf_rand_int_general Generates a vector of pseudorandom integers from a general discrete distribution 
G05TE  nagf_rand_int_hypergeom Generates a vector of pseudorandom integers from a hypergeometric distribution 
G05TF  nagf_rand_int_log Generates a vector of pseudorandom integers from a logarithmic distribution 
G05TG  nagf_rand_int_multinomial Generates a vector of pseudorandom integers from a multinomial distribution 
G05TH  nagf_rand_int_negbin Generates a vector of pseudorandom integers from a negative binomial distribution 
G05TJ  nagf_rand_int_poisson Generates a vector of pseudorandom integers from a Poisson distribution 
G05TK  nagf_rand_int_poisson_varmean Generates a vector of pseudorandom integers from a Poisson distribution with varying mean 
G05TL  nagf_rand_int_uniform Generates a vector of pseudorandom integers from a uniform distribution 
G05XA  nagf_rand_bb_init Initializes the Brownian bridge generator 
G05XB  nagf_rand_bb Generate paths for a free or nonfree Wiener process using the Brownian bridge algorithm 
G05XC  nagf_rand_bb_inc_init Initializes the generator which backs out the increments of sample paths generated by a Brownian bridge algorithm 
G05XD  nagf_rand_bb_inc Backs out the increments from sample paths generated by a Brownian bridge algorithm 
G05XE  nagf_rand_bb_make_bridge_order Creates a Brownian bridge construction order out of a set of input times 
G05YJ  nagf_rand_quasi_normal Generates a Normal quasirandom number sequence 
G05YK  nagf_rand_quasi_lognormal Generates a lognormal quasirandom number sequence 
G05YL  nagf_rand_quasi_init Initializes a quasirandom number generator 
G05YM  nagf_rand_quasi_uniform Generates a uniform quasirandom number sequence 
G05YN  nagf_rand_quasi_init_scrambled Initializes a scrambled quasirandom number generator 
G05ZM  nagf_rand_field_1d_user_setup Setup for simulating onedimensional random fields, userdefined variogram 
G05ZN  nagf_rand_field_1d_predef_setup Setup for simulating onedimensional random fields 
G05ZP  nagf_rand_field_1d_generate Generates realizations of a onedimensional random field 
G05ZQ  nagf_rand_field_2d_user_setup Setup for simulating twodimensional random fields, userdefined variogram 
G05ZR  nagf_rand_field_2d_predef_setup Setup for simulating twodimensional random fields, preset variogram 
G05ZS  nagf_rand_field_2d_generate Generates realizations of a twodimensional random field 
G05ZT  nagf_rand_field_fracbm_generate Generates realizations of fractional Brownian motion 
G07 – Univariate Estimation
Examples of routines and methods in this chapter.
G07AA  nagf_univar_ci_binomial Computes confidence interval for the parameter of a binomial distribution 
G07AB  nagf_univar_ci_poisson Computes confidence interval for the parameter of a Poisson distribution 
G07BB  nagf_univar_estim_normal Computes maximum likelihood estimates for parameters of the Normal distribution from grouped and/or censored data 
G07BE  nagf_univar_estim_weibull Computes maximum likelihood estimates for parameters of the Weibull distribution 
G07BF  nagf_univar_estim_genpareto Estimates parameter values of the generalized Pareto distribution 
G07CA  nagf_univar_ttest_2normal Computes ttest statistic for a difference in means between two Normal populations, confidence interval 
G07DA  nagf_univar_robust_1var_median Robust estimation, median, median absolute deviation, robust standard deviation 
G07DB  nagf_univar_robust_1var_mestim Robust estimation, Mestimates for location and scale parameters, standard weight functions 
G07DC  nagf_univar_robust_1var_mestim_wgt Robust estimation, Mestimates for location and scale parameters, userdefined weight functions 
G07DD  nagf_univar_robust_1var_trimmed Computes a trimmed and winsorized mean of a single sample with estimates of their variance 
G07EA  nagf_univar_robust_1var_ci Robust confidence intervals, onesample 
G07EB  nagf_univar_robust_2var_ci Robust confidence intervals, twosample 
G07GA  nagf_univar_outlier_peirce_1var Outlier detection using method of Peirce, raw data or single variance supplied 
G07GB  nagf_univar_outlier_peirce_2var Outlier detection using method of Peirce, two variances supplied 
G08 – Nonparametric Statistics
Examples of routines and methods in this chapter.
G08AA  nagf_nonpar_test_sign Sign test on two paired samples 
G08AC  nagf_nonpar_test_median Median test on two samples of unequal size 
G08AE  nagf_nonpar_test_friedman Friedman twoway analysis of variance on k matched samples 
G08AF  nagf_nonpar_test_kruskal Kruskal–Wallis oneway analysis of variance on k samples of unequal size 
G08AG  nagf_nonpar_test_wilcoxon Performs the Wilcoxon onesample (matched pairs) signed rank test 
G08AH  nagf_nonpar_test_mwu Performs the Mann–Whitney U test on two independent samples 
G08AJ  nagf_nonpar_prob_mwu_noties Computes the exact probabilities for the Mann–Whitney U statistic, no ties in pooled sample 
G08AK  nagf_nonpar_prob_mwu_ties Computes the exact probabilities for the Mann–Whitney U statistic, ties in pooled sample 
G08AL  nagf_nonpar_test_cochranq Performs the Cochran Q test on crossclassified binary data 
G08BA  nagf_nonpar_test_mooddavid Mood's and David's tests on two samples of unequal size 
G08CB  nagf_nonpar_test_ks_1sample Performs the onesample Kolmogorov–Smirnov test for standard distributions 
G08CC  nagf_nonpar_test_ks_1sample_user Performs the onesample Kolmogorov–Smirnov test for a usersupplied distribution 
G08CD  nagf_nonpar_test_ks_2sample Performs the twosample Kolmogorov–Smirnov test 
G08CG  nagf_nonpar_test_chisq Performs the χ^{2} goodnessoffit test, for standard continuous distributions 
G08CH  nagf_nonpar_gofstat_anddar Calculates the Anderson–Darling goodnessoffit test statistic 
G08CJ  nagf_nonpar_gofstat_anddar_unif Calculates the Anderson–Darling goodnessoffit test statistic and its probability for the case of uniformly distributed data 
G08CK  nagf_nonpar_gofstat_anddar_normal Calculates the Anderson–Darling goodnessoffit test statistic and its probability for the case of a fullyunspecified Normal distribution 
G08CL  nagf_nonpar_gofstat_anddar_exp Calculates the Anderson–Darling goodnessoffit test statistic and its probability for the case of an unspecified exponential distribution 
G08DA  nagf_nonpar_concordance_kendall Kendall's coefficient of concordance 
G08EA  nagf_nonpar_randtest_runs Performs the runs up or runs down test for randomness 
G08EB  nagf_nonpar_randtest_pairs Performs the pairs (serial) test for randomness 
G08EC  nagf_nonpar_randtest_triplets Performs the triplets test for randomness 
G08ED  nagf_nonpar_randtest_gaps Performs the gaps test for randomness 
G08RA  nagf_nonpar_rank_regsn Regression using ranks, uncensored data 
G08RB  nagf_nonpar_rank_regsn_censored Regression using ranks, rightcensored data 
G10 – Smoothing in Statistics
Examples of routines and methods in this chapter.
G10AB  nagf_smooth_fit_spline Fit cubic smoothing spline, smoothing parameter given 
G10AC  nagf_smooth_fit_spline_parest Fit cubic smoothing spline, smoothing parameter estimated 
G10BB  nagf_smooth_kerndens_gauss Kernel density estimate using Gaussian kernel (thread safe) 
G10CA  nagf_smooth_data_runningmedian Compute smoothed data sequence using running median smoothers 
G10ZA  nagf_smooth_data_order Reorder data to give ordered distinct observations 
G11 – Contingency Table Analysis
Examples of routines and methods in this chapter.
G11AA  nagf_contab_chisq χ^{2} statistics for twoway contingency table 
G11BA  nagf_contab_tabulate_stat Computes multiway table from set of classification factors using selected statistic 
G11BB  nagf_contab_tabulate_percentile Computes multiway table from set of classification factors using given percentile/quantile 
G11BC  nagf_contab_tabulate_margin Computes marginal tables for multiway table computed by G11BA or G11BB 
G11CA  nagf_contab_condl_logistic Returns parameter estimates for the conditional analysis of stratified data 
G11SA  nagf_contab_binary Contingency table, latent variable model for binary data 
G11SB  nagf_contab_binary_service Frequency count for G11SA 
G12 – Survival Analysis
Examples of routines and methods in this chapter.
G12AA  nagf_surviv_kaplanmeier Computes Kaplan–Meier (productlimit) estimates of survival probabilities 
G12AB  nagf_surviv_logrank Computes rank statistics for comparing survival curves 
G12BA  nagf_surviv_coxmodel Fits Cox's proportional hazard model 
G12ZA  nagf_surviv_coxmodel_risksets Creates the risk sets associated with the Cox proportional hazards model for fixed covariates 
G13 – Time Series Analysis
Examples of routines and methods in this chapter.
G13AA  nagf_tsa_uni_diff Univariate time series, seasonal and nonseasonal differencing 
G13AB  nagf_tsa_uni_autocorr Univariate time series, sample autocorrelation function 
G13AC  nagf_tsa_uni_autocorr_part Univariate time series, partial autocorrelations from autocorrelations 
G13AD  nagf_tsa_uni_arima_prelim Univariate time series, preliminary estimation, seasonal ARIMA model 
G13AE  nagf_tsa_uni_arima_estim Univariate time series, estimation, seasonal ARIMA model (comprehensive) 
G13AF  nagf_tsa_uni_arima_estim_easy Univariate time series, estimation, seasonal ARIMA model (easytouse) 
G13AG  nagf_tsa_uni_arima_update Univariate time series, update state set for forecasting 
G13AH  nagf_tsa_uni_arima_forecast_state Univariate time series, forecasting from state set 
G13AJ  nagf_tsa_uni_arima_forcecast Univariate time series, state set and forecasts, from fully specified seasonal ARIMA model 
G13AM  nagf_tsa_uni_smooth_exp Univariate time series, exponential smoothing 
G13AS  nagf_tsa_uni_arima_resid Univariate time series, diagnostic checking of residuals, following G13AE or G13AF 
G13AU  nagf_tsa_uni_means Computes quantities needed for rangemean or standard deviationmean plot 
G13AW  nagf_tsa_uni_dickey_fuller_unit Computes (augmented) Dickey–Fuller unit root test statistic 
G13BA  nagf_tsa_multi_filter_arima Multivariate time series, filtering (prewhitening) by an ARIMA model 
G13BB  nagf_tsa_multi_filter_transf Multivariate time series, filtering by a transfer function model 
G13BC  nagf_tsa_multi_xcorr Multivariate time series, crosscorrelations 
G13BD  nagf_tsa_multi_transf_prelim Multivariate time series, preliminary estimation of transfer function model 
G13BE  nagf_tsa_multi_inputmod_estim Multivariate time series, estimation of multiinput model 
G13BG  nagf_tsa_multi_inputmod_update Multivariate time series, update state set for forecasting from multiinput model 
G13BH  nagf_tsa_multi_inputmod_forecast_state Multivariate time series, forecasting from state set of multiinput model 
G13BJ  nagf_tsa_multi_inputmod_forecast Multivariate time series, state set and forecasts from fully specified multiinput model 
G13CA  nagf_tsa_uni_spectrum_lag Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window 
G13CB  nagf_tsa_uni_spectrum_daniell Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window 
G13CC  nagf_tsa_multi_spectrum_lag Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window 
G13CD  nagf_tsa_multi_spectrum_daniell Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window 
G13CE  nagf_tsa_multi_spectrum_bivar Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra 
G13CF  nagf_tsa_multi_gain_bivar Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra 
G13CG  nagf_tsa_multi_noise_bivar Multivariate time series, noise spectrum, bounds, impulse response function and its standard error 
G13DB  nagf_tsa_multi_autocorr_part Multivariate time series, multiple squared partial autocorrelations 
G13DD  nagf_tsa_multi_varma_estimate Multivariate time series, estimation of VARMA model 
G13DJ  nagf_tsa_multi_varma_forecast Multivariate time series, forecasts and their standard errors 
G13DK  nagf_tsa_multi_varma_update Multivariate time series, updates forecasts and their standard errors 
G13DL  nagf_tsa_multi_diff Multivariate time series, differences and/or transforms 
G13DM  nagf_tsa_multi_corrmat_cross Multivariate time series, sample crosscorrelation or crosscovariance matrices 
G13DN  nagf_tsa_multi_corrmat_partlag Multivariate time series, sample partial lag correlation matrices, χ^{2} statistics and significance levels 
G13DP  nagf_tsa_multi_regmat_partial Multivariate time series, partial autoregression matrices 
G13DS  nagf_tsa_multi_varma_diag Multivariate time series, diagnostic checking of residuals, following G13DD 
G13DX  nagf_tsa_uni_arma_roots Calculates the zeros of a vector autoregressive (or moving average) operator 
G13EA  nagf_tsa_multi_kalman_sqrt_var Combined measurement and time update, one iteration of Kalman filter, timevarying, square root covariance filter 
G13EB  nagf_tsa_multi_kalman_sqrt_invar Combined measurement and time update, one iteration of Kalman filter, timeinvariant, square root covariance filter 
G13EJ  nagf_tsa_kalman_unscented_state_revcom Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise (reverse communication) 
G13EK  nagf_tsa_kalman_unscented_state Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise 
G13FA  nagf_tsa_uni_garch_asym1_estim Univariate time series, parameter estimation for either a symmetric GARCH process or a GARCH process with asymmetry of the form (ε_{t1}+γ)^{2} 
G13FB  nagf_tsa_uni_garch_asym1_forecast Univariate time series, forecast function for either a symmetric GARCH process or a GARCH process with asymmetry of the form (ε_{t1}+γ)^{2} 
G13FC  nagf_tsa_uni_garch_asym2_estim Univariate time series, parameter estimation for a GARCH process with asymmetry of the form (ε_{t1}+γε_{t1})^{2} 
G13FD  nagf_tsa_uni_garch_asym2_forecast Univariate time series, forecast function for a GARCH process with asymmetry of the form (ε_{t1}+γε_{t1})^{2} 
G13FE  nagf_tsa_uni_garch_GJR_estim Univariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process 
G13FF  nagf_tsa_uni_garch_GJR_forecast Univariate time series, forecast function for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process 
G13FG  nagf_tsa_uni_garch_exp_estim Univariate time series, parameter estimation for an exponential GARCH (EGARCH) process 
G13FH  nagf_tsa_uni_garch_exp_forecast Univariate time series, forecast function for an exponential GARCH (EGARCH) process 
G13ME  nagf_tsa_inhom_iema Computes the iterated exponential moving average for a univariate inhomogeneous time series 
G13MF  nagf_tsa_inhom_iema_all Computes the iterated exponential moving average for a univariate inhomogeneous time series, intermediate results are also returned 
G13MG  nagf_tsa_inhom_ma Computes the exponential moving average for a univariate inhomogeneous time series 
G13NA  nagf_tsa_cp_pelt Change point detection, using the PELT algorithm 
G13NB  nagf_tsa_cp_pelt_user Change points detection using the PELT algorithm, user supplied cost function 
G13ND  nagf_tsa_cp_binary Change point detection, using binary segmentation 
G13NE  nagf_tsa_cp_binary_user Change point detection, using binary segmentation, user supplied cost function 
G22 – Linear Model Specification
Examples of routines and methods in this chapter.
H – Operations Research
Examples of routines and methods in this chapter.
H02BB  nagf_mip_ilp_dense Integer LP problem (dense) 
H02BF  nagf_mip_ilp_mpsx Interpret MPSX data file defining IP or LP problem, optimize and print solution 
H02BU  nagf_mip_ilp_mpsx_convert Convert MPSX data file defining IP or LP problem to format required by H02BB or E04MF 
H02BV  nagf_mip_ilp_print Print IP or LP solutions with userspecified names for rows and columns 
H02BZ  nagf_mip_ilp_info Integer programming solution, supplies further information on solution obtained by H02BB 
H02CB  nagf_mip_iqp_dense Integer QP problem (dense) 
H02CB  nagf_mip_iqp_dense_dummy_monit dummy 
H02CC  nagf_mip_iqp_dense_optfile Read optional parameter values for H02CB from external file 
H02CD  nagf_mip_iqp_dense_optstr Supply optional parameter values to H02CB 
H02CE  nagf_mip_iqp_sparse Integer LP or QP problem (sparse), using E04NK 
H02CE  nagf_mip_iqp_sparse_dummy_monit dummy 
H02CF  nagf_mip_iqp_sparse_optfile Read optional parameter values for H02CE from external file 
H02CG  nagf_mip_iqp_sparse_optstr Supply optional parameter values to H02CE 
H02DA  nagf_mip_sqp Mixed integer nonlinear programming 
H02ZK  nagf_mip_optset Option setting routine for H02DA 
H02ZL  nagf_mip_optget Option getting routine for H02DA 
H03AB  nagf_mip_transportation Transportation problem, modified 'stepping stone' method 
H03AD  nagf_mip_shortestpath Shortest path problem, Dijkstra's algorithm 
H03BB  nagf_mip_tsp_simann Travelling Salesman Problem, simulated annealing 
H05AA  nagf_best_subset_given_size_revcomm Best n subsets of size p (reverse communication) 
H05AB  nagf_best_subset_given_size Best n subsets of size p (direct communication) 
J10 –
Examples of routines and methods in this chapter.
M01 – Sorting and Searching
Examples of routines and methods in this chapter.
M01CA  nagf_sort_realvec_sort Sort a vector, real numbers 
M01CB  nagf_sort_intvec_sort Sort a vector, integer numbers 
M01CC  nagf_sort_charvec_sort Sort a vector, character data 
M01DA  nagf_sort_realvec_rank Rank a vector, real numbers 
M01DB  nagf_sort_intvec_rank Rank a vector, integer numbers 
M01DC  nagf_sort_charvec_rank Rank a vector, character data 
M01DE  nagf_sort_realmat_rank_rows Rank rows of a matrix, real numbers 
M01DF  nagf_sort_intmat_rank_rows Rank rows of a matrix, integer numbers 
M01DJ  nagf_sort_realmat_rank_columns Rank columns of a matrix, real numbers 
M01DK  nagf_sort_intmat_rank_columns Rank columns of a matrix, integer numbers 
M01DZ  nagf_sort_arbitrary_rank Rank arbitrary data 
M01EA  nagf_sort_realvec_rank_rearrange Rearrange a vector according to given ranks, real numbers 
M01EB  nagf_sort_intvec_rank_rearrange Rearrange a vector according to given ranks, integer numbers 
M01EC  nagf_sort_charvec_rank_rearrange Rearrange a vector according to given ranks, character data 
M01ED  nagf_sort_cmplxvec_rank_rearrange Rearrange a vector according to given ranks, complex numbers 
M01NA  nagf_sort_realvec_search Binary search in set of real numbers 
M01NB  nagf_sort_intvec_search Binary search in set of integer numbers 
M01NC  nagf_sort_charvec_search Binary search in set of character data 
M01ZA  nagf_sort_permute_invert Invert a permutation 
M01ZB  nagf_sort_permute_check Check validity of a permutation 
M01ZC  nagf_sort_permute_decompose Decompose a permutation into cycles 
P01 – Error Trapping
Examples of routines and methods in this chapter.
S – Approximations of Special Functions
Examples of routines and methods in this chapter.
S01BA  nagf_specfun_log_shifted ln (1+x) 
S01EA  nagf_specfun_exp_complex Complex exponential, e^{z} 
S07AA  nagf_specfun_tan tan x 
S09AA  nagf_specfun_arcsin arcsin x 
S09AB  nagf_specfun_arccos arccos x 
S10AA  nagf_specfun_tanh tanh x 
S10AB  nagf_specfun_sinh sinh x 
S10AC  nagf_specfun_cosh cosh x 
S11AA  nagf_specfun_arctanh arctanh x 
S11AB  nagf_specfun_arcsinh arcsinh x 
S11AC  nagf_specfun_arccosh arccosh x 
S13AA  nagf_specfun_integral_exp Exponential integral E_{1}(x) 
S13AC  nagf_specfun_integral_cos Cosine integral Ci (x) 
S13AD  nagf_specfun_integral_sin Sine integral Si (x) 
S14AA  nagf_specfun_gamma Gamma function 
S14AB  nagf_specfun_gamma_log_real Log gamma function, real argument 
S14AC  nagf_specfun_polygamma ψ(x)ln x 
S14AD  nagf_specfun_polygamma_deriv Scaled derivatives of ψ(x) 
S14AE  nagf_specfun_psi_deriv_real Polygamma function ψ^{(n)}(x) for real x 
S14AF  nagf_specfun_psi_deriv_complex Polygamma function ψ^{(n)}(z) for complex z 
S14AG  nagf_specfun_gamma_log_complex Logarithm of the gamma function ln Γ(z), complex argument 
S14AH  nagf_specfun_gamma_log_scaled_real Scaled log gamma function 
S14BA  nagf_specfun_gamma_incomplete Incomplete gamma functions P(a,x) and Q(a,x) 
S14CB  nagf_specfun_beta_log_real Logarithm of the beta function ln B(a,b) 
S14CC  nagf_specfun_beta_incomplete Incomplete beta function I_{x}(a,b) and its complement 1I_{x} 
S15AB  nagf_specfun_cdf_normal Cumulative Normal distribution function P(x) 
S15AC  nagf_specfun_compcdf_normal Complement of cumulative Normal distribution function Q(x) 
S15AD  nagf_specfun_erfc_real Complement of error function erfc (x) 
S15AE  nagf_specfun_erf_real Error function erf (x) 
S15AF  nagf_specfun_dawson Dawson's integral 
S15AG  nagf_specfun_erfcx_real Scaled complement of error function, erfcx (x) 
S15DD  nagf_specfun_erfc_complex Scaled complex complement of error function, exp (z^{2})erfc (iz) 
S17AC  nagf_specfun_bessel_y0_real Bessel function Y_{0}(x) 
S17AD  nagf_specfun_bessel_y1_real Bessel function Y_{1}(x) 
S17AE  nagf_specfun_bessel_j0_real Bessel function J_{0}(x) 
S17AF  nagf_specfun_bessel_j1_real Bessel function J_{1}(x) 
S17AG  nagf_specfun_airy_ai_real Airy function Ai (x) 
S17AH  nagf_specfun_airy_bi_real Airy function Bi (x) 
S17AJ  nagf_specfun_airy_ai_deriv Airy function Ai^{′} (x) 
S17AK  nagf_specfun_airy_bi_deriv Airy function Bi^{′} (x) 
S17AL  nagf_specfun_bessel_zeros Zeros of Bessel functions J_{α}(x), J_{α}^{′}(x), Y_{α}(x) or Y_{α}^{′}(x) 
S17AQ  nagf_specfun_bessel_y0_real_vector Bessel function vectorized Y_{0}(x) 
S17AR  nagf_specfun_bessel_y1_real_vector Bessel function vectorized Y_{1}(x) 
S17AS  nagf_specfun_bessel_j0_real_vector Bessel function vectorized J_{0}(x) 
S17AT  nagf_specfun_bessel_j1_real_vector Bessel function vectorized J_{1}(x) 
S17AU  nagf_specfun_airy_ai_real_vector Airy function vectorized Ai (x) 
S17AV  nagf_specfun_airy_bi_real_vector Airy function vectorized Bi (x) 
S17AW  nagf_specfun_airy_ai_deriv_vector Derivatives of the Airy function, vectorized Ai^{′} (x) 
S17AX  nagf_specfun_airy_bi_deriv_vector Derivatives of the Airy function, vectorized Bi^{′} (x) 
S17DC  nagf_specfun_bessel_y_complex Bessel functions Y_{ν+a}(z), real a≥0, complex z, ν=0,1,2,… 
S17DE  nagf_specfun_bessel_j_complex Bessel functions J_{ν+a}(z), real a≥0, complex z, ν=0,1,2,… 
S17DG  nagf_specfun_airy_ai_complex Airy functions Ai (z) and Ai^{′} (z), complex z 
S17DH  nagf_specfun_airy_bi_complex Airy functions Bi (z) and Bi^{′} (z), complex z 
S17DL  nagf_specfun_hankel_complex Hankel functions H_{ν+a}^{(j)}(z), j=1,2, real a≥0, complex z, ν=0,1,2,… 
S18AC  nagf_specfun_bessel_k0_real Modified Bessel function K_{0}(x) 
S18AD  nagf_specfun_bessel_k1_real Modified Bessel function K_{1}(x) 
S18AE  nagf_specfun_bessel_i0_real Modified Bessel function I_{0}(x) 
S18AF  nagf_specfun_bessel_i1_real Modified Bessel function I_{1}(x) 
S18AQ  nagf_specfun_bessel_k0_real_vector Modified Bessel function vectorized K_{0}(x) 
S18AR  nagf_specfun_bessel_k1_real_vector Modified Bessel function vectorized K_{1}(x) 
S18AS  nagf_specfun_bessel_i0_real_vector Modified Bessel function vectorized I_{0}(x) 
S18AT  nagf_specfun_bessel_i1_real_vector Modified Bessel function vectorized I_{1}(x) 
S18CC  nagf_specfun_bessel_k0_scaled Scaled modified Bessel function e^{x}K_{0}(x) 
S18CD  nagf_specfun_bessel_k1_scaled Scaled modified Bessel function e^{x}K_{1}(x) 
S18CE  nagf_specfun_bessel_i0_scaled Scaled modified Bessel function e^{x}I_{0}(x) 
S18CF  nagf_specfun_bessel_i1_scaled Scaled modified Bessel function e^{x}I_{1}(x) 
S18CQ  nagf_specfun_bessel_k0_scaled_vector Scaled modified Bessel function vectorized e^{x}K_{0}(x) 
S18CR  nagf_specfun_bessel_k1_scaled_vector Scaled modified Bessel function vectorized e^{x}K_{1}(x) 
S18CS  nagf_specfun_bessel_i0_scaled_vector Scaled modified Bessel function vectorized e^{x}I_{0}(x) 
S18CT  nagf_specfun_bessel_i1_scaled_vector Scaled modified Bessel function vectorized e^{x}I_{1}(x) 
S18DC  nagf_specfun_bessel_k_complex Modified Bessel functions K_{ν+a}(z), real a≥0, complex z, ν=0,1,2,… 
S18DE  nagf_specfun_bessel_i_complex Modified Bessel functions I_{ν+a}(z), real a≥0, complex z, ν=0,1,2,… 
S18GK  nagf_specfun_bessel_j_seq_complex Bessel function of the 1st kind J_{α±n}(z) 
S19AA  nagf_specfun_kelvin_ber Kelvin function ber x 
S19AB  nagf_specfun_kelvin_bei Kelvin function bei x 
S19AC  nagf_specfun_kelvin_ker Kelvin function ker x 
S19AD  nagf_specfun_kelvin_kei Kelvin function kei x 
S19AN  nagf_specfun_kelvin_ber_vector Kelvin function vectorized ber x 
S19AP  nagf_specfun_kelvin_bei_vector Kelvin function vectorized bei x 
S19AQ  nagf_specfun_kelvin_ker_vector Kelvin function vectorized ker x 
S19AR  nagf_specfun_kelvin_kei_vector Kelvin function vectorized kei x 
S20AC  nagf_specfun_fresnel_s Fresnel integral S(x) 
S20AD  nagf_specfun_fresnel_c Fresnel integral C(x) 
S20AQ  nagf_specfun_fresnel_s_vector Fresnel integral vectorized S(x) 
S20AR  nagf_specfun_fresnel_c_vector Fresnel integral vectorized C(x) 
S21BA  nagf_specfun_ellipint_symm_1_degen Degenerate symmetrised elliptic integral of 1st kind R_{C}(x,y) 
S21BB  nagf_specfun_ellipint_symm_1 Symmetrised elliptic integral of 1st kind R_{F}(x,y,z) 
S21BC  nagf_specfun_ellipint_symm_2 Symmetrised elliptic integral of 2nd kind R_{D}(x,y,z) 
S21BD  nagf_specfun_ellipint_symm_3 Symmetrised elliptic integral of 3rd kind R_{J}(x,y,z,r) 
S21BE  nagf_specfun_ellipint_legendre_1 Elliptic integral of 1st kind, Legendre form, F(ϕ∣m) 
S21BF  nagf_specfun_ellipint_legendre_2 Elliptic integral of 2nd kind, Legendre form, E(ϕ∣m) 
S21BG  nagf_specfun_ellipint_legendre_3 Elliptic integral of 3rd kind, Legendre form, Π(n;ϕ∣m) 
S21BH  nagf_specfun_ellipint_complete_1 Complete elliptic integral of 1st kind, Legendre form, K(m) 
S21BJ  nagf_specfun_ellipint_complete_2 Complete elliptic integral of 2nd kind, Legendre form, E(m) 
S21CA  nagf_specfun_jacellip_real Jacobian elliptic functions sn, cn and dn of real argument 
S21CB  nagf_specfun_jacellip_complex Jacobian elliptic functions sn, cn and dn of complex argument 
S21CC  nagf_specfun_jactheta_real Jacobian theta functions θ_{k}(x,q) of real argument 
S21DA  nagf_specfun_ellipint_general_2 General elliptic integral of 2nd kind F(z,k^{′},a,b) of complex argument 
S22AA  nagf_specfun_legendre_p Legendre functions of 1st kind P_{n}^{m}(x) or P_{n}^{m}^{}(x) 
S22BA  nagf_specfun_1f1_real Real confluent hypergeometric function _{1}F_{1}(a;b;x) 
S22BB  nagf_specfun_1f1_real_scaled Real confluent hypergeometric function _{1}F_{1}(a;b;x) in scaled form 
S22BE  nagf_specfun_2f1_real Real Gauss hypergeometric function _{2}F_{1}(a,b;c;x) 
S22BF  nagf_specfun_2f1_real_scaled Real Gauss hypergeometric function _{2}F_{1}(a,b;c;x) in scaled form 
S30AA  nagf_specfun_opt_bsm_price Black–Scholes–Merton option pricing formula 
S30AB  nagf_specfun_opt_bsm_greeks Black–Scholes–Merton option pricing formula with Greeks 
S30BA  nagf_specfun_opt_lookback_fls_price Floatingstrike lookback option pricing formula in the BlackScholesMerton model 
S30BB  nagf_specfun_opt_lookback_fls_greeks Floatingstrike lookback option pricing formula with Greeks in the BlackScholesMerton model 
S30CA  nagf_specfun_opt_binary_con_price Binary option, cashornothing pricing formula 
S30CB  nagf_specfun_opt_binary_con_greeks Binary option, cashornothing pricing formula with Greeks 
S30CC  nagf_specfun_opt_binary_aon_price Binary option, assetornothing pricing formula 
S30CD  nagf_specfun_opt_binary_aon_greeks Binary option, assetornothing pricing formula with Greeks 
S30FA  nagf_specfun_opt_barrier_std_price Standard barrier option pricing formula 
S30JA  nagf_specfun_opt_jumpdiff_merton_price Jumpdiffusion, Merton's model, option pricing formula 
S30JB  nagf_specfun_opt_jumpdiff_merton_greeks Jumpdiffusion, Merton's model, option pricing formula with Greeks 
S30NA  nagf_specfun_opt_heston_price Heston's model option pricing formula 
S30NB  nagf_specfun_opt_heston_greeks Heston's model option pricing formula with Greeks 
S30NC  nagf_specfun_opt_heston_term Heston's model option pricing with term structure 
S30QC  nagf_specfun_opt_amer_bs_price American option, Bjerksund and Stensland pricing formula 
S30SA  nagf_specfun_opt_asian_geom_price Asian option, geometric continuous average rate pricing formula 
S30SB  nagf_specfun_opt_asian_geom_greeks Asian option, geometric continuous average rate pricing formula with Greeks 
X01 – Mathematical Constants
Examples of routines and methods in this chapter.
X01AA  nagf_math_pi Provides the mathematical constant π 
X01AB  nagf_math_euler Provides the mathematical constant γ (Euler's constant) 
X02 – Machine Constants
Examples of routines and methods in this chapter.
X02AH  nagf_machine_sinarg_max The largest permissible argument for sin and cos 
X02AJ  nagf_machine_precision The machine precision 
X02AK  nagf_machine_real_smallest The smallest positive model number 
X02AL  nagf_machine_real_largest The largest positive model number 
X02AM  nagf_machine_real_safe The safe range parameter 
X02AN  nagf_machine_complex_safe The safe range parameter for complex floatingpoint arithmetic 
X02BB  nagf_machine_integer_max The largest representable integer 
X02BE  nagf_machine_decimal_digits The maximum number of decimal digits that can be represented 
X02BH  nagf_machine_model_base The floatingpoint model parameter, b 
X02BJ  nagf_machine_model_digits The floatingpoint model parameter, p 
X02BK  nagf_machine_model_minexp The floatingpoint model parameter e_{min} 
X02BL  nagf_machine_model_maxexp The floatingpoint model parameter e_{max} 
X03 – Inner Products
Examples of routines and methods in this chapter.
X03AA  nagf_dot_real_prec Real inner product added to initial value, basic/additional precision 
X03AB  nagf_dot_complex_prec Complex inner product added to initial value, basic/additional precision 
X04 – Input/Output Utilities
Examples of routines and methods in this chapter.
X04AA  nagf_file_set_unit_error Return or set unit number for error messages 
X04AB  nagf_file_set_unit_advisory Return or set unit number for advisory messages 
X04AC  nagf_file_open Open unit number for reading, writing or appending, and associate unit with named file 
X04AD  nagf_file_close Close file associated with given unit number 
X04BA  nagf_file_line_write Write formatted record to external file 
X04BB  nagf_file_line_read Read formatted record from external file 
X04CA  nagf_file_print_matrix_real_gen Print real general matrix (easytouse) 
X04CB  nagf_file_print_matrix_real_gen_comp Print real general matrix (comprehensive) 
X04CC  nagf_file_print_matrix_real_packed Print real packed triangular matrix (easytouse) 
X04CD  nagf_file_print_matrix_real_packed_comp Print real packed triangular matrix (comprehensive) 
X04CE  nagf_file_print_matrix_real_band Print real packed banded matrix (easytouse) 
X04CF  nagf_file_print_matrix_real_band_comp Print real packed banded matrix (comprehensive) 
X04DA  nagf_file_print_matrix_complex_gen Print complex general matrix (easytouse) 
X04DB  nagf_file_print_matrix_complex_gen_comp Print complex general matrix (comprehensive) 
X04DC  nagf_file_print_matrix_complex_packed Print complex packed triangular matrix (easytouse) 
X04DD  nagf_file_print_matrix_complex_packed_comp Print complex packed triangular matrix (comprehensive) 
X04DE  nagf_file_print_matrix_complex_band Print complex packed banded matrix (easytouse) 
X04DF  nagf_file_print_matrix_complex_band_comp Print complex packed banded matrix (comprehensive) 
X04EA  nagf_file_print_matrix_integer Print integer matrix (easytouse) 
X04EB  nagf_file_print_matrix_integer_comp Print integer matrix (comprehensive) 
X05 – Date and Time Utilities
Examples of routines and methods in this chapter.
X05AA  nagf_time_date_array Return date and time as an array of integers 
X05AB  nagf_time_date_array_string Convert array of integers representing date and time to character string 
X05AC  nagf_time_date_string_compare Compare two character strings representing date and time 
X05BA  nagf_time_cpu Return the CPU time 
X06 – OpenMP Utilities
Examples of routines and methods in this chapter.
X06AA  nagf_omp_set_num_threads Sets the number of threads for OpenMP parallel regions 
X06AB  nagf_omp_get_num_threads The number of OpenMP threads in the current team 
X06AC  nagf_omp_get_max_threads An upper bound on the number of threads in the next parallel region 
X06AD  nagf_omp_get_thread_num The OpenMP thread number of the calling thread 
X06AF  nagf_omp_in_parallel Tests for an active OpenMP parallel region 
X06AG  nagf_omp_set_nested Enables or disables nested OpenMP parallelism 
X06AH  nagf_omp_get_nested Tests the status of nested OpenMP parallelism 
X06XA  nagf_omp_using_threaded_impl Tests whether a threaded NAG Library is being used 
X07 – IEEE Arithmetic
Examples of routines and methods in this chapter.
X07AA  nagf_is_finite Determines whether its argument has a finite value 
X07AB  nagf_is_nan Determines whether its argument is a NaN (Not A Number) 
X07BA  nagf_create_infinity Creates a signed infinite value 
X07BB  nagf_create_nan Creates a NaN (Not A Number) 
X07CA  nagf_get_ieee_exception_mode Gets current behaviour of floatingpoint exceptions 
X07CB  nagf_set_ieee_exception_mode Sets behaviour of floatingpoint exceptions 