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').
This chapter provides facilities for arithmetic operations involving complex numbers.
This chapter is concerned with computing the zeros of a polynomial with real or complex coefficients.
This chapter is concerned with the calculation of zeros of continuous functions of one or more variables. The majority of problems considered are for real-valued functions of real variables, in which case complex equations must be expressed in terms of the equivalent larger system of real equations.
This chapter is concerned with the following tasks.
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((t-b)/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}t-k).
The continuous real valued, one-dimensional wavelet transform (CWT) is included in this chapter. The discrete wavelet transform (DWT) at a single level together with its inverse and the multi-level DWT with inverse are also provided for one, two and three dimensions. The Maximal Overlap DWT (MODWT) together with its inverse and the multi-level 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.
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.
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, two-point boundary value problems and Sturm–Liouville eigenvalue problems.
This chapter is concerned with the numerical solution of partial differential equations.
This chapter is concerned with calculating approximations to derivatives of a function f.
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:
This chapter is concerned with automatic mesh generation
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 lowest-order 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.
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).
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.
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.
This chapter provides facilities for four types of problem:
See the Chapter Introduction where these problems are discussed.
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.
This chapter is concerned with the calculation of determinants of square matrices.
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 right-hand 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.
This chapter is concerned with the orthogonalization of vectors in a finite dimensional space.
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).
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 high-performance computers, without compromising efficiency on conventional serial machines.
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 high-performance computers, without compromising efficiency on conventional serial machines.
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 non-Hermitian and Hermitian linear systems and direct methods for general real linear systems. Further direct methods are currently available in Chapters F01 and F04.
This chapter provides routines for computing some eigenvalues and eigenvectors of large-scale (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 Large-scale 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 Large-scale 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.
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.
This chapter covers three topics:
This chapter is concerned with two techniques
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.
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 variable-directed methods, and those that seek to examine the relationships between the objects (e.g., cluster analysis), known as individual-directed 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.
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.
This chapter is concerned with the generation of sequences of independent pseudorandom and quasi-random numbers from various distributions, and models.
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.
The routines in this chapter perform nonparametric statistical tests which are based on distribution-free 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.
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.
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 two-way contingency tables, conditional logistic models and one-factor 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.
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.
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.
This chapter provides routines to solve certain integer programming, transportation and shortest path problems. Additionally 'best subset' routines are included.
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.
This chapter is concerned with the provision of some commonly occurring physical and mathematical functions.
This chapter is concerned with the provision of mathematical constants required by other routines within the Library.
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 floating-point 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.
This chapter is concerned with the calculation of innerproducts required by other routines within the Library.
This chapter contains utility routines concerned with input and output to or from an external file.
This chapter provides routines to obtain the current real time, and the amount of processor time used.
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.
This chapter provides routines to handle various aspects of IEEE floating-point arithmetic behaviour.
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 |
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 |
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 |
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 (easy-to-use) |
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 (easy-to-use) |
C05RB | nagf_roots_sys_deriv_easy Solution of a system of nonlinear equations using first derivatives (easy-to-use) |
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 |
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 one-dimensional real discrete Fourier transform, extra workspace for greater speed |
C06FB | nagf_sum_fft_hermitian_1d_rfmt Single one-dimensional Hermitian discrete Fourier transform, extra workspace for greater speed |
C06FC | nagf_sum_fft_complex_1d_sep Single one-dimensional complex discrete Fourier transform, extra workspace for greater speed |
C06FF | nagf_sum_fft_complex_multid_1d_sep One-dimensional 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 Three-dimensional 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 one-dimensional real and Hermitian complex discrete Fourier transform, using complex storage format for Hermitian sequences |
C06PC | nagf_sum_fft_complex_1d Single one-dimensional complex discrete Fourier transform, complex data type |
C06PF | nagf_sum_fft_complex_multid_1d One-dimensional 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 one-dimensional 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 one-dimensional 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 one-dimensional complex discrete Fourier transforms using complex data type |
C06PS | nagf_sum_fft_complex_1d_multi_col Multiple one-dimensional complex discrete Fourier transforms, complex data type |
C06PU | nagf_sum_fft_complex_2d Two-dimensional complex discrete Fourier transform, complex data type |
C06PV | nagf_sum_fft_real_2d Two-dimensional real-to-complex discrete Fourier transform |
C06PW | nagf_sum_fft_hermitian_2d Two-dimensional complex-to-real discrete Fourier transform |
C06PX | nagf_sum_fft_complex_3d Three-dimensional complex discrete Fourier transform, complex data type |
C06PY | nagf_sum_fft_real_3d Three-dimensional real-to-complex discrete Fourier transform |
C06PZ | nagf_sum_fft_hermitian_3d Three-dimensional complex-to-real discrete Fourier transform |
C06RA | nagf_sum_fft_real_sine_simple Discrete sine transform (easy-to-use) |
C06RB | nagf_sum_fft_real_cosine_simple Discrete cosine transform (easy-to-use) |
C06RC | nagf_sum_fft_real_qtrsine_simple Discrete quarter-wave sine transform (easy-to-use) |
C06RD | nagf_sum_fft_real_qtrcosine_simple Discrete quarter-wave cosine transform (easy-to-use) |
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 quarter-wave sine transforms, simple |
C06RH | nagf_sum_fft_qtrcosine Multiple discrete quarter-wave cosine transforms, simple |
Examples of routines and methods in this chapter.
C09AA | nagf_wav_1d_init One-dimensional wavelet filter initialization |
C09AB | nagf_wav_2d_init Two-dimensional wavelet filter initialization |
C09AC | nagf_wav_3d_init Three-dimensional wavelet filter initialization |
C09BA | nagf_wav_1d_cont One-dimensional real continuous wavelet transform |
C09CA | nagf_wav_1d_sngl_fwd One-dimensional discrete wavelet transform |
C09CB | nagf_wav_1d_sngl_inv One-dimensional inverse discrete wavelet transform |
C09CC | nagf_wav_1d_multi_fwd One-dimensional multi-level discrete wavelet transform |
C09CD | nagf_wav_1d_multi_inv One-dimensional inverse multi-level discrete wavelet transform |
C09DA | nagf_wav_1d_mxolap_fwd One-dimensional maximal overlap discrete wavelet transform (MODWT) |
C09DB | nagf_wav_1d_mxolap_inv One-dimensional inverse maximal overlap discrete wavelet transform (IMODWT) |
C09DC | nagf_wav_1d_mxolap_multi_fwd One-dimensional multi-level maximal overlap discrete wavelet transform (MODWT) |
C09DD | nagf_wav_1d_mxolap_multi_inv One-dimensional inverse multi-level maximal overlap discrete wavelet transform (IMODWT) |
C09EA | nagf_wav_2d_sngl_fwd Two-dimensional discrete wavelet transform |
C09EB | nagf_wav_2d_sngl_inv Two-dimensional inverse discrete wavelet transform |
C09EC | nagf_wav_2d_multi_fwd Two-dimensional multi-level discrete wavelet transform |
C09ED | nagf_wav_2d_multi_inv Two-dimensional inverse multi-level discrete wavelet transform |
C09EY | nagf_wav_2d_coeff_ext Two-dimensional discrete wavelet transform coefficient extraction |
C09EZ | nagf_wav_2d_coeff_ins Two-dimensional discrete wavelet transform coefficient insertion |
C09FA | nagf_wav_3d_sngl_fwd Three-dimensional discrete wavelet transform |
C09FB | nagf_wav_3d_sngl_inv Three-dimensional inverse discrete wavelet transform |
C09FC | nagf_wav_3d_multi_fwd Three-dimensional multi-level discrete wavelet transform |
C09FD | nagf_wav_3d_mxolap_multi_inv Three-dimensional inverse multi-level discrete wavelet transform |
C09FY | nagf_wav_3d_coeff_ext Three-dimensional discrete wavelet transform coefficient extraction |
C09FZ | nagf_wav_3d_coeff_ins Three-dimensional discrete wavelet transform coefficient insertion |
Examples of routines and methods in this chapter.
D01AH | nagf_quad_1d_fin_well One-dimensional quadrature, adaptive, finite interval, strategy due to Patterson, suitable for well-behaved integrands |
D01AJ | nagf_quad_1d_fin_bad One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands |
D01AK | nagf_quad_1d_fin_osc One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions |
D01AL | nagf_quad_1d_fin_sing One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points |
D01AM | nagf_quad_1d_inf One-dimensional quadrature, adaptive, infinite or semi-infinite interval |
D01AN | nagf_quad_1d_fin_wtrig One-dimensional quadrature, adaptive, finite interval, weight function cos (ωx) or sin (ωx) |
D01AP | nagf_quad_1d_fin_wsing One-dimensional quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type |
D01AQ | nagf_quad_1d_fin_wcauchy One-dimensional quadrature, adaptive, finite interval, weight function 1/(x-c), Cauchy principal value (Hilbert transform) |
D01AR | nagf_quad_1d_indef One-dimensional quadrature, non-adaptive, finite interval with provision for indefinite integrals |
D01AS | nagf_quad_1d_inf_wtrig One-dimensional quadrature, adaptive, semi-infinite interval, weight function cos (ωx) or sin (ωx) |
D01AT | nagf_quad_1d_fin_bad_vec One-dimensional quadrature, adaptive, finite interval, variant of D01AJ efficient on vector machines |
D01AU | nagf_quad_1d_fin_osc_vec One-dimensional 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 One-dimensional quadrature, non-adaptive, finite interval |
D01DA | nagf_quad_2d_fin Two-dimensional quadrature, finite region |
D01EA | nagf_quad_md_adapt_multi Multidimensional adaptive quadrature over hyper-rectangle, multiple integrands |
D01ES | nagf_quad_md_sgq_multi_vec Multi-dimensional quadrature using sparse grids |
D01FB | nagf_quad_md_gauss Multidimensional Gaussian quadrature over hyper-rectangle |
D01FC | nagf_quad_md_adapt Multidimensional adaptive quadrature over hyper-rectangle |
D01FD | nagf_quad_md_sphere Multidimensional quadrature, Sag–Szekeres method, general product region or n-sphere |
D01FD | nagf_quad_md_sphere_dummy_region dummy |
D01GA | nagf_quad_1d_data One-dimensional quadrature, integration of function defined by data values, Gill–Miller method |
D01GB | nagf_quad_md_mcarlo Multidimensional quadrature over hyper-rectangle, Monte–Carlo method |
D01GC | nagf_quad_md_numth Multidimensional quadrature, general product region, number-theoretic method |
D01GD | nagf_quad_md_numth_vec Multidimensional quadrature, general product region, number-theoretic 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 n-sphere, allowing for badly behaved integrands |
D01PA | nagf_quad_md_simplex Multidimensional quadrature over an n-simplex |
D01RA | nagf_quad_1d_gen_vec_multi_rcomm One-dimensional 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 One-dimensional quadrature, adaptive, finite interval, strategy due to Gonnet, allowing for badly behaved integrands |
D01TB | nagf_quad_1d_gauss_wres Pre-computed 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 One-dimensional Gaussian quadrature, choice of weight functions (vectorized) |
D01UB | nagf_quad_1d_inf_exp_wt Non-automatic 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 |
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 nth-order linear equation |
D02JB | nagf_ode_bvp_coll_sys Ordinary differential equations, boundary value problem, collocation and least squares, system of first-order linear equations |
D02KA | nagf_ode_sl2_reg_finite Second-order Sturm–Liouville problem, regular system, finite range, eigenvalue only |
D02KA | nagf_ode_sl2_reg_finite_dummy_monit dummy |
D02KD | nagf_ode_sl2_breaks_vals Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, user-specified break-points |
D02KE | nagf_ode_sl2_breaks_funs Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points |
D02LA | nagf_ode_ivp_2nd_rkn Second-order ordinary differential equations, initial value problem, Runge–Kutta–Nystrom method |
D02LX | nagf_ode_ivp_2nd_rkn_setup Second-order ordinary differential equations, initial value problem, setup for D02LA |
D02LY | nagf_ode_ivp_2nd_rkn_diag Second-order ordinary differential equations, initial value problem, diagnostics for D02LA |
D02LZ | nagf_ode_ivp_2nd_rkn_interp Second-order 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 root-finding (direct communication, comprehensive) |
D02QG | nagf_ode_ivp_adams_roots_revcom Ordinary differential equations, initial value problem, Adams' method with root-finding (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, root-finding 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 nth-order 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 low-order-derivative 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 |
Examples of routines and methods in this chapter.
D03EA | nagf_pde_2d_laplace Elliptic PDE, Laplace's equation, two-dimensional arbitrary domain |
D03EB | nagf_pde_2d_ellip_fd Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, iterate to convergence |
D03EC | nagf_pde_3d_ellip_fd Elliptic PDE, solution of finite difference equations by SIP for seven-point three-dimensional 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 second-order elliptic PDE on a rectangle |
D03FA | nagf_pde_3d_ellip_helmholtz Elliptic PDE, Helmholtz equation, three-dimensional 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 first-order 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 convection-diffusion 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 first-order PDEs, coupled DAEs, method of lines, Keller box discretization, one space variable |
D03PL | nagf_pde_1d_parab_convdiff_dae General system of convection-diffusion 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 first-order PDEs, coupled DAEs, method of lines, Keller box discretization, remeshing, one space variable |
D03PS | nagf_pde_1d_parab_convdiff_remesh General system of convection-diffusion 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 second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectangular region |
D03RB | nagf_pde_2d_gen_order2_rectilinear General system of second-order 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, five-point two-dimensional molecule, one iteration |
D03UB | nagf_pde_3d_ellip_fd_iter Elliptic PDE, solution of finite difference equations by SIP, seven-point three-dimensional molecule, one iteration |
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, user-supplied 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 |
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 Abel-type equations |
Examples of routines and methods in this chapter.
D06AA | nagf_mesh_2d_gen_inc Generates a two-dimensional mesh using a simple incremental method |
D06AB | nagf_mesh_2d_gen_delaunay Generates a two-dimensional mesh using a Delaunay–Voronoi process |
D06AC | nagf_mesh_2d_gen_front Generates a two-dimensional mesh using an Advancing-front 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 |
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, monotonicity-preserving, 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 two-dimensional scattered grid, method of Renka and Cline |
E01EB | nagf_interp_2d_triang_bary_eval Barycentric interpolation on function values provided on a two-dimensional 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 |
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 two-stage 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 two-dimensional data into panels for fitting bicubic splines |
E02ZK | nagf_fit_opt_set Option setting routine |
E02ZL | nagf_fit_opt_get Option getting routine |
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 (easy-to-use) |
E04GB | nagf_opt_lsq_uncon_quasi_deriv_comp Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton 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 quasi-Newton algorithm, using first derivatives (easy-to-use) |
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 (easy-to-use) |
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 (easy-to-use) |
E04JC | nagf_opt_bounds_bobyqa_func Bound constrained minimum, model-based algorithm, using function values only |
E04JY | nagf_opt_bounds_quasi_func_easy Bound constrained minimum, quasi-Newton algorithm, using function values only (easy-to-use) |
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, quasi-Newton algorithm, using first derivatives (easy-to-use) |
E04KZ | nagf_opt_bounds_mod_deriv_easy Bound constrained minimum, modified Newton algorithm, using first derivatives (easy-to-use) |
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 (easy-to-use) |
E04MF | nagf_opt_lp_solve_old Linear programming (LP), dense, active-set 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 linearly-constrained 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 non-convex) quadratic programming (QP) , dense, active-set 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, active-set 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, active-set 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 (BMI-SDP) |
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, active-set 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, active-set, SQP method, using function values and optionally first derivatives (reverse communication, comprehensive) |
E04UG | nagf_opt_nlp1_sparse_solve_old Nonlinear programming (NLP), sparse, active-set 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, active-set 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, active-set 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, active-set 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 |
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 multi-level 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 multi-start, 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 multi-start, 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 |
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 Pseudo-inverse 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 symmetric-definite 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 user-supplied derivatives) |
F01EN | nagf_matop_real_gen_matrix_sqrt Real matrix square root |
F01EP | nagf_matop_real_tri_matrix_sqrt Real upper quasi-triangular 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 user-supplied 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 user-supplied 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 user-supplied 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 variable-bandwidth 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 |
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) |
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 |
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 error-bound to a real system of linear equations |
F04BB | nagf_linsys_real_band_solve Computes the solution, estimated condition number and error-bound to a real banded system of linear equations |
F04BC | nagf_linsys_real_tridiag_solve Computes the solution, estimated condition number and error-bound to a real tridiagonal system of linear equations |
F04BD | nagf_linsys_real_posdef_solve Computes the solution, estimated condition number and error-bound to a real symmetric positive definite system of linear equations |
F04BE | nagf_linsys_real_posdef_packed_solve Computes the solution, estimated condition number and error-bound 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 error-bound 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 error-bound to a real symmetric positive definite tridiagonal system of linear equations |
F04BH | nagf_linsys_real_symm_solve Computes the solution, estimated condition number and error-bound to a real symmetric system of linear equations |
F04BJ | nagf_linsys_real_symm_packed_solve Computes the solution, estimated condition number and error-bound to a real symmetric system of linear equations, packed storage |
F04CA | nagf_linsys_complex_square_solve Computes the solution, estimated condition number and error-bound to a complex system of linear equations |
F04CB | nagf_linsys_complex_band_solve Computes the solution, estimated condition number and error-bound to a complex banded system of linear equations |
F04CC | nagf_linsys_complex_tridiag_solve Computes the solution, estimated condition number and error-bound to a complex tridiagonal system of linear equations |
F04CD | nagf_linsys_complex_posdef_solve Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite system of linear equations |
F04CE | nagf_linsys_complex_posdef_packed_solve Computes the solution, estimated condition number and error-bound 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 error-bound 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 error-bound to a complex Hermitian positive definite tridiagonal system of linear equations |
F04CH | nagf_linsys_complex_herm_solve Computes the solution and error-bound to a complex Hermitian system of linear equations |
F04CJ | nagf_linsys_complex_herm_packed_solve Computes the solution, estimated condition number and error-bound to a complex Hermitian system of linear equations, packed storage |
F04DH | nagf_linsys_complex_symm_solve Computes the solution, estimated condition number and error-bound to a complex symmetric system of linear equations |
F04DJ | nagf_linsys_complex_symm_packed_solve Computes the solution, estimated condition number and error-bound 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 right-hand side |
F04FF | nagf_linsys_real_toeplitz_solve Solution of real symmetric positive definite Toeplitz system, one right-hand 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 variable-bandwidth 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 |
Examples of routines and methods in this chapter.
F05AA | nagf_orthog_real_gram_schmidt Gram–Schmidt orthogonalization of n vectors of order m |
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 non-negligible element of real vector |
F06KP | nagf_blas_zdrot Apply real plane rotation to two complex vectors |
F06PA | nagf_blas_dgemv Matrix-vector product, real rectangular matrix |
F06PB | nagf_blas_dgbmv Matrix-vector product, real rectangular band matrix |
F06PC | nagf_blas_dsymv Matrix-vector product, real symmetric matrix |
F06PD | nagf_blas_dsbmv Matrix-vector product, real symmetric band matrix |
F06PE | nagf_blas_dspmv Matrix-vector product, real symmetric packed matrix |
F06PF | nagf_blas_dtrmv Matrix-vector product, real triangular matrix |
F06PG | nagf_blas_dtbmv Matrix-vector product, real triangular band matrix |
F06PH | nagf_blas_dtpmv Matrix-vector 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 Rank-1 update, real rectangular matrix |
F06PP | nagf_blas_dsyr Rank-1 update, real symmetric matrix |
F06PQ | nagf_blas_dspr Rank-1 update, real symmetric packed matrix |
F06PR | nagf_blas_dsyr2 Rank-2 update, real symmetric matrix |
F06PS | nagf_blas_dspr2 Rank-2 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, rank-1 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 1-norm, ∞-norm, Frobenius norm, largest absolute element, real general matrix |
F06RB | nagf_blas_dlangb 1-norm, ∞-norm, Frobenius norm, largest absolute element, real band matrix |
F06RC | nagf_blas_dlansy 1-norm, ∞-norm, Frobenius norm, largest absolute element, real symmetric matrix |
F06RD | nagf_blas_dlansp 1-norm, ∞-norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage |
F06RE | nagf_blas_dlansb 1-norm, ∞-norm, Frobenius norm, largest absolute element, real symmetric band matrix |
F06RJ | nagf_blas_dlantr 1-norm, ∞-norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix |
F06RK | nagf_blas_dlantp 1-norm, ∞-norm, Frobenius norm, largest absolute element, real triangular matrix, packed storage |
F06RL | nagf_blas_dlantb 1-norm, ∞-norm, Frobenius norm, largest absolute element, real triangular band matrix |
F06RM | nagf_blas_dlanhs 1-norm, ∞-norm, Frobenius norm, largest absolute element, real upper Hessenberg matrix |
F06RN | nagf_blas_dlangt 1-norm, ∞-norm, Frobenius norm, largest absolute element, real tridiagonal matrix |
F06RP | nagf_blas_dlanst 1-norm, ∞-norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix |
F06SA | nagf_blas_zgemv Matrix-vector product, complex rectangular matrix |
F06SB | nagf_blas_zgbmv Matrix-vector product, complex rectangular band matrix |
F06SC | nagf_blas_zhemv Matrix-vector product, complex Hermitian matrix |
F06SD | nagf_blas_zhbmv Matrix-vector product, complex Hermitian band matrix |
F06SE | nagf_blas_zhpmv Matrix-vector product, complex Hermitian packed matrix |
F06SF | nagf_blas_ztrmv Matrix-vector product, complex triangular matrix |
F06SG | nagf_blas_ztbmv Matrix-vector product, complex triangular band matrix |
F06SH | nagf_blas_ztpmv Matrix-vector 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 Rank-1 update, complex rectangular matrix, unconjugated vector |
F06SN | nagf_blas_zgerc Rank-1 update, complex rectangular matrix, conjugated vector |
F06SP | nagf_blas_zher Rank-1 update, complex Hermitian matrix |
F06SQ | nagf_blas_zhpr Rank-1 update, complex Hermitian packed matrix |
F06SR | nagf_blas_zher2 Rank-2 update, complex Hermitian matrix |
F06SS | nagf_blas_zhpr2 Rank-2 update, complex Hermitian packed matrix |
F06TA | nagf_blas_zsymv Matrix-vector product, complex symmetric matrix |
F06TB | nagf_blas_zsyr Rank-1 update, complex symmetric matrix |
F06TC | nagf_blas_zspmv Matrix-vector product, complex symmetric packed matrix |
F06TD | nagf_blas_zspr Rank-1 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, rank-1 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 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex general matrix |
F06UB | nagf_blas_zlangb 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex band matrix |
F06UC | nagf_blas_zlanhe 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex Hermitian matrix |
F06UD | nagf_blas_zlanhp 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex Hermitian matrix, packed storage |
F06UE | nagf_blas_zlanhb 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex Hermitian band matrix |
F06UF | nagf_blas_zlansy 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex symmetric matrix |
F06UG | nagf_blas_zlansp 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage |
F06UH | nagf_blas_zlansb 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex symmetric band matrix |
F06UJ | nagf_blas_zlantr 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex trapezoidal/triangular matrix |
F06UK | nagf_blas_zlantp 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex triangular matrix, packed storage |
F06UL | nagf_blas_zlantb 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex triangular band matrix |
F06UM | nagf_blas_zlanhs 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex Hessenberg matrix |
F06UN | nagf_blas_zlangt 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex tridiagonal matrix |
F06UP | nagf_blas_zlanht 1-norm, ∞-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 1-norm, ∞-norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format |
F06WB | nagf_blas_dtfsm Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix, Rectangular Full Packed format |
F06WC | nagf_blas_dsfrk Rank-k update of a real symmetric matrix, Rectangular Full Packed format |
F06WN | nagf_blas_zlanhf 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex Hermitian matrix, Rectangular Full Packed format |
F06WP | nagf_blas_ztfsm Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix, Rectangular Full Packed format |
F06WQ | nagf_blas_zhfrk Rank-k update of a complex Hermitian matrix, Rectangular Full Packed format |
F06YA | nagf_blas_dgemm Matrix-matrix product, two real rectangular matrices |
F06YC | nagf_blas_dsymm Matrix-matrix product, one real symmetric matrix, one real rectangular matrix |
F06YF | nagf_blas_dtrmm Matrix-matrix product, one real triangular matrix, one real rectangular matrix |
F06YJ | nagf_blas_dtrsm Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix |
F06YP | nagf_blas_dsyrk Rank-k update of a real symmetric matrix |
F06YR | nagf_blas_dsyr2k Rank-2k update of a real symmetric matrix |
F06ZA | nagf_blas_zgemm Matrix-matrix product, two complex rectangular matrices |
F06ZC | nagf_blas_zhemm Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix |
F06ZF | nagf_blas_ztrmm Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix |
F06ZJ | nagf_blas_ztrsm Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix |
F06ZP | nagf_blas_zherk Rank-k update of a complex Hermitian matrix |
F06ZR | nagf_blas_zher2k Rank-2k update of a complex Hermitian matrix |
F06ZT | nagf_blas_zsymm Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix |
F06ZU | nagf_blas_zsyrk Rank-k update of a complex symmetric matrix |
F06ZW | nagf_blas_zsyr2k Rank-2k update of a complex symmetric matrix |
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, error-bound 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 right-hand 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 right-hand 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, error-bound 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 right-hand 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 right-hand 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, error-bound 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 right-hand 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 right-hand 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, error-bound 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 right-hand 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 right-hand 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, error-bound 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 right-hand 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, error-bound 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 right-hand 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, error-bound 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 right-hand 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 right-hand 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, error-bound 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 right-hand 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 right-hand 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, error-bound 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 right-hand 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 right-hand 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, error-bound 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 right-hand 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 right-hand 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, error-bound 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 right-hand 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 right-hand 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, error-bound 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 right-hand 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 right-hand 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, error-bound 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 right-hand 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, error-bound 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 right-hand 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 right-hand 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 right-hand 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 right-hand 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 right-hand 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 right-hand 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 right-hand 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 right-hand 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 right-hand 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 right-hand 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 right-hand 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 right-hand 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 right-hand 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 right-hand 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 right-hand sides |
F07TJ | nagf_lapack_dtrtri Inverse of real triangular matrix |
F07TS | nagf_lapack_ztrtrs Solution of complex triangular system of linear equations, multiple right-hand 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 right-hand sides |
F07TW | nagf_lapack_ztrtri Inverse of complex triangular matrix |
F07UE | nagf_lapack_dtptrs Solution of real triangular system of linear equations, multiple right-hand 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 right-hand 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 right-hand 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 right-hand 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 right-hand 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 right-hand sides |
F07VS | nagf_lapack_ztbtrs Solution of complex band triangular system of linear equations, multiple right-hand 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 right-hand 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 right-hand 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 right-hand 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 |
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 minimum-norm solution to a real linear least squares problem |
F08BB | nagf_lapack_dtpqrt QR factorization of real general triangular-pentagonal 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 BLAS-3, 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 minimum-norm solution to a complex linear least squares problem |
F08BP | nagf_lapack_ztpqrt QR factorization of complex triangular-pentagonal 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 BLAS-3, 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 (divide-and-conquer) |
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 (divide-and-conquer) |
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 (divide-and-conquer 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 (divide-and-conquer 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 (divide-and-conquer 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 (divide-and-conquer) |
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 (divide-and-conquer) |
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, root-free 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 (divide-and-conquer) |
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 (divide-and-conquer) |
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 minimum-norm 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 minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer) |
F08KD | nagf_lapack_dgesdd Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer) |
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 minimum-norm 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 minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer) |
F08KR | nagf_lapack_zgesdd Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer) |
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 (divide-and-conquer) |
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 quasi-triangular or transposes |
F08QK | nagf_lapack_dtrevc Computes left and right eigenvectors of real upper quasi-triangular matrix |
F08QL | nagf_lapack_dtrsna Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular 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 conjugate-transposes |
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 symmetric-definite eigenproblem |
F08SB | nagf_lapack_dsygvx Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |
F08SC | nagf_lapack_dsygvd Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer) |
F08SE | nagf_lapack_dsygst Performs a reduction to standard form of real symmetric-definite 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 Hermitian-definite eigenproblem |
F08SP | nagf_lapack_zhegvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |
F08SQ | nagf_lapack_zhegvd Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer) |
F08SS | nagf_lapack_zhegst Performs a reduction to standard form of complex Hermitian-definite 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 symmetric-definite eigenproblem, packed storage |
F08TB | nagf_lapack_dspgvx Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage |
F08TC | nagf_lapack_dspgvd Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer) |
F08TE | nagf_lapack_dspgst Performs a reduction to standard form of real symmetric-definite 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 Hermitian-definite eigenproblem, packed storage |
F08TP | nagf_lapack_zhpgvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage |
F08TQ | nagf_lapack_zhpgvd Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer) |
F08TS | nagf_lapack_zhpgst Performs a reduction to standard form of complex Hermitian-definite 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 symmetric-definite eigenproblem |
F08UB | nagf_lapack_dsbgvx Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem |
F08UC | nagf_lapack_dsbgvd Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer) |
F08UE | nagf_lapack_dsbgst Performs a reduction of real symmetric-definite 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 Hermitian-definite eigenproblem |
F08UP | nagf_lapack_zhbgvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem |
F08UQ | nagf_lapack_zhbgvd Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer) |
F08US | nagf_lapack_zhbgst Performs a reduction of complex Hermitian-definite 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 BLAS-3, 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 BLAS-3, 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 BLAS-3, 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 BLAS-3, 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 BLAS-3, 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 BLAS-3, 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 BLAS-3, 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 BLAS-3, 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 BLAS-3, 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 BLAS-3, 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 real-valued, generalized, quasi-trangular, 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 equality-constrained 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 equality-constrained 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 |
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, Bi-CGSTAB 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 non-Hermitian linear systems, setup for F11BS |
F11BS | nagf_sparse_complex_gen_basic_solver Complex sparse non-Hermitian linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method |
F11BT | nagf_sparse_complex_gen_basic_diag Complex sparse non-Hermitian 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, Bi-CGSTAB 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, Bi-CGSTAB, 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, Bi-CGSTAB 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 non-Hermitian 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 non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB 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 non-Hermitian matrix |
F11DS | nagf_sparse_complex_gen_solve_jacssor Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner Black Box |
F11DT | nagf_sparse_complex_gen_precon_bdilu Complex, sparse, non-Hermitian linear system, incomplete LU factorization of local or overlapping diagonal blocks |
F11DU | nagf_sparse_complex_gen_solve_bdilu Solution of complex, sparse, non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete LU block diagonal preconditioner computed by F11DT |
F11DX | nagf_sparse_complex_gen_precon_jacobi Complex, sparse, Hermitian or non-Hermitian, 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 right-hand sides |
F11MK | nagf_sparse_direct_real_gen_matmul Real sparse nonsymmetric matrix-matrix multiply, compressed column storage |
F11ML | nagf_sparse_direct_real_gen_norm 1-norm, ∞-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 matrix-vector multiply |
F11XE | nagf_sparse_real_symm_matvec Real sparse symmetric matrix-vector multiply |
F11XN | nagf_sparse_complex_gen_matvec Complex sparse non-Hermitian matrix-vector multiply |
F11XS | nagf_sparse_complex_herm_matvec Complex sparse Hermitian matrix-vector 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 non-Hermitian matrix reorder routine |
F11ZP | nagf_sparse_complex_herm_sort Complex sparse Hermitian matrix reorder routine |
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 non-Hermitian 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 |
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 1-norm, ∞-norm, Frobenius norm, largest absolute element, real band matrix |
F16UB | nagf_blast_zgb_norm 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex band matrix |
Examples of routines and methods in this chapter.
G01AB | nagf_stat_summary_2var Means, corrected sums of squares and cross-products, 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 Two-way contingency table analysis, with χ^{2}/Fisher's exact test |
G01AL | nagf_stat_5pt_summary Computes a five-point 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 variance-covariance 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 t-distribution |
G01EC | nagf_stat_prob_chisq Computes probabilities for χ^{2} distribution |
G01ED | nagf_stat_prob_f Computes probabilities for F-distribution |
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 one-sample Kolmogorov–Smirnov distribution |
G01EZ | nagf_stat_prob_kolmogorov2 Computes probabilities for the two-sample 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 t-distribution |
G01FC | nagf_stat_inv_cdf_chisq Computes deviates for the χ^{2} distribution |
G01FD | nagf_stat_inv_cdf_f Computes deviates for the F-distribution |
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 non-central Student's t-distribution |
G01GC | nagf_stat_prob_chisq_noncentral Computes probabilities for the non-central χ^{2} distribution |
G01GD | nagf_stat_prob_f_noncentral Computes probabilities for the non-central F-distribution |
G01GE | nagf_stat_prob_beta_noncentral Computes probabilities for the non-central 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 t-distribution |
G01HD | nagf_stat_prob_multi_students_t Computes the probability for the multivariate Student's t-distribution |
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 t-distribution |
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 F-distribution |
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 t-distribution |
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 F-distribution |
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 |
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 k-factor structure to a real square matrix |
G02AJ | nagf_nearest_correlation_h_weight Computes the nearest correlation matrix to a real square matrix, using element-wise 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 product-moment correlation coefficients, all variables, no missing values |
G02BB | nagf_correg_coeffs_pearson_miss_case Pearson product-moment correlation coefficients, all variables, casewise treatment of missing values |
G02BC | nagf_correg_coeffs_pearson_miss_pair Pearson product-moment correlation coefficients, all variables, pairwise treatment of missing values |
G02BD | nagf_correg_coeffs_zero Correlation-like coefficients (about zero), all variables, no missing values |
G02BE | nagf_correg_coeffs_zero_miss_case Correlation-like coefficients (about zero), all variables, casewise treatment of missing values |
G02BF | nagf_correg_coeffs_zero_miss_pair Correlation-like coefficients (about zero), all variables, pairwise treatment of missing values |
G02BG | nagf_correg_coeffs_pearson_subset Pearson product-moment correlation coefficients, subset of variables, no missing values |
G02BH | nagf_correg_coeffs_pearson_subset_miss_case Pearson product-moment correlation coefficients, subset of variables, casewise treatment of missing values |
G02BJ | nagf_correg_coeffs_pearson_subset_miss_pair Pearson product-moment correlation coefficients, subset of variables, pairwise treatment of missing values |
G02BK | nagf_correg_coeffs_zero_subset Correlation-like coefficients (about zero), subset of variables, no missing values |
G02BL | nagf_correg_coeffs_zero_subset_miss_case Correlation-like coefficients (about zero), subset of variables, casewise treatment of missing values |
G02BM | nagf_correg_coeffs_zero_subset_miss_pair Correlation-like coefficients (about zero), subset of variables, pairwise treatment of missing values |
G02BN | nagf_correg_coeffs_kspearman_overwrite Kendall/Spearman non-parametric rank correlation coefficients, no missing values, overwriting input data |
G02BP | nagf_correg_coeffs_kspearman_miss_case_overwrite Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, overwriting input data |
G02BQ | nagf_correg_coeffs_kspearman Kendall/Spearman non-parametric rank correlation coefficients, no missing values, preserving input data |
G02BR | nagf_correg_coeffs_kspearman_miss_case Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, preserving input data |
G02BS | nagf_correg_coeffs_kspearman_miss_pair Kendall/Spearman non-parametric 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/variance-covariance matrix from correlation/variance-covariance 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 correlation-like 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 M-estimates |
G02HB | nagf_correg_robustm_wts Robust regression, compute weights for use with G02HD |
G02HD | nagf_correg_robustm_user Robust regression, compute regression with user-supplied functions and weights |
G02HF | nagf_correg_robustm_user_varmat Robust regression, variance-covariance 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, user-supplied weight function plus derivatives |
G02HM | nagf_correg_robustm_corr_user Calculates a robust estimation of a covariance matrix, user-supplied 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 cross-products 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 |
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 within-group covariance matrices and matrices for discriminant analysis |
G03DB | nagf_mv_discrim_mahal Computes Mahalanobis squared distances for group or pooled variance-covariance 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 K-means 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 non-metric (ordinal) multidimensional scaling |
G03GA | nagf_mv_gaussian_mixture Fits a Gaussian mixture model |
G03ZA | nagf_mv_z_scores Produces standardized values (z-scores) for a data matrix |
Examples of routines and methods in this chapter.
G04AG | nagf_anova_hier2 Two-way 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 |
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 non-repeatable sequence |
G05KH | nagf_rand_init_leapfrog Primes a pseudorandom number generator for generating multiple streams using leap-frog |
G05KJ | nagf_rand_init_skipahead Primes a pseudorandom number generator for generating multiple streams using skip-ahead |
G05KK | nagf_rand_init_skipahead_power2 Primes a pseudorandom number generator for generating multiple streams using skip-ahead, 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_{t-1}+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_{t-1}|+γε_{t-1})^{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 K-fold cross validation |
G05PW | nagf_rand_subsamp_xyw Permutes a matrix, vector, vector triplet into a form suitable for random sub-sampling 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 two-way table |
G05RC | nagf_rand_copula_students_t Generates a matrix of pseudorandom numbers from a Student's t-copula |
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 t-distribution |
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 F-distribution |
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 log-normal distribution |
G05SN | nagf_rand_dist_students_t Generates a vector of pseudorandom numbers from a Student's t-distribution |
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 non-free 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 quasi-random number sequence |
G05YK | nagf_rand_quasi_lognormal Generates a log-normal quasi-random number sequence |
G05YL | nagf_rand_quasi_init Initializes a quasi-random number generator |
G05YM | nagf_rand_quasi_uniform Generates a uniform quasi-random number sequence |
G05YN | nagf_rand_quasi_init_scrambled Initializes a scrambled quasi-random number generator |
G05ZM | nagf_rand_field_1d_user_setup Setup for simulating one-dimensional random fields, user-defined variogram |
G05ZN | nagf_rand_field_1d_predef_setup Setup for simulating one-dimensional random fields |
G05ZP | nagf_rand_field_1d_generate Generates realizations of a one-dimensional random field |
G05ZQ | nagf_rand_field_2d_user_setup Setup for simulating two-dimensional random fields, user-defined variogram |
G05ZR | nagf_rand_field_2d_predef_setup Setup for simulating two-dimensional random fields, preset variogram |
G05ZS | nagf_rand_field_2d_generate Generates realizations of a two-dimensional random field |
G05ZT | nagf_rand_field_fracbm_generate Generates realizations of fractional Brownian motion |
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 t-test 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, M-estimates for location and scale parameters, standard weight functions |
G07DC | nagf_univar_robust_1var_mestim_wgt Robust estimation, M-estimates for location and scale parameters, user-defined 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, one-sample |
G07EB | nagf_univar_robust_2var_ci Robust confidence intervals, two-sample |
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 |
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 two-way analysis of variance on k matched samples |
G08AF | nagf_nonpar_test_kruskal Kruskal–Wallis one-way analysis of variance on k samples of unequal size |
G08AG | nagf_nonpar_test_wilcoxon Performs the Wilcoxon one-sample (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 cross-classified 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 one-sample Kolmogorov–Smirnov test for standard distributions |
G08CC | nagf_nonpar_test_ks_1sample_user Performs the one-sample Kolmogorov–Smirnov test for a user-supplied distribution |
G08CD | nagf_nonpar_test_ks_2sample Performs the two-sample Kolmogorov–Smirnov test |
G08CG | nagf_nonpar_test_chisq Performs the χ^{2} goodness-of-fit test, for standard continuous distributions |
G08CH | nagf_nonpar_gofstat_anddar Calculates the Anderson–Darling goodness-of-fit test statistic |
G08CJ | nagf_nonpar_gofstat_anddar_unif Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of uniformly distributed data |
G08CK | nagf_nonpar_gofstat_anddar_normal Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of a fully-unspecified Normal distribution |
G08CL | nagf_nonpar_gofstat_anddar_exp Calculates the Anderson–Darling goodness-of-fit 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, right-censored data |
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 |
Examples of routines and methods in this chapter.
G11AA | nagf_contab_chisq χ^{2} statistics for two-way 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 |
Examples of routines and methods in this chapter.
G12AA | nagf_surviv_kaplanmeier Computes Kaplan–Meier (product-limit) 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 |
Examples of routines and methods in this chapter.
G13AA | nagf_tsa_uni_diff Univariate time series, seasonal and non-seasonal 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 (easy-to-use) |
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 range-mean or standard deviation-mean 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 (pre-whitening) 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, cross-correlations |
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 multi-input model |
G13BG | nagf_tsa_multi_inputmod_update Multivariate time series, update state set for forecasting from multi-input model |
G13BH | nagf_tsa_multi_inputmod_forecast_state Multivariate time series, forecasting from state set of multi-input model |
G13BJ | nagf_tsa_multi_inputmod_forecast Multivariate time series, state set and forecasts from fully specified multi-input 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 cross-correlation or cross-covariance 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, time-varying, square root covariance filter |
G13EB | nagf_tsa_multi_kalman_sqrt_invar Combined measurement and time update, one iteration of Kalman filter, time-invariant, 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_{t-1}+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_{t-1}+γ)^{2} |
G13FC | nagf_tsa_uni_garch_asym2_estim Univariate time series, parameter estimation for a GARCH process with asymmetry of the form (|ε_{t-1}|+γε_{t-1})^{2} |
G13FD | nagf_tsa_uni_garch_asym2_forecast Univariate time series, forecast function for a GARCH process with asymmetry of the form (|ε_{t-1}|+γε_{t-1})^{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 |
Examples of routines and methods in this chapter.
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 user-specified 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) |
Examples of routines and methods in this chapter.
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 |
Examples of routines and methods in this chapter.
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 1-I_{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 Floating-strike lookback option pricing formula in the Black-Scholes-Merton model |
S30BB | nagf_specfun_opt_lookback_fls_greeks Floating-strike lookback option pricing formula with Greeks in the Black-Scholes-Merton model |
S30CA | nagf_specfun_opt_binary_con_price Binary option, cash-or-nothing pricing formula |
S30CB | nagf_specfun_opt_binary_con_greeks Binary option, cash-or-nothing pricing formula with Greeks |
S30CC | nagf_specfun_opt_binary_aon_price Binary option, asset-or-nothing pricing formula |
S30CD | nagf_specfun_opt_binary_aon_greeks Binary option, asset-or-nothing pricing formula with Greeks |
S30FA | nagf_specfun_opt_barrier_std_price Standard barrier option pricing formula |
S30JA | nagf_specfun_opt_jumpdiff_merton_price Jump-diffusion, Merton's model, option pricing formula |
S30JB | nagf_specfun_opt_jumpdiff_merton_greeks Jump-diffusion, 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 |
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) |
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 floating-point 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 floating-point model parameter, b |
X02BJ | nagf_machine_model_digits The floating-point model parameter, p |
X02BK | nagf_machine_model_minexp The floating-point model parameter e_{min} |
X02BL | nagf_machine_model_maxexp The floating-point model parameter e_{max} |
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 |
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 (easy-to-use) |
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 (easy-to-use) |
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 (easy-to-use) |
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 (easy-to-use) |
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 (easy-to-use) |
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 (easy-to-use) |
X04DF | nagf_file_print_matrix_complex_band_comp Print complex packed banded matrix (comprehensive) |
X04EA | nagf_file_print_matrix_integer Print integer matrix (easy-to-use) |
X04EB | nagf_file_print_matrix_integer_comp Print integer matrix (comprehensive) |
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 |
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 |
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 floating-point exceptions |
X07CB | nagf_set_ieee_exception_mode Sets behaviour of floating-point exceptions |
© The Numerical Algorithms Group Ltd, Oxford, UK. 2016