%insert a pointer to reference section % Page pointed to from top level menu \begin{page}{htxl}{The AXIOM Link to NAG Software} \beginscroll \beginmenu \menumemolink{Introduction to the NAG Library Link}{nagLinkIntroPage} \menumemolink{Access the Link from HyperDoc}{htxl1} \menulispmemolink{Browser pages for individual routines}{(|kSearch| "Nag*")} \menumemolink{NAG Library Documentation}{FoundationLibraryDocPage} \endmenu \endscroll \end{page} \begin{page}{htxl1}{Use of the Link from HyperDoc} Click on the chapter of routines that you would like to use. \beginscroll \beginmenu \menumemolink{C02}{c02}\tab{8} Zeros of Polynomials \menumemolink{C05}{c05}\tab{8} Roots of One or More Transcendental Equations \menumemolink{C06}{c06}\tab{8} Summation of Series \menumemolink{D01}{d01}\tab{8} Quadrature \menumemolink{D02}{d02}\tab{8} Ordinary Differential Equations \menumemolink{D03}{d03}\tab{8} Partial Differential Equations \menumemolink{E01}{e01}\tab{8} Interpolation \menumemolink{E02}{e02}\tab{8} Curve and Surface Fitting \menumemolink{E04}{e04}\tab{8} Minimizing or Maximizing a Function \menumemolink{F01}{f01}\tab{8} Matrix Operations, Including Inversion \menumemolink{F02}{f02}\tab{8} Eigenvalues and Eigenvectors \menumemolink{F04}{f04}\tab{8} Simultaneous Linear Equations \menumemolink{F07}{f07}\tab{8} Linear Equations (LAPACK) \menumemolink{S}{s}\tab{8} Approximations of Special Functions \endmenu \endscroll \end{page} \begin{page}{c02}{C02 Zeros of Polynomials} \beginscroll \centerline{What would you like to do?} \newline \beginmenu \item Read \menuwindowlink{Foundation Library Chapter c02 Manual Page}{manpageXXc02} \item or \menulispwindowlink{Browse}{(|kSearch| "NagPolynomialRootsPackage")}\tab{10} through this chapter \item or use the routines: \menulispdownlink{C02AFF}{(|c02aff|)}\space{} \tab{10} All zeros of a complex polynomial \menulispdownlink{C02AGF}{(|c02agf|)}\space{} \tab{10} All zeros of a real polynomial \endmenu \endscroll \autobuttons \end{page} \begin{page}{c05}{C05 Roots of One or More Transcendental Equations} \beginscroll \centerline{What would you like to do?} \newline \beginmenu \item Read \menuwindowlink{Foundation Library Chapter c05 Manual Page}{manpageXXc05} \item or \menulispwindowlink{Browse}{(|kSearch| "NagRootFindingPackage")}\tab{10} through this chapter \item or use the routines: \menulispdownlink{C05ADF}{(|c05adf|)}\space{} \tab{10} Zero of continuous function in given interval, Bus and Dekker algorithm \menulispdownlink{C05NBF}{(|c05nbf|)}\space{} \tab{10} Solution of system of nonlinear equations using function values only \menulispdownlink{C05PBF}{(|c05pbf|)}\space{} \tab{10} Solution of system of nonlinear equations using 1st derivatives \endmenu \endscroll \autobuttons \end{page} \begin{page}{c06}{C06 Summation of Series} \beginscroll \centerline{What would you like to do?} \newline \beginmenu \item Read \menuwindowlink{Foundation Library Chapter c06 Manual Page}{manpageXXc06} \item or \menulispwindowlink{Browse}{(|kSearch| "NagSeriesSummationPackage")}\tab{10} through this chapter \item or use the routines: \menulispdownlink{C06EAF}{(|c06eaf|)}\space{} \tab{10} Single 1-D real discrete Fourier transform, no extra workspace \menulispdownlink{C06EBF}{(|c06ebf|)}\space{} \tab{10} Single 1-D Hermitian discrete Fourier transform, no extra workspace \menulispdownlink{C06ECF}{(|c06ecf|)}\space{} \tab{10} Single 1-D complex discrete Fourier transform, no extra workspace \menulispdownlink{C06EKF}{(|c06ekf|)}\space{} \tab{10} Circular convolution or correlation of two real vectors, no extra workspace \menulispdownlink{C06FPF}{(|c06fpf|)}\space{} \tab{10} Multiple 1-D real discrete Fourier transforms \menulispdownlink{C06FQF}{(|c06fqf|)}\space{} \tab{10} Multiple 1-D Hermitian discrete Fourier transforms \menulispdownlink{C06FRF}{(|c06frf|)}\space{} \tab{10} Multiple 1-D complex discrete Fourier transforms \menulispdownlink{C06FUF}{(|c06fuf|)}\space{} \tab{10} 2-D complex discrete Fourier transforms \menulispdownlink{C06GBF}{(|c06gbf|)}\space{} \tab{10} Complex conjugate of Hermitian sequence \menulispdownlink{C06GCF}{(|c06gcf|)}\space{} \tab{10} Complex conjugate of complex sequence \menulispdownlink{C06GQF}{(|c06gqf|)}\space{} \tab{10} Complex conjugate of multiple Hermitian sequences \menulispdownlink{C06GSF}{(|c06gsf|)}\space{} \tab{10} Convert Hermitian sequences to general complex sequences \endmenu \endscroll \autobuttons \end{page} \begin{page}{d01}{D01 Quadrature} \beginscroll \centerline{What would you like to do?} \newline \beginmenu \item Read \menuwindowlink{Foundation Library Chapter d01 Manual Page}{manpageXXd01} \item or \menulispwindowlink{Browse}{(|kSearch| "NagIntegrationPackage")}\tab{10} through this chapter \item or use the routines: \menulispdownlink{D01AJF}{(|d01ajf|)}\space{} \tab{10} 1-D quadrature, adaptive, finite interval, strategy due to Plessens and de Doncker, allowing for badly-behaved integrands \menulispdownlink{D01AKF}{(|d01akf|)}\space{} \tab{10} 1-D quadrature, adaptive, finite interval, method suitable for oscillating functions \menulispdownlink{D01ALF}{(|d01alf|)}\space{} \tab{10} 1-D quadrature, adaptive, finite interval, allowing for singularities at user specified points \menulispdownlink{D01AMF}{(|d01amf|)}\space{} \tab{10} 1-D quadrature, adaptive, infinite or semi-finite interval \menulispdownlink{D01ANF}{(|d01anf|)}\space{} \tab{10} 1-D quadrature, adaptive, finite interval, weight function cos(\omega x) or sin(\omega x) \menulispdownlink{D01APF}{(|d01apf|)}\space{} \tab{10} 1-D quadrature, adaptive, finite interval, weight function with end point singularities of algebraico-logarithmic type \menulispdownlink{D01AQF}{(|d01aqf|)}\space{} \tab{10} 1-D quadrature, adaptive, finite interval, weight function 1/(x-c), Cauchy principle value (Hilbert transform) \menulispdownlink{D01ASF}{(|d01asf|)}\space{} \tab{10} 1-D quadrature, adaptive, semi-infinite interval, weight function cos(\omega x) or sin(\omega x) \menulispdownlink{D01BBF}{(|d01bbf|)}\space{} \tab{10} Pre-computed weights and abscissae for Gaussian quadrature rules, restricted choice of rule \menulispdownlink{D01FCF}{(|d01fcf|)}\space{} \tab{10} Multi-dimensional adaptive quadrature over hyper-rectangle \menulispdownlink{D01GAF}{(|d01gaf|)}\space{} \tab{10} 1-D quadrature, integration of function defined by data values, Gill-Miller method \menulispdownlink{D01GBF}{(|d01gbf|)}\space{} \tab{10} Multi-dimensional quadrature over hyper-rectangle, Monte Carlo method \endmenu \endscroll \autobuttons \end{page} \begin{page}{d02}{D02 Ordinary Differential Equations} \beginscroll \centerline{What would you like to do?} \newline \beginmenu \item Read \menuwindowlink{Foundation Library Chapter d02 Manual Page}{manpageXXd02} \item or \menulispwindowlink{Browse}{(|kSearch| "NagOrdinaryDifferentialEquationsPackage")}\tab{10} through this chapter \item or use the routines: \menulispdownlink{D02BBF}{(|d02bbf|)}\space{} \tab{10} ODEs, IVP, Runge-Kutta-Merson method, over a range, intermediate output \menulispdownlink{D02BHF}{(|d02bhf|)}\space{} \tab{10} ODEs, IVP, Runge-Kutta-Merson method, until function of solution is zero \menulispdownlink{D02CJF}{(|d02cjf|)}\space{} \tab{10} ODEs, IVP, Adams method, until function of solution is zero, intermediate output \menulispdownlink{D02EJF}{(|d02ejf|)}\space{} \tab{10} ODEs, stiff IVP, BDF method, until function of solution is zero, intermediate output \menulispdownlink{D02GAF}{(|d02gaf|)}\space{} \tab{10} ODEs, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem \menulispdownlink{D02GBF}{(|d02gbf|)}\space{} \tab{10} ODEs, boundary value problem, finite difference technique with deferred correction, general nonlinear problem \menulispdownlink{D02KEF}{(|d02kef|)}\space{} \tab{10} 2nd order Sturm-Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points \menulispdownlink{D02RAF}{(|d02raf|)}\space{} \tab{10} ODEs, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility \endmenu \endscroll \autobuttons \end{page} \begin{page}{d03}{D03 Partial Differential Equations} \beginscroll \centerline{What would you like to do?} \newline \beginmenu \item Read \menuwindowlink{Foundation Library Chapter d03 Manual Page}{manpageXXd03} \item or \menulispwindowlink{Browse}{(|kSearch| "NagPartialDifferentialEquationsPackage")}\tab{10} through this chapter \item or use the routines: \menulispdownlink{D03EDF}{(|d03edf|)}\space{} \tab{10} Elliptic PDE, solution of finite difference equations by a multigrid technique \menulispdownlink{D03EEF}{(|d03eef|)}\space{} \tab{10} Discretize a 2nd order elliptic PDE on a rectangle \menulispdownlink{D03FAF}{(|d03faf|)}\space{} \tab{10} Elliptic PDE, Helmholtz equation, 3-D Cartesian co-ordinates \endmenu \endscroll \autobuttons \end{page} \begin{page}{e01}{E01 Interpolation} \beginscroll \centerline{What would you like to do?} \beginmenu \item Read \menuwindowlink{Foundation Library Chapter e01 Manual Page}{manpageXXe01} \item or \menulispwindowlink{Browse}{(|kSearch| "NagInterpolationPackage")}\tab{10} through this chapter \item or use the routines: \menulispdownlink{E01BAF}{(|e01baf|)}\space{} \tab{10} Interpolating functions, cubic spline interpolant, one variable \menulispdownlink{E01BEF}{(|e01bef|)}\space{} \tab{10} Interpolating functions, monotonicity-preserving, piecewise cubic Hermite, one variable \menulispdownlink{E01BFF}{(|e01bff|)}\space{} \tab{10} Interpolated values, interpolant computed by E01BEF, function only, one variable \menulispdownlink{E01BGF}{(|e01bgf|)}\space{} \tab{10} Interpolated values, interpolant computed by E01BEF, function and 1st derivative, one variable \menulispdownlink{E01BHF}{(|e01bhf|)}\space{} \tab{10} Interpolated values, interpolant computed by E01BEF, definite integral, one variable \menulispdownlink{E01DAF}{(|e01daf|)}\space{} \tab{10} Interpolating functions, fitting bicubic spline, data on a rectangular grid \menulispdownlink{E01SAF}{(|e01saf|)}\space{} \tab{10} Interpolating functions, method of Renka and Cline, two variables \menulispdownlink{E01SEF}{(|e01sef|)}\space{} \tab{10} Interpolating functions, modified Shepherd's method, two variables \endmenu \endscroll \autobuttons \end{page} \begin{page}{e02}{E02 Curve and Surface Fitting} \beginscroll \centerline{What would you like to do?} \beginmenu \item Read \menuwindowlink{Foundation Library Chapter e02 Manual Page}{manpageXXe02} \item or \menulispwindowlink{Browse}{(|kSearch| "NagFittingPackage")}\tab{10} through this chapter \item or use the routines: \menulispdownlink{E02ADF}{(|e02adf|)}\space{} \tab{10} Least-squares curve fit, by polynomials, arbitrary data points \menulispdownlink{E02AEF}{(|e02aef|)}\space{} \tab{10} Evaluation of fitted polynomial in one variable from Chebyshev series form (simplified parameter list) \menulispdownlink{E02AGF}{(|e02agf|)}\space{} \tab{10} Least-squares polynomial fit, values and derivatives may be constrained, arbitrary data points \menulispdownlink{E02AHF}{(|e02ahf|)}\space{} \tab{10} Derivative of fitted polynomial in Chebyshev series form \menulispdownlink{E02AJF}{(|e02ajf|)}\space{} \tab{10} Integral of fitted polynomial in Chebyshev series form \menulispdownlink{E02AKF}{(|e02akf|)}\space{} \tab{10} Evaluation of fitted polynomial in one variable, from Chebyshev series form \menulispdownlink{E02BAF}{(|e02baf|)}\space{} \tab{10} Least-squares curve cubic spline fit (including interpolation) \menulispdownlink{E02BBF}{(|e02bbf|)}\space{} \tab{10} Evaluation of fitted cubic spline, function only \menulispdownlink{E02BCF}{(|e02bcf|)}\space{} \tab{10} Evaluation of fitted cubic spline, function and derivatives \menulispdownlink{E02BDF}{(|e02bdf|)}\space{} \tab{10} Evaluation of fitted cubic spline, definite integral \menulispdownlink{E02BEF}{(|e02bef|)}\space{} \tab{10} Least-squares curve cubic spline fit, automatic knot placement \menulispdownlink{E02DAF}{(|e02daf|)}\space{} \tab{10} Least-squares surface fit, bicubic splines \menulispdownlink{E02DCF}{(|e02dcf|)}\space{} \tab{10} Least-squares surface fit by bicubic splines with automatic knot placement, data on a rectangular grid \menulispdownlink{E02DDF}{(|e02ddf|)}\space{} \tab{10} Least-squares surface fit by bicubic splines with automatic knot placement, scattered data \menulispdownlink{E02DEF}{(|e02def|)}\space{} \tab{10} Evaluation of a fitted bicubic spline at a vector of points \menulispdownlink{E02DFF}{(|e02dff|)}\space{} \tab{10} Evaluation of a fitted bicubic spline at a mesh of points \menulispdownlink{E02GAF}{(|e02gaf|)}\space{} \tab{10} \htbitmap{l1}-approximation by general linear function \menulispdownlink{E02ZAF}{(|e02zaf|)}\space{} \tab{10} Sort 2-D sata into panels for fitting bicubic splines \endmenu \endscroll \autobuttons \end{page} \begin{page}{e04}{E04 Minimizing or Maximizing a Function} \beginscroll \centerline{What would you like to do?} \newline \beginmenu \item Read \menuwindowlink{Foundation Library Chapter e04 Manual Page}{manpageXXe04} \item or \menulispwindowlink{Browse}{(|kSearch| "NagOptimisationPackage")}\tab{10} through this chapter \item or use the routines: \menulispdownlink{E04DGF}{(|e04dgf|)}\space{} \tab{10} Unconstrained minimum, pre-conditioned conjugate gradient algorithm, function of several variables using 1st derivatives \menulispdownlink{E04FDF}{(|e04fdf|)}\space{} \tab{10} Unconstrained minimum of a sum of squares, combined Gauss-Newton and modified Newton algorithm using function values only \menulispdownlink{E04GCF}{(|e04gcf|)}\space{} \tab{10} Unconstrained minimum, of a sum of squares, combined Gauss-Newton and modified Newton algorithm using 1st derivatives \menulispdownlink{E04JAF}{(|e04jaf|)}\space{} \tab{10} Minimum, function of several variables, quasi-Newton algorithm, simple bounds, using function values only \menulispdownlink{E04MBF}{(|e04mbf|)}\space{} \tab{10} Linear programming problem \menulispdownlink{E04NAF}{(|e04naf|)}\space{} \tab{10} Quadratic programming problem \menulispdownlink{E04UCF}{(|e04ucf|)}\space{} \tab{10} Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally 1st derivatives \menulispdownlink{E04YCF}{(|e04ycf|)}\space{} \tab{10} Covariance matrix for non-linear least-squares problem \endmenu \endscroll \autobuttons \end{page} \begin{page}{f01}{F01 Matrix Operations - Including Inversion} \beginscroll \centerline{What would you like to do?} \beginmenu \item Read \menuwindowlink{Foundation Library Chapter f Manual Page}{manpageXXf} \menuwindowlink{Foundation Library Chapter f01 Manual Page}{manpageXXf01} \item or \menulispwindowlink{Browse}{(|kSearch| "NagMatrixOperationsPackage")}\tab{10} through this chapter \item or use the routines: \menulispdownlink{F01BRF}{(|f01brf|)}\space{} \tab{10} {\it LU} factorization of real sparse matrix \menulispdownlink{F01BSF}{(|f01bsf|)}\space{} \tab{10} {\it LU} factorization of real sparse matrix with known sparsity pattern \menulispdownlink{F01MAF}{(|f01maf|)}\space{} \tab{10} \htbitmap{llt} factorization of real sparse symmetric positive-definite matrix \menulispdownlink{F01MCF}{(|f01mcf|)}\space{} \tab{10} \htbitmap{ldlt} factorization of real symmetric positive-definite variable-bandwith matrix \menulispdownlink{F01QCF}{(|f01qcf|)}\space{} \tab{10} {\it QR} factorization of real {\it m} by {\it n} matrix (m \htbitmap{great=} n) \menulispdownlink{F01QDF}{(|f01qdf|)}\space{} \tab{10} Operations with orthogonal matrices, compute {\it QB} or \htbitmap{f01qdf} after factorization by F01QCF or F01QFF \menulispdownlink{F01QEF}{(|f01qef|)}\space{} \tab{10} Operations with orthogonal matrices, form columns of {\it Q} after factorization by F01QCF or F01QFF \menulispdownlink{F01RCF}{(|f01rcf|)}\space{} \tab{10} {\it QR} factorization of complex {\it m} by {\it n} matrix (m \htbitmap{great=} n) \menulispdownlink{F01RDF}{(|f01rdf|)}\space{} \tab{10} Operations with unitary matrices, compute {\it QB} or \htbitmap{f01rdf} after factorization by F01RCF \menulispdownlink{F01REF}{(|f01ref|)}\space{} \tab{10} Operations with unitary matrices, form columns of {\it Q} after factorization by F01RCF \endmenu \endscroll \autobuttons \end{page} \begin{page}{f02}{F02 Eigenvalues and Eigenvectors} \beginscroll \centerline{What would you like to do?} \beginmenu \item Read \menuwindowlink{Foundation Library Chapter f Manual Page}{manpageXXf} \menuwindowlink{Foundation Library Chapter f02 Manual Page}{manpageXXf02} \item or \menulispwindowlink{Browse}{(|kSearch| "NagEigenPackage")}\tab{10} through this chapter \item or use the routines: \menulispdownlink{F02AAF}{(|f02aaf|)}\space{} \tab{10} All eigenvalues of real symmetric matrix (Black box) \menulispdownlink{F02ABF}{(|f02abf|)}\space{} \tab{10} All eigenvalues and eigenvectors of real symmetric matrix (Black box) \menulispdownlink{F02ADF}{(|f02adf|)}\space{} \tab{10} All eigenvalues of generalized real eigenproblem of the form Ax = \lambda Bx where A and B are symmetric and B is positive definite \menulispdownlink{F02AEF}{(|f02aef|)}\space{} \tab{10} All eigenvalues and eigenvectors of generalized real eigenproblem of the form Ax = \lambda Bx where A and B are symmetric and B is positive definite \menulispdownlink{F02AFF}{(|f02aff|)}\space{} \tab{10} All eigenvalues of real matrix (Black box) \menulispdownlink{F02AGF}{(|f02agf|)}\space{} \tab{10} All eigenvalues and eigenvectors of real matrix (Black box) \menulispdownlink{F02AJF}{(|f02ajf|)}\space{} \tab{10} All eigenvalues of complex matrix (Black box) \menulispdownlink{F02AKF}{(|f02akf|)}\space{} \tab{10} All eigenvalues and eigenvectors of complex matrix (Black box) \menulispdownlink{F02AWF}{(|f02awf|)}\space{} \tab{10} All eigenvalues of complex Hermitian matrix (Black box) \menulispdownlink{F02AXF}{(|f02axf|)}\space{} \tab{10} All eigenvalues and eigenvectors of complex Hermitian matrix (Black box) \menulispdownlink{F02BBF}{(|f02bbf|)}\space{} \tab{10} Selected eigenvalues and eigenvectors of real symmetric matrix (Black box) \menulispdownlink{F02BJF}{(|f02bjf|)}\space{} \tab{10} All eigenvalues and optionally eigenvectors of generalized eigenproblem by {\it QZ} algorithm, real matrices (Black box) \menulispdownlink{F02FJF}{(|f02fjf|)}\space{} \tab{10} Selected eigenvalues and eigenvectors of sparse symmetric eigenproblem \menulispdownlink{F02WEF}{(|f02wef|)}\space{} \tab{10} SVD of real matrix \menulispdownlink{F02XEF}{(|f02xef|)}\space{} \tab{10} SVD of complex matrix \endmenu \endscroll \autobuttons \end{page} \begin{page}{f04}{F04 Simultaneous Linear Equations} \beginscroll \centerline{What would you like to do?} \beginmenu \item Read \menuwindowlink{Foundation Library Chapter f Manual Page}{manpageXXf} \menuwindowlink{Foundation Library Chapter f04 Manual Page}{manpageXXf04} \item or \menulispwindowlink{Browse}{(|kSearch| "NagLinearEquationSolvingPackage")}\tab{10} through this chapter \item or use the routines: \menulispdownlink{F04ADF}{(|f04adf|)}\space{} \tab{10} Solution of complex simultaneous linear equations, with multiple right-hand sides (Black box) \menulispdownlink{F04ARF}{(|f04arf|)}\space{} \tab{10} Solution of real simultaneous linear equations, one right-hand side (Black box) \menulispdownlink{F04ASF}{(|f04asf|)}\space{} \tab{10} Solution of real symmetric positive-definite simultaneous linear equations, one right-hand side using iterative refinement (Black box) \menulispdownlink{F04ATF}{(|f04atf|)}\space{} \tab{10} Solution of real simultaneous linear equations, one right-hand side using iterative refinement (Black box) \menulispdownlink{F04AXF}{(|f04axf|)}\space{} \tab{10} Approximate solution of real sparse simultaneous linear equations (coefficient matrix already factorized by F01BRF or F01BSF) \menulispdownlink{F04FAF}{(|f04faf|)}\space{} \tab{10} Solution of real symmetric positive-definite tridiagonal simultaneous linear equations, one right-hand side (Black box) \menulispdownlink{F04JGF}{(|f04jgf|)}\space{} \tab{10} Least-squares (if rank = n) or minimal least-squares (if rank < n) solution of m real equations in n unknowns, rank \htbitmap{less=} n, m \htbitmap{great=} n \menulispdownlink{F04MAF}{(|f04maf|)}\space{} \tab{10} Real sparse symmetric positive-definite simultaneous linear equations(coefficient matrix already factorized) \menulispdownlink{F04MBF}{(|f04mbf|)}\space{} \tab{10} Real sparse symmetric simultaneous linear equations \menulispdownlink{F04MCF}{(|f04mcf|)}\space{} \tab{10} Approximate solution of real symmetric positive-definite variable-bandwidth simultaneous linear equations (coefficient matrix already factorized) \menulispdownlink{F04QAF}{(|f04qaf|)}\space{} \tab{10} Sparse linear least-squares problem, {\it m} real equations in {\it n} unknowns \endmenu \endscroll \autobuttons \end{page} \begin{page}{f07}{F07 Linear Equations (LAPACK)} \beginscroll \centerline{What would you like to do?} \beginmenu \item Read \menuwindowlink{Foundation Library Chapter f Manual Page}{manpageXXf} \menuwindowlink{Foundation Library Chapter f07 Manual Page}{manpageXXf07} \item or \menulispwindowlink{Browse}{(|kSearch| "NagLapack")}\tab{10} through this chapter \item or use the routines: \menulispdownlink{F07ADF}{(|f07adf|)}\space{} \tab{10} (DGETRF) {\it LU} factorization of real {\it m} by {\it n} matrix \menulispdownlink{F07AEF}{(|f07aef|)}\space{} \tab{10} (DGETRS) Solution of real system of linear equations, multiple right hand sides, matrix factorized by F07ADF \menulispdownlink{F07FDF}{(|f07fdf|)}\space{} \tab{10} (DPOTRF) Cholesky factorization of real symmetric positive-definite matrix \menulispdownlink{F07FEF}{(|f07fef|)}\space{} \tab{10} (DPOTRS) Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FDF \endmenu \endscroll \autobuttons \end{page} \begin{page}{s}{S \space{2} Approximations of Special Functions} \beginscroll \centerline{What would you like to do?} \beginmenu \item Read \menuwindowlink{Foundation Library Chapter s Manual Page}{manpageXXs} \item or \menulispwindowlink{Browse}{(|kSearch| "NagSpecialFunctionsPackage")}\tab{10} through this chapter \item or use the routines: \menulispdownlink{S01EAF}{(|s01eaf|)}\space{} \tab{10} Complex exponential {\em exp(z)} \menulispdownlink{S13AAF}{(|s13aaf|)}\space{} \tab{10} Exponential integral \htbitmap{s13aaf2} \menulispdownlink{S13ACF}{(|s13acf|)}\space{} \tab{10} Cosine integral {\em Ci(x)} \menulispdownlink{S13ADF}{(|s13adf|)}\space{} \tab{10} Sine integral {\em Si(x)} \menulispdownlink{S14AAF}{(|s14aaf|)}\space{} \tab{10} Gamma function \Gamma \menulispdownlink{S14ABF}{(|s14abf|)}\space{} \tab{10} Log Gamma function {\em ln \Gamma} \menulispdownlink{S14BAF}{(|s14baf|)}\space{} \tab{10} Incomplete gamma functions P(a,x) and Q(a,x) \menulispdownlink{S15ADF}{(|s15adf|)}\space{} \tab{10} Complement of error function {\em erfc x } \menulispdownlink{S15AEF}{(|s15aef|)}\space{} \tab{10} Error function {\em erf x} \menulispdownlink{S17ACF}{(|s17acf|)}\space{} \tab{10} Bessel function \space{1} \htbitmap{s17acf} \menulispdownlink{S17ADF}{(|s17adf|)}\space{} \tab{10} Bessel function \space{1} \htbitmap{s17adf} \menulispdownlink{S17AEF}{(|s17aef|)}\space{} \tab{10} Bessel function \space{1} \htbitmap{s17aef1} \menulispdownlink{S17AFF}{(|s17aff|)}\space{} \tab{10} Bessel function \space{1} \htbitmap{s17aff1} \menulispdownlink{S17AGF}{(|s17agf|)} \tab{10} Airy function {\em Ai(x)} \menulispdownlink{S17AHF}{(|s17ahf|)} \tab{10} Airy function {\em Bi(x)} \menulispdownlink{S17AJF}{(|s17ajf|)} \tab{10} Airy function {\em Ai'(x)} \menulispdownlink{S17AKF}{(|s17akf|)} \tab{10} Airy function {\em Bi'(x)} \menulispdownlink{S17DCF}{(|s17dcf|)} \tab{10} Bessel function \htbitmap{s17dcf}, real a \space{1} \htbitmap{great=} 0, complex z, v = 0,1,2,... \menulispdownlink{S17DEF}{(|s17def|)} \tab{10} Bessel function \htbitmap{s17def}, real a \space{1} \htbitmap{great=} 0, complex z, v = 0,1,2,... \menulispdownlink{S17DGF}{(|s17dgf|)} \tab{10} Airy function {\em Ai(z)} and {\em Ai'(z)}, complex z \menulispdownlink{S17DHF}{(|s17dhf|)} \tab{10} Airy function {\em Bi(z)} and {\em Bi'(z)}, complex z \menulispdownlink{S17DLF}{(|s17dlf|)} \tab{10} Hankel function \vspace{-32} \htbitmap{s17dlf} \vspace{-37}, j = 1,2, real a \space{1} \htbitmap{great=} 0, complex z, v = 0,1,2,... \newline \menulispdownlink{S18ACF}{(|s18acf|)} \tab{10} Modified Bessel function \space{1} \htbitmap{s18acf1} \menulispdownlink{S18ADF}{(|s18adf|)} \tab{10} Modified Bessel function \space{1} \htbitmap{s18adf1} \menulispdownlink{S18AEF}{(|s18aef|)} \tab{10} Modified Bessel function \space{1} \htbitmap{s18aef1} \menulispdownlink{S18AFF}{(|s18aff|)} \tab{10} Modified Bessel function \space{1} \htbitmap{s18aff1} \menulispdownlink{S18DCF}{(|s18dcf|)} \tab{10} Modified bessel function \htbitmap{s18dcf}, real a \space{1} \htbitmap{great=} 0, complex z, v = 0,1,2,... \menulispdownlink{S18DEF}{(|s18def|)} \tab{10} Modified bessel function \htbitmap{s18def}, real a \space{1} \htbitmap{great=} 0, complex z, v = 0,1,2,... \menulispdownlink{S19AAF}{(|s19aaf|)} \tab{10} Kelvin function {\em ber x} \menulispdownlink{S19ABF}{(|s19abf|)} \tab{10} Kelvin function {\em bei x} \menulispdownlink{S19ACF}{(|s19acf|)} \tab{10} Kelvin function {\em ker x} \menulispdownlink{S19ADF}{(|s19adf|)} \tab{10} Kelvin function {\em kei x} \menulispdownlink{S20ACF}{(|s20acf|)} \tab{10} Fresnel integral {\em S(x)} \menulispdownlink{S20ADF}{(|s20adf|)} \tab{10} Fresnel integral {\em C(x)} \menulispdownlink{S21BAF}{(|s21baf|)} \tab{10} Degenerate symmetrised elliptic integral of 1st kind \space{1} \htbitmap{s21baf1} \menulispdownlink{S21BBF}{(|s21bbf|)} \tab{10} Symmetrised elliptic integral of 1st kind \space{1} \vspace{-28} \htbitmap{s21bbf1} \vspace{-40} \menulispdownlink{S21BCF}{(|s21bcf|)} \tab{10} Symmetrised elliptic integral of 2nd kind \space{1} \vspace{-28} \htbitmap{s21bcf1} \vspace{-40} \menulispdownlink{S21BDF}{(|s21bdf|)} \tab{10} Symmetrised elliptic integral of 3rd kind \space{1} \vspace{-26} \htbitmap{s21bdf1} \vspace{-40} \endmenu \endscroll \autobuttons \end{page}