Mark 20 Library Contents

A00: Library Identification

A00AAF

Prints details of the NAG Fortran Library implementation

A02: Complex Arithmetic

Chapter Introduction
A02AAF	Square root of complex number
A02ABF	Modulus of complex number
A02ACF	Quotient of two complex numbers

C02: Zeros of Polynomials

Chapter Introduction
C02AFF	All zeros of complex polynomial, modified Laguerre method
C02AGF	All zeros of real polynomial, modified Laguerre method
C02AHF	All zeros of complex quadratic equation
C02AJF	All zeros of real quadratic equation
C02AKF	All zeros of real cubic equation
C02ALF	All zeros of real quartic equation
C02AMF	All zeros of complex cubic equation
C02ANF	All zeros of complex quartic equation

C05: Roots of One or More Transcendental Equations

Chapter Introduction
C05ADF	Zero of continuous function in given interval, Bus and Dekker algorithm
C05AGF	Zero of continuous function, Bus and Dekker algorithm, from given starting value, binary search for interval
C05AJF	Zero of continuous function, continuation method, from a given starting value
C05AVF	Binary search for interval containing zero of continuous function (reverse communication)
C05AXF	Zero of continuous function by continuation method, from given starting value (reverse communication)
C05AZF	Zero in given interval of continuous function by Bus and Dekker algorithm (reverse communication)
C05NBF	Solution of system of nonlinear equations using function values only (easy-to-use)
C05NCF	Solution of system of nonlinear equations using function values only (comprehensive)
C05NDF	Solution of system of nonlinear equations using function values only (reverse communication)
C05PBF	Solution of system of nonlinear equations using first derivatives (easy-to-use)
C05PCF	Solution of system of nonlinear equations using first derivatives (comprehensive)
C05PDF	Solution of system of nonlinear equations using first derivatives (reverse communication)
C05ZAF	Check user's routine for calculating first derivatives

C06: Summation of Series

Chapter Introduction
C06BAF	Acceleration of convergence of sequence, Shanks' transformation and epsilon algorithm
C06DBF	Sum of a Chebyshev series
C06EAF	Single one-dimensional real discrete Fourier transform, no extra workspace
C06EBF	Single one-dimensional Hermitian discrete Fourier transform, no extra workspace
C06ECF	Single one-dimensional complex discrete Fourier transform, no extra workspace
C06EKF	Circular convolution or correlation of two real vectors, no extra workspace
C06FAF	Single one-dimensional real discrete Fourier transform, extra workspace for greater speed
C06FBF	Single one-dimensional Hermitian discrete Fourier transform, extra workspace for greater speed
C06FCF	Single one-dimensional complex discrete Fourier transform, extra workspace for greater speed
C06FFF	One-dimensional complex discrete Fourier transform of multi-dimensional data
C06FJF	Multi-dimensional complex discrete Fourier transform of multi-dimensional data
C06FKF	Circular convolution or correlation of two real vectors, extra workspace for greater speed
C06FPF	Multiple one-dimensional real discrete Fourier transforms
C06FQF	Multiple one-dimensional Hermitian discrete Fourier transforms
C06FRF	Multiple one-dimensional complex discrete Fourier transforms
C06FUF	Two-dimensional complex discrete Fourier transform
C06FXF	Three-dimensional complex discrete Fourier transform
C06GBF	Complex conjugate of Hermitian sequence
C06GCF	Complex conjugate of complex sequence
C06GQF	Complex conjugate of multiple Hermitian sequences
C06GSF	Convert Hermitian sequences to general complex sequences
C06HAF	Discrete sine transform
C06HBF	Discrete cosine transform
C06HCF	Discrete quarter-wave sine transform
C06HDF	Discrete quarter-wave cosine transform
C06LAF	Inverse Laplace transform, Crump's method
C06LBF	Inverse Laplace transform, modified Weeks' method
C06LCF	Evaluate inverse Laplace transform as computed by C06LBF
C06PAF	Single one-dimensional real and Hermitian complex discrete Fourier transform, using complex data format for Hermitian sequences
C06PCF	Single one-dimensional complex discrete Fourier transform, complex data format
C06PFF	One-dimensional complex discrete Fourier transform of multi-dimensional data (using complex data type)
C06PJF	Multi-dimensional complex discrete Fourier transform of multi-dimensional data (using complex data type)
C06PKF	Circular convolution or correlation of two complex vectors
C06PPF	Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using complex data format for Hermitian sequences
C06PQF	Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using complex data format for Hermitian sequences
C06PRF	Multiple one-dimensional complex discrete Fourier transforms using complex data format
C06PSF	Multiple one-dimensional complex discrete Fourier transforms using complex data format and sequences stored as columns
C06PUF	Two-dimensional complex discrete Fourier transform, complex data format
C06PXF	Three-dimensional complex discrete Fourier transform, complex data format
C06RAF	Discrete sine transform (easy-to-use)
C06RBF	Discrete cosine transform (easy-to-use)
C06RCF	Discrete quarter-wave sine transform (easy-to-use)
C06RDF	Discrete quarter-wave cosine transform (easy-to-use)

D01: Quadrature

Chapter Introduction
D01AHF	One-dimensional quadrature, adaptive, finite interval, strategy due to Patterson, suitable for well-behaved integrands
D01AJF	One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly-behaved integrands
D01AKF	One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions
D01ALF	One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points
D01AMF	One-dimensional quadrature, adaptive, infinite or semi-infinite interval
D01ANF	One-dimensional quadrature, adaptive, finite interval, weight function cos(omega x) or sin(omega x)
D01APF	One-dimensional quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type
D01AQF	One-dimensional quadrature, adaptive, finite interval, weight function 1/(x-c), Cauchy principal value (Hilbert transform)
D01ARF	One-dimensional quadrature, non-adaptive, finite interval with provision for indefinite integrals
D01ASF	One-dimensional quadrature, adaptive, semi-infinite interval, weight function cos(omega x) or sin(omega x)
D01ATF	One-dimensional quadrature, adaptive, finite interval, variant of D01AJF efficient on vector machines
D01AUF	One-dimensional quadrature, adaptive, finite interval, variant of D01AKF efficient on vector machines
D01BAF	One-dimensional Gaussian quadrature
D01BBF	Pre-computed weights and abscissae for Gaussian quadrature rules, restricted choice of rule
D01BCF	Calculation of weights and abscissae for Gaussian quadrature rules, general choice of rule
D01BDF	One-dimensional quadrature, non-adaptive, finite interval
D01DAF	Two-dimensional quadrature, finite region
D01EAF	Multi-dimensional adaptive quadrature over hyper-rectangle, multiple integrands
D01FBF	Multi-dimensional Gaussian quadrature over hyper-rectangle
D01FCF	Multi-dimensional adaptive quadrature over hyper-rectangle
D01FDF	Multi-dimensional quadrature, Sag–Szekeres method, general product region or n-sphere
D01GAF	One-dimensional quadrature, integration of function defined by data values, Gill–Miller method
D01GBF	Multi-dimensional quadrature over hyper-rectangle, Monte Carlo method
D01GCF	Multi-dimensional quadrature, general product region, number-theoretic method
D01GDF	Multi-dimensional quadrature, general product region, number-theoretic method, variant of D01GCF efficient on vector machines
D01GYF	Korobov optimal coefficients for use in D01GCF or D01GDF, when number of points is prime
D01GZF	Korobov optimal coefficients for use in D01GCF or D01GDF, when number of points is product of two primes
D01JAF	Multi-dimensional quadrature over an n-sphere, allowing for badly-behaved integrands
D01PAF	Multi-dimensional quadrature over an n-simplex

D02: Ordinary Differential Equations

Chapter Introduction
D02AGF	ODEs, boundary value problem, shooting and matching technique, allowing interior matching point, general parameters to be determined
D02BGF	ODEs, IVP, Runge–Kutta–Merson method, until a component attains given value (simple driver)
D02BHF	ODEs, IVP, Runge–Kutta–Merson method, until function of solution is zero (simple driver)
D02BJF	ODEs, IVP, Runge–Kutta method, until function of solution is zero, integration over range with intermediate output (simple driver)
D02CJF	ODEs, IVP, Adams method, until function of solution is zero, intermediate output (simple driver)
D02EJF	ODEs, stiff IVP, BDF method, until function of solution is zero, intermediate output (simple driver)
D02GAF	ODEs, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem
D02GBF	ODEs, boundary value problem, finite difference technique with deferred correction, general linear problem
D02HAF	ODEs, boundary value problem, shooting and matching, boundary values to be determined
D02HBF	ODEs, boundary value problem, shooting and matching, general parameters to be determined
D02JAF	ODEs, boundary value problem, collocation and least-squares, single nth-order linear equation
D02JBF	ODEs, boundary value problem, collocation and least-squares, system of first-order linear equations
D02KAF	Second-order Sturm–Liouville problem, regular system, finite range, eigenvalue only
D02KDF	Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, user-specified break-points
D02KEF	Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points
D02LAF	Second-order ODEs, IVP, Runge–Kutta–Nystrom method
D02LXF	Second-order ODEs, IVP, setup for D02LAF
D02LYF	Second-order ODEs, IVP, diagnostics for D02LAF
D02LZF	Second-order ODEs, IVP, interpolation for D02LAF
D02M/N Introduction
D02MVF	ODEs, IVP, DASSL method, setup for D02M–N routines
D02MZF	ODEs, IVP, interpolation for D02M–N routines, natural interpolant
D02NBF	Explicit ODEs, stiff IVP, full Jacobian (comprehensive)
D02NCF	Explicit ODEs, stiff IVP, banded Jacobian (comprehensive)
D02NDF	Explicit ODEs, stiff IVP, sparse Jacobian (comprehensive)
D02NGF	Implicit/algebraic ODEs, stiff IVP, full Jacobian (comprehensive)
D02NHF	Implicit/algebraic ODEs, stiff IVP, banded Jacobian (comprehensive)
D02NJF	Implicit/algebraic ODEs, stiff IVP, sparse Jacobian (comprehensive)
D02NMF	Explicit ODEs, stiff IVP (reverse communication, comprehensive)
D02NNF	Implicit/algebraic ODEs, stiff IVP (reverse communication, comprehensive)
D02NRF	ODEs, IVP, for use with D02M–N routines, sparse Jacobian, enquiry routine
D02NSF	ODEs, IVP, for use with D02M–N routines, full Jacobian, linear algebra set up
D02NTF	ODEs, IVP, for use with D02M–N routines, banded Jacobian, linear algebra set up
D02NUF	ODEs, IVP, for use with D02M–N routines, sparse Jacobian, linear algebra set up
D02NVF	ODEs, IVP, BDF method, setup for D02M–N routines
D02NWF	ODEs, IVP, Blend method, setup for D02M–N routines
D02NXF	ODEs, IVP, sparse Jacobian, linear algebra diagnostics, for use with D02M–N routines
D02NYF	ODEs, IVP, integrator diagnostics, for use with D02M–N routines
D02NZF	ODEs, IVP, setup for continuation calls to integrator, for use with D02M–N routines
D02PCF	ODEs, IVP, Runge–Kutta method, integration over range with output
D02PDF	ODEs, IVP, Runge–Kutta method, integration over one step
D02PVF	ODEs, IVP, setup for D02PCF and D02PDF
D02PWF	ODEs, IVP, resets end of range for D02PDF
D02PXF	ODEs, IVP, interpolation for D02PDF
D02PYF	ODEs, IVP, integration diagnostics for D02PCF and D02PDF
D02PZF	ODEs, IVP, error assessment diagnostics for D02PCF and D02PDF
D02QFF	ODEs, IVP, Adams method with root-finding (forward communication, comprehensive)
D02QGF	ODEs, IVP, Adams method with root-finding (reverse communication, comprehensive)
D02QWF	ODEs, IVP, setup for D02QFF and D02QGF
D02QXF	ODEs, IVP, diagnostics for D02QFF and D02QGF
D02QYF	ODEs, IVP, root-finding diagnostics for D02QFF and D02QGF
D02QZF	ODEs, IVP, interpolation for D02QFF or D02QGF
D02RAF	ODEs, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility
D02SAF	ODEs, boundary value problem, shooting and matching technique, subject to extra algebraic equations, general parameters to be determined
D02TGF	nth-order linear ODEs, boundary value problem, collocation and least-squares
D02TKF	ODEs, general nonlinear boundary value problem, collocation technique
D02TVF	ODEs, general nonlinear boundary value problem, setup for D02TKF
D02TXF	ODEs, general nonlinear boundary value problem, continuation facility for D02TKF
D02TYF	ODEs, general nonlinear boundary value problem, interpolation for D02TKF
D02TZF	ODEs, general nonlinear boundary value problem, diagnostics for D02TKF
D02XJF	ODEs, IVP, interpolation for D02M–N routines, natural interpolant
D02XKF	ODEs, IVP, interpolation for D02M–N routines, C₁ interpolant
D02ZAF	ODEs, IVP, weighted norm of local error estimate for D02M–N routines

D03: Partial Differential Equations

Chapter Introduction
D03EAF	Elliptic PDE, Laplace's equation, two-dimensional arbitrary domain
D03EBF	Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, iterate to convergence
D03ECF	Elliptic PDE, solution of finite difference equations by SIP for seven-point three-dimensional molecule, iterate to convergence
D03EDF	Elliptic PDE, solution of finite difference equations by a multigrid technique
D03EEF	Discretize a second-order elliptic PDE on a rectangle
D03FAF	Elliptic PDE, Helmholtz equation, three-dimensional Cartesian co-ordinates
D03MAF	Triangulation of plane region
D03NCF	Finite difference solution of the Black–Scholes equations
D03NDF	Analytic solution of the Black–Scholes equations
D03NEF	Compute average values for D03NDF
D03PCF	General system of parabolic PDEs, method of lines, finite differences, one space variable
D03PDF	General system of parabolic PDEs, method of lines, Chebyshev C⁰ collocation, one space variable
D03PEF	General system of first-order PDEs, method of lines, Keller box discretisation, one space variable
D03PFF	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
D03PHF	General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable
D03PJF	General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C⁰ collocation, one space variable
D03PKF	General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, one space variable
D03PLF	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
D03PPF	General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable
D03PRF	General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, remeshing, one space variable
D03PSF	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, remeshing, one space variable
D03PUF	Roe's approximate Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
D03PVF	Osher's approximate Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
D03PWF	Modified HLL Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
D03PXF	Exact Riemann Solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
D03PYF	PDEs, spatial interpolation with D03PDF or D03PJF
D03PZF	PDEs, spatial interpolation with D03PCF, D03PEF, D03PFF, D03PHF, D03PKF, D03PLF, D03PPF, D03PRF or D03PSF
D03RAF	General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectangular region
D03RBF	General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectilinear region
D03RYF	Check initial grid data in D03RBF
D03RZF	Extract grid data from D03RBF
D03UAF	Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, one iteration
D03UBF	Elliptic PDE, solution of finite difference equations by SIP, seven-point three-dimensional molecule, one iteration

D04: Numerical Differentiation

Chapter Introduction
D04AAF	Numerical differentiation, derivatives up to order 14, function of one real variable

D05: Integral Equations

Chapter Introduction
D05AAF	Linear non-singular Fredholm integral equation, second kind, split kernel
D05ABF	Linear non-singular Fredholm integral equation, second kind, smooth kernel
D05BAF	Nonlinear Volterra convolution equation, second kind
D05BDF	Nonlinear convolution Volterra–Abel equation, second kind, weakly singular
D05BEF	Nonlinear convolution Volterra–Abel equation, first kind, weakly singular
D05BWF	Generate weights for use in solving Volterra equations
D05BYF	Generate weights for use in solving weakly singular Abel-type equations

D06: Mesh Generation

Chapter Introduction
D06AAF	Generates a two-dimensional mesh using a simple incremental method
D06ABF	Generates a two-dimensional mesh using a Delaunay–Voronoi process
D06ACF	Generates a two-dimensional mesh using an Advancing-front method
D06BAF	Generates a boundary mesh
D06CAF	Uses a barycentering technique to smooth a given mesh
D06CBF	Generates a sparsity pattern of a Finite Element matrix associated with a given mesh
D06CCF	Renumbers a given mesh using Gibbs method
D06DAF	Generates a mesh resulting from an affine transformation of a given mesh
D06DBF	Joins together two given adjacent (possibly overlapping) meshes

E01: Interpolation

Chapter Introduction
E01AAF	Interpolated values, Aitken's technique, unequally spaced data, one variable
E01ABF	Interpolated values, Everett's formula, equally spaced data, one variable
E01AEF	Interpolating functions, polynomial interpolant, data may include derivative values, one variable
E01BAF	Interpolating functions, cubic spline interpolant, one variable
E01BEF	Interpolating functions, monotonicity-preserving, piecewise cubic Hermite, one variable
E01BFF	Interpolated values, interpolant computed by E01BEF, function only, one variable
E01BGF	Interpolated values, interpolant computed by E01BEF, function and first derivative, one variable
E01BHF	Interpolated values, interpolant computed by E01BEF, definite integral, one variable
E01DAF	Interpolating functions, fitting bicubic spline, data on rectangular grid
E01RAF	Interpolating functions, rational interpolant, one variable
E01RBF	Interpolated values, evaluate rational interpolant computed by E01RAF, one variable
E01SAF	Interpolating functions, method of Renka and Cline, two variables
E01SBF	Interpolated values, evaluate interpolant computed by E01SAF, two variables
E01SGF	Interpolating functions, modified Shepard's method, two variables
E01SHF	Interpolated values, evaluate interpolant computed by E01SGF, function and first derivatives, two variables
E01TGF	Interpolating functions, modified Shepard's method, three variables
E01THF	Interpolated values, evaluate interpolant computed by E01TGF, function and first derivatives, three variables

E02: Curve and Surface Fitting

Chapter Introduction
E02ACF	Minimax curve fit by polynomials
E02ADF	Least-squares curve fit, by polynomials, arbitrary data points
E02AEF	Evaluation of fitted polynomial in one variable from Chebyshev series form (simplified parameter list)
E02AFF	Least-squares polynomial