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 fit, special data points (including interpolation)
E02AGF    Least-squares polynomial fit, values and derivatives may be constrained, arbitrary data points
E02AHF    Derivative of fitted polynomial in Chebyshev series form
E02AJF    Integral of fitted polynomial in Chebyshev series form
E02AKF    Evaluation of fitted polynomial in one variable from Chebyshev series form
E02BAF    Least-squares curve cubic spline fit (including interpolation)
E02BBF    Evaluation of fitted cubic spline, function only
E02BCF    Evaluation of fitted cubic spline, function and derivatives
E02BDF    Evaluation of fitted cubic spline, definite integral
E02BEF    Least-squares cubic spline curve fit, automatic knot placement
E02CAF    Least-squares surface fit by polynomials, data on lines
E02CBF    Evaluation of fitted polynomial in two variables
E02DAF    Least-squares surface fit, bicubic splines
E02DCF    Least-squares surface fit by bicubic splines with automatic knot placement, data on rectangular grid
E02DDF    Least-squares surface fit by bicubic splines with automatic knot placement, scattered data
E02DEF    Evaluation of fitted bicubic spline at a vector of points
E02DFF    Evaluation of fitted bicubic spline at a mesh of points
E02GAF    L1-approximation by general linear function
E02GBF    L1-approximation by general linear function subject to linear inequality constraints
E02GCF    L-approximation by general linear function
E02RAF    Padé-approximants
E02RBF    Evaluation of fitted rational function as computed by E02RAF
E02ZAF    Sort two-dimensional data into panels for fitting bicubic splines

E04:  Minimizing or Maximizing a Function

Chapter Introduction
E04ABF    Minimum, function of one variable using function values only
E04BBF    Minimum, function of one variable, using first derivative
E04CCF    Unconstrained minimum, simplex algorithm, function of several variables using function values only (comprehensive)
E04DGF    Unconstrained minimum, preconditioned conjugate gradient algorithm, function of several variables using first derivatives (comprehensive)
E04DJF    Read optional parameter values for E04DGF from external file
E04DKF    Supply optional parameter values to E04DGF
E04FCF    Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using function values only (comprehensive)
E04FYF    Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using function values only (easy-to-use)
E04GBF    Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm using first derivatives (comprehensive)
E04GDF    Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using first derivatives (comprehensive)
E04GYF    Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use)
E04GZF    Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using first derivatives (easy-to-use)
E04HCF    Check user's routine for calculating first derivatives of function
E04HDF    Check user's routine for calculating second derivatives of function
E04HEF    Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (comprehensive)
E04HYF    Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (easy-to-use)
E04JYF    Minimum, function of several variables, quasi-Newton algorithm, simple bounds, using function values only (easy-to-use)
E04KDF    Minimum, function of several variables, modified Newton algorithm, simple bounds, using first derivatives (comprehensive)
E04KYF    Minimum, function of several variables, quasi-Newton algorithm, simple bounds, using first derivatives (easy-to-use)
E04KZF    Minimum, function of several variables, modified Newton algorithm, simple bounds, using first derivatives (easy-to-use)
E04LBF    Minimum, function of several variables, modified Newton algorithm, simple bounds, using first and second derivatives (comprehensive)
E04LYF    Minimum, function of several variables, modified Newton algorithm, simple bounds, using first and second derivatives (easy-to-use)
E04MFF    LP problem (dense)
E04MGF    Read optional parameter values for E04MFF from external file
E04MHF    Supply optional parameter values to E04MFF
E04MZF    Converts MPSX data file defining LP or QP problem to format required by E04NKF
E04NCF    Convex QP problem or linearly-constrained linear least-squares problem (dense)
E04NDF    Read optional parameter values for E04NCF from external file
E04NEF    Supply optional parameter values to E04NCF
E04NFF    QP problem (dense)
E04NGF    Read optional parameter values for E04NFF from external file
E04NHF    Supply optional parameter values to E04NFF
E04NKF    LP or QP problem (sparse)
E04NLF    Read optional parameter values for E04NKF from external file
E04NMF    Supply optional parameter values to E04NKF
E04UCF    Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (forward communication, comprehensive)
E04UDF    Read optional parameter values for E04UCF or E04UFF from external file
E04UEF    Supply optional parameter values to E04UCF or E04UFF
E04UFF    Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (reverse communication, comprehensive)
E04UGF    NLP problem (sparse)
E04UHF    Read optional parameter values for E04UGF from external file
E04UJF    Supply optional parameter values to E04UGF
E04UNF * Minimum of a sum of squares, nonlinear constraints, sequential QP method, using function values and optionally first derivatives (comprehensive)
E04UQF    Read optional parameter values for E04UNF from external file
E04URF    Supply optional parameter values to E04UNF
E04USF    Minimum of a sum of squares, nonlinear constraints, sequential QP method, using function values and optionally first derivatives (comprehensive)
E04WBF    Initialization routine for E04DGA, E04MFA, E04NCA, E04NFA, E04NKA, E04UCA, E04UFA, E04UGA and E04USA
E04XAF    Estimate (using numerical differentiation) gradient and/or Hessian of a function
E04YAF    Check user's routine for calculating Jacobian of first derivatives
E04YBF    Check user's routine for calculating Hessian of a sum of squares
E04YCF    Covariance matrix for nonlinear least-squares problem (unconstrained)
E04ZCF    Check user's routines for calculating first derivatives of function and constraints

F:  Linear Algebra

Chapter Introduction

F01:  Matrix Factorizations

Chapter Introduction
F01ABF    Inverse of real symmetric positive-definite matrix using iterative refinement
F01ADF    Inverse of real symmetric positive-definite matrix
F01BLF    Pseudo-inverse and rank of real m by n matrix (m ≥ n)
F01BRF    LU factorization of real sparse matrix
F01BSF    LU factorization of real sparse matrix with known sparsity pattern
F01BUF    ULD LT UT factorization of real symmetric positive-definite band matrix
F01BVF    Reduction to standard form, generalized real symmetric-definite banded eigenproblem
F01CKF    Matrix multiplication
F01CRF    Matrix transposition
F01CTF    Sum or difference of two real matrices, optional scaling and transposition
F01CWF    Sum or difference of two complex matrices, optional scaling and transposition
F01LEF    LU factorization of real tridiagonal matrix
F01LHF    LU factorization of real almost block diagonal matrix
F01MCF    LDLT factorization of real symmetric positive-definite variable-bandwidth matrix
F01QGF    RQ factorization of real m by n upper trapezoidal matrix (m ≤ n)
F01QJF    RQ factorization of real m by n matrix (m ≤ n)
F01QKF    Operations with orthogonal matrices, form rows of Q, after RQ factorization by F01QJF
F01RGF    RQ factorization of complex m by n upper trapezoidal matrix (m ≤ n)
F01RJF    RQ factorization of complex m by n matrix (m ≤ n)
F01RKF    Operations with unitary matrices, form rows of Q, after RQ factorization by F01RJF
F01ZAF    Convert real matrix between packed triangular and square storage schemes
F01ZBF    Convert complex matrix between packed triangular and square storage schemes
F01ZCF    Convert real matrix between packed banded and rectangular storage schemes
F01ZDF    Convert complex matrix between packed banded and rectangular storage schemes

F02:  Eigenvalues and Eigenvectors

Chapter Introduction
F02BJF    All eigenvalues and optionally eigenvectors of generalized eigenproblem by QZ algorithm, real matrices (Black Box)
F02EAF    All eigenvalues and Schur factorization of real general matrix (Black Box)
F02EBF    All eigenvalues and eigenvectors of real general matrix (Black Box)
F02ECF    Selected eigenvalues and eigenvectors of real nonsymmetric matrix (Black Box)
F02FAF    All eigenvalues and eigenvectors of real symmetric matrix (Black Box)
F02FCF    Selected eigenvalues and eigenvectors of real symmetric matrix (Black Box)
F02FDF    All eigenvalues and eigenvectors of real symmetric-definite generalized problem (Black Box)
F02FHF    All eigenvalues of generalized banded real symmetric-definite eigenproblem (Black Box)
F02FJF    Selected eigenvalues and eigenvectors of sparse symmetric eigenproblem (Black Box)
F02GAF    All eigenvalues and Schur factorization of complex general matrix (Black Box)
F02GBF    All eigenvalues and eigenvectors of complex general matrix (Black Box)
F02GCF    Selected eigenvalues and eigenvectors of complex nonsymmetric matrix (Black Box)
F02GJF    All eigenvalues and optionally eigenvectors of generalized complex eigenproblem by QZ algorithm (Black Box)
F02HAF    All eigenvalues and eigenvectors of complex Hermitian matrix (Black Box)
F02HCF    Selected eigenvalues and eigenvectors of complex Hermitian matrix (Black Box)
F02HDF    All eigenvalues and eigenvectors of complex Hermitian-definite generalized problem (Black Box)
F02SDF    Eigenvector of generalized real banded eigenproblem by inverse iteration
F02WDF    QR factorization, possibly followed by SVD
F02WEF    SVD of real matrix (Black Box)
F02WUF    SVD of real upper triangular matrix (Black Box)
F02XEF    SVD of complex matrix (Black Box)
F02XUF    SVD of complex upper triangular matrix (Black Box)

F03:  Determinants

Chapter Introduction
F03AAF    Determinant of real matrix (Black Box)
F03ABF    Determinant of real symmetric positive-definite matrix (Black Box)
F03ACF    Determinant of real symmetric positive-definite band matrix (Black Box)
F03ADF    Determinant of complex matrix (Black Box)
F03AEF    LLT factorization and determinant of real symmetric positive-definite matrix
F03AFF    LU factorization and determinant of real matrix

F04:  Simultaneous Linear Equations

Chapter Introduction
F04AAF    Solution of real simultaneous linear equations with multiple right-hand sides (Black Box)
F04ABF    Solution of real symmetric positive-definite simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box)
F04ACF    Solution of real symmetric positive-definite banded simultaneous linear equations with multiple right-hand sides (Black Box)
F04ADF    Solution of complex simultaneous linear equations with multiple right-hand sides (Black Box)
F04AEF    Solution of real simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box)
F04AFF    Solution of real symmetric positive-definite simultaneous linear equations using iterative refinement (coefficient matrix already factorized by F03AEF)
F04AGF    Solution of real symmetric positive-definite simultaneous linear equations (coefficient matrix already factorized by F03AEF)
F04AHF    Solution of real simultaneous linear equations using iterative refinement (coefficient matrix already factorized by F03AFF)
F04AJF    Solution of real simultaneous linear equations (coefficient matrix already factorized by F03AFF)
F04AMF    Least-squares solution of m real equations in n unknowns, rank = n, m ≥ n using iterative refinement (Black Box)
F04ARF    Solution of real simultaneous linear equations, one right-hand side (Black Box)
F04ASF    Solution of real symmetric positive-definite simultaneous linear equations, one right-hand side using iterative refinement (Black Box)
F04ATF    Solution of real simultaneous linear equations, one right-hand side using iterative refinement (Black Box)
F04AXF    Solution of real sparse simultaneous linear equations (coefficient matrix already factorized)
F04EAF    Solution of real tridiagonal simultaneous linear equations, one right-hand side (Black Box)
F04FAF    Solution of real symmetric positive-definite tridiagonal simultaneous linear equations, one right-hand side (Black Box)
F04FEF    Solution of the Yule–Walker equations for real symmetric positive-definite Toeplitz matrix, one right-hand side
F04FFF    Solution of real symmetric positive-definite Toeplitz system, one right-hand side
F04JAF    Minimal least-squares solution of m real equations in n unknowns, rank ≤ n, m ≥ n
F04JDF    Minimal least-squares solution of m real equations in n unknowns, rank ≤ n, m ≥ n
F04JGF    Least-squares (if rank = n) or minimal least-squares (if rank < n) solution of m real equations in n unknowns, rank ≤ n, m ≥ n
F04JLF    Real general Gauss–Markov linear model (including weighted least-squares)
F04JMF    Equality-constrained real linear least-squares problem
F04KLF    Complex general Gauss–Markov linear model (including weighted least-squares)
F04KMF    Equality-constrained complex linear least-squares problem
F04LEF    Solution of real tridiagonal simultaneous linear equations (coefficient matrix already factorized by F01LEF)
F04LHF    Solution of real almost block diagonal simultaneous linear equations (coefficient matrix already factorized by F01LHF)
F04MCF    Solution of real symmetric positive-definite variable-bandwidth simultaneous linear equations (coefficient matrix already factorized by F01MCF)
F04MEF    Update solution of the Yule–Walker equations for real symmetric positive-definite Toeplitz matrix
F04MFF    Update solution of real symmetric positive-definite Toeplitz system
F04QAF    Sparse linear least-squares problem, m real equations in n unknowns
F04YAF    Covariance matrix for linear least-squares problems, m real equations in n unknowns
F04YCF    Norm estimation (for use in condition estimation), real matrix
F04ZCF    Norm estimation (for use in condition estimation), complex matrix

F05:  Orthogonalisation

Chapter Introduction
F05AAF    Gram–Schmidt orthogonalisation of n vectors of order m

F06:  Linear Algebra Support Routines

Chapter Introduction
F06AAF    Generate real plane rotation
F06BAF    Generate real plane rotation, storing tangent
F06BCF    Recover cosine and sine from given real tangent
F06BEF    Generate real Jacobi plane rotation
F06BHF    Apply real similarity rotation to 2 by 2 symmetric matrix
F06BLF    Compute quotient of two real scalars, with overflow flag
F06BMF    Compute Euclidean norm from scaled form
F06BNF    Compute square root of (a2 + b2), real a and b
F06BPF    Compute eigenvalue of 2 by 2 real symmetric matrix
F06CAF    Generate complex plane rotation, storing tangent, real cosine
F06CBF    Generate complex plane rotation, storing tangent, real sine
F06CCF    Recover cosine and sine from given complex tangent, real cosine
F06CDF    Recover cosine and sine from given complex tangent, real sine
F06CHF    Apply complex similarity rotation to 2 by 2 Hermitian matrix
F06CLF    Compute quotient of two complex scalars, with overflow flag
F06DBF    Broadcast scalar into integer vector
F06DFF    Copy integer vector
F06EAF    Dot product of two real vectors
F06ECF    Add scalar times real vector to real vector
F06EDF    Multiply real vector by scalar
F06EFF    Copy real vector
F06EGF    Swap two real vectors
F06EJF    Compute Euclidean norm of real vector
F06EKF    Sum absolute values of real vector elements
F06EPF    Apply real plane rotation
F06ERF    Dot product of two real sparse vectors
F06ETF    Add scalar times real sparse vector to real sparse vector
F06EUF    Gather real sparse vector
F06EVF    Gather and set to zero real sparse vector
F06EWF    Scatter real sparse vector
F06EXF    Apply plane rotation to two real sparse vectors
F06FAF    Compute cosine of angle between two real vectors
F06FBF    Broadcast scalar into real vector
F06FCF    Multiply real vector by diagonal matrix
F06FDF    Multiply real vector by scalar, preserving input vector
F06FGF    Negate real vector
F06FJF    Update Euclidean norm of real vector in scaled form
F06FKF    Compute weighted Euclidean norm of real vector
F06FLF    Elements of real vector with largest and smallest absolute value
F06FPF    Apply real symmetric plane rotation to two vectors
F06FQF    Generate sequence of real plane rotations
F06FRF    Generate real elementary reflection, NAG style
F06FSF    Generate real elementary reflection, LINPACK style
F06FTF    Apply real elementary reflection, NAG style
F06FUF    Apply real elementary reflection, LINPACK style
F06GAF    Dot product of two complex vectors, unconjugated
F06GBF    Dot product of two complex vectors, conjugated
F06GCF    Add scalar times complex vector to complex vector
F06GDF    Multiply complex vector by complex scalar
F06GFF    Copy complex vector
F06GGF    Swap two complex vectors
F06GRF    Dot product of two complex sparse vector, unconjugated
F06GSF    Dot product of two complex sparse vector, conjugated
F06GTF    Add scalar times complex sparse vector to complex sparse vector
F06GUF    Gather complex sparse vector
F06GVF    Gather and set to zero complex sparse vector
F06GWF    Scatter complex sparse vector
F06HBF    Broadcast scalar into complex vector
F06HCF    Multiply complex vector by complex diagonal matrix
F06HDF    Multiply complex vector by complex scalar, preserving input vector
F06HGF    Negate complex vector
F06HPF    Apply complex plane rotation
F06HQF    Generate sequence of complex plane rotations
F06HRF    Generate complex elementary reflection
F06HTF    Apply complex elementary reflection
F06JDF    Multiply complex vector by real scalar
F06JJF    Compute Euclidean norm of complex vector
F06JKF    Sum absolute values of complex vector elements
F06JLF    Index, real vector element with largest absolute value
F06JMF    Index, complex vector element with largest absolute value
F06KCF    Multiply complex vector by real diagonal matrix
F06KDF    Multiply complex vector by real scalar, preserving input vector
F06KFF    Copy real vector to complex vector
F06KJF    Update Euclidean norm of complex vector in scaled form
F06KLF    Last non-negligible element of real vector
F06KPF    Apply real plane rotation to two complex vectors
F06PAF    Matrix-vector product, real rectangular matrix
F06PBF    Matrix-vector product, real rectangular band matrix
F06PCF    Matrix-vector product, real symmetric matrix
F06PDF    Matrix-vector product, real symmetric band matrix
F06PEF    Matrix-vector product, real symmetric packed matrix
F06PFF    Matrix-vector product, real triangular matrix
F06PGF    Matrix-vector product, real triangular band matrix
F06PHF    Matrix-vector product, real triangular packed matrix
F06PJF    System of equations, real triangular matrix
F06PKF    System of equations, real triangular band matrix
F06PLF    System of equations, real triangular packed matrix
F06PMF    Rank-1 update, real rectangular matrix
F06PPF    Rank-1 update, real symmetric matrix
F06PQF    Rank-1 update, real symmetric packed matrix
F06PRF    Rank-2 update, real symmetric matrix
F06PSF    Rank-2 update, real symmetric packed matrix
F06QFF    Matrix copy, real rectangular or trapezoidal matrix
F06QHF    Matrix initialisation, real rectangular matrix
F06QJF    Permute rows or columns, real rectangular matrix, permutations represented by an integer array
F06QKF    Permute rows or columns, real rectangular matrix, permutations represented by a real array
F06QMF    Orthogonal similarity transformation of real symmetric matrix as a sequence of plane rotations
F06QPF    QR factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix
F06QQF    QR factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row
F06QRF    QR or RQ factorization by sequence of plane rotations, real upper Hessenberg matrix
F06QSF    QR or RQ factorization by sequence of plane rotations, real upper spiked matrix
F06QTF    QR factorization of UZ or RQ factorization of ZU, U real upper triangular, Z a sequence of plane rotations
F06QVF    Compute upper Hessenberg matrix by sequence of plane rotations, real upper triangular matrix
F06QWF    Compute upper spiked matrix by sequence of plane rotations, real upper triangular matrix
F06QXF    Apply sequence of plane rotations, real rectangular matrix
F06RAF    1-norm, -norm, Frobenius norm, largest absolute element, real general matrix
F06RBF    1-norm, -norm, Frobenius norm, largest absolute element, real band matrix
F06RCF    1-norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix
F06RDF    1-norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage
F06REF    1-norm, -norm, Frobenius norm, largest absolute element, real symmetric band matrix
F06RJF    1-norm, -norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix
F06RKF    1-norm, -norm, Frobenius norm, largest absolute element, real triangular matrix, packed storage
F06RLF    1-norm, -norm, Frobenius norm, largest absolute element, real triangular band matrix
F06RMF    1-norm, -norm, Frobenius norm, largest absolute element, real Hessenberg matrix
F06SAF    Matrix-vector product, complex rectangular matrix
F06SBF    Matrix-vector product, complex rectangular band matrix
F06SCF    Matrix-vector product, complex Hermitian matrix
F06SDF    Matrix-vector product, complex Hermitian band matrix
F06SEF    Matrix-vector product, complex Hermitian packed matrix
F06SFF    Matrix-vector product, complex triangular matrix
F06SGF    Matrix-vector product, complex triangular band matrix
F06SHF    Matrix-vector product, complex triangular packed matrix
F06SJF    System of equations, complex triangular matrix
F06SKF    System of equations, complex triangular band matrix
F06SLF    System of equations, complex triangular packed matrix
F06SMF    Rank-1 update, complex rectangular matrix, unconjugated vector
F06SNF    Rank-1 update, complex rectangular matrix, conjugated vector
F06SPF    Rank-1 update, complex Hermitian matrix
F06SQF    Rank-1 update, complex Hermitian packed matrix
F06SRF    Rank-2 update, complex Hermitian matrix
F06SSF    Rank-2 update, complex Hermitian packed matrix
F06TFF    Matrix copy, complex rectangular or trapezoidal matrix
F06THF    Matrix initialisation, complex rectangular matrix
F06TMF    Unitary similarity transformation of Hermitian matrix as a sequence of plane rotations
F06TPF    QR factorization by sequence of plane rotations, rank-1 update of complex upper triangular matrix
F06TQF    QR × k factorization by sequence of plane rotations, complex upper triangular matrix augmented by a full row
F06TRF    QR or RQ factorization by sequence of plane rotations, complex upper Hessenberg matrix
F06TSF    QR or RQ factorization by sequence of plane rotations, complex upper spiked matrix
F06TTF    QR factorization of UZ or RQ factorization of ZU, U complex upper triangular, Z a sequence of plane rotations
F06TVF    Compute upper Hessenberg matrix by sequence of plane rotations, complex upper triangular matrix
F06TWF    Compute upper spiked matrix by sequence of plane rotations, complex upper triangular matrix
F06TXF    Apply sequence of plane rotations, complex rectangular matrix, real cosine and complex sine
F06TYF    Apply sequence of plane rotations, complex rectangular matrix, complex cosine and real sine
F06UAF    1-norm, -norm, Frobenius norm, largest absolute element, complex general matrix
F06UBF    1-norm, -norm, Frobenius norm, largest absolute element, complex band matrix
F06UCF    1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix
F06UDF    1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, packed storage
F06UEF    1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian band matrix
F06UFF    1-norm, -norm, Frobenius norm, largest absolute element, complex symmetric matrix
F06UGF    1-norm, -norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage
F06UHF    1-norm, -norm, Frobenius norm, largest absolute element, complex symmetric band matrix
F06UJF    1-norm, -norm, Frobenius norm, largest absolute element, complex trapezoidal/triangular matrix
F06UKF    1-norm, -norm, Frobenius norm, largest absolute element, complex triangular matrix, packed storage
F06ULF    1-norm, -norm, Frobenius norm, largest absolute element, complex triangular band matrix
F06UMF    1-norm, -norm, Frobenius norm, largest absolute element, complex Hessenberg matrix
F06VJF    Permute rows or columns, complex rectangular matrix, permutations represented by an integer array
F06VKF    Permute rows or columns, complex rectangular matrix, permutations represented by a real array
F06VXF    Apply sequence of plane rotations, complex rectangular matrix, real cosine and sine
F06YAF    Matrix-matrix product, two real rectangular matrices
F06YCF    Matrix-matrix product, one real symmetric matrix, one real rectangular matrix
F06YFF    Matrix-matrix product, one real triangular matrix, one real rectangular matrix
F06YJF    Solves system of equations with multiple right-hand sides, real triangular coefficient matrix
F06YPF    Rank-k update of real symmetric matrix
F06YRF    Rank-2k update of real symmetric matrix
F06ZAF    Matrix-matrix product, two complex rectangular matrices
F06ZCF    Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix
F06ZFF    Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix
F06ZJF    Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix
F06ZPF    Rank-k update of complex Hermitian matrix
F06ZRF    Rank-2k update of complex Hermitian matrix
F06ZTF    Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix
F06ZUF    Rank-k update of complex symmetric matrix
F06ZWF    Rank-2k update of complex symmetric matrix

F07:  Linear Equations (LAPACK)

A list of the LAPACK equivalent names is included in the Chapter F07 Introduction.

Chapter Introduction
F07ADF    LU factorization of real m by n matrix
F07AEF    Solution of real system of linear equations, multiple right-hand sides, matrix already factorized by F07ADF
F07AGF    Estimate condition number of real matrix, matrix already factorized by F07ADF
F07AHF    Refined solution with error bounds of real system of linear equations, multiple right-hand sides
F07AJF    Inverse of real matrix, matrix already factorized by F07ADF
F07ARF    LU factorization of complex m by n matrix
F07ASF    Solution of complex system of linear equations, multiple right-hand sides, matrix already factorized by F07ARF
F07AUF    Estimate condition number of complex matrix, matrix already factorized by F07ARF
F07AVF    Refined solution with error bounds of complex system of linear equations, multiple right-hand sides
F07AWF    Inverse of complex matrix, matrix already factorized by F07ARF
F07BDF    LU factorization of real m by n band matrix
F07BEF    Solution of real band system of linear equations, multiple right-hand sides, matrix already factorized by F07BDF
F07BGF    Estimate condition number of real band matrix, matrix already factorized by F07BDF
F07BHF    Refined solution with error bounds of real band system of linear equations, multiple right-hand sides
F07BRF    LU factorization of complex m by n band matrix
F07BSF    Solution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by F07BRF
F07BUF    Estimate condition number of complex band matrix, matrix already factorized by F07BRF
F07BVF    Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides
F07FDF    Cholesky factorization of real symmetric positive-definite matrix
F07FEF    Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FDF
F07FGF    Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by F07FDF
F07FHF    Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides
F07FJF    Inverse of real symmetric positive-definite matrix, matrix already factorized by F07FDF
F07FRF    Cholesky factorization of complex Hermitian positive-definite matrix
F07FSF    Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FRF
F07FUF    Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by F07FRF
F07FVF    Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides
F07FWF    Inverse of complex Hermitian positive-definite matrix, matrix already factorized by F07FRF
F07GDF    Cholesky factorization of real symmetric positive-definite matrix, packed storage
F07GEF    Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GDF, packed storage
F07GGF    Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by F07GDF, packed storage
F07GHF    Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides, packed storage
F07GJF    Inverse of real symmetric positive-definite matrix, matrix already factorized by F07GDF, packed storage
F07GRF    Cholesky factorization of complex Hermitian positive-definite matrix, packed storage
F07GSF    Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GRF, packed storage
F07GUF    Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by F07GRF, packed storage
F07GVF    Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, packed storage
F07GWF    Inverse of complex Hermitian positive-definite matrix, matrix already factorized by F07GRF, packed storage
F07HDF    Cholesky factorization of real symmetric positive-definite band matrix
F07HEF    Solution of real symmetric positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HDF
F07HGF    Estimate condition number of real symmetric positive-definite band matrix, matrix already factorized by F07HDF
F07HHF    Refined solution with error bounds of real symmetric positive-definite band system of linear equations, multiple right-hand sides
F07HRF    Cholesky factorization of complex Hermitian positive-definite band matrix
F07HSF    Solution of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HRF
F07HUF    Estimate condition number of complex Hermitian positive-definite band matrix, matrix already factorized by F07HRF
F07HVF    Refined solution with error bounds of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides
F07MDF    Bunch–Kaufman factorization of real symmetric indefinite matrix
F07MEF    Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MDF
F07MGF    Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07MDF
F07MHF    Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides
F07MJF    Inverse of real symmetric indefinite matrix, matrix already factorized by F07MDF
F07MRF    Bunch–Kaufman factorization of complex Hermitian indefinite matrix
F07MSF    Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MRF
F07MUF    Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07MRF
F07MVF    Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides
F07MWF    Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07MRF
F07NRF    Bunch–Kaufman factorization of complex symmetric matrix
F07NSF    Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07NRF
F07NUF    Estimate condition number of complex symmetric matrix, matrix already factorized by F07NRF
F07NVF    Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides
F07NWF    Inverse of complex symmetric matrix, matrix already factorized by F07NRF
F07PDF    Bunch–Kaufman factorization of real symmetric indefinite matrix, packed storage
F07PEF    Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PDF, packed storage
F07PGF    Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage
F07PHF    Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage
F07PJF    Inverse of real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage
F07PRF    Bunch–Kaufman factorization of complex Hermitian indefinite matrix, packed storage
F07PSF    Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PRF, packed storage
F07PUF    Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07PRF, packed storage
F07PVF    Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage
F07PWF    Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07PRF, packed storage
F07QRF    Bunch–Kaufman factorization of complex symmetric matrix, packed storage
F07QSF    Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07QRF, packed storage
F07QUF    Estimate condition number of complex symmetric matrix, matrix already factorized by F07QRF, packed storage
F07QVF    Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage
F07QWF    Inverse of complex symmetric matrix, matrix already factorized by F07QRF, packed storage
F07TEF    Solution of real triangular system of linear equations, multiple right-hand sides
F07TGF    Estimate condition number of real triangular matrix
F07THF    Error bounds for solution of real triangular system of linear equations, multiple right-hand sides
F07TJF    Inverse of real triangular matrix
F07TSF    Solution of complex triangular system of linear equations, multiple right-hand sides
F07TUF    Estimate condition number of complex triangular matrix
F07TVF    Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides
F07TWF    Inverse of complex triangular matrix
F07UEF    Solution of real triangular system of linear equations, multiple right-hand sides, packed storage
F07UGF    Estimate condition number of real triangular matrix, packed storage
F07UHF    Error bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage
F07UJF    Inverse of real triangular matrix, packed storage
F07USF    Solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
F07UUF    Estimate condition number of complex triangular matrix, packed storage
F07UVF    Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
F07UWF    Inverse of complex triangular matrix, packed storage
F07VEF    Solution of real band triangular system of linear equations, multiple right-hand sides
F07VGF    Estimate condition number of real band triangular matrix
F07VHF    Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides
F07VSF    Solution of complex band triangular system of linear equations, multiple right-hand sides
F07VUF    Estimate condition number of complex band triangular matrix
F07VVF    Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides

F08:  Least-squares and Eigenvalue Problems (LAPACK)

A list of the LAPACK equivalent names is included in the Chapter F08 Introduction.

Chapter Introduction
F08AEF    QR factorization of real general rectangular matrix
F08AFF    Form all or part of orthogonal Q from QR factorization determined by F08AEF or F08BEF
F08AGF    Apply orthogonal transformation determined by F08AEF or F08BEF
F08AHF    LQ factorization of real general rectangular matrix
F08AJF    Form all or part of orthogonal Q from LQ factorization determined by F08AHF
F08AKF    Apply orthogonal transformation determined by F08AHF
F08ASF    QR factorization of complex general rectangular matrix
F08ATF    Form all or part of unitary Q from QR factorization determined by F08ASF or F08BSF
F08AUF    Apply unitary transformation determined by F08ASF or F08BSF
F08AVF    LQ factorization of complex general rectangular matrix
F08AWF    Form all or part of unitary Q from LQ factorization determined by F08AVF
F08AXF    Apply unitary transformation determined by F08AVF
F08BEF    QR factorization of real general rectangular matrix with column pivoting
F08BSF    QR factorization of complex general rectangular matrix with column pivoting
F08FCF    All eigenvalues and optionally all eigenvectors of real symmetric matrix, using divide and conquer
F08FEF    Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
F08FFF    Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF
F08FGF    Apply orthogonal transformation determined by F08FEF
F08FQF    All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, using divide and conquer
F08FSF    Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
F08FTF    Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF
F08FUF    Apply unitary transformation matrix determined by F08FSF
F08GCF    All eigenvalues and optionally all eigenvectors of real symmetric matrix, packed storage, using divide and conquer
F08GEF    Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
F08GFF    Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF
F08GGF    Apply orthogonal transformation determined by F08GEF
F08GQF    All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, packed storage, using divide and conquer
F08GSF    Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
F08GTF    Generate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF
F08GUF    Apply unitary transformation matrix determined by F08GSF
F08HCF    All eigenvalues and optionally all eigenvectors of real symmetric band matrix, using divide and conquer
F08HEF    Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
F08HQF    All eigenvalues and optionally all eigenvectors of complex Hermitian band matrix, using divide and conquer
F08HSF    Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
F08JCF    All eigenvalues and optionally all eigenvectors of real symmetric tridiagonal matrix, using divide and conquer
F08JEF    All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using implicit QL or QR
F08JFF    All eigenvalues of real symmetric tridiagonal matrix, root-free variant of QL or QR
F08JGF    All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from real symmetric positive-definite matrix
F08JJF    Selected eigenvalues of real symmetric tridiagonal matrix by bisection
F08JKF    Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
F08JSF    All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using implicit QL or QR
F08JUF    All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from complex Hermitian positive-definite matrix
F08JXF    Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
F08KEF    Orthogonal reduction of real general rectangular matrix to bidiagonal form
F08KFF    Generate orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF
F08KGF    Apply orthogonal transformations from reduction to bidiagonal form determined by F08KEF
F08KSF    Unitary reduction of complex general rectangular matrix to bidiagonal form
F08KTF    Generate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF
F08KUF    Apply unitary transformations from reduction to bidiagonal form determined by F08KSF
F08LEF    Reduction of real rectangular band matrix to upper bidiagonal form
F08LSF    Reduction of complex rectangular band matrix to upper bidiagonal form
F08MEF    SVD of real bidiagonal matrix reduced from real general matrix
F08MSF    SVD of real bidiagonal matrix reduced from complex general matrix
F08NEF    Orthogonal reduction of real general matrix to upper Hessenberg form
F08NFF    Generate orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF
F08NGF    Apply orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF
F08NHF    Balance real general matrix
F08NJF    Transform eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF
F08NSF    Unitary reduction of complex general matrix to upper Hessenberg form
F08NTF    Generate unitary transformation matrix from reduction to Hessenberg form determined by F08NSF
F08NUF    Apply unitary transformation matrix from reduction to Hessenberg form determined by F08NSF
F08NVF    Balance complex general matrix
F08NWF    Transform eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF
F08PEF    Eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
F08PKF    Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
F08PSF    Eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
F08PXF    Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
F08QFF    Reorder Schur factorization of real matrix using orthogonal similarity transformation
F08QGF    Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QHF    Solve real Sylvester matrix equation AX + XB = C, A and B are upper quasi-triangular or transposes
F08QKF    Left and right eigenvectors of real upper quasi-triangular matrix
F08QLF    Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
F08QTF    Reorder Schur factorization of complex matrix using unitary similarity transformation
F08QUF    Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QVF    Solve complex Sylvester matrix equation AX + XB = C, A and B are upper triangular or conjugate-transposes
F08QXF    Left and right eigenvectors of complex upper triangular matrix
F08QYF    Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
F08SEF    Reduction to standard form of real symmetric-definite generalized eigenproblem Ax = λ Bx, ABx = λ x or BAx = λ x, B factorized by F07FDF
F08SSF    Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax = λ Bx, ABx = λ x or BAx = λ x, B factorized by F07FRF
F08TEF    Reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λ Bx, ABx = λ x or BAx = λ x, packed storage, B factorized by F07GDF
F08TSF    Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λ Bx, ABx = lamda x or BAx = λ x, packed storage, B factorized by F07GRF
F08UEF    Reduction of real symmetric-definite banded generalized eigenproblem Ax = λ Bx to standard form Cy = λ y, such that C has the same bandwidth as A
F08UFF    Computes a split Cholesky factorization of real symmetric positive-definite band matrix A
F08USF    Reduction of complex Hermitian-definite banded generalized eigenproblem Ax = λ Bx to standard form Cy = λ y, such that C has the same bandwidth as A
F08UTF    Computes a split Cholesky factorization of complex Hermitian positive-definite band matrix A
F08WEF    Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
F08WHF    Balance a pair of real general matrices
F08WJF    Transform eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF
F08WSF    Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
F08WVF    Balance a pair of complex general matrices
F08WWF    Transform eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF
F08XEF    Eigenvalues and generalized Schur factorization of real generalized upper Hessenberg matrix reduced from a pair of real general matrices
F08XSF    Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg matrix reduced from a pair of complex general matrices
F08YKF    Left and right eigenvectors of a pair of real upper quasi-triangular matrices
F08YXF    Left and right eigenvectors of a pair of complex upper triangular matrices

F11:  Sparse Linear Algebra

Chapter Introduction
F11BAF ** Real sparse nonsymmetric linear systems, setup for F11BBF
F11BBF ** Real sparse nonsymmetric linear systems, preconditioned RGMRES, CGS or Bi-CGSTAB
F11BCF ** Real sparse nonsymmetric linear systems, diagnostic for F11BBF
F11BDF    Real sparse nonsymmetric linear systems, setup for F11BEF
F11BEF    Real sparse nonsymmetric linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
F11BFF    Real sparse nonsymmetric linear systems, diagnostic for F11BEF
F11BRF    Complex sparse non-Hermitian linear systems, setup for F11BSF
F11BSF    Complex sparse non-Hermitian linear systems, preconditioned RGMRES, CGS,Bi-CGSTAB or TFQMR method
F11BTF    Complex sparse non-Hermitian linear systems, diagnostic for F11BSF
F11DAF    Real sparse nonsymmetric linear systems, incomplete LU factorization
F11DBF    Solution of linear system involving incomplete LU preconditioning matrix generated by F11DAF
F11DCF    Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DAF
F11DDF    Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse nonsymmetric matrix
F11DEF    Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB, or TFQMR method, Jacobi or SSOR preconditioner (Black Box)
F11DKF    Real sparse nonsymmetric linear systems, line Jacobi preconditioner
F11DNF    Complex sparse non-Hermitian linear systems, incomplete LU factorization
F11DPF    Solution of complex linear system involving incomplete LU preconditioning matrix generated by F11DNF
F11DQF    Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DNF (Black Box)
F11DRF    Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse non-Hermitian matrix
F11DSF    Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner Black Box
F11DXF    Complex sparse nonsymmetric linear systems, line Jacobi preconditioner
F11GAF * Real sparse symmetric linear systems, setup for F11GBF
F11GBF * Real sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos
F11GCF * Real sparse symmetric linear systems, diagnostic for F11GBF
F11GDF    Real sparse symmetric linear systems, setup for F11GEF
F11GEF    Real sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos
F11GFF    Real sparse symmetric linear systems, diagnostic for F11GEF
F11GRF    Complex sparse symmetric linear systems, setup for F11GEF
F11GSF    Complex sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos
F11GTF    Complex sparse symmetric linear systems, diagnostic for F11GEF
F11JAF    Real sparse symmetric matrix, incomplete Cholesky factorization
F11JBF    Solution of linear system involving incomplete Cholesky preconditioning matrix generated by F11JAF
F11JCF    Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JAF (Black Box)
F11JDF    Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse symmetric matrix
F11JEF    Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
F11JNF    Complex sparse Hermitian matrix, incomplete Cholesky factorization
F11JPF    Solution of complex linear system involving incomplete Cholesky preconditioning matrix generated by F11JNF
F11JQF    Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JNF (Black Box)
F11JRF    Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse Hermitian matrix
F11JSF    Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
F11XAF    Real sparse nonsymmetric matrix vector multiply
F11XEF    Real sparse symmetric matrix vector multiply
F11XNF    Complex sparse non-Hermitian matrix vector multiply
F11XSF    Complex sparse Hermitian matrix vector multiply
F11ZAF    Real sparse nonsymmetric matrix reorder routine
F11ZBF    Real sparse symmetric matrix reorder routine
F11ZNF    Complex sparse non-Hermitian matrix reorder routine
F11ZPF    Complex sparse Hermitian matrix reorder routine

G01:  Simple Calculations on Statistical Data

Chapter Introduction
G01AAF    Mean, variance, skewness, kurtosis, etc, one variable, from raw data
G01ABF    Mean, variance, skewness, kurtosis, etc, two variables, from raw data
G01ADF    Mean, variance, skewness, kurtosis, etc, one variable, from frequency table
G01AEF    Frequency table from raw data
G01AFF    Two-way contingency table analysis, with χ2/Fisher's exact test
G01AGF    Lineprinter scatterplot of two variables
G01AHF    Lineprinter scatterplot of one variable against Normal scores
G01AJF    Lineprinter histogram of one variable
G01ALF    Computes a five-point summary (median, hinges and extremes)
G01ARF    Constructs a stem and leaf plot
G01ASF    Constructs a box and whisker plot
G01BJF    Binomial distribution function
G01BKF    Poisson distribution function
G01BLF    Hypergeometric distribution function
G01DAF    Normal scores, accurate values
G01DBF    Normal scores, approximate values
G01DCF    Normal scores, approximate variance-covariance matrix
G01DDF    Shapiro and Wilk's W test for Normality
G01DHF    Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores
G01EAF    Computes probabilities for the standard Normal distribution
G01EBF    Computes probabilities for Student's t-distribution
G01ECF    Computes probabilities for χ2 distribution
G01EDF    Computes probabilities for F-distribution
G01EEF    Computes upper and lower tail probabilities and probability density function for the beta distribution
G01EFF    Computes probabilities for the gamma distribution
G01EMF    Computes probability for the Studentized range statistic
G01EPF    Computes bounds for the significance of a Durbin–Watson statistic
G01ERF    Computes probability for von Mises distribution
G01EYF    Computes probabilities for the one-sample Kolmogorov–Smirnov distribution
G01EZF    Computes probabilities for the two-sample Kolmogorov–Smirnov distribution
G01FAF    Computes deviates for the standard Normal distribution
G01FBF    Computes deviates for Student's t-distribution
G01FCF    Computes deviates for the χ2 distribution
G01FDF    Computes deviates for the F-distribution
G01FEF    Computes deviates for the beta distribution
G01FFF    Computes deviates for the gamma distribution
G01FMF    Computes deviates for the Studentized range statistic
G01GBF    Computes probabilities for the non-central Student's t-distribution
G01GCF    Computes probabilities for the non-central χ2 distribution
G01GDF    Computes probabilities for the non-central F-distribution
G01GEF    Computes probabilities for the non-central beta distribution
G01HAF    Computes probability for the bivariate Normal distribution
G01HBF    Computes probabilities for the multivariate Normal distribution
G01JCF    Computes probability for a positive linear combination of χ2 variables
G01JDF    Computes lower tail probability for a linear combination of (central) χ2 variables
G01MBF    Computes reciprocal of Mills' Ratio
G01NAF    Cumulants and moments of quadratic forms in Normal variables
G01NBF    Moments of ratios of quadratic forms in Normal variables, and related statistics

G02:  Correlation and Regression Analysis

Chapter Introduction
G02BAF    Pearson product-moment correlation coefficients, all variables, no missing values
G02BBF    Pearson product-moment correlation coefficients, all variables, casewise treatment of missing values
G02BCF    Pearson product-moment correlation coefficients, all variables, pairwise treatment of missing values
G02BDF    Correlation-like coefficients (about zero), all variables, no missing values
G02BEF    Correlation-like coefficients (about zero), all variables, casewise treatment of missing values
G02BFF    Correlation-like coefficients (about zero), all variables, pairwise treatment of missing values
G02BGF    Pearson product-moment correlation coefficients, subset of variables, no missing values
G02BHF    Pearson product-moment correlation coefficients, subset of variables, casewise treatment of missing values
G02BJF    Pearson product-moment correlation coefficients, subset of variables, pairwise treatment of missing values
G02BKF    Correlation-like coefficients (about zero), subset of variables, no missing values
G02BLF    Correlation-like coefficients (about zero), subset of variables, casewise treatment of missing values
G02BMF    Correlation-like coefficients (about zero), subset of variables, pairwise treatment of missing values
G02BNF    Kendall/Spearman non-parametric rank correlation coefficients, no missing values, overwriting input data
G02BPF    Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, overwriting input data
G02BQF    Kendall/Spearman non-parametric rank correlation coefficients, no missing values, preserving input data
G02BRF    Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, preserving input data
G02BSF    Kendall/Spearman non-parametric rank correlation coefficients, pairwise treatment of missing values
G02BTF    Update a weighted sum of squares matrix with a new observation
G02BUF    Computes a weighted sum of squares matrix
G02BWF    Computes a correlation matrix from a sum of squares matrix
G02BXF    Computes (optionally weighted) correlation and covariance matrices
G02BYF    Computes partial correlation/variance-covariance matrix from correlation/variance-covariance matrix computed by G02BXF
G02CAF    Simple linear regression with constant term, no missing values
G02CBF    Simple linear regression without constant term, no missing values
G02CCF    Simple linear regression with constant term, missing values
G02CDF    Simple linear regression without constant term, missing values
G02CEF    Service routines for multiple linear regression, select elements from vectors and matrices
G02CFF    Service routines for multiple linear regression, re-order elements of vectors and matrices
G02CGF    Multiple linear regression, from correlation coefficients, with constant term
G02CHF    Multiple linear regression, from correlation-like coefficients, without constant term
G02DAF    Fits a general (multiple) linear regression model
G02DCF    Add/delete an observation to/from a general linear regression model
G02DDF    Estimates of linear parameters and general linear regression model from updated model
G02DEF    Add a new variable to a general linear regression model
G02DFF    Delete a variable from a general linear regression model
G02DGF    Fits a general linear regression model for new dependent variable
G02DKF    Estimates and standard errors of parameters of a general linear regression model for given constraints
G02DNF    Computes estimable function of a general linear regression model and its standard error
G02EAF    Computes residual sums of squares for all possible linear regressions for a set of independent variables
G02ECF    Calculates R2 and CP values from residual sums of squares
G02EEF    Fits a linear regression model by forward selection
G02FAF    Calculates standardized residuals and influence statistics
G02FCF    Computes Durbin–Watson test statistic
G02GAF    Fits a generalized linear model with Normal errors
G02GBF    Fits a generalized linear model with binomial errors
G02GCF    Fits a generalized linear model with Poisson errors
G02GDF    Fits a generalized linear model with gamma errors
G02GKF    Estimates and standard errors of parameters of a general linear model for given constraints
G02GNF    Computes estimable function of a generalized linear model and its standard error
G02HAF    Robust regression, standard M-estimates
G02HBF    Robust regression, compute weights for use with G02HDF
G02HDF    Robust regression, compute regression with user-supplied functions and weights
G02HFF    Robust regression, variance-covariance matrix following G02HDF
G02HKF    Calculates a robust estimation of a correlation matrix, Huber's weight function
G02HLF    Calculates a robust estimation of a correlation matrix, user-supplied weight function plus derivatives
G02HMF    Calculates a robust estimation of a correlation matrix, user-supplied weight function

G03:  Multivariate Methods

Chapter Introduction
G03AAF    Performs principal component analysis
G03ACF    Performs canonical variate analysis
G03ADF    Performs canonical correlation analysis
G03BAF    Computes orthogonal rotations for loading matrix, generalized orthomax criterion
G03BCF    Computes Procrustes rotations
G03CAF    Computes maximum likelihood estimates of the parameters of a factor analysis model, factor loadings, communalities and residual correlations
G03CCF    Computes factor score coefficients (for use after G03CAF)
G03DAF    Computes test statistic for equality of within-group covariance matrices and matrices for discriminant analysis
G03DBF    Computes Mahalanobis squared distances for group or pooled variance-covariance matrices (for use after G03DAF)
G03DCF    Allocates observations to groups according to selected rules (for use after G03DAF)
G03EAF    Computes distance matrix
G03ECF    Hierarchical cluster analysis
G03EFF    K-means cluster analysis
G03EHF    Constructs dendrogram (for use after G03ECF)
G03EJF    Computes cluster indicator variable (for use after G03ECF)
G03FAF    Performs principal co-ordinate analysis, classical metric scaling
G03FCF    Performs non-metric (ordinal) multidimensional scaling
G03ZAF    Produces standardized values (z-scores) for a data matrix

G04:  Analysis of Variance

Chapter Introduction
G04AGF    Two-way analysis of variance, hierarchical classification, subgroups of unequal size
G04BBF    Analysis of variance, randomized block or completely randomized design, treatment means and standard errors
G04BCF    Analysis of variance, general row and column design, treatment means and standard errors
G04CAF    Analysis of variance, complete factorial design, treatment means and standard errors
G04DAF    Computes sum of squares for contrast between means
G04DBF    Computes confidence intervals for differences between means computed by G04BBF or G04BCF
G04EAF    Computes orthogonal polynomials or dummy variables for factor/classification variable

G05:  Random Number Generators

Chapter Introduction
G05CAF * Pseudo-random real numbers, uniform distribution over (0,1)
G05CBF * Initialise random number generating routines to give repeatable sequence
G05CCF * Initialise random number generating routines to give non-repeatable sequence
G05CFF * Save state of random number generating routines
G05CGF * Restore state of random number generating routines
G05DAF * Pseudo-random real numbers, uniform distribution over (a,b)
G05DBF * Pseudo-random real numbers, (negative) exponential distribution
G05DCF * Pseudo-random real numbers, logistic distribution
G05DDF * Pseudo-random real numbers, Normal distribution
G05DEF * Pseudo-random real numbers, log-normal distribution
G05DFF * Pseudo-random real numbers, Cauchy distribution
G05DHF * Pseudo-random real numbers, χ2 distribution
G05DJF * Pseudo-random real numbers, Student's t-distribution
G05DKF * Pseudo-random real numbers, F-distribution
G05DPF * Pseudo-random real numbers, Weibull distribution
G05DRF * Pseudo-random integer, Poisson distribution
G05DYF * Pseudo-random integer from uniform distribution
G05DZF * Pseudo-random logical (boolean) value
G05EAF * Set up reference vector for multivariate Normal distribution
G05EBF * Set up reference vector for generating pseudo-random integers, uniform distribution
G05ECF * Set up reference vector for generating pseudo-random integers, Poisson distribution
G05EDF * Set up reference vector for generating pseudo-random integers, binomial distribution
G05EEF * Set up reference vector for generating pseudo-random integers, negative binomial distribution
G05EFF * Set up reference vector for generating pseudo-random integers, hypergeometric distribution
G05EGF * Set up reference vector for univariate ARMA time series model
G05EHF * Pseudo-random permutation of an integer vector
G05EJF * Pseudo-random sample from an integer vector
G05EWF * Generate next term from reference vector for ARMA time series model
G05EXF * Set up reference vector from supplied cumulative distribution function or probability distribution function
G05EYF * Pseudo-random integer from reference vector
G05EZF * Pseudo-random multivariate Normal vector from reference vector
G05FAF * Generates a vector of random numbers from a uniform distribution
G05FBF * Generates a vector of random numbers from an (negative) exponential distribution
G05FDF * Generates a vector of random numbers from a Normal distribution
G05FEF * Generates a vector of pseudo-random numbers from a beta distribution
G05FFF * Generates a vector of pseudo-random numbers from a gamma distribution
G05FSF * Generates a vector of pseudo-random variates from von Mises distribution
G05GAF * Computes a random orthogonal matrix
G05GBF * Computes a random correlation matrix
G05HDF * Generates a realisation of a multivariate time series from a VARMA model
G05HKF    Univariate time series, generate n terms of either a symmetric GARCH process or a GARCH process with asymmetry of the form t-1 + γ)2
G05HLF    Univariate time series, generate n terms of a GARCH process with asymmetry of the form (|εt-1| + γ εt-1)2
G05HMF    Univariate time series, generate n terms of an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
G05HNF    Univariate time series, generate n terms of an exponential GARCH (EGARCH) process
G05KAF    Pseudo-random real numbers, uniform distribution over (0,1), seeds and generator number passed explicitly
G05KBF    Initialise seeds of a given generator for random number generating routines (that pass seeds expicitly) to give a repeatable sequence
G05KCF    Initialise seeds of a given generator for random number generating routines (that pass seeds expicitly) to give non-repeatable sequence
G05KEF    Pseudo-random logical (boolean) value, seeds and generator number passed explicitly
G05LAF    Generates a vector of random numbers from a Normal distribution, seeds and generator number passed explicitly
G05LBF    Generates a vector of random numbers from a Student's t-distribution, seeds and generator number passed explicitly
G05LCF    Generates a vector of random numbers from a χ2 distribution, seeds and generator number passed explicitly
G05LDF    Generates a vector of random numbers from an F-distribution, seeds and generator number passed explicitly
G05LEF    Generates a vector of random numbers from a beta distribution, seeds and generator number passed explicitly
G05LFF    Generates a vector of random numbers from a γ distribution, seeds and generator number passed explicitly
G05LGF    Generates a vector of random numbers from a uniform distribution, seeds and generator number passed explicitly
G05LHF    Generates a vector of random numbers from a triangular distribution, seeds and generator number passed explicitly
G05LJF    Generates a vector of random numbers from an exponential distribution, seeds and generator number passed explicitly
G05LKF    Generates a vector of random numbers from a lognormal distribution, seeds and generator number passed explicitly
G05LLF    Generates a vector of random numbers from a Cauchy distribution, seeds and generator number passed explicitly
G05LMF    Generates a vector of random numbers from a Weibull distribution, seeds and generator number passed explicitly
G05LNF    Generates a vector of random numbers from a logistic distribution, seeds and generator number passed explicitly
G05LPF    Generates a vector of random numbers from a Von Mises distribution, seeds and generator number passed explicitly
G05LQF    Generates a vector of random numbers from an exponential mixture distribution, seeds and generator number passed explicitly
G05LZF    Generates a vector of random numbers from a multivariate Normal distribution, seeds and generator number passed explicitly
G05MAF    Generates a vector of random integers from a uniform distribution, seeds and generator number passed explicitly
G05MBF    Generates a vector of random integers from a geometric distribution, seeds and generator number passed explicitly
G05MCF    Generates a vector of random integers from a negative binomial distribution, seeds and generator number passed explicitly
G05MDF    Generates a vector of random integers from a logarithmic distribution, seeds and generator number passed explicitly
G05MEF    Generates a vector of random integers from a Poisson distribution with varying mean, seeds and generator number passed explicitly
G05MJF    Generates a vector of random integers from a binomial distribution, seeds and generator number passed explicitly
G05MKF    Generates a vector of random integers from a Poisson distribution, seeds and generator number passed explicitly
G05MLF    Generates a vector of random integers from a hypergeometric distribution, seeds and generator number passed explicitly
G05MRF    Generates a vector of random integers from a multinomial distribution, seeds and generator number passed explicitly
G05MZF    Generates a vector of random integers from a general discrete distribution, seeds and generator number passed explicitly
G05NAF    Pseudo-random permutation of an integer vector
G05NBF    Pseudo-random sample from an integer vector
G05PAF    Generates a realisation of a time series from an ARMA model
G05PCF    Generates a realisation of a multivariate time series from a VARMA model
G05QAF    Computes a random orthogonal matrix
G05QBF    Computes a random correlation matrix
G05QDF    Generates a random table matrix
G05YAF    Multi-dimensional quasi-random number generator with a uniform probability distribution
G05YBF    Multi-dimensional quasi-random number generator with a Gaussian or log-normal probability distribution
G05ZAF    Selects either the basic generator or the Wichmann–Hill generator for those routines using internal communication

G07:  Univariate Estimation

Chapter Introduction
G07AAF    Computes confidence interval for the parameter of a binomial distribution
G07ABF    Computes confidence interval for the parameter of a Poisson distribution
G07BBF    Computes maximum likelihood estimates for parameters of the Normal distribution from grouped and/or censored data
G07BEF    Computes maximum likelihood estimates for parameters of the Weibull distribution
G07CAF    Computes t-test statistic for a difference in means between two Normal populations, confidence interval
G07DAF    Robust estimation, median, median absolute deviation, robust standard deviation
G07DBF    Robust estimation, M-estimates for location and scale parameters, standard weight functions
G07DCF    Robust estimation, M-estimates for location and scale parameters, user-defined weight functions
G07DDF    Computes a trimmed and winsorized mean of a single sample with estimates of their variance
G07EAF    Robust confidence intervals, one-sample
G07EBF    Robust confidence intervals, two-sample

G08:  Nonparametric Statistics

Chapter Introduction
G08AAF    Sign test on two paired samples
G08ACF    Median test on two samples of unequal size
G08AEF    Friedman two-way analysis of variance on k matched samples
G08AFF    Kruskal–Wallis one-way analysis of variance on k samples of unequal size
G08AGF    Performs the Wilcoxon one-sample (matched pairs) signed rank test
G08AHF    Performs the Mann–Whitney U test on two independent samples
G08AJF    Computes the exact probabilities for the Mann–Whitney U statistic, no ties in pooled sample
G08AKF    Computes the exact probabilities for the Mann–Whitney U statistic, ties in pooled sample
G08ALF    Performs the Cochran Q test on cross-classified binary data
G08BAF    Mood's and David's tests on two samples of unequal size
G08CBF    Performs the one-sample Kolmogorov–Smirnov test for standard distributions
G08CCF    Performs the one-sample Kolmogorov–Smirnov test for a user-supplied distribution
G08CDF    Performs the two-sample Kolmogorov–Smirnov test
G08CGF    Performs the χ2 goodness of fit test, for standard continuous distributions
G08DAF    Kendall's coefficient of concordance
G08EAF    Performs the runs up or runs down test for randomness
G08EBF    Performs the pairs (serial) test for randomness
G08ECF    Performs the triplets test for randomness
G08EDF    Performs the gaps test for randomness
G08RAF    Regression using ranks, uncensored data
G08RBF    Regression using ranks, right-censored data

G10:  Smoothing in Statistics

Chapter Introduction
G10ABF    Fit cubic smoothing spline, smoothing parameter given
G10ACF    Fit cubic smoothing spline, smoothing parameter estimated
G10BAF    Kernel density estimate using Gaussian kernel
G10CAF    Compute smoothed data sequence using running median smoothers
G10ZAF    Reorder data to give ordered distinct observations

G11:  Contingency Table Analysis

Chapter Introduction
G11AAF    χ2 statistics for two-way contingency table
G11BAF    Computes multiway table from set of classification factors using selected statistic
G11BBF    Computes multiway table from set of classification factors using given percentile/quantile
G11BCF    Computes marginal tables for multiway table computed by G11BAF or G11BBF
G11CAF    Returns parameter estimates for theconditional analysis of stratified data
G11SAF    Contingency table, latent variable model for binary data
G11SBF    Frequency count for G11SAF

G12:  Survival Analysis

Chapter Introduction
G12AAF    Computes Kaplan–Meier (product-limit) estimates of survival probabilities
G12BAF    Fits Cox's proportional hazard model
G12ZAF    Creates the risk sets associated with the Cox proportional hazards model for fixed covariates

G13:  Time Series Analysis

Chapter Introduction
G13AAF    Univariate time series, seasonal and non-seasonal differencing
G13ABF    Univariate time series, sample autocorrelation function
G13ACF    Univariate time series, partial autocorrelations from autocorrelations
G13ADF    Univariate time series, preliminary estimation, seasonal ARIMA model
G13AEF    Univariate time series, estimation, seasonal ARIMA model (comprehensive)
G13AFF    Univariate time series, estimation, seasonal ARIMA model (easy-to-use)
G13AGF    Univariate time series, update state set for forecasting
G13AHF    Univariate time series, forecasting from state set
G13AJF    Univariate time series, state set and forecasts, from fully specified seasonal ARIMA model
G13ASF    Univariate time series, diagnostic checking of residuals, following G13AEF or G13AFF
G13AUF    Computes quantities needed for range-mean or standard deviation-mean plot
G13BAF    Multivariate time series, filtering (pre-whitening) by an ARIMA model
G13BBF    Multivariate time series, filtering by a transfer function model
G13BCF    Multivariate time series, cross-correlations
G13BDF    Multivariate time series, preliminary estimation of transfer function model
G13BEF    Multivariate time series, estimation of multi-input model
G13BGF    Multivariate time series, update state set for forecasting from multi-input model
G13BHF    Multivariate time series, forecasting from state set of multi-input model
G13BJF    Multivariate time series, state set and forecasts from fully specified multi-input model
G13CAF    Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window
G13CBF    Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window
G13CCF    Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window
G13CDF    Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window
G13CEF    Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra
G13CFF    Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra
G13CGF    Multivariate time series, noise spectrum, bounds, impulse response function and its standard error
G13DBF    Multivariate time series, multiple squared partial autocorrelations
G13DCF    Multivariate time series, estimation of VARMA model
G13DJF    Multivariate time series, forecasts and their standard errors
G13DKF    Multivariate time series, updates forecasts and their standard errors
G13DLF    Multivariate time series, differences and/or transforms (for use before G13DCF)
G13DMF    Multivariate time series, sample cross-correlation or cross-covariance matrices
G13DNF    Multivariate time series, sample partial lag correlation matrices, χ2 statistics and significance levels
G13DPF    Multivariate time series, partial autoregression matrices
G13DSF    Multivariate time series, diagnostic checking of residuals, following G13DCF
G13DXF    Calculates the zeros of a vector autoregressive (or moving average) operator
G13EAF    Combined measurement and time update, one iteration of Kalman filter, time-varying, square root covariance filter
G13EBF    Combined measurement and time update, one iteration of Kalman filter, time-invariant, square root covariance filter
G13FAF    Univariate time series, parameter estimation for either a symmetric GARCH process or a GARCH process with asymmetry of the form t-1 + γ)2
G13FBF    Univariate time series, forecast function for either a symmetric GARCH process or a GARCH process with asymmetry of the form t-1 + γ)2
G13FCF    Univariate time series, parameter estimation for a GARCH process with asymmetry of the form (|εt-1| + γ εt-1)2
G13FDF    Univariate time series, forecast function for a GARCH process with asymmetry of the form (|εt-1| + γ εt-1)2
G13FEF    Univariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
G13FFF    Univariate time series, forecast function for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
G13FGF    Univariate time series, forecast function for an exponential GARCH (EGARCH) process
G13FHF    Univariate time series, forecast function for an exponential GARCH (EGARCH) process

H:  Operations Research

Chapter Introduction
H02BBF    Integer LP problem (dense)
H02BFF    Interpret MPSX data file defining IP or LP problem, optimize and print solution
H02BUF    Convert MPSX data file defining IP or LP problem to format required by H02BBF or E04MFF
H02BVF    Print IP or LP solutions with user specified names for rows and columns
H02BZF    Integer programming solution, supplies further information on solution obtained by H02BBF
H02CBF    Integer QP problem (dense)
H02CCF    Read optional parameter values for H02CBF from external file
H02CDF    Supply optional parameter values to H02CBF
H02CEF    Integer LP or QP problem (sparse)
H02CFF    Read optional parameter values for H02CEF from external file
H02CGF    Supply optional parameter values to H02CEF
H03ABF    Transportation problem, modified stepping stone method
H03ADF    Shortest path problem, Dijkstra's algorithm

M01:  Sorting

Chapter Introduction
M01CAF    Sort a vector, real numbers
M01CBF    Sort a vector, integer numbers
M01CCF    Sort a vector, character data
M01DAF    Rank a vector, real numbers
M01DBF    Rank a vector, integer numbers
M01DCF    Rank a vector, character data
M01DEF    Rank rows of a matrix, real numbers
M01DFF    Rank rows of a matrix, integer numbers
M01DJF    Rank columns of a matrix, real numbers
M01DKF    Rank columns of a matrix, integer numbers
M01DZF    Rank arbitrary data
M01EAF    Rearrange a vector according to given ranks, real numbers
M01EBF    Rearrange a vector according to given ranks, integer numbers
M01ECF    Rearrange a vector according to given ranks, character data
M01EDF    Rearrange a vector according to given ranks, complex numbers
M01ZAF    Invert a permutation
M01ZBF    Check validity of a permutation
M01ZCF    Decompose a permutation into cycles

P01:  Error Trapping

Chapter Introduction
P01ABF    Return value of error indicator/terminate with error message

S:  Approximations of Special Functions

Chapter Introduction
S01BAF    ln (1+x)
S01EAF    Complex exponential, e^z
S07AAF    tan x
S09AAF    arcsin x
S09ABF    arccos x
S10AAF    tanh x
S10ABF    sinh x
S10ACF    cosh x
S11AAF    arctanh x
S11ABF    arcsinh x
S11ACF    arccosh x
S13AAF    Exponential integral E1 (x)
S13ACF    Cosine integral Ci(x)
S13ADF    Sine integral Si(x)
S14AAF    Gamma function
S14ABF    Log Gamma function
S14ACF    ψ (x) - ln x
S14ADF    Scaled derivatives of ψ (x)
S14AEF    Polygamma function ψ(n)(x) for real x
S14AFF    Polygamma function ψ(n)(z) for complex z
S14BAF    Incomplete Gamma functions P(a,x) and Q(a,x)
S15ABF    Cumulative Normal distribution function P(x)
S15ACF    Complement of cumulative Normal distribution function Q(x)
S15ADF    Complement of error function erfc(x)
S15AEF    Error function erf(x)
S15AFF    Dawson's integral
S15DDF    Scaled complex complement of error function, exp(-z2) erfc(-iz)
S17ACF    Bessel function Y0 (x)
S17ADF    Bessel function Y1 (x)
S17AEF    Bessel function J0 (x)
S17AFF    Bessel function J1 (x)
S17AGF    Airy function Ai(x)
S17AHF    Airy function Bi(x)
S17AJF    Airy function Ai'(x)
S17AKF    Airy function Bi'(x)
S17ALF    Zeros of Bessel functions Jα(x), J'α(x), Yα(x) or Y'α(x)
S17DCF    Bessel functions Yν+a(z), real a ≥ 0, complex z, ν =0,1, 2,...
S17DEF    Bessel functions Jν+a(z), real a ≥ 0, complex z, ν =0,1, 2,...
S17DGF    Airy functions Ai(z) and Ai'(z), complex z
S17DHF    Airy functions Bi(z) and Bi'(z), complex z
S17DLF    Hankel functions Hν+a(j)(z), j=1,2, real a ≥ 0, complex z, ν =0,1,2,...
S18ACF    Modified Bessel function K0 (x)
S18ADF    Modified Bessel function K1 (x)
S18AEF    Modified Bessel function I0 (x)
S18AFF    Modified Bessel function I1(x)
S18CCF    Modified Bessel function exK0(x)
S18CDF    Modified Bessel function exK1(x)
S18CEF    Modified Bessel function e-|x|I0(x)
S18CFF    Modified Bessel function e-|x|I1(x)
S18DCF    Modified Bessel functions Kν+a(z), real a ≥ 0, complex z, ν =0,1,2,...
S18DEF    Modified Bessel functions Iν+a(z), real a ≥ 0, complex z, ν =0,1,2,...
S19AAF    Kelvin function ber x
S19ABF    Kelvin function bei x
S19ACF    Kelvin function ker x
S19ADF    Kelvin function kei x
S20ACF    Fresnel integral S(x)
S20ADF    Fresnel integral C(x)
S21BAF    Degenerate symmetrised elliptic integral of 1st kind RC(x,y)
S21BBF    Symmetrised elliptic integral of 1st kind RF(x,y,z)
S21BCF    Symmetrised elliptic integral of 2nd kind RD(x,y,z)
S21BDF    Symmetrised elliptic integral of 3rd kind RJ(x,y,z,r)
S21CAF    Jacobian elliptic functions sn, cn and dn of real argument
S21CBF    Jacobian elliptic functions sn, cn and dn of complex argument
S21CCF    Jacobian theta functions θk (x,q) of real argument
S21DAF    General elliptic integral of 2nd kind F(z,k',a,b) of complex argument
S22AAF    Legendre functions of 1st kind Pnm (x) or Pnmx

X01:  Mathematical Constants

Chapter Introduction
X01AAF    Provides the mathematical constant π
X01ABF    Provides the mathematical constant γ (Euler's Constant)

X02:  Machine Constants

Chapter Introduction
X02AHF    The largest permissible argument for sin and cos
X02AJF    The machine precision
X02AKF    The smallest positive model number
X02ALF    The largest positive model number
X02AMF    The safe range parameter
X02ANF    The safe range parameter for complex floating-point arithmetic
X02BBF    The largest representable integer
X02BEF    The maximum number of decimal digits that can be represented
X02BHF    The floating-point model parameter, b
X02BJF    The floating-point model parameter, p
X02BKF    The floating-point model parameter emin
X02BLF    The floating-point model parameter emax
X02DAF    Switch for taking precautions to avoid underflow
X02DJF    The floating-point model parameter ROUNDS

X03:  Inner Products

Chapter Introduction
X03AAF    Real inner product added to initial value, basic/additional precision
X03ABF    Complex inner product added to initial value, basic/additional precision

X04:  Input/Output Utilities

Chapter Introduction
X04AAF    Return or set unit number for error messages
X04ABF    Return or set unit number for advisory messages
X04ACF    Open unit number for reading, writing or appending, and associate unit with named file
X04ADF    Close file associated with given unit number
X04BAF    Write formatted record to external file
X04BBF    Read formatted record from external file
X04CAF    Print real general matrix (easy-to-use)
X04CBF    Print real general matrix (comprehensive)
X04CCF    Print real packed triangular matrix (easy-to-use)
X04CDF    Print real packed triangular matrix (comprehensive)
X04CEF    Print real packed banded matrix (easy-to-use)
X04CFF    Print real packed banded matrix (comprehensive)
X04DAF    Print complex general matrix (easy-to-use)
X04DBF    Print complex general matrix (comprehensive)
X04DCF    Print complex packed triangular matrix (easy-to-use)
X04DDF    Print complex packed triangular matrix (comprehensive)
X04DEF    Print complex packed banded matrix (easy-to-use)
X04DFF    Print complex packed banded matrix (comprehensive)
X04EAF    Print integer matrix (easy-to-use)
X04EBF    Print integer matrix (comprehensive)

X05:  Date and Time Utilities

Chapter Introduction
X05AAF    Return date and time as an array of integers
X05ABF    Convert array of integers representing date and time to character string
X05ACF    Compare two character strings representing date and time
X05BAF    Return the CPU time