Mark 21 Library Contents (pdf version)
NAG Library Manual

Mark 21 Library Contents

A00 – Library Identification


Routine Name
Mark of
Introduction

Purpose
A00AAF 18 Library identification, details of implementation and mark
A00ACF 21 Check availability of a valid licence key

A02 – Complex Arithmetic


Routine Name
Mark of
Introduction

Purpose
A02AAF 2 Square root of complex number
A02ABF 2 Modulus of complex number
A02ACF 2 Quotient of two complex numbers

C02 – Zeros of Polynomials


Routine Name
Mark of
Introduction

Purpose
C02AFF 14 All zeros of complex polynomial, modified Laguerre method
C02AGF 13 All zeros of real polynomial, modified Laguerre method
C02AHF 14 All zeros of complex quadratic equation
C02AJF 14 All zeros of real quadratic equation
C02AKF 20 All zeros of real cubic equation
C02ALF 20 All zeros of real quartic equation
C02AMF 20 All zeros of complex cubic equation
C02ANF 20 All zeros of complex quartic equation

C05 – Roots of One or More Transcendental Equations


Routine Name
Mark of
Introduction

Purpose
C05ADF 8 Zero of continuous function in given interval, Bus and Dekker algorithm
C05AGF 8 Zero of continuous function, Bus and Dekker algorithm, from given starting value, binary search for interval
C05AJF 8 Zero of continuous function, continuation method, from a given starting value
C05AVF 8 Binary search for interval containing zero of continuous function (reverse communication)
C05AXF 8 Zero of continuous function by continuation method, from given starting value (reverse communication)
C05AZF 7 Zero in given interval of continuous function by Bus and Dekker algorithm (reverse communication)
C05NBF 9 Solution of system of nonlinear equations using function values only (easy-to-use)
C05NCF 9 Solution of system of nonlinear equations using function values only (comprehensive)
C05NDF 14 Solution of system of nonlinear equations using function values only (reverse communication)
C05PBF 9 Solution of system of nonlinear equations using first derivatives (easy-to-use)
C05PCF 9 Solution of system of nonlinear equations using first derivatives (comprehensive)
C05PDF/C05PDA 14 Solution of system of nonlinear equations using first derivatives (reverse communication)
C05ZAF 9 Check user's routine for calculating first derivatives

C06 – Summation of Series


Routine Name
Mark of
Introduction

Purpose
C06BAF 10 Acceleration of convergence of sequence, Shanks' transformation and epsilon algorithm
C06DBF 6 Sum of a Chebyshev series
C06EAF 8 Single one-dimensional real discrete Fourier transform, no extra workspace
C06EBF 8 Single one-dimensional Hermitian discrete Fourier transform, no extra workspace
C06ECF 8 Single one-dimensional complex discrete Fourier transform, no extra workspace
C06EKF 11 Circular convolution or correlation of two real vectors, no extra workspace
C06FAF 8 Single one-dimensional real discrete Fourier transform, extra workspace for greater speed
C06FBF 8 Single one-dimensional Hermitian discrete Fourier transform, extra workspace for greater speed
C06FCF 8 Single one-dimensional complex discrete Fourier transform, extra workspace for greater speed
C06FFF 11 One-dimensional complex discrete Fourier transform of multi-dimensional data
C06FJF 11 Multi-dimensional complex discrete Fourier transform of multi-dimensional data
C06FKF 11 Circular convolution or correlation of two real vectors, extra workspace for greater speed
C06FPF 12 Multiple one-dimensional real discrete Fourier transforms
C06FQF 12 Multiple one-dimensional Hermitian discrete Fourier transforms
C06FRF 12 Multiple one-dimensional complex discrete Fourier transforms
C06FUF 13 Two-dimensional complex discrete Fourier transform
C06FXF 17 Three-dimensional complex discrete Fourier transform
C06GBF 8 Complex conjugate of Hermitian sequence
C06GCF 8 Complex conjugate of complex sequence
C06GQF 12 Complex conjugate of multiple Hermitian sequences
C06GSF 12 Convert Hermitian sequences to general complex sequences
C06HAF 13 Discrete sine transform
C06HBF 13 Discrete cosine transform
C06HCF 13 Discrete quarter-wave sine transform
C06HDF 13 Discrete quarter-wave cosine transform
C06LAF 12 Inverse Laplace transform, Crump's method
C06LBF 14 Inverse Laplace transform, modified Weeks' method
C06LCF 14 Evaluate inverse Laplace transform as computed by C06LBF
C06PAF 19 Single one-dimensional real and Hermitian complex discrete Fourier transform, using complex data format for Hermitian sequences
C06PCF 19 Single one-dimensional complex discrete Fourier transform, complex data format
C06PFF 19 One-dimensional complex discrete Fourier transform of multi-dimensional data (using complex data type)
C06PJF 19 Multi-dimensional complex discrete Fourier transform of multi-dimensional data (using complex data type)
C06PKF 19 Circular convolution or correlation of two complex vectors
C06PPF 19 Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using complex data format for Hermitian sequences
C06PQF 19 Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using complex data format for Hermitian sequences
C06PRF 19 Multiple one-dimensional complex discrete Fourier transforms using complex data format
C06PSF 19 Multiple one-dimensional complex discrete Fourier transforms using complex data format and sequences stored as columns
C06PUF 19 Two-dimensional complex discrete Fourier transform, complex data format
C06PXF 19 Three-dimensional complex discrete Fourier transform, complex data format
C06RAF 19 Discrete sine transform (easy-to-use)
C06RBF 19 Discrete cosine transform (easy-to-use)
C06RCF 19 Discrete quarter-wave sine transform (easy-to-use)
C06RDF 19 Discrete quarter-wave cosine transform (easy-to-use)

D01 – Quadrature


Routine Name
Mark of
Introduction

Purpose
D01AHF 8 One-dimensional quadrature, adaptive, finite interval, strategy due to Patterson, suitable for well-behaved integrands
D01AJF 8 One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands
D01AKF 8 One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions
D01ALF 8 One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points
D01AMF 2 One-dimensional quadrature, adaptive, infinite or semi-infinite interval
D01ANF 8 One-dimensional quadrature, adaptive, finite interval, weight function cos(ωx)  or sin(ωx)  
D01APF 8 One-dimensional quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type
D01AQF 8 One-dimensional quadrature, adaptive, finite interval, weight function 1 / (x-c) , Cauchy principal value (Hilbert transform)
D01ARF 10 One-dimensional quadrature, non-adaptive, finite interval with provision for indefinite integrals
D01ASF 13 One-dimensional quadrature, adaptive, semi-infinite interval, weight function cos(ωx)  or sin(ωx)  
D01ATF 13 One-dimensional quadrature, adaptive, finite interval, variant of D01AJF efficient on vector machines
D01AUF 13 One-dimensional quadrature, adaptive, finite interval, variant of D01AKF efficient on vector machines
D01BAF 7 One-dimensional Gaussian quadrature
D01BBF 7 Pre-computed weights and abscissae for Gaussian quadrature rules, restricted choice of rule
D01BCF 8 Calculation of weights and abscissae for Gaussian quadrature rules, general choice of rule
D01BDF 8 One-dimensional quadrature, non-adaptive, finite interval
D01DAF 5 Two-dimensional quadrature, finite region
D01EAF 12 Multi-dimensional adaptive quadrature over hyper-rectangle, multiple integrands
D01FBF 8 Multi-dimensional Gaussian quadrature over hyper-rectangle
D01FCF 8 Multi-dimensional adaptive quadrature over hyper-rectangle
D01FDF 10 Multi-dimensional quadrature, Sag–Szekeres method, general product region or n -sphere
D01GAF 5 One-dimensional quadrature, integration of function defined by data values, Gill–Miller method
D01GBF 10 Multi-dimensional quadrature over hyper-rectangle, Monte Carlo method
D01GCF 10 Multi-dimensional quadrature, general product region, number-theoretic method
D01GDF 14 Multi-dimensional quadrature, general product region, number-theoretic method, variant of D01GCF efficient on vector machines
D01GYF 10 Korobov optimal coefficients for use in D01GCF or D01GDF, when number of points is prime
D01GZF 10 Korobov optimal coefficients for use in D01GCF or D01GDF, when number of points is product of two primes
D01JAF 10 Multi-dimensional quadrature over an n -sphere, allowing for badly behaved integrands
D01PAF 10 Multi-dimensional quadrature over an n -simplex

D02 – Ordinary Differential Equations


Routine Name
Mark of
Introduction

Purpose
D02AGF 2 ODEs, boundary value problem, shooting and matching technique, allowing interior matching point, general parameters to be determined
D02BGF 7 ODEs, IVP, Runge–Kutta–Merson method, until a component attains given value (simple driver)
D02BHF 7 ODEs, IVP, Runge–Kutta–Merson method, until function of solution is zero (simple driver)
D02BJF 18 ODEs, IVP, Runge–Kutta method, until function of solution is zero, integration over range with intermediate output (simple driver)
D02CJF 13 ODEs, IVP, Adams method, until function of solution is zero, intermediate output (simple driver)
D02EJF 12 ODEs, stiff IVP, BDF method, until function of solution is zero, intermediate output (simple driver)
D02GAF 8 ODEs, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem
D02GBF 8 ODEs, boundary value problem, finite difference technique with deferred correction, general linear problem
D02HAF 8 ODEs, boundary value problem, shooting and matching, boundary values to be determined
D02HBF 8 ODEs, boundary value problem, shooting and matching, general parameters to be determined
D02JAF 8 ODEs, boundary value problem, collocation and least-squares, single n th-order linear equation
D02JBF 8 ODEs, boundary value problem, collocation and least-squares, system of first-order linear equations
D02KAF 7 Second-order Sturm–Liouville problem, regular system, finite range, eigenvalue only
D02KDF 7 Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, user-specified break-points
D02KEF 8 Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points
D02LAF 13 Second-order ODEs, IVP, Runge–Kutta–Nystrom method
D02LXF 13 Second-order ODEs, IVP, setup for D02LAF
D02LYF 13 Second-order ODEs, IVP, diagnostics for D02LAF
D02LZF 13 Second-order ODEs, IVP, interpolation for D02LAF
D02MVF 14 ODEs, IVP, DASSL method, setup for D02M–N routines
D02MZF 14 ODEs, IVP, interpolation for D02M–N routines, natural interpolant
D02NBF 12 Explicit ODEs, stiff IVP, full Jacobian (comprehensive)
D02NCF 12 Explicit ODEs, stiff IVP, banded Jacobian (comprehensive)
D02NDF 12 Explicit ODEs, stiff IVP, sparse Jacobian (comprehensive)
D02NGF 12 Implicit/algebraic ODEs, stiff IVP, full Jacobian (comprehensive)
D02NHF 12 Implicit/algebraic ODEs, stiff IVP, banded Jacobian (comprehensive)
D02NJF 12 Implicit/algebraic ODEs, stiff IVP, sparse Jacobian (comprehensive)
D02NMF 12 Explicit ODEs, stiff IVP (reverse communication, comprehensive)
D02NNF 12 Implicit/algebraic ODEs, stiff IVP (reverse communication, comprehensive)
D02NRF 12 ODEs, IVP, for use with D02M–N routines, sparse Jacobian, enquiry routine
D02NSF 12 ODEs, IVP, for use with D02M–N routines, full Jacobian, linear algebra set up
D02NTF 12 ODEs, IVP, for use with D02M–N routines, banded Jacobian, linear algebra set up
D02NUF 12 ODEs, IVP, for use with D02M–N routines, sparse Jacobian, linear algebra set up
D02NVF 12 ODEs, IVP, BDF method, setup for D02M–N routines
D02NWF 12 ODEs, IVP, Blend method, setup for D02M–N routines
D02NXF 12 ODEs, IVP, sparse Jacobian, linear algebra diagnostics, for use with D02M–N routines
D02NYF 12 ODEs, IVP, integrator diagnostics, for use with D02M–N routines
D02NZF 12 ODEs, IVP, setup for continuation calls to integrator, for use with D02M–N routines
D02PCF 16 ODEs, IVP, Runge–Kutta method, integration over range with output
D02PDF 16 ODEs, IVP, Runge–Kutta method, integration over one step
D02PVF 16 ODEs, IVP, setup for D02PCF and D02PDF
D02PWF 16 ODEs, IVP, resets end of range for D02PDF
D02PXF 16 ODEs, IVP, interpolation for D02PDF
D02PYF 16 ODEs, IVP, integration diagnostics for D02PCF and D02PDF
D02PZF 16 ODEs, IVP, error assessment diagnostics for D02PCF and D02PDF
D02QFF 13 ODEs, IVP, Adams method with root-finding (forward communication, comprehensive)
D02QGF 13 ODEs, IVP, Adams method with root-finding (reverse communication, comprehensive)
D02QWF 13 ODEs, IVP, setup for D02QFF and D02QGF
D02QXF 13 ODEs, IVP, diagnostics for D02QFF and D02QGF
D02QYF 13 ODEs, IVP, root-finding diagnostics for D02QFF and D02QGF
D02QZF 13 ODEs, IVP, interpolation for D02QFF or D02QGF
D02RAF 8 ODEs, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility
D02SAF 8 ODEs, boundary value problem, shooting and matching technique, subject to extra algebraic equations, general parameters to be determined
D02TGF 8 n th-order linear ODEs, boundary value problem, collocation and least-squares
D02TKF 17 ODEs, general nonlinear boundary value problem, collocation technique
D02TVF 17 ODEs, general nonlinear boundary value problem, setup for D02TKF
D02TXF 17 ODEs, general nonlinear boundary value problem, continuation facility for D02TKF
D02TYF 17 ODEs, general nonlinear boundary value problem, interpolation for D02TKF
D02TZF 17 ODEs, general nonlinear boundary value problem, diagnostics for D02TKF
D02XJF 12 ODEs, IVP, interpolation for D02M–N routines, natural interpolant
D02XKF 12 ODEs, IVP, interpolation for D02M–N routines, C1  interpolant
D02ZAF 12 ODEs, IVP, weighted norm of local error estimate for D02M–N routines

D03 – Partial Differential Equations


Routine Name
Mark of
Introduction

Purpose
D03EAF 7 Elliptic PDE, Laplace's equation, two-dimensional arbitrary domain
D03EBF 7 Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, iterate to convergence
D03ECF 8 Elliptic PDE, solution of finite difference equations by SIP for seven-point three-dimensional molecule, iterate to convergence
D03EDF 12 Elliptic PDE, solution of finite difference equations by a multigrid technique
D03EEF 13 Discretize a second-order elliptic PDE on a rectangle
D03FAF 14 Elliptic PDE, Helmholtz equation, three-dimensional Cartesian co-ordinates
D03MAF 7 Triangulation of plane region
D03NCF 20 Finite difference solution of the Black–Scholes equations
D03NDF 20 Analytic solution of the Black–Scholes equations
D03NEF 20 Compute average values for D03NDF
D03PCF/D03PCA 15 General system of parabolic PDEs, method of lines, finite differences, one space variable
D03PDF/D03PDA 15 General system of parabolic PDEs, method of lines, Chebyshev C0  collocation, one space variable
D03PEF 16 General system of first-order PDEs, method of lines, Keller box discretisation, one space variable
D03PFF 17 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/D03PHA 15 General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable
D03PJF/D03PJA 15 General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C0  collocation, one space variable
D03PKF 16 General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, one space variable
D03PLF 17 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/D03PPA 16 General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable
D03PRF 16 General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, remeshing, one space variable
D03PSF 17 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 17 Roe's approximate Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
D03PVF 17 Osher's approximate Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
D03PWF 18 Modified HLL Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
D03PXF 18 Exact Riemann Solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
D03PYF 15 PDEs, spatial interpolation with D03PDF/D03PDA or D03PJF/D03PJA
D03PZF 15 PDEs, spatial interpolation with D03PCF/D03PCA, D03PEF, D03PFF, D03PHF/D03PHA, D03PKF, D03PLF, D03PPF/D03PPA, D03PRF or D03PSF
D03RAF 18 General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectangular region
D03RBF 18 General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectilinear region
D03RYF 18 Check initial grid data in D03RBF
D03RZF 18 Extract grid data from D03RBF
D03UAF 7 Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, one iteration
D03UBF 8 Elliptic PDE, solution of finite difference equations by SIP, seven-point three-dimensional molecule, one iteration

D04 – Numerical Differentiation


Routine Name
Mark of
Introduction

Purpose
D04AAF 5 Numerical differentiation, derivatives up to order 14, function of one real variable

D05 – Integral Equations


Routine Name
Mark of
Introduction

Purpose
D05AAF 5 Linear non-singular Fredholm integral equation, second kind, split kernel
D05ABF 6 Linear non-singular Fredholm integral equation, second kind, smooth kernel
D05BAF 14 Nonlinear Volterra convolution equation, second kind
D05BDF 16 Nonlinear convolution Volterra–Abel equation, second kind, weakly singular
D05BEF 16 Nonlinear convolution Volterra–Abel equation, first kind, weakly singular
D05BWF 16 Generate weights for use in solving Volterra equations
D05BYF 16 Generate weights for use in solving weakly singular Abel-type equations

D06 – Mesh Generation


Routine Name
Mark of
Introduction

Purpose
D06AAF 20 Generates a two-dimensional mesh using a simple incremental method
D06ABF 20 Generates a two-dimensional mesh using a Delaunay–Voronoi process
D06ACF 20 Generates a two-dimensional mesh using an Advancing-front method
D06BAF 20 Generates a boundary mesh
D06CAF 20 Uses a barycentering technique to smooth a given mesh
D06CBF 20 Generates a sparsity pattern of a Finite Element matrix associated with a given mesh
D06CCF 20 Renumbers a given mesh using Gibbs method
D06DAF 20 Generates a mesh resulting from an affine transformation of a given mesh
D06DBF 20 Joins together two given adjacent (possibly overlapping) meshes

E01 – Interpolation


Routine Name
Mark of
Introduction

Purpose
E01AAF 1 Interpolated values, Aitken's technique, unequally spaced data, one variable
E01ABF 1 Interpolated values, Everett's formula, equally spaced data, one variable
E01AEF 8 Interpolating functions, polynomial interpolant, data may include derivative values, one variable
E01BAF 8 Interpolating functions, cubic spline interpolant, one variable
E01BEF 13 Interpolating functions, monotonicity-preserving, piecewise cubic Hermite, one variable
E01BFF 13 Interpolated values, interpolant computed by E01BEF, function only, one variable
E01BGF 13 Interpolated values, interpolant computed by E01BEF, function and first derivative, one variable
E01BHF 13 Interpolated values, interpolant computed by E01BEF, definite integral, one variable
E01DAF 14 Interpolating functions, fitting bicubic spline, data on rectangular grid
E01RAF 9 Interpolating functions, rational interpolant, one variable
E01RBF 9 Interpolated values, evaluate rational interpolant computed by E01RAF, one variable
E01SAF 13 Interpolating functions, method of Renka and Cline, two variables
E01SBF 13 Interpolated values, evaluate interpolant computed by E01SAF, two variables
E01SGF 18 Interpolating functions, modified Shepard's method, two variables
E01SHF 18 Interpolated values, evaluate interpolant computed by E01SGF, function and first derivatives, two variables
E01TGF 18 Interpolating functions, modified Shepard's method, three variables
E01THF 18 Interpolated values, evaluate interpolant computed by E01TGF, function and first derivatives, three variables

E02 – Curve and Surface Fitting


Routine Name
Mark of
Introduction

Purpose
E02ACF 1 Minimax curve fit by polynomials
E02ADF 5 Least-squares curve fit, by polynomials, arbitrary data points
E02AEF 5 Evaluation of fitted polynomial in one variable from Chebyshev series form (simplified parameter list)
E02AFF 5 Least-squares polynomial fit, special data points (including interpolation)
E02AGF 8 Least-squares polynomial fit, values and derivatives may be constrained, arbitrary data points
E02AHF 8 Derivative of fitted polynomial in Chebyshev series form
E02AJF 8 Integral of fitted polynomial in Chebyshev series form
E02AKF 8 Evaluation of fitted polynomial in one variable from Chebyshev series form
E02BAF 5 Least-squares curve cubic spline fit (including interpolation)
E02BBF 5 Evaluation of fitted cubic spline, function only
E02BCF 7 Evaluation of fitted cubic spline, function and derivatives
E02BDF 7 Evaluation of fitted cubic spline, definite integral
E02BEF 13 Least-squares cubic spline curve fit, automatic knot placement
E02CAF 7 Least-squares surface fit by polynomials, data on lines
E02CBF 7 Evaluation of fitted polynomial in two variables
E02DAF 6 Least-squares surface fit, bicubic splines
E02DCF 13 Least-squares surface fit by bicubic splines with automatic knot placement, data on rectangular grid
E02DDF 13 Least-squares surface fit by bicubic splines with automatic knot placement, scattered data
E02DEF 14 Evaluation of fitted bicubic spline at a vector of points
E02DFF 14 Evaluation of fitted bicubic spline at a mesh of points
E02GAF 7 L1 -approximation by general linear function
E02GBF 7 L1 -approximation by general linear function subject to linear inequality constraints
E02GCF 8 L -approximation by general linear function
E02RAF 7 Padé approximants
E02RBF 7 Evaluation of fitted rational function as computed by E02RAF
E02ZAF 6 Sort two-dimensional data into panels for fitting bicubic splines

E04 – Minimizing or Maximizing a Function


Routine Name
Mark of
Introduction

Purpose
E04ABF/E04ABA 6 Minimum, function of one variable using function values only
E04BBF/E04BBA 6 Minimum, function of one variable, using first derivative
E04CCF/E04CCA 1 Unconstrained minimum, simplex algorithm, function of several variables using function values only (comprehensive)
E04DGF/E04DGA 12 Unconstrained minimum, preconditioned conjugate gradient algorithm, function of several variables using first derivatives (comprehensive)
E04DJF/E04DJA 12 Supply optional parameter values for E04DGF/E04DGA from external file
E04DKF/E04DKA 12 Supply optional parameter values to E04DGF/E04DGA
E04FCF 7 Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using function values only (comprehensive)
E04FYF 18 Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using function values only (easy-to-use)
E04GBF 7 Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm using first derivatives (comprehensive)
E04GDF 7 Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using first derivatives (comprehensive)
E04GYF 18 Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use)
E04GZF 18 Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using first derivatives (easy-to-use)
E04HCF 6 Check user's routine for calculating first derivatives of function
E04HDF 6 Check user's routine for calculating second derivatives of function
E04HEF 7 Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (comprehensive)
E04HYF 18 Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (easy-to-use)
E04JYF 18 Minimum, function of several variables, quasi-Newton algorithm, simple bounds, using function values only (easy-to-use)
E04KDF 6 Minimum, function of several variables, modified Newton algorithm, simple bounds, using first derivatives (comprehensive)
E04KYF 18 Minimum, function of several variables, quasi-Newton algorithm, simple bounds, using first derivatives (easy-to-use)
E04KZF 18 Minimum, function of several variables, modified Newton algorithm, simple bounds, using first derivatives (easy-to-use)
E04LBF 6 Minimum, function of several variables, modified Newton algorithm, simple bounds, using first and second derivatives (comprehensive)
E04LYF 18 Minimum, function of several variables, modified Newton algorithm, simple bounds, using first and second derivatives (easy-to-use)
E04MFF/E04MFA 16 LP problem (dense)
E04MGF/E04MGA 16 Supply optional parameter values for E04MFF/E04MFA from external file
E04MHF/E04MHA 16 Supply optional parameter values to E04MFF/E04MFA
E04MZF 18 Converts MPSX data file defining LP or QP problem to format required by E04NQF
E04NCF/E04NCA 12 Convex QP problem or linearly-constrained linear least-squares problem (dense)
E04NDF/E04NDA 12 Supply optional parameter values for E04NCF/E04NCA from external file
E04NEF/E04NEA 12 Supply optional parameter values to E04NCF/E04NCA
E04NFF/E04NFA 16 QP problem (dense)
E04NGF/E04NGA 16 Supply optional parameter values for E04NFF/E04NFA from external file
E04NHF/E04NHA 16 Supply optional parameter values to E04NFF/E04NFA
E04NPF 21 Initialization routine for E04NQF
E04NQF 21 LP or QP problem (suitable for sparse problems)
E04NRF 21 Supply optional parameter values for E04NQF from external file
E04NSF 21 Set a single option for E04NQF from a character string
E04NTF 21 Set a single option for E04NQF from an INTEGER argument
E04NUF 21 Set a single option for E04NQF from a double precision argument
E04NXF 21 Get the setting of an INTEGER valued option of E04NQF
E04NYF 21 Get the setting of a double precision valued option of E04NQF
E04UDF/E04UDA 12 Supply optional parameter values for E04UCF/E04UCA or E04UFF/E04UFA from external file
E04UEF/E04UEA 12 Supply optional parameter values to E04UCF/E04UCA or E04UFF/E04UFA
E04UFF/E04UFA 18 Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (reverse communication, comprehensive)
E04UGF/E04UGA 19 NLP problem (sparse)
E04UHF/E04UHA 19 Supply optional parameter values for E04UGF/E04UGA from external file
E04UJF/E04UJA 19 Supply optional parameter values to E04UGF/E04UGA
E04UQF/E04UQA 14 Supply optional parameter values for E04USF/E04USA from external file
E04URF/E04URA 14 Supply optional parameter values to E04USF/E04USA
E04USF/E04USA 20 Minimum of a sum of squares, nonlinear constraints, sequential QP method, using function values and optionally first derivatives (comprehensive)
E04VGF 21 Initialization routine for E04VHF
E04VHF 21 General sparse nonlinear optimizer
E04VJF 21 Determine the pattern of nonzeros in the Jacobian matrix for E04VHF
E04VKF 21 Supply optional parameter values for E04VHF from external file
E04VLF 21 Set a single option for E04VHF from a character string
E04VMF 21 Set a single option for E04VHF from an INTEGER argument
E04VNF 21 Set a single option for E04VHF from a double precision argument
E04VRF 21 Get the setting of an INTEGER valued option of E04VHF
E04VSF 21 Get the setting of a double precision valued option of E04VHF
E04WBF 20 Initialization routine for E04DGA E04MFA E04NCA E04NFA E04UFA E04UGA E04USA
E04WCF 21 Initialization routine for E04WDF
E04WDF 21 Solves the nonlinear programming (NP) problem
E04WEF 21 Supply optional parameter values for E04WDF from external file
E04WFF 21 Set a single option for E04WDF from a character string
E04WGF 21 Set a single option for E04WDF from an INTEGER argument
E04WHF 21 Set a single option for E04WDF from a double precision argument
E04WJF 21 Determine whether an E04WDF option has been set or not
E04WKF 21 Get the setting of an INTEGER valued option of E04WDF
E04WLF 21 Get the setting of a double precision valued option of E04WDF
E04XAF/E04XAA 12 Estimate (using numerical differentiation) gradient and/or Hessian of a function
E04YAF 7 Check user's routine for calculating Jacobian of first derivatives
E04YBF 7 Check user's routine for calculating Hessian of a sum of squares
E04YCF 11 Covariance matrix for nonlinear least-squares problem (unconstrained)
E04ZCF/E04ZCA 11 Check user's routines for calculating first derivatives of function and constraints

F01 – Matrix Operations, Including Inversion


Routine Name
Mark of
Introduction

Purpose
F01ABF 1 Inverse of real symmetric positive-definite matrix using iterative refinement
F01ADF 2 Inverse of real symmetric positive-definite matrix
F01BLF 5 Pseudo-inverse and rank of real m  by n  matrix (mn)  
F01BRF 7 L U  factorization of real sparse matrix
F01BSF 7 L U  factorization of real sparse matrix with known sparsity pattern
F01BUF 7 U L D LT UT  factorization of real symmetric positive-definite band matrix
F01BVF 7 Reduction to standard form, generalized real symmetric-definite banded eigenproblem
F01CKF 2 Matrix multiplication
F01CRF 7 Matrix transposition
F01CTF 14 Sum or difference of two real matrices, optional scaling and transposition
F01CWF 14 Sum or difference of two complex matrices, optional scaling and transposition
F01LEF 11 L U  factorization of real tridiagonal matrix
F01LHF 13 L U  factorization of real almost block diagonal matrix
F01MCF 8 L D LT  factorization of real symmetric positive-definite variable-bandwidth matrix
F01QGF 14 R Q  factorization of real m  by n  upper trapezoidal matrix (mn)  
F01QJF 14 R Q  factorization of real m  by n  matrix (mn)  
F01QKF 14 Operations with orthogonal matrices, form rows of Q , after R Q  factorization by F01QJF
F01RGF 14 R Q  factorization of complex m  by n  upper trapezoidal matrix (mn)  
F01RJF 14 R Q  factorization of complex m  by n  matrix (mn)  
F01RKF 14 Operations with unitary matrices, form rows of Q , after R Q  factorization by F01RJF
F01ZAF 14 Convert real matrix between packed triangular and square storage schemes
F01ZBF 14 Convert complex matrix between packed triangular and square storage schemes
F01ZCF 14 Convert real matrix between packed banded and rectangular storage schemes
F01ZDF 14 Convert complex matrix between packed banded and rectangular storage schemes

F02 – Eigenvalues and Eigenvectors


Routine Name
Mark of
Introduction

Purpose
F02ECF 17 Selected eigenvalues and eigenvectors of real nonsymmetric matrix (Black Box)
F02FJF 11 Selected eigenvalues and eigenvectors of sparse symmetric eigenproblem (Black Box)
F02GCF 17 Selected eigenvalues and eigenvectors of complex nonsymmetric matrix (Black Box)
F02SDF 8 Eigenvector of generalized real banded eigenproblem by inverse iteration
F02WDF 8 Q R  factorization, possibly followed by SVD
F02WUF 14 SVD of real upper triangular matrix (Black Box)
F02XUF 13 SVD of complex upper triangular matrix (Black Box)

F03 – Determinants


Routine Name
Mark of
Introduction

Purpose
F03AAF 1 Determinant of real matrix (Black Box)
F03ABF 1 Determinant of real symmetric positive-definite matrix (Black Box)
F03ACF 1 Determinant of real symmetric positive-definite band matrix (Black Box)
F03ADF 1 Determinant of complex matrix (Black Box)
F03AEF 2 L LT  factorization and determinant of real symmetric positive-definite matrix
F03AFF 2 L U  factorization and determinant of real matrix

F04 – Simultaneous Linear Equations


Routine Name
Mark of
Introduction

Purpose
F04ABF 2 Solution of real symmetric positive-definite simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box)
F04AEF 2 Solution of real simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box)
F04AFF 2 Solution of real symmetric positive-definite simultaneous linear equations using iterative refinement (coefficient matrix already factorized by F03AEF)
F04AGF 2 Solution of real symmetric positive-definite simultaneous linear equations (coefficient matrix already factorized by F03AEF)
F04AHF 2 Solution of real simultaneous linear equations using iterative refinement (coefficient matrix already factorized by F03AFF)
F04AJF 2 Solution of real simultaneous linear equations (coefficient matrix already factorized by F03AFF)
F04AMF 2 Least-squares solution of m  real equations in n  unknowns, rank = n , m n  using iterative refinement (Black Box)
F04ASF 4 Solution of real symmetric positive-definite simultaneous linear equations, one right-hand side using iterative refinement (Black Box)
F04ATF 4 Solution of real simultaneous linear equations, one right-hand side using iterative refinement (Black Box)
F04AXF 7 Solution of real sparse simultaneous linear equations (coefficient matrix already factorized)
F04BAF 21 Computes the solution and error-bound to a real system of linear equations
F04BBF 21 Computes the solution and error-bound to a real banded system of linear equations
F04BCF 21 Computes the solution and error-bound to a real tridiagonal system of linear equations
F04BDF 21 Computes the solution and error-bound to a real symmetric positive-definite system of linear equations
F04BEF 21 Computes the solution and error-bound to a real symmetric positive-definite system of linear equations, packed storage
F04BFF 21 Computes the solution and error-bound to a real symmetric positive-definite banded system of linear equations
F04BGF 21 Computes the solution and error-bound to a real symmetric positive-definite tridiagonal system of linear equations
F04BHF 21 Computes the solution and error-bound to a real symmetric system of linear equations
F04BJF 21 Computes the solution and error-bound to a real symmetric system of linear equations, packed storage
F04CAF 21 Computes the solution and error-bound to a complex system of linear equations
F04CBF 21 Computes the solution and error-bound to a complex banded system of linear equations
F04CCF 21 Computes the solution and error-bound to a complex tridiagonal system of linear equations
F04CDF 21 Computes the solution and error-bound to a complex Hermitian positive-definite system of linear equations
F04CEF 21 Computes the solution and error-bound to a complex Hermitian positive-definite system of linear equations, packed storage
F04CFF 21 Computes the solution and error-bound to a complex Hermitian positive-definite banded system of linear equations
F04CGF 21 Computes the solution and error-bound to a complex Hermitian positive-definite tridiagonal system of linear equations
F04CHF 21 Computes the solution and error-bound to a complex Hermitian system of linear equations
F04CJF 21 Computes the solution and error-bound to a complex Hermitian system of linear equations, packed storage
F04DHF 21 Computes the solution and error-bound to a complex symmetric system of linear equations
F04DJF 21 Computes the solution and error-bound to a complex symmetric system of linear equations, packed storage.
F04FEF 15 Solution of the Yule–Walker equations for real symmetric positive-definite Toeplitz matrix, one right-hand side
F04FFF 15 Solution of real symmetric positive-definite Toeplitz system, one right-hand side
F04JGF 8 Least-squares (if rank = n ) or minimal least-squares (if rank < n ) solution of m  real equations in n  unknowns, rank n , m n  
F04LEF 11 Solution of real tridiagonal simultaneous linear equations (coefficient matrix already factorized by F01LEF)
F04LHF 13 Solution of real almost block diagonal simultaneous linear equations (coefficient matrix already factorized by F01LHF)
F04MCF 8 Solution of real symmetric positive-definite variable-bandwidth simultaneous linear equations (coefficient matrix already factorized by F01MCF)
F04MEF 15 Update solution of the Yule–Walker equations for real symmetric positive-definite Toeplitz matrix
F04MFF 15 Update solution of real symmetric positive-definite Toeplitz system
F04QAF 11 Sparse linear least-squares problem, m  real equations in n  unknowns
F04YAF 11 Covariance matrix for linear least-squares problems, m  real equations in n  unknowns
F04YCF 13 Norm estimation (for use in condition estimation), real matrix
F04ZCF 13 Norm estimation (for use in condition estimation), complex matrix

F05 – Orthogonalisation


Routine Name
Mark of
Introduction

Purpose
F05AAF 5 Gram–Schmidt orthogonalisation of n  vectors of order m  

F06 – Linear Algebra Support Routines


Routine Name
Mark of
Introduction

Purpose
F06AAF (DROTG) 12 Generate real plane rotation
F06BAF 12 Generate real plane rotation, storing tangent
F06BCF 12 Recover cosine and sine from given real tangent
F06BEF 12 Generate real Jacobi plane rotation
F06BHF 12 Apply real similarity rotation to 2 by 2 symmetric matrix
F06BLF 12 Compute quotient of two real scalars, with overflow flag
F06BMF 12 Compute Euclidean norm from scaled form
F06BNF 12 Compute square root of (a2+b2) , real a  and b  
F06BPF 12 Compute eigenvalue of 2 by 2 real symmetric matrix
F06CAF 12 Generate complex plane rotation, storing tangent, real cosine
F06CBF 12 Generate complex plane rotation, storing tangent, real sine
F06CCF 12 Recover cosine and sine from given complex tangent, real cosine
F06CDF 12 Recover cosine and sine from given complex tangent, real sine
F06CHF 12 Apply complex similarity rotation to 2 by 2 Hermitian matrix
F06CLF 12 Compute quotient of two complex scalars, with overflow flag
F06DBF 12 Broadcast scalar into integer vector
F06DFF 12 Copy integer vector
F06EAF (DDOT) 12 Dot product of two real vectors
F06ECF (DAXPY) 12 Add scalar times real vector to real vector
F06EDF (DSCAL) 12 Multiply real vector by scalar
F06EFF (DCOPY) 12 Copy real vector
F06EGF (DSWAP) 12 Swap two real vectors
F06EJF (DNRM2) 12 Compute Euclidean norm of real vector
F06EKF (DASUM) 12 Sum absolute values of real vector elements
F06EPF (DROT) 12 Apply real plane rotation
F06ERF (DDOTI) 14 Dot product of two real sparse vectors
F06ETF (DAXPYI) 14 Add scalar times real sparse vector to real sparse vector
F06EUF (DGTHR) 14 Gather real sparse vector
F06EVF (DGTHRZ) 14 Gather and set to zero real sparse vector
F06EWF (DSCTR) 14 Scatter real sparse vector
F06EXF (DROTI) 14 Apply plane rotation to two real sparse vectors
F06FAF 12 Compute cosine of angle between two real vectors
F06FBF 12 Broadcast scalar into real vector
F06FCF 12 Multiply real vector by diagonal matrix
F06FDF 12 Multiply real vector by scalar, preserving input vector
F06FEF (DRSCL) 21 Multiply real vector by reciprocal of scalar
F06FGF 12 Negate real vector
F06FJF 12 Update Euclidean norm of real vector in scaled form
F06FKF 12 Compute weighted Euclidean norm of real vector
F06FLF 12 Elements of real vector with largest and smallest absolute value
F06FPF 12 Apply real symmetric plane rotation to two vectors
F06FQF 12 Generate sequence of real plane rotations
F06FRF 12 Generate real elementary reflection, NAG style
F06FSF 12 Generate real elementary reflection, LINPACK style
F06FTF 12 Apply real elementary reflection, NAG style
F06FUF 12 Apply real elementary reflection, LINPACK style
F06GAF (ZDOTU) 12 Dot product of two complex vectors, unconjugated
F06GBF (ZDOTC) 12 Dot product of two complex vectors, conjugated
F06GCF (ZAXPY) 12 Add scalar times complex vector to complex vector
F06GDF (ZSCAL) 12 Multiply complex vector by complex scalar
F06GFF (ZCOPY) 12 Copy complex vector
F06GGF (ZSWAP) 12 Swap two complex vectors
F06GRF (ZDOTUI) 14 Dot product of two complex sparse vector, unconjugated
F06GSF (ZDOTCI) 14 Dot product of two complex sparse vector, conjugated
F06GTF (ZAXPYI) 14 Add scalar times complex sparse vector to complex sparse vector
F06GUF (ZGTHR) 14 Gather complex sparse vector
F06GVF (ZGTHRZ) 14 Gather and set to zero complex sparse vector
F06GWF (ZSCTR) 14 Scatter complex sparse vector
F06HBF 12 Broadcast scalar into complex vector
F06HCF 12 Multiply complex vector by complex diagonal matrix
F06HDF 12 Multiply complex vector by complex scalar, preserving input vector
F06HGF 12 Negate complex vector
F06HPF 12 Apply complex plane rotation
F06HQF 12 Generate sequence of complex plane rotations
F06HRF 12 Generate complex elementary reflection
F06HTF 12 Apply complex elementary reflection
F06JDF (ZDSCAL) 12 Multiply complex vector by real scalar
F06JJF (DZNRM2) 12 Compute Euclidean norm of complex vector
F06JKF (DZASUM) 12 Sum absolute values of complex vector elements
F06JLF (IDAMAX) 12 Index, real vector element with largest absolute value
F06JMF (IZAMAX) 12 Index, complex vector element with largest absolute value
F06KCF 12 Multiply complex vector by real diagonal matrix
F06KDF 12 Multiply complex vector by real scalar, preserving input vector
F06KEF (ZDRSCL) 21 Multiply complex vector by reciprocal of real scalar
F06KFF 12 Copy real vector to complex vector
F06KJF 12 Update Euclidean norm of complex vector in scaled form
F06KLF 12 Last non-negligible element of real vector
F06KPF 12 Apply real plane rotation to two complex vectors
F06PAF (DGEMV) 12 Matrix-vector product, real rectangular matrix
F06PBF (DGBMV) 12 Matrix-vector product, real rectangular band matrix
F06PCF (DSYMV) 12 Matrix-vector product, real symmetric matrix
F06PDF (DSBMV) 12 Matrix-vector product, real symmetric band matrix
F06PEF (DSPMV) 12 Matrix-vector product, real symmetric packed matrix
F06PFF (DTRMV) 12 Matrix-vector product, real triangular matrix
F06PGF (DTBMV) 12 Matrix-vector product, real triangular band matrix
F06PHF (DTPMV) 12 Matrix-vector product, real triangular packed matrix
F06PJF (DTRSV) 12 System of equations, real triangular matrix
F06PKF (DTBSV) 12 System of equations, real triangular band matrix
F06PLF (DTPSV) 12 System of equations, real triangular packed matrix
F06PMF (DGER) 12 Rank-1 update, real rectangular matrix
F06PPF (DSYR) 12 Rank-1 update, real symmetric matrix
F06PQF (DSPR) 12 Rank-1 update, real symmetric packed matrix
F06PRF (DSYR2) 12 Rank-2 update, real symmetric matrix
F06PSF (DSPR2) 12 Rank-2 update, real symmetric packed matrix
F06QFF 13 Matrix copy, real rectangular or trapezoidal matrix
F06QHF 13 Matrix initialization, real rectangular matrix
F06QJF 13 Permute rows or columns, real rectangular matrix, permutations represented by an integer array
F06QKF 13 Permute rows or columns, real rectangular matrix, permutations represented by a real array
F06QMF 13 Orthogonal similarity transformation of real symmetric matrix as a sequence of plane rotations
F06QPF 13 Q R  factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix
F06QQF 13 Q R  factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row
F06QRF 13 Q R  or R Q  factorization by sequence of plane rotations, real upper Hessenberg matrix
F06QSF 13 Q R  or R Q  factorization by sequence of plane rotations, real upper spiked matrix
F06QTF 13 Q R  factorization of U Z  or R Q  factorization of Z U , U  real upper triangular, Z  a sequence of plane rotations
F06QVF 13 Compute upper Hessenberg matrix by sequence of plane rotations, real upper triangular matrix
F06QWF 13 Compute upper spiked matrix by sequence of plane rotations, real upper triangular matrix
F06QXF 13 Apply sequence of plane rotations, real rectangular matrix
F06RAF 15 1 -norm, -norm, Frobenius norm, largest absolute element, real general matrix
F06RBF 15 1 -norm, -norm, Frobenius norm, largest absolute element, real band matrix
F06RCF 15 1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix
F06RDF 15 1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage
F06REF 15 1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric band matrix
F06RJF 15 1 -norm, -norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix
F06RKF 15 1 -norm, -norm, Frobenius norm, largest absolute element, real triangular matrix, packed storage
F06RLF 15 1 -norm, -norm, Frobenius norm, largest absolute element, real triangular band matrix
F06RMF 15 1 -norm, -norm, Frobenius norm, largest absolute element, real Hessenberg matrix
F06RNF 21 1 -norm, -norm, Frobenius norm, largest absolute element, real tridiagonal matrix
F06RPF 21 1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix
F06SAF (ZGEMV) 12 Matrix-vector product, complex rectangular matrix
F06SBF (ZGBMV) 12 Matrix-vector product, complex rectangular band matrix
F06SCF (ZHEMV) 12 Matrix-vector product, complex Hermitian matrix
F06SDF (ZHBMV) 12 Matrix-vector product, complex Hermitian band matrix
F06SEF (ZHPMV) 12 Matrix-vector product, complex Hermitian packed matrix
F06SFF (ZTRMV) 12 Matrix-vector product, complex triangular matrix
F06SGF (ZTBMV) 12 Matrix-vector product, complex triangular band matrix
F06SHF (ZTPMV) 12 Matrix-vector product, complex triangular packed matrix
F06SJF (ZTRSV) 12 System of equations, complex triangular matrix
F06SKF (ZTBSV) 12 System of equations, complex triangular band matrix
F06SLF (ZTPSV) 12 System of equations, complex triangular packed matrix
F06SMF (ZGERU) 12 Rank-1 update, complex rectangular matrix, unconjugated vector
F06SNF (ZGERC) 12 Rank-1 update, complex rectangular matrix, conjugated vector
F06SPF (ZHER) 12 Rank-1 update, complex Hermitian matrix
F06SQF (ZHPR) 12 Rank-1 update, complex Hermitian packed matrix
F06SRF (ZHER2) 12 Rank-2 update, complex Hermitian matrix
F06SSF (ZHPR2) 12 Rank-2 update, complex Hermitian packed matrix
F06TAF (ZSYMV) 21 Matrix-vector product, complex symmetric matrix
F06TBF (ZSYR) 21 Rank-1 update, complex symetric matrix
F06TCF (ZSPMV) 21 Matrix-vector product, complex symmetric packed matrix
F06TDF (ZSPR) 21 Rank-1 update, complex symetric packed matrix
F06TFF 13 Matrix copy, complex rectangular or trapezoidal matrix
F06THF 13 Matrix initialization, complex rectangular matrix
F06TMF 13 Unitary similarity transformation of Hermitian matrix as a sequence of plane rotations
F06TPF 13 Q R  factorization by sequence of plane rotations, rank-1 update of complex upper triangular matrix
F06TQF 13 Q R × k  factorization by sequence of plane rotations, complex upper triangular matrix augmented by a full row
F06TRF 13 Q R  or R Q  factorization by sequence of plane rotations, complex upper Hessenberg matrix
F06TSF 13 Q R  or R Q  factorization by sequence of plane rotations, complex upper spiked matrix
F06TTF 13 Q R  factorization of U Z  or R Q  factorization of Z U , U  complex upper triangular, Z  a sequence of plane rotations
F06TVF 13 Compute upper Hessenberg matrix by sequence of plane rotations, complex upper triangular matrix
F06TWF 13 Compute upper spiked matrix by sequence of plane rotations, complex upper triangular matrix
F06TXF 13 Apply sequence of plane rotations, complex rectangular matrix, real cosine and complex sine
F06TYF 13 Apply sequence of plane rotations, complex rectangular matrix, complex cosine and real sine
F06UAF 15 1 -norm, -norm, Frobenius norm, largest absolute element, complex general matrix
F06UBF 15 1 -norm, -norm, Frobenius norm, largest absolute element, complex band matrix
F06UCF 15 1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix
F06UDF 15 1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, packed storage
F06UEF 15 1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian band matrix
F06UFF 15 1 -norm, -norm, Frobenius norm, largest absolute element, complex symmetric matrix
F06UGF 15 1 -norm, -norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage
F06UHF 15 1 -norm, -norm, Frobenius norm, largest absolute element, complex symmetric band matrix
F06UJF 15 1 -norm, -norm, Frobenius norm, largest absolute element, complex trapezoidal/triangular matrix
F06UKF 15 1 -norm, -norm, Frobenius norm, largest absolute element, complex triangular matrix, packed storage
F06ULF 15 1 -norm, -norm, Frobenius norm, largest absolute element, complex triangular band matrix
F06UMF 15 1 -norm, -norm, Frobenius norm, largest absolute element, complex Hessenberg matrix
F06UNF 21 1 -norm, -norm, Frobenius norm, largest absolute element, complex tridiagonal matrix
F06UPF 21 1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian tridiagonal matrix
F06VJF 13 Permute rows or columns, complex rectangular matrix, permutations represented by an integer array
F06VKF 13 Permute rows or columns, complex rectangular matrix, permutations represented by a real array
F06VXF 13 Apply sequence of plane rotations, complex rectangular matrix, real cosine and sine
F06YAF (DGEMM) 14 Matrix-matrix product, two real rectangular matrices
F06YCF (DSYMM) 14 Matrix-matrix product, one real symmetric matrix, one real rectangular matrix
F06YFF (DTRMM) 14 Matrix-matrix product, one real triangular matrix, one real rectangular matrix
F06YJF (DTRSM) 14 Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix
F06YPF (DSYRK) 14 Rank- k  update of a real symmetric matrix
F06YRF (DSYR2K) 14 Rank- 2 k  update of a real symmetric matrix
F06ZAF (ZGEMM) 14 Matrix-matrix product, two complex rectangular matrices
F06ZCF (ZHEMM) 14 Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix
F06ZFF (ZTRMM) 14 Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix
F06ZJF (ZTRSM) 14 Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix
F06ZPF (ZHERK) 14 Rank- k  update of a complex Hermitian matrix
F06ZRF (ZHER2K) 14 Rank- 2 k  update of a complex Hermitian matrix
F06ZTF (ZSYMM) 14 Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix
F06ZUF (ZSYRK) 14 Rank- k  update of a complex symmetric matrix
F06ZWF (ZSYR2K) 14 Rank- 2 k  update of a complex symmetric matrix

F07 – Linear Equations (LAPACK)

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

Routine Name
Mark of
Introduction

Purpose
F07AAF (DGESV) 21 Computes the solution to a real system of linear equations
F07ABF (DGESVX) 21 Uses the L U  factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
F07ADF (DGETRF) 15 L U  factorization of real m  by n  matrix
F07AEF (DGETRS) 15 Solution of real system of linear equations, multiple right-hand sides, matrix already factorized by F07ADF (DGETRF)
F07AFF (DGEEQU) 21 Computes row and column scalings intended to equilibrate a general real matrix and reduce its condition number
F07AGF (DGECON) 15 Estimate condition number of real matrix, matrix already factorized by F07ADF (DGETRF)
F07AHF (DGERFS) 15 Refined solution with error bounds of real system of linear equations, multiple right-hand sides
F07AJF (DGETRI) 15 Inverse of real matrix, matrix already factorized by F07ADF (DGETRF)
F07ANF (ZGESV) 21 Computes the solution to a complex system of linear equations
F07APF (ZGESVX) 21 Uses the L U  factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
F07ARF (ZGETRF) 15 L U  factorization of complex m  by n  matrix
F07ASF (ZGETRS) 15 Solution of complex system of linear equations, multiple right-hand sides, matrix already factorized by F07ARF (ZGETRF)
F07ATF (ZGEEQU) 21 Computes row and column scalings intended to equilibrate a general complex matrix and reduce its condition number
F07AUF (ZGECON) 15 Estimate condition number of complex matrix, matrix already factorized by F07ARF (ZGETRF)
F07AVF (ZGERFS) 15 Refined solution with error bounds of complex system of linear equations, multiple right-hand sides
F07AWF (ZGETRI) 15 Inverse of complex matrix, matrix already factorized by F07ARF (ZGETRF)
F07BAF (DGBSV) 21 Computes the solution to a real banded system of linear equations
F07BBF (DGBSVX) 21 Uses the L U  factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations
F07BDF (DGBTRF) 15 L U  factorization of real m  by n  band matrix
F07BEF (DGBTRS) 15 Solution of real band system of linear equations, multiple right-hand sides, matrix already factorized by F07BDF (DGBTRF)
F07BFF (DGBEQU) 21 Computes row and column scalings intended to equilibrate a real banded matrix and reduce its condition number
F07BGF (DGBCON) 15 Estimate condition number of real band matrix, matrix already factorized by F07BDF (DGBTRF)
F07BHF (DGBRFS) 15 Refined solution with error bounds of real band system of linear equations, multiple right-hand sides
F07BNF (ZGBSV) 21 Computes the solution to a complex banded system of linear equations
F07BPF (ZGBSVX) 21 Uses the L U  factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations
F07BRF (ZGBTRF) 15 L U  factorization of complex m  by n  band matrix
F07BSF (ZGBTRS) 15 Solution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by F07BRF (ZGBTRF)
F07BTF (ZGBEQU) 21 Computes row and column scalings intended to equilibrate a complex banded matrix and reduce its condition number
F07BUF (ZGBCON) 15 Estimate condition number of complex band matrix, matrix already factorized by F07BRF (ZGBTRF)
F07BVF (ZGBRFS) 15 Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides
F07CAF (DGTSV) 21 Computes the solution to a real tridiagonal system of linear equations
F07CBF (DGTSVX) 21 Uses the L U  factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations
F07CDF (DGTTRF) 21 L U  factorization of real tridiagonal matrix
F07CEF (DGTTRS) 21 Solves a real tridiagonal system of linear equations using the L U  factorization computed by F07CDF (DGTTRF)
F07CGF (DGTCON) 21 Estimates the reciprocal of the condition number of a real tridiagonal matrix using the L U  factorization computed by F07CDF (DGTTRF)
F07CHF (DGTRFS) 21 Refined solution with error bounds of real tridiagonal system of linear equations, multiple right-hand sides
F07CNF (ZGTSV) 21 Computes the solution to a complex tridiagonal system of linear equations
F07CPF (ZGTSVX) 21 Uses the L U  factorization to compute the solution, error-bound and condition estimate for a complex tridiagonal system of linear equations
F07CRF (ZGTTRF) 21 L U  factorization of complex tridiagonal matrix
F07CSF (ZGTTRS) 21 Solves a complex tridiagonal system of linear equations using the L U  factorization computed by F07CDF (DGTTRF)
F07CUF (ZGTCON) 21 Estimates the reciprocal of the condition number of a complex tridiagonal matrix using the L U  factorization computed by F07CDF (DGTTRF)
F07CVF (ZGTRFS) 21 Refined solution with error bounds of complex tridiagonal system of linear equations, multiple right-hand sides
F07FAF (DPOSV) 21 Computes the solution to a real symmetric positive-definite system of linear equations
F07FBF (DPOSVX) 21 Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite system of linear equations
F07FDF (DPOTRF) 15 Cholesky factorization of real symmetric positive-definite matrix
F07FEF (DPOTRS) 15 Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FDF (DPOTRF)
F07FFF (DPOEQU) 21 Computes row and column scalings intended to equilibrate a real symmetric positive-definite matrix and reduce its condition number
F07FGF (DPOCON) 15 Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by F07FDF (DPOTRF)
F07FHF (DPORFS) 15 Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides
F07FJF (DPOTRI) 15 Inverse of real symmetric positive-definite matrix, matrix already factorized by F07FDF (DPOTRF)
F07FNF (ZPOSV) 21 Computes the solution to a complex Hermitian positive-definite system of linear equations
F07FPF (ZPOSVX) 21 Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite system of linear equations
F07FRF (ZPOTRF) 15 Cholesky factorization of complex Hermitian positive-definite matrix
F07FSF (ZPOTRS) 15 Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FRF (ZPOTRF)
F07FTF (ZPOEQU) 21 Computes row and column scalings intended to equilibrate a complex Hermitian positive-definite matrix and reduce its condition number
F07FUF (ZPOCON) 15 Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by F07FRF (ZPOTRF)
F07FVF (ZPORFS) 15 Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides
F07FWF (ZPOTRI) 15 Inverse of complex Hermitian positive-definite matrix, matrix already factorized by F07FRF (ZPOTRF)
F07GAF (DPPSV) 21 Computes the solution to a real symmetric positive-definite system of linear equations, packed storage
F07GBF (DPPSVX) 21 Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite system of linear equations, packed storage
F07GDF (DPPTRF) 15 Cholesky factorization of real symmetric positive-definite matrix, packed storage
F07GEF (DPPTRS) 15 Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GDF (DPPTRF), packed storage
F07GFF (DPPEQU) 21 Computes row and column scalings intended to equilibrate a real symmetric positive-definite matrix and reduce its condition number, packed storage
F07GGF (DPPCON) 15 Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by F07GDF (DPPTRF), packed storage
F07GHF (DPPRFS) 15 Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides, packed storage
F07GJF (DPPTRI) 15 Inverse of real symmetric positive-definite matrix, matrix already factorized by F07GDF (DPPTRF), packed storage
F07GNF (ZPPSV) 21 Computes the solution to a complex Hermitian positive-definite system of linear equations, packed storage
F07GPF (ZPPSVX) 21 Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite system of linear equations, packed storage
F07GRF (ZPPTRF) 15 Cholesky factorization of complex Hermitian positive-definite matrix, packed storage
F07GSF (ZPPTRS) 15 Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GRF (ZPPTRF), packed storage
F07GTF (ZPPEQU) 21 Computes row and column scalings intended to equilibrate a complex Hermitian positive-definite matrix and reduce its condition number, packed storage
F07GUF (ZPPCON) 15 Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by F07GRF (ZPPTRF), packed storage
F07GVF (ZPPRFS) 15 Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, packed storage
F07GWF (ZPPTRI) 15 Inverse of complex Hermitian positive-definite matrix, matrix already factorized by F07GRF (ZPPTRF), packed storage
F07HAF (DPBSV) 21 Computes the solution to a real symmetric positive-definite banded system of linear equations
F07HBF (DPBSVX) 21 Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite banded system of linear equations
F07HDF (DPBTRF) 15 Cholesky factorization of real symmetric positive-definite band matrix
F07HEF (DPBTRS) 15 Solution of real symmetric positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HDF (DPBTRF)
F07HFF (DPBEQU) 21 Computes row and column scalings intended to equilibrate a real symmetric positive-definite banded matrix and reduce its condition number
F07HGF (DPBCON) 15 Estimate condition number of real symmetric positive-definite band matrix, matrix already factorized by F07HDF (DPBTRF)
F07HHF (DPBRFS) 15 Refined solution with error bounds of real symmetric positive-definite band system of linear equations, multiple right-hand sides
F07HNF (ZPBSV) 21 Computes the solution to a complex Hermitian positive-definite banded system of linear equations
F07HPF (ZPBSVX) 21 Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite banded system of linear equations
F07HRF (ZPBTRF) 15 Cholesky factorization of complex Hermitian positive-definite band matrix
F07HSF (ZPBTRS) 15 Solution of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HRF (ZPBTRF)
F07HTF (ZPBEQU) 21 Computes row and column scalings intended to equilibrate a complex Hermitian positive-definite banded matrix and reduce its condition number
F07HUF (ZPBCON) 15 Estimate condition number of complex Hermitian positive-definite band matrix, matrix already factorized by F07HRF (ZPBTRF)
F07HVF (ZPBRFS) 15 Refined solution with error bounds of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides
F07JAF (DPTSV) 21 Computes the solution to a real symmetric positive-definite tridiagonal system of linear equations
F07JBF (DPTSVX) 21 Uses the modified Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite tridiagonal system of linear equations
F07JDF (DPTTRF) 21 Computes the modified Cholesky factorization of a real symmetric positive-definite tridiagonal matrix
F07JEF (DPTTRS) 21 Solves a real symmetric positive-definite tridiagonal system using the modified Cholesky factorization computed by F07JDF (DPTTRF)
F07JGF (DPTCON) 21 Computes the reciprocal of the condition number of a real symmetric positive-definite tridiagonal system using the modified Cholesky factorization computed by F07JDF (DPTTRF)
F07JHF (DPTRFS) 21 Refined solution with error bounds of real symmetric positive-definite tridiagonal system of linear equations, multiple right-hand sides
F07JNF (ZPTSV) 21 Computes the solution to a complex Hermitian positive-definite tridiagonal system of linear equations
F07JPF (ZPTSVX) 21 Uses the modified Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite tridiagonal system of linear equations
F07JRF (ZPTTRF) 21 Computes the modified Cholesky factorization of a complex Hermitian positive-definite tridiagonal matrix
F07JSF (ZPTTRS) 21 Solves a complex Hermitian positive-definite tridiagonal system using the modified Cholesky factorization computed by F07JRF (ZPTTRF)
F07JUF (ZPTCON) 21 Computes the reciprocal of the condition number of a complex Hermitian positive-definite tridiagonal system using the modified Cholesky factorization computed by F07JRF (ZPTTRF)
F07JVF (ZPTRFS) 21 Refined solution with error bounds of complex Hermitian positive-definite tridiagonal system of linear equations, multiple right-hand sides
F07MAF (DSYSV) 21 Computes the solution to a real symmetric system of linear equations
F07MBF (DSYSVX) 21 Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations
F07MDF (DSYTRF) 15 Bunch–Kaufman factorization of real symmetric indefinite matrix
F07MEF (DSYTRS) 15 Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MDF (DSYTRF)
F07MGF (DSYCON) 15 Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07MDF (DSYTRF)
F07MHF (DSYRFS) 15 Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides
F07MJF (DSYTRI) 15 Inverse of real symmetric indefinite matrix, matrix already factorized by F07MDF (DSYTRF)
F07MNF (ZHESV) 21 Computes the solution to a complex Hermitian system of linear equations
F07MPF (ZHESVX) 21 Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations
F07MRF (ZHETRF) 15 Bunch–Kaufman factorization of complex Hermitian indefinite matrix
F07MSF (ZHETRS) 15 Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MRF (ZHETRF)
F07MUF (ZHECON) 15 Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07MRF (ZHETRF)
F07MVF (ZHERFS) 15 Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides
F07MWF (ZHETRI) 15 Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07MRF (ZHETRF)
F07NNF (ZSYSV) 21 Computes the solution to a complex symmetric system of linear equations
F07NPF (ZSYSVX) 21 Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations
F07NRF (ZSYTRF) 15 Bunch–Kaufman factorization of complex symmetric matrix
F07NSF (ZSYTRS) 15 Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07NRF (ZSYTRF)
F07NUF (ZSYCON) 15 Estimate condition number of complex symmetric matrix, matrix already factorized by F07NRF (ZSYTRF)
F07NVF (ZSYRFS) 15 Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides
F07NWF (ZSYTRI) 15 Inverse of complex symmetric matrix, matrix already factorized by F07NRF (ZSYTRF)
F07PAF (DSPSV) 21 Computes the solution to a real symmetric system of linear equations, packed storage
F07PBF (DSPSVX) 21 Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage
F07PDF (DSPTRF) 15 Bunch–Kaufman factorization of real symmetric indefinite matrix, packed storage
F07PEF (DSPTRS) 15 Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PDF (DSPTRF), packed storage
F07PGF (DSPCON) 15 Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07PDF (DSPTRF), packed storage
F07PHF (DSPRFS) 15 Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage
F07PJF (DSPTRI) 15 Inverse of real symmetric indefinite matrix, matrix already factorized by F07PDF (DSPTRF), packed storage
F07PNF (ZHPSV) 21 Computes the solution to a complex Hermitian system of linear equations, packed storage
F07PPF (ZHPSVX) 21 Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations, packed storage
F07PRF (ZHPTRF) 15 Bunch–Kaufman factorization of complex Hermitian indefinite matrix, packed storage
F07PSF (ZHPTRS) 15 Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PRF (ZHPTRF), packed storage
F07PUF (ZHPCON) 15 Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07PRF (ZHPTRF), packed storage
F07PVF (ZHPRFS) 15 Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage
F07PWF (ZHPTRI) 15 Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07PRF (ZHPTRF), packed storage
F07QNF (ZSPSV) 21 Computes the solution to a complex symmetric system of linear equations, packed storage
F07QPF (ZSPSVX) 21 Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations, packed storage
F07QRF (ZSPTRF) 15 Bunch–Kaufman factorization of complex symmetric matrix, packed storage
F07QSF (ZSPTRS) 15 Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07QRF (ZSPTRF), packed storage
F07QUF (ZSPCON) 15 Estimate condition number of complex symmetric matrix, matrix already factorized by F07QRF (ZSPTRF), packed storage
F07QVF (ZSPRFS) 15 Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage
F07QWF (ZSPTRI) 15 Inverse of complex symmetric matrix, matrix already factorized by F07QRF (ZSPTRF), packed storage
F07TEF (DTRTRS) 15 Solution of real triangular system of linear equations, multiple right-hand sides
F07TGF (DTRCON) 15 Estimate condition number of real triangular matrix
F07THF (DTRRFS) 15 Error bounds for solution of real triangular system of linear equations, multiple right-hand sides
F07TJF (DTRTRI) 15 Inverse of real triangular matrix
F07TSF (ZTRTRS) 15 Solution of complex triangular system of linear equations, multiple right-hand sides
F07TUF (ZTRCON) 15 Estimate condition number of complex triangular matrix
F07TVF (ZTRRFS) 15 Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides
F07TWF (ZTRTRI) 15 Inverse of complex triangular matrix
F07UEF (DTPTRS) 15 Solution of real triangular system of linear equations, multiple right-hand sides, packed storage
F07UGF (DTPCON) 15 Estimate condition number of real triangular matrix, packed storage
F07UHF (DTPRFS) 15 Error bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage
F07UJF (DTPTRI) 15 Inverse of real triangular matrix, packed storage
F07USF (ZTPTRS) 15 Solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
F07UUF (ZTPCON) 15 Estimate condition number of complex triangular matrix, packed storage
F07UVF (ZTPRFS) 15 Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
F07UWF (ZTPTRI) 15 Inverse of complex triangular matrix, packed storage
F07VEF (DTBTRS) 15 Solution of real band triangular system of linear equations, multiple right-hand sides
F07VGF (DTBCON) 15 Estimate condition number of real band triangular matrix
F07VHF (DTBRFS) 15 Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides
F07VSF (ZTBTRS) 15 Solution of complex band triangular system of linear equations, multiple right-hand sides
F07VUF (ZTBCON) 15 Estimate condition number of complex band triangular matrix
F07VVF (ZTBRFS) 15 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 F08 Chapter Introduction.

Routine Name
Mark of
Introduction

Purpose
F08AAF (DGELS) 21 Solves an overdetermined or underdetermined real linear system
F08AEF (DGEQRF) 16 Q R  factorization of real general rectangular matrix
F08AFF (DORGQR) 16 Form all or part of orthogonal Q  from Q R  factorization determined by F08AEF (DGEQRF) or F08BEF (DGEQPF)
F08AGF (DORMQR) 16 Apply orthogonal transformation determined by F08AEF (DGEQRF) or F08BEF (DGEQPF)
F08AHF (DGELQF) 16 L Q  factorization of real general rectangular matrix
F08AJF (DORGLQ) 16 Form all or part of orthogonal Q  from L Q  factorization determined by F08AHF (DGELQF)
F08AKF (DORMLQ) 16 Apply orthogonal transformation determined by F08AHF (DGELQF)
F08ANF (ZGELS) 21 Solves an overdetermined or underdetermined complex linear system
F08ASF (ZGEQRF) 16 Q R  factorization of complex general rectangular matrix
F08ATF (ZUNGQR) 16 Form all or part of unitary Q  from Q R  factorization determined by F08ASF (ZGEQRF) or F08BSF (ZGEQPF)
F08AUF (ZUNMQR) 16 Apply unitary transformation determined by F08ASF (ZGEQRF) or F08BSF (ZGEQPF)
F08AVF (ZGELQF) 16 L Q  factorization of complex general rectangular matrix
F08AWF (ZUNGLQ) 16 Form all or part of unitary Q  from L Q  factorization determined by F08AVF (ZGELQF)
F08AXF (ZUNMLQ) 16 Apply unitary transformation determined by F08AVF (ZGELQF)
F08BAF (DGELSY) 21 Computes the minimum-norm solution to a real linear least-squares problem
F08BEF (DGEQPF) 16 Q R  factorization of real general rectangular matrix with column pivoting
F08BFF (DGEQP3) 21 Q R  factorization of real general rectangular matrix with column pivoting, using BLAS-3
F08BHF (DTZRZF) 21 Reduces a real upper trapezoidal matrix to upper triangular form
F08BKF (DORMRZ) 21 Apply orthogonal transformation determined by F08BHF (DTZRZF)
F08BNF (ZGELSY) 21 Computes the minimum-norm solution to a complex linear least-squares problem
F08BSF (ZGEQPF) 16 Q R  factorization of complex general rectangular matrix with column pivoting
F08BTF (ZGEQP3) 21 Q R  factorization of complex general rectangular matrix with column pivoting, using BLAS-3
F08BVF (ZTZRZF) 21 Reduces a complex upper trapezoidal matrix to upper triangular form
F08BXF (ZUNMRZ) 21 Apply unitary transformation determined by F08BVF (ZTZRZF)
F08CEF (DGEQLF) 21 Q L  factorization of real general rectangular matrix
F08CFF (DORGQL) 21 Form all or part of orthogonal Q  from Q L  factorization determined by F08CEF (DGEQLF)
F08CGF (DORMQL) 21 Apply orthogonal transformation determined by F08CEF (DGEQLF)
F08CHF (DGERQF) 21 R Q  factorization of real general rectangular matrix
F08CJF (DORGRQ) 21 Form all or part of orthogonal Q  from R Q  factorization determined by F08CHF (DGERQF)
F08CKF (DORMRQ) 21 Apply orthogonal transformation determined by F08CHF (DGERQF)
F08CSF (ZGEQLF) 21 Q L  factorization of complex general rectangular matrix
F08CTF (ZUNGQL) 21 Form all or part of orthogonal Q  from Q L  factorization determined by F08CSF (ZGEQLF)
F08CUF (ZUNMQL) 21 Apply unitary transformation determined by F08CSF (ZGEQLF)
F08CVF (ZGERQF) 21 R Q  factorization of complex general rectangular matrix
F08CWF (ZUNGRQ) 21 Form all or part of orthogonal Q  from R Q  factorization determined by F08CVF (ZGERQF)
F08CXF (ZUNMRQ) 21 Apply unitary transformation determined by F08CVF (ZGERQF)
F08FAF (DSYEV) 21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
F08FBF (DSYEVX) 21 Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
F08FCF (DSYEVD) 19 All eigenvalues and optionally all eigenvectors of real symmetric matrix (divide-and-conquer)
F08FDF (DSYEVR) 21 Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
F08FEF (DSYTRD) 16 Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
F08FFF (DORGTR) 16 Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF (DSYTRD)
F08FGF (DORMTR) 16 Apply orthogonal transformation determined by F08FEF (DSYTRD)
F08FLF (DDISNA) 21 Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix
F08FNF (ZHEEV) 21 Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
F08FPF (ZHEEVX) 21 Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
F08FQF (ZHEEVD) 19 All eigenvalues and optionally all eigenvectors of complex Hermitian matrix (divide-and-conquer)
F08FRF (ZHEEVR) 21 Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
F08FSF (ZHETRD) 16 Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
F08FTF (ZUNGTR) 16 Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF (ZHETRD)
F08FUF (ZUNMTR) 16 Apply unitary transformation matrix determined by F08FSF (ZHETRD)
F08GAF (DSPEV) 21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
F08GBF (DSPEVX) 21 Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
F08GCF (DSPEVD) 19 All eigenvalues and optionally all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer)
F08GEF (DSPTRD) 16 Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
F08GFF (DOPGTR) 16 Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF (DSPTRD)
F08GGF (DOPMTR) 16 Apply orthogonal transformation determined by F08GEF (DSPTRD)
F08GNF (ZHPEV) 21 Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
F08GPF (ZHPEVX) 21 Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
F08GQF (ZHPEVD) 19 All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer)
F08GSF (ZHPTRD) 16 Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
F08GTF (ZUPGTR) 16 Generate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF (ZHPTRD)
F08GUF (ZUPMTR) 16 Apply unitary transformation matrix determined by F08GSF (ZHPTRD)
F08HAF (DSBEV) 21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
F08HBF (DSBEVX) 21 Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
F08HCF (DSBEVD) 19 All eigenvalues and optionally all eigenvectors of real symmetric band matrix (divide-and-conquer)
F08HEF (DSBTRD) 16 Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
F08HNF (ZHBEV) 21 Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
F08HPF (ZHBEVX) 21 Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
F08HQF (ZHBEVD) 19 All eigenvalues and optionally all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
F08HSF (ZHBTRD) 16 Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
F08JAF (DSTEV) 21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
F08JBF (DSTEVX) 21 Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
F08JCF (DSTEVD) 19 All eigenvalues and optionally all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
F08JDF (DSTEVR) 21 Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
F08JEF (DSTEQR) 16 All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using implicit Q L  or Q R  
F08JFF (DSTERF) 16 All eigenvalues of real symmetric tridiagonal matrix, root-free variant of Q L  or Q R  
F08JGF (DPTEQR) 16 All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from real symmetric positive-definite matrix
F08JHF (DSTEDC) 21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
F08JJF (DSTEBZ) 16 Selected eigenvalues of real symmetric tridiagonal matrix by bisection
F08JKF (DSTEIN) 16 Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
F08JLF (DSTEGR) 21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
F08JSF (ZSTEQR) 16 All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using implicit Q L  or Q R  
F08JUF (ZPTEQR) 16 All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from complex Hermitian positive-definite matrix
F08JVF (ZSTEDC) 21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
F08JXF (ZSTEIN) 16 Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
F08JYF (ZSTEGR) 21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
F08KAF (DGELSS) 21 Computes the minimum-norm solution to a real linear least-squares problem using singular value decomposition
F08KBF (DGESVD) 21 Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
F08KCF (DGELSD) 21 Computes the minimum-norm solution to a real linear least-squares problem using singular value decomposition (divide-and-conquer)
F08KDF (DGESDD) 21 Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
F08KEF (DGEBRD) 16 Orthogonal reduction of real general rectangular matrix to bidiagonal form
F08KFF (DORGBR) 16 Generate orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF (DGEBRD)
F08KGF (DORMBR) 16 Apply orthogonal transformations from reduction to bidiagonal form determined by F08KEF (DGEBRD)
F08KNF (ZGELSS) 21 Computes the minimum-norm solution to a complex linear least-squares problem using singular value decomposition
F08KPF (ZGESVD) 21 Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
F08KQF (ZGELSD) 21 Computes the minimum-norm solution to a complex linear least-squares problem using singular value decomposition (divide-and-conquer)
F08KRF (ZGESDD) 21 Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
F08KSF (ZGEBRD) 16 Unitary reduction of complex general rectangular matrix to bidiagonal form
F08KTF (ZUNGBR) 16 Generate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF (ZGEBRD)
F08KUF (ZUNMBR) 16 Apply unitary transformations from reduction to bidiagonal form determined by F08KSF (ZGEBRD)
F08LEF (DGBBRD) 19 Reduction of real rectangular band matrix to upper bidiagonal form
F08LSF (ZGBBRD) 19 Reduction of complex rectangular band matrix to upper bidiagonal form
F08MDF (DBDSDC) 21 Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
F08MEF (DBDSQR) 16 SVD of real bidiagonal matrix reduced from real general matrix
F08MSF (ZBDSQR) 16 SVD of real bidiagonal matrix reduced from complex general matrix
F08NAF (DGEEV) 21 Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
F08NBF (DGEEVX) 21 Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
F08NEF (DGEHRD) 16 Orthogonal reduction of real general matrix to upper Hessenberg form
F08NFF (DORGHR) 16 Generate orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD)
F08NGF (DORMHR) 16 Apply orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD)
F08NHF (DGEBAL) 16 Balance real general matrix
F08NJF (DGEBAK) 16 Transform eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF (DGEBAL)
F08NNF (ZGEEV) 21 Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
F08NPF (ZGEEVX) 21 Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
F08NSF (ZGEHRD) 16 Unitary reduction of complex general matrix to upper Hessenberg form
F08NTF (ZUNGHR) 16 Generate unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD)
F08NUF (ZUNMHR) 16 Apply unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD)
F08NVF (ZGEBAL) 16 Balance complex general matrix
F08NWF (ZGEBAK) 16 Transform eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF (ZGEBAL)
F08PAF (DGEES) 21 Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
F08PBF (DGEESX) 21 Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
F08PEF (DHSEQR) 16 Eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
F08PKF (DHSEIN) 16 Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
F08PNF (ZGEES) 21 Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
F08PPF (ZGEESX) 21 Computes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
F08PSF (ZHSEQR) 16 Eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
F08PXF (ZHSEIN) 16 Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
F08QFF (DTREXC) 16 Reorder Schur factorization of real matrix using orthogonal similarity transformation
F08QGF (DTRSEN) 16 Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QHF (DTRSYL) 16 Solve real Sylvester matrix equation A X + X B = C , A  and B  are upper quasi-triangular or transposes
F08QKF (DTREVC) 16 Left and right eigenvectors of real upper quasi-triangular matrix
F08QLF (DTRSNA) 16 Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
F08QTF (ZTREXC) 16 Reorder Schur factorization of complex matrix using unitary similarity transformation
F08QUF (ZTRSEN) 16 Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QVF (ZTRSYL) 16 Solve complex Sylvester matrix equation A X + X B = C , A  and B  are upper triangular or conjugate-transposes
F08QXF (ZTREVC) 16 Left and right eigenvectors of complex upper triangular matrix
F08QYF (ZTRSNA) 16 Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
F08SAF (DSYGV) 21 Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
F08SBF (DSYGVX) 21 Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
F08SCF (DSYGVD) 21 Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
F08SEF (DSYGST) 16 Reduction to standard form of real symmetric-definite generalized eigenproblem A x = λ B x , A B x = λ x  or B A x = λ x , B  factorized by F07FDF (DPOTRF)
F08SNF (ZHEGV) 21 Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
F08SPF (ZHEGVX) 21 Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
F08SQF (ZHEGVD) 21 Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
F08SSF (ZHEGST) 16 Reduction to standard form of complex Hermitian-definite generalized eigenproblem A x = λ B x , A B x = λ x  or B A x = λ x , B  factorized by F07FRF (ZPOTRF)
F08TAF (DSPGV) 21 Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
F08TBF (DSPGVX) 21 Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
F08TCF (DSPGVD) 21 Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
F08TEF (DSPGST) 16 Reduction to standard form of real symmetric-definite generalized eigenproblem A x = λ B x , A B x = λ x  or B A x = λ x , packed storage, B  factorized by F07GDF (DPPTRF)
F08TNF (ZHPGV) 21 Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
F08TPF (ZHPGVX) 21 Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
F08TQF (ZHPGVD) 21 Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
F08TSF (ZHPGST) 16 Reduction to standard form of complex Hermitian-definite generalized eigenproblem A x = λ B x , A B x = λ x  or B A x = λ x , packed storage, B  factorized by F07GRF (ZPPTRF)
F08UAF (DSBGV) 21 Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
F08UBF (DSBGVX) 21 Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
F08UCF (DSBGVD) 21 Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
F08UEF (DSBGST) 19 Reduction of real symmetric-definite banded generalized eigenproblem A x = λ B x  to standard form C y = λ y , such that C  has the same bandwidth as A  
F08UFF (DPBSTF) 19 Computes a split Cholesky factorization of real symmetric positive-definite band matrix A  
F08UNF (ZHBGV) 21 Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
F08UPF (ZHBGVX) 21 Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
F08UQF (ZHBGVD) 21 Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
F08USF (ZHBGST) 19 Reduction of complex Hermitian-definite banded generalized eigenproblem A x = λ B x  to standard form C y = λ y , such that C  has the same bandwidth as A  
F08UTF (ZPBSTF) 19 Computes a split Cholesky factorization of complex Hermitian positive-definite band matrix A  
F08VAF (DGGSVD) 21 Computes the generalized singular value decomposition of a real matrix pair
F08VEF (DGGSVP) 21 Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a real matrix pair
F08VNF (ZGGSVD) 21 Computes the generalized singular value decomposition of a complex matrix pair
F08VSF (ZGGSVP) 21 Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a complex matrix pair
F08WAF (DGGEV) 21 Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
F08WBF (DGGEVX) 21 Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
F08WEF (DGGHRD) 20 Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
F08WHF (DGGBAL) 20 Balance a pair of real general matrices
F08WJF (DGGBAK) 20 Transform eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF (DGGBAL)
F08WNF (ZGGEV) 21 Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
F08WPF (ZGGEVX) 21 Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
F08WSF (ZGGHRD) 20 Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
F08WVF (ZGGBAL) 20 Balance a pair of complex general matrices
F08WWF (ZGGBAK) 20 Transform eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF (ZGGBAL)
F08XAF (DGGES) 21 Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
F08XBF (DGGESX) 21 Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
F08XEF (DHGEQZ) 20 Eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
F08XNF (ZGGES) 21 Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
F08XPF (ZGGESX) 21 Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
F08XSF (ZHGEQZ) 20 Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex general matrices
F08YEF (DTGSJA) 21 Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
F08YFF (DTGEXC) 21 Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
F08YGF (DTGSEN) 21 Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
F08YHF (DTGSYL) 21 Solves the real-valued generalized Sylvester equation
F08YKF (DTGEVC) 20 Left and right eigenvectors of a pair of real upper quasi-triangular matrices
F08YLF (DTGSNA) 21 Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form
F08YSF (ZTGSJA) 21 Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
F08YTF (ZTGEXC) 21 Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
F08YUF (ZTGSEN) 21 Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
F08YVF (ZTGSYL) 21 Solves the complex generalized Sylvester equation
F08YXF (ZTGEVC) 20 Left and right eigenvectors of a pair of complex upper triangular matrices
F08YYF (ZTGSNA) 21 Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form
F08ZAF (DGGLSE) 21 Solves the real linear equality-constrained least-squares (LSE) problem
F08ZBF (DGGGLM) 21 Solves a real general Gauss–Markov linear model (GLM) problem
F08ZEF (DGGQRF) 21 Computes a generalized Q R  factorization of a real matrix pair
F08ZFF (DGGRQF) 21 Computes a generalized R Q  factorization of a real matrix pair
F08ZNF (ZGGLSE) 21 Solves the complex linear equality-constrained least-squares (LSE) problem
F08ZPF (ZGGGLM) 21 Solves a complex general Gauss–Markov linear model (GLM) problem
F08ZSF (ZGGQRF) 21 Computes a generalized Q R  factorization of a complex matrix pair
F08ZTF (ZGGRQF) 21 Computes a generalized R Q  factorization of a complex matrix pair

F11 – Large Scale Linear Systems


Routine Name
Mark of
Introduction

Purpose
F11BDF 19 Real sparse nonsymmetric linear systems, setup for F11BEF
F11BEF 19 Real sparse nonsymmetric linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
F11BFF 19 Real sparse nonsymmetric linear systems, diagnostic for F11BEF
F11BRF 19 Complex sparse non-Hermitian linear systems, setup for F11BSF
F11BSF 19 Complex sparse non-Hermitian linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
F11BTF 19 Complex sparse non-Hermitian linear systems, diagnostic for F11BSF
F11DAF 18 Real sparse nonsymmetric linear systems, incomplete L U  factorization
F11DBF 18 Solution of linear system involving incomplete L U  preconditioning matrix generated by F11DAF
F11DCF 18 Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DAF
F11DDF 18 Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse nonsymmetric matrix
F11DEF 18 Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB, or TFQMR method, Jacobi or SSOR preconditioner (Black Box)
F11DKF 20 Real sparse nonsymmetric linear systems, line Jacobi preconditioner
F11DNF 19 Complex sparse non-Hermitian linear systems, incomplete L U  factorization
F11DPF 19 Solution of complex linear system involving incomplete L U  preconditioning matrix generated by F11DNF
F11DQF 19 Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DNF (Black Box)
F11DRF 19 Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse non-Hermitian matrix
F11DSF 19 Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner Black Box
F11DXF 20 Complex sparse nonsymmetric linear systems, line Jacobi preconditioner
F11GDF 20 Real sparse symmetric linear systems, setup for F11GEF
F11GEF 20 Real sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos
F11GFF 20 Real sparse symmetric linear systems, diagnostic for F11GEF
F11GRF 20 Complex sparse Hermitian linear systems, setup for F11GSF
F11GSF 20 Complex sparse Hermitian linear systems, preconditioned conjugate gradient or Lanczos
F11GTF 20 Complex sparse Hermitian linear systems, diagnostic for F11GSF
F11JAF 17 Real sparse symmetric matrix, incomplete Cholesky factorization
F11JBF 17 Solution of linear system involving incomplete Cholesky preconditioning matrix generated by F11JAF
F11JCF 17 Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JAF (Black Box)
F11JDF 17 Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse symmetric matrix
F11JEF 17 Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
F11JNF 19 Complex sparse Hermitian matrix, incomplete Cholesky factorization
F11JPF 19 Solution of complex linear system involving incomplete Cholesky preconditioning matrix generated by F11JNF
F11JQF 19 Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JNF (Black Box)
F11JRF 19 Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse Hermitian matrix
F11JSF 19 Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
F11MDF 21 Real sparse nonsymmetric linear systems, setup for F11MEF
F11MEF 21 L U  factorization of real sparse matrix
F11MFF 21 Solution of real sparse simultaneous linear equations (coefficient matrix already factorized)
F11MGF 21 Estimate condition number of real matrix, matrix already factorized by F11MEF
F11MHF 21 Refined solution with error bounds of real system of linear equations, multiple right-hand sides
F11MKF 21 Real sparse nonsymmetric matrix matrix multiply, compressed column storage
F11MLF 21 1 -norm, -norm, largest absolute element, real general matrix
F11MMF 21 Real sparse nonsymmetric linear systems, diagnostic for F11MEF
F11XAF 18 Real sparse nonsymmetric matrix vector multiply
F11XEF 17 Real sparse symmetric matrix vector multiply
F11XNF 19 Complex sparse non-Hermitian matrix vector multiply
F11XSF 19 Complex sparse Hermitian matrix vector multiply
F11ZAF 18 Real sparse nonsymmetric matrix reorder routine
F11ZBF 17 Real sparse symmetric matrix reorder routine
F11ZNF 19 Complex sparse non-Hermitian matrix reorder routine
F11ZPF 19 Complex sparse Hermitian matrix reorder routine

F12 – Large Scale Eigenproblems


Routine Name
Mark of
Introduction

Purpose
F12AAF 21 Initialization routine for (F12ABF) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse (standard or generalized) eigenproblem
F12ABF 21 Implements a reverse communication interface for the Implicitly Restarted Arnoldi iteration for computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse (standard or generalized) eigenproblem
F12ACF 21 Returns the converged approximations (as determined by F12ABF) to eigenvalues of a real nonsymmetric sparse (standard or generalized) eigenproblem and, optionally, the corresponding approximate eigenvectors and/or an orthonormal basis for the associated approximate invariant subspace
F12ADF 21 Set a single option from a string (F12ABF/F12ACF/F12AGF)
F12AEF 21 Provides monitoring information for F12ABF
F12AFF 21 Initialization routine for (F12AGF) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded (standard or generalized) eigenproblem
F12AGF 21 Computes approximations to selected eigenvalues of a real nonsymmetric banded (standard or generalized) eigenproblem and, optionally, the corresponding approximate eigenvectors and/or an orthonormal basis for the associated approximate invariant subspace
F12ANF 21 Initialization routine for (F12APF) computing selected eigenvalues and, optionally, eigenvectors of a complex sparse (standard or generalized) eigenproblem
F12APF 21 Implements a reverse communication interface for the Implicitly Restarted Arnoldi iteration for computing selected eigenvalues and, optionally, eigenvectors of a complex sparse (standard or generalized) eigenproblem
F12AQF 21 Returns the converged approximations (as determined by F12ABF) to eigenvalues of a complex sparse (standard or generalized) eigenproblem and, optionally, the corresponding approximate eigenvectors and/or an orthonormal basis for the associated approximate invariant subspace
F12ARF 21 Set a single option from a string (F12APF/F12AQF)
F12ASF 21 Provides monitoring information for F12APF
F12FAF 21 Initialization routine for (F12FBF) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse (standard or generalized) eigenproblem
F12FBF 21 Implements a reverse communication interface for the Implicitly Restarted Arnoldi iteration for computing selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse (standard or generalized) eigenproblem
F12FCF 21 Returns the converged approximations (as determined by F12ABF) to eigenvalues of a real symmetric sparse (standard or generalized) eigenproblem and, optionally, the corresponding approximate eigenvectors and/or an orthonormal basis for the associated approximate invariant subspace
F12FDF 21 Set a single option from a string (F12FBF/F12FCF/F12FGF)
F12FEF 21 Provides monitoring information for F12FBF
F12FFF 21 Initialization routine for (F12FGF) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric banded (standard or generalized) eigenproblem
F12FGF 21 Computes approximations to selected eigenvalues of a real symmetric banded (standard or generalized) eigenproblem and, optionally, the corresponding approximate eigenvectors and/or an orthonormal basis for the associated approximate invariant subspace

G01 – Simple Calculations on Statistical Data


Routine Name
Mark of
Introduction

Purpose
G01AAF 4 Mean, variance, skewness, kurtosis, etc., one variable, from raw data
G01ABF 4 Mean, variance, skewness, kurtosis, etc., two variables, from raw data
G01ADF 4 Mean, variance, skewness, kurtosis, etc., one variable, from frequency table
G01AEF 4 Frequency table from raw data
G01AFF 4 Two-way contingency table analysis, with χ2 /Fisher's exact test
G01AGF 8 Lineprinter scatterplot of two variables
G01AHF 8 Lineprinter scatterplot of one variable against Normal scores
G01AJF 10 Lineprinter histogram of one variable
G01ALF 14 Computes a five-point summary (median, hinges and extremes)
G01ARF 14 Constructs a stem and leaf plot
G01ASF 14 Constructs a box and whisker plot
G01BJF 13 Binomial distribution function
G01BKF 13 Poisson distribution function
G01BLF 13 Hypergeometric distribution function
G01DAF 8 Normal scores, accurate values
G01DBF 12 Normal scores, approximate values
G01DCF 12 Normal scores, approximate variance-covariance matrix
G01DDF 12 Shapiro and Wilk's W  test for Normality
G01DHF 15 Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores
G01EAF 15 Computes probabilities for the standard Normal distribution
G01EBF 14 Computes probabilities for Student's t -distribution
G01ECF 14 Computes probabilities for χ2  distribution
G01EDF 14 Computes probabilities for F -distribution
G01EEF 14 Computes upper and lower tail probabilities and probability density function for the beta distribution
G01EFF 14 Computes probabilities for the gamma distribution
G01EMF 15 Computes probability for the Studentized range statistic
G01EPF 15 Computes bounds for the significance of a Durbin–Watson statistic
G01ERF 16 Computes probability for von Mises distribution
G01ETF 21 Landau distribution function Φ (λ)  
G01EUF 21 Vavilov distribution function ΦV ( λ ; κ ,β2)  
G01EYF 14 Computes probabilities for the one-sample Kolmogorov–Smirnov distribution
G01EZF 14 Computes probabilities for the two-sample Kolmogorov–Smirnov distribution
G01FAF 15 Computes deviates for the standard Normal distribution
G01FBF 14 Computes deviates for Student's t -distribution
G01FCF 14 Computes deviates for the χ2  distribution
G01FDF 14 Computes deviates for the F -distribution
G01FEF 14 Computes deviates for the beta distribution
G01FFF 14 Computes deviates for the gamma distribution
G01FMF 15 Computes deviates for the Studentized range statistic
G01FTF 21 Landau inverse function Ψ (x)  
G01GBF 14 Computes probabilities for the non-central Student's t -distribution
G01GCF 14 Computes probabilities for the non-central χ2  distribution
G01GDF 14 Computes probabilities for the non-central F -distribution
G01GEF 14 Computes probabilities for the non-central beta distribution
G01HAF 14 Computes probability for the bivariate Normal distribution
G01HBF 15 Computes probabilities for the multivariate Normal distribution
G01JCF 14 Computes probability for a positive linear combination of χ2  variables
G01JDF 15 Computes lower tail probability for a linear combination of (central) χ2  variables
G01MBF 15 Computes reciprocal of Mills' Ratio
G01MTF 21 Landau density function φ (λ)  
G01MUF 21 Vavilov density function φV ( λ ; κ ,β2)  
G01NAF 16 Cumulants and moments of quadratic forms in Normal variables
G01NBF 16 Moments of ratios of quadratic forms in Normal variables, and related statistics
G01PTF 21 Landau first moment function Φ1 (x)  
G01QTF 21 Landau second moment function Φ2 (x)  
G01RTF 21 Landau derivative function φ (λ)  
G01ZUF 21 Initialization routine for G01MUF and G01EUF

G02 – Correlation and Regression Analysis


Routine Name
Mark of
Introduction

Purpose
G02BAF 4 Pearson product-moment correlation coefficients, all variables, no missing values
G02BBF 4 Pearson product-moment correlation coefficients, all variables, casewise treatment of missing values
G02BCF 4 Pearson product-moment correlation coefficients, all variables, pairwise treatment of missing values
G02BDF 4 Correlation-like coefficients (about zero), all variables, no missing values
G02BEF 4 Correlation-like coefficients (about zero), all variables, casewise treatment of missing values
G02BFF 4 Correlation-like coefficients (about zero), all variables, pairwise treatment of missing values
G02BGF 4 Pearson product-moment correlation coefficients, subset of variables, no missing values
G02BHF 4 Pearson product-moment correlation coefficients, subset of variables, casewise treatment of missing values
G02BJF 4 Pearson product-moment correlation coefficients, subset of variables, pairwise treatment of missing values
G02BKF 4 Correlation-like coefficients (about zero), subset of variables, no missing values
G02BLF 4 Correlation-like coefficients (about zero), subset of variables, casewise treatment of missing values
G02BMF 4 Correlation-like coefficients (about zero), subset of variables, pairwise treatment of missing values
G02BNF 4 Kendall/Spearman non-parametric rank correlation coefficients, no missing values, overwriting input data
G02BPF 4 Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, overwriting input data
G02BQF 4 Kendall/Spearman non-parametric rank correlation coefficients, no missing values, preserving input data
G02BRF 4 Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, preserving input data
G02BSF 4 Kendall/Spearman non-parametric rank correlation coefficients, pairwise treatment of missing values
G02BTF 14 Update a weighted sum of squares matrix with a new observation
G02BUF 14 Computes a weighted sum of squares matrix
G02BWF 14 Computes a correlation matrix from a sum of squares matrix
G02BXF 14 Computes (optionally weighted) correlation and covariance matrices
G02BYF 17 Computes partial correlation/variance-covariance matrix from correlation/variance-covariance matrix computed by G02BXF
G02CAF 4 Simple linear regression with constant term, no missing values
G02CBF 4 Simple linear regression without constant term, no missing values
G02CCF 4 Simple linear regression with constant term, missing values
G02CDF 4 Simple linear regression without constant term, missing values
G02CEF 4 Service routines for multiple linear regression, select elements from vectors and matrices
G02CFF 4 Service routines for multiple linear regression, re-order elements of vectors and matrices
G02CGF 4 Multiple linear regression, from correlation coefficients, with constant term
G02CHF 4 Multiple linear regression, from correlation-like coefficients, without constant term
G02DAF 14 Fits a general (multiple) linear regression model
G02DCF 14 Add/delete an observation to/from a general linear regression model
G02DDF 14 Estimates of linear parameters and general linear regression model from updated model
G02DEF 14 Add a new independent variable to a general linear regression model
G02DFF 14 Delete an independent variable from a general linear regression model
G02DGF 14 Fits a general linear regression model to new dependent variable
G02DKF 14 Estimates and standard errors of parameters of a general linear regression model for given constraints
G02DNF 14 Computes estimable function of a general linear regression model and its standard error
G02EAF 14 Computes residual sums of squares for all possible linear regressions for a set of independent variables
G02ECF 14 Calculates R2  and CP  values from residual sums of squares
G02EEF 14 Fits a linear regression model by forward selection
G02EFF 21 Stepwise linear regression
G02FAF 14 Calculates standardized residuals and influence statistics
G02FCF 15 Computes Durbin–Watson test statistic
G02GAF 14 Fits a generalized linear model with Normal errors
G02GBF 14 Fits a generalized linear model with binomial errors
G02GCF 14 Fits a generalized linear model with Poisson errors
G02GDF 14 Fits a generalized linear model with gamma errors
G02GKF 14 Estimates and standard errors of parameters of a general linear model for given constraints
G02GNF 14 Computes estimable function of a generalized linear model and its standard error
G02HAF 13 Robust regression, standard M -estimates
G02HBF 13 Robust regression, compute weights for use with G02HDF
G02HDF 13 Robust regression, compute regression with user-supplied functions and weights
G02HFF 13 Robust regression, variance-covariance matrix following G02HDF
G02HKF 14 Calculates a robust estimation of a correlation matrix, Huber's weight function
G02HLF 14 Calculates a robust estimation of a correlation matrix, user-supplied weight function plus derivatives
G02HMF 14 Calculates a robust estimation of a correlation matrix, user-supplied weight function
G02JAF 21 Linear mixed effects regression using Restricted Maximum Likelihood (REML)
G02JBF 21 Linear mixed effects regression using Maximum Likelihood (ML)

G03 – Multivariate Methods


Routine Name
Mark of
Introduction

Purpose
G03AAF 14 Performs principal component analysis
G03ACF 14 Performs canonical variate analysis
G03ADF 14 Performs canonical correlation analysis
G03BAF 15 Computes orthogonal rotations for loading matrix, generalized orthomax criterion
G03BCF 15 Computes Procrustes rotations
G03CAF 15 Computes maximum likelihood estimates of the parameters of a factor analysis model, factor loadings, communalities and residual correlations
G03CCF 15 Computes factor score coefficients (for use after G03CAF)
G03DAF 15 Computes test statistic for equality of within-group covariance matrices and matrices for discriminant analysis
G03DBF 15 Computes Mahalanobis squared distances for group or pooled variance-covariance matrices (for use after G03DAF)
G03DCF 15 Allocates observations to groups according to selected rules (for use after G03DAF)
G03EAF 16 Computes distance matrix
G03ECF 16 Hierarchical cluster analysis
G03EFF 16 K -means cluster analysis
G03EHF 16 Constructs dendrogram (for use after G03ECF)
G03EJF 16 Computes cluster indicator variable (for use after G03ECF)
G03FAF 17 Performs principal co-ordinate analysis, classical metric scaling
G03FCF 17 Performs non-metric (ordinal) multidimensional scaling
G03ZAF 15 Produces standardized values ( z -scores) for a data matrix

G04 – Analysis of Variance


Routine Name
Mark of
Introduction

Purpose
G04AGF 8 Two-way analysis of variance, hierarchical classification, subgroups of unequal size
G04BBF 16 Analysis of variance, randomized block or completely randomized design, treatment means and standard errors
G04BCF 17 Analysis of variance, general row and column design, treatment means and standard errors
G04CAF 16 Analysis of variance, complete factorial design, treatment means and standard errors
G04DAF 17 Computes sum of squares for contrast between means
G04DBF 17 Computes confidence intervals for differences between means computed by G04BBF or G04BCF
G04EAF 17 Computes orthogonal polynomials or dummy variables for factor/classification variable

G05 – Random Number Generators


Routine Name
Mark of
Introduction

Purpose
G05HKF 20 Univariate time series, generate n  terms of either a symmetric GARCH process or a GARCH process with asymmetry of the form (ε t - 1 +γ)2  
G05HLF 20 Univariate time series, generate n  terms of a GARCH process with asymmetry of the form (|ε t - 1 |+γε t - 1 )2  
G05HMF 20 Univariate time series, generate n  terms of an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
G05HNF 20 Univariate time series, generate n  terms of an exponential GARCH (EGARCH) process
G05KAF 20 Pseudo-random real numbers, uniform distribution over (0,1), seeds and generator number passed explicitly
G05KBF 20 Initialize seeds of a given generator for random number generating routines (that pass seeds explicitly) to give a repeatable sequence
G05KCF 20 Initialize seeds of a given generator for random number generating routines (that pass seeds expicitly) to give non-repeatable sequence
G05KEF 20 Pseudo-random logical (boolean) value, seeds and generator number passed explicitly
G05LAF 20 Generates a vector of random numbers from a Normal distribution, seeds and generator number passed explicitly
G05LBF 20 Generates a vector of random numbers from a Student's t -distribution, seeds and generator number passed explicitly
G05LCF 20 Generates a vector of random numbers from a χ2  distribution, seeds and generator number passed explicitly
G05LDF 20 Generates a vector of random numbers from an F -distribution, seeds and generator number passed explicitly
G05LEF 20 Generates a vector of random numbers from a β  distribution, seeds and generator number passed explicitly
G05LFF 20 Generates a vector of random numbers from a γ  distribution, seeds and generator number passed explicitly
G05LGF 20 Generates a vector of random numbers from a uniform distribution, seeds and generator number passed explicitly
G05LHF 20 Generates a vector of random numbers from a triangular distribution, seeds and generator number passed explicitly
G05LJF 20 Generates a vector of random numbers from an exponential distribution, seeds and generator number passed explicitly
G05LKF 20 Generates a vector of random numbers from a lognormal distribution, seeds and generator number passed explicitly
G05LLF 20 Generates a vector of random numbers from a Cauchy distribution, seeds and generator number passed explicitly
G05LMF 20 Generates a vector of random numbers from a Weibull distribution, seeds and generator number passed explicitly
G05LNF 20 Generates a vector of random numbers from a logistic distribution, seeds and generator number passed explicitly
G05LPF 20 Generates a vector of random numbers from a von Mises distribution, seeds and generator number passed explicitly
G05LQF 20 Generates a vector of random numbers from an exponential mixture distribution, seeds and generator number passed explicitly
G05LXF 21 Generates a matrix of random numbers from a multivariate Student's t -distribution, seeds and generator passed explicitly
G05LYF 21 Generates a matrix of random numbers from a multivariate Normal distribution, seeds and generator passed explicitly
G05LZF 20 Generates a vector of random numbers from a multivariate Normal distribution, seeds and generator number passed explicitly
G05MAF 20 Generates a vector of random integers from a uniform distribution, seeds and generator number passed explicitly
G05MBF 20 Generates a vector of random integers from a geometric distribution, seeds and generator number passed explicitly
G05MCF 20 Generates a vector of random integers from a negative binomial distribution, seeds and generator number passed explicitly
G05MDF 20 Generates a vector of random integers from a logarithmic distribution, seeds and generator number passed explicitly
G05MEF 20 Generates a vector of random integers from a Poisson distribution with varying mean, seeds and generator number passed explicitly
G05MJF 20 Generates a vector of random integers from a binomial distribution, seeds and generator number passed explicitly
G05MKF 20 Generates a vector of random integers from a Poisson distribution, seeds and generator number passed explicitly
G05MLF 20 Generates a vector of random integers from a hypergeometric distribution, seeds and generator number passed explicitly
G05MRF 20 Generates a vector of random integers from a multinomial distribution, seeds and generator number passed explicitly
G05MZF 20 Generates a vector of random integers from a general discrete distribution, seeds and generator number passed explicitly
G05NAF 20 Pseudo-random permutation of an integer vector
G05NBF 20 Pseudo-random sample from an integer vector
G05PAF 20 Generates a realisation of a time series from an ARMA model
G05PCF 20 Generates a realisation of a multivariate time series from a VARMA model
G05QAF 20 Computes a random orthogonal matrix
G05QBF 20 Computes a random correlation matrix
G05QDF 20 Generates a random table matrix
G05RAF 21 Generates a matrix of random numbers from a Gaussian Copula, seeds and generator passed explicitly
G05RBF 21 Generates a matrix of random numbers from a Student's t -Copula, seeds and generator passed explicitly
G05YCF 21 Initializes the Faure generator (G05YDF/G05YJF/G05YKF)
G05YDF 21 Generates a sequence of quasi-random numbers using Faure's method
G05YEF 21 Initializes the Sobol generator (G05YFF/G05YJF/G05YKF)
G05YFF 21 Generates a sequence of quasi-random numbers using Sobol's method
G05YGF 21 Initializes the Neiderreiter generator (G05YHF/G05YJF/G05YKF)
G05YHF 21 Generates a sequence of quasi-random numbers using Neiderreiter's method
G05YJF 21 Generates a Normal quasi-random number sequence using Faure's, Sobol's or Neiderreiter's method
G05YKF 21 Generates a log-Normal quasi-random number sequence using Faure's, Sobol's or Neiderreiter's method

G07 – Univariate Estimation


Routine Name
Mark of
Introduction

Purpose
G07AAF 15 Computes confidence interval for the parameter of a binomial distribution
G07ABF 15 Computes confidence interval for the parameter of a Poisson distribution
G07BBF 15 Computes maximum likelihood estimates for parameters of the Normal distribution from grouped and/or censored data
G07BEF 15 Computes maximum likelihood estimates for parameters of the Weibull distribution
G07CAF 15 Computes t -test statistic for a difference in means between two Normal populations, confidence interval
G07DAF 13 Robust estimation, median, median absolute deviation, robust standard deviation
G07DBF 13 Robust estimation, M -estimates for location and scale parameters, standard weight functions
G07DCF 13 Robust estimation, M -estimates for location and scale parameters, user-defined weight functions
G07DDF 14 Computes a trimmed and winsorized mean of a single sample with estimates of their variance
G07EAF 16 Robust confidence intervals, one-sample
G07EBF 16 Robust confidence intervals, two-sample

G08 – Nonparametric Statistics


Routine Name
Mark of
Introduction

Purpose
G08AAF 8 Sign test on two paired samples
G08ACF 8 Median test on two samples of unequal size
G08AEF 8 Friedman two-way analysis of variance on k  matched samples
G08AFF 8 Kruskal–Wallis one-way analysis of variance on k  samples of unequal size
G08AGF 14 Performs the Wilcoxon one-sample (matched pairs) signed rank test
G08AHF 14 Performs the Mann–Whitney U  test on two independent samples
G08AJF 14 Computes the exact probabilities for the Mann–Whitney U  statistic, no ties in pooled sample
G08AKF 14 Computes the exact probabilities for the Mann–Whitney U  statistic, ties in pooled sample
G08ALF 15 Performs the Cochran Q  test on cross-classified binary data
G08BAF 8 Mood's and David's tests on two samples of unequal size
G08CBF 14 Performs the one-sample Kolmogorov–Smirnov test for standard distributions
G08CCF 14 Performs the one-sample Kolmogorov–Smirnov test for a user-supplied distribution
G08CDF 14 Performs the two-sample Kolmogorov–Smirnov test
G08CGF 14 Performs the χ2  goodness of fit test, for standard continuous distributions
G08DAF 8 Kendall's coefficient of concordance
G08EAF 14 Performs the runs up or runs down test for randomness
G08EBF 14 Performs the pairs (serial) test for randomness
G08ECF 14 Performs the triplets test for randomness
G08EDF 14 Performs the gaps test for randomness
G08RAF 12 Regression using ranks, uncensored data
G08RBF 12 Regression using ranks, right-censored data

G10 – Smoothing in Statistics


Routine Name
Mark of
Introduction

Purpose
G10ABF 16 Fit cubic smoothing spline, smoothing parameter given
G10ACF 16 Fit cubic smoothing spline, smoothing parameter estimated
G10BAF 16 Kernel density estimate using Gaussian kernel
G10CAF 16 Compute smoothed data sequence using running median smoothers
G10ZAF 16 Reorder data to give ordered distinct observations

G11 – Contingency Table Analysis


Routine Name
Mark of
Introduction

Purpose
G11AAF 16 χ2  statistics for two-way contingency table
G11BAF 17 Computes multiway table from set of classification factors using selected statistic
G11BBF 17 Computes multiway table from set of classification factors using given percentile/quantile
G11BCF 17 Computes marginal tables for multiway table computed by G11BAF or G11BBF
G11CAF 19 Returns parameter estimates for the conditional analysis of stratified data
G11SAF 12 Contingency table, latent variable model for binary data
G11SBF 12 Frequency count for G11SAF

G12 – Survival Analysis


Routine Name
Mark of
Introduction

Purpose
G12AAF 15 Computes Kaplan–Meier (product-limit) estimates of survival probabilities
G12BAF 17 Fits Cox's proportional hazard model
G12ZAF 19 Creates the risk sets associated with the Cox proportional hazards model for fixed covariates

G13 – Time Series Analysis


Routine Name
Mark of
Introduction

Purpose
G13AAF 9 Univariate time series, seasonal and non-seasonal differencing
G13ABF 9 Univariate time series, sample autocorrelation function
G13ACF 9 Univariate time series, partial autocorrelations from autocorrelations
G13ADF 9 Univariate time series, preliminary estimation, seasonal ARIMA model
G13AEF 9 Univariate time series, estimation, seasonal ARIMA model (comprehensive)
G13AFF 9 Univariate time series, estimation, seasonal ARIMA model (easy-to-use)
G13AGF 9 Univariate time series, update state set for forecasting
G13AHF 9 Univariate time series, forecasting from state set
G13AJF 10 Univariate time series, state set and forecasts, from fully specified seasonal ARIMA model
G13ASF 13 Univariate time series, diagnostic checking of residuals, following G13AEF or G13AFF
G13AUF 14 Computes quantities needed for range-mean or standard deviation-mean plot
G13BAF 10 Multivariate time series, filtering (pre-whitening) by an ARIMA model
G13BBF 11 Multivariate time series, filtering by a transfer function model
G13BCF 10 Multivariate time series, cross-correlations
G13BDF 11 Multivariate time series, preliminary estimation of transfer function model
G13BEF 11 Multivariate time series, estimation of multi-input model
G13BGF 11 Multivariate time series, update state set for forecasting from multi-input model
G13BHF 11 Multivariate time series, forecasting from state set of multi-input model
G13BJF 11 Multivariate time series, state set and forecasts from fully specified multi-input model
G13CAF 10 Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window
G13CBF 10 Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window
G13CCF 10 Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window
G13CDF 10 Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window
G13CEF 10 Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra
G13CFF 10 Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra
G13CGF 10 Multivariate time series, noise spectrum, bounds, impulse response function and its standard error
G13DBF 11 Multivariate time series, multiple squared partial autocorrelations
G13DCF 12 Multivariate time series, estimation of VARMA model
G13DJF 15 Multivariate time series, forecasts and their standard errors
G13DKF 15 Multivariate time series, updates forecasts and their standard errors
G13DLF 15 Multivariate time series, differences and/or transforms
G13DMF 15 Multivariate time series, sample cross-correlation or cross-covariance matrices
G13DNF 15 Multivariate time series, sample partial lag correlation matrices, χ2  statistics and significance levels
G13DPF 16 Multivariate time series, partial autoregression matrices
G13DSF 13 Multivariate time series, diagnostic checking of residuals, following G13DCF
G13DXF 15 Calculates the zeros of a vector autoregressive (or moving average) operator
G13EAF 17 Combined measurement and time update, one iteration of Kalman filter, time-varying, square root covariance filter
G13EBF 17 Combined measurement and time update, one iteration of Kalman filter, time-invariant, square root covariance filter
G13FAF 20 Univariate time series, parameter estimation for either a symmetric GARCH process or a GARCH process with asymmetry of the form (ε t - 1 +γ)2  
G13FBF 20 Univariate time series, forecast function for either a symmetric GARCH process or a GARCH process with asymmetry of the form (ε t - 1 +γ)2  
G13FCF 20 Univariate time series, parameter estimation for a GARCH process with asymmetry of the form (|ε t - 1 |+γε t - 1 )2  
G13FDF 20 Univariate time series, forecast function for a GARCH process with asymmetry of the form (|ε t - 1 |+γε t - 1 )2  
G13FEF 20 Univariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
G13FFF 20 Univariate time series, forecast function for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
G13FGF 20 Univariate time series, parameter estimation for an exponential GARCH (EGARCH) process
G13FHF 20 Univariate time series, forecast function for an exponential GARCH (EGARCH) process

H – Operations Research


Routine Name
Mark of
Introduction

Purpose
H02BBF 14 Integer LP problem (dense)
H02BFF 16 Interpret MPSX data file defining IP or LP problem, optimize and print solution
H02BUF 16 Convert MPSX data file defining IP or LP problem to format required by H02BBF or E04MFF/E04MFA
H02BVF 16 Print IP or LP solutions with user specified names for rows and columns
H02BZF 15 Integer programming solution, supplies further information on solution obtained by H02BBF
H02CBF 19 Integer QP problem (dense)
H02CCF 19 Read optional parameter values for H02CBF from external file
H02CDF 19 Supply optional parameter values to H02CBF
H02CEF 19 Integer LP or QP problem (sparse)
H02CFF 19 Read optional parameter values for H02CEF from external file
H02CGF 19 Supply optional parameter values to H02CEF
H03ABF 4 Transportation problem, modified ‘stepping stone’ method
H03ADF 18 Shortest path problem, Dijkstra's algorithm

M01 – Sorting


Routine Name
Mark of
Introduction

Purpose
M01CAF 12 Sort a vector, real numbers
M01CBF 12 Sort a vector, integer numbers
M01CCF 12 Sort a vector, character data
M01DAF 12 Rank a vector, real numbers
M01DBF 12 Rank a vector, integer numbers
M01DCF 12 Rank a vector, character data
M01DEF 12 Rank rows of a matrix, real numbers
M01DFF 12 Rank rows of a matrix, integer numbers
M01DJF 12 Rank columns of a matrix, real numbers
M01DKF 12 Rank columns of a matrix, integer numbers
M01DZF 12 Rank arbitrary data
M01EAF 12 Rearrange a vector according to given ranks, real numbers
M01EBF 12 Rearrange a vector according to given ranks, integer numbers
M01ECF 12 Rearrange a vector according to given ranks, character data
M01EDF 19 Rearrange a vector according to given ranks, complex numbers
M01ZAF 12 Invert a permutation
M01ZBF 12 Check validity of a permutation
M01ZCF 12 Decompose a permutation into cycles

P01 – Error Trapping


Routine Name
Mark of
Introduction

Purpose
P01ABF 12 Return value of error indicator/terminate with error message

S – Approximations of Special Functions


Routine Name
Mark of
Introduction

Purpose
S01BAF 14 ln(1+x)  
S01EAF 14 Complex exponential, ez  
S07AAF 1 tanx  
S09AAF 1 arcsinx  
S09ABF 3 arccosx  
S10AAF 3 tanhx  
S10ABF 4 sinhx  
S10ACF 4 coshx  
S11AAF 4 arctanhx  
S11ABF 4 arcsinhx  
S11ACF 4 arccoshx  
S13AAF 1 Exponential integral E1 (x)  
S13ACF 2 Cosine integral Ci(x)  
S13ADF 5 Sine integral Si(x)  
S14AAF 1 Gamma function
S14ABF 8 Log Gamma function
S14ACF 14 ψ (x) - lnx  
S14ADF 14 Scaled derivatives of ψ (x)  
S14AEF 20 Polygamma function ψ(n) (x)  for real x  
S14AFF 20 Polygamma function ψ(n) (z)  for complex z  
S14AGF 21 Logarithm of the Gamma function lnΓ (z)  
S14BAF 14 Incomplete Gamma functions P (a,x)  and Q (a,x)  
S15ABF 3 Cumulative Normal distribution function P (x)  
S15ACF 4 Complement of cumulative Normal distribution function Q (x)  
S15ADF 4 Complement of error function erfc(x)  
S15AEF 4 Error function erf(x)  
S15AFF 7 Dawson's integral
S15DDF 14 Scaled complex complement of error function, exp(-z2) erfc(-iz)  
S17ACF 1 Bessel function Y0 (x)  
S17ADF 1 Bessel function Y1 (x)  
S17AEF 5 Bessel function J0 (x)  
S17AFF 5 Bessel function J1 (x)  
S17AGF 8 Airy function Ai(x)  
S17AHF 8 Airy function Bi(x)  
S17AJF 8 Airy function Ai (x)  
S17AKF 8 Airy function Bi (x)  
S17ALF 20 Zeros of Bessel functions Jα (x) , Jα (x) , Yα (x)  or Yα (x)  
S17DCF 13 Bessel functions Y ν + a (z) , real a 0 , complex z , ν = 0 , 1 , 2 ,  
S17DEF 13 Bessel functions J ν + a (z) , real a 0 , complex z , ν = 0 , 1 , 2 ,  
S17DGF 13 Airy functions Ai(z)  and Ai (z) , complex z  
S17DHF 13 Airy functions Bi(z)  and Bi (z) , complex z  
S17DLF 13 Hankel functions H ν + a (j) (z) , j = 1 , 2 , real a 0 , complex z , ν = 0 , 1 , 2 ,  
S18ACF 1 Modified Bessel function K0 (x)  
S18ADF 1 Modified Bessel function K1 (x)  
S18AEF 5 Modified Bessel function I0 (x)  
S18AFF 5 Modified Bessel function I1 (x)  
S18CCF 10 Scaled modified Bessel function ex K0 (x)  
S18CDF 10 Scaled modified Bessel function ex K1 (x)  
S18CEF 10 Scaled modified Bessel function e - |x| I0 (x)  
S18CFF 10 Scaled modified Bessel function e - |x| I1 (x)  
S18DCF 13 Modified Bessel functions K ν + a (z) , real a 0 , complex z , ν = 0 , 1 , 2 ,  
S18DEF 13 Modified Bessel functions I ν + a (z) , real a 0 , complex z , ν = 0 , 1 , 2 ,  
S18GKF 21 Bessel function of the 1st kind J α ± n (z)  
S19AAF 11 Kelvin function berx  
S19ABF 11 Kelvin function beix  
S19ACF 11 Kelvin function kerx  
S19ADF 11 Kelvin function keix  
S20ACF 5 Fresnel integral S (x)  
S20ADF 5 Fresnel integral C (x)  
S21BAF 8 Degenerate symmetrised elliptic integral of 1st kind RC (x,y)  
S21BBF 8 Symmetrised elliptic integral of 1st kind RF (x,y,z)  
S21BCF 8 Symmetrised elliptic integral of 2nd kind RD (x,y,z)  
S21BDF 8 Symmetrised elliptic integral of 3rd kind RJ (x,y,z,r)  
S21CAF 15 Jacobian elliptic functions sn, cn and dn of real argument
S21CBF 20 Jacobian elliptic functions sn, cn and dn of complex argument
S21CCF 20 Jacobian theta functions θk (x,q)  of real argument
S21DAF 20 General elliptic integral of 2nd kind F (z, k ,a,b)  of complex argument
S22AAF 20 Legendre functions of 1st kind Pnm (x)  or Pnm (x)  

X01 – Mathematical Constants


Routine Name
Mark of
Introduction

Purpose
X01AAF 5 Provides the mathematical constant π  
X01ABF 5 Provides the mathematical constant γ  (Euler's Constant)

X02 – Machine Constants


Routine Name
Mark of
Introduction

Purpose
X02AHF 9 The largest permissible argument for sin and cos
X02AJF 12 The machine precision
X02AKF 12 The smallest positive model number
X02ALF 12 The largest positive model number
X02AMF 12 The safe range parameter
X02ANF 15 The safe range parameter for complex floating-point arithmetic
X02BBF 5 The largest representable integer
X02BEF 5 The maximum number of decimal digits that can be represented
X02BHF 12 The floating-point model parameter, b  
X02BJF 12 The floating-point model parameter, p  
X02BKF 12 The floating-point model parameter emin  
X02BLF 12 The floating-point model parameter emax  
X02DAF 8 Switch for taking precautions to avoid underflow
X02DJF 12 The floating-point model parameter ROUNDS

X03 – Inner Products


Routine Name
Mark of
Introduction

Purpose
X03AAF 5 Real inner product added to initial value, basic/additional precision
X03ABF 5 Complex inner product added to initial value, basic/additional precision

X04 – Input/Output Utilities


Routine Name
Mark of
Introduction

Purpose
X04AAF 7 Return or set unit number for error messages
X04ABF 7 Return or set unit number for advisory messages
X04ACF 19 Open unit number for reading, writing or appending, and associate unit with named file
X04ADF 19 Close file associated with given unit number
X04BAF 12 Write formatted record to external file
X04BBF 12 Read formatted record from external file
X04CAF 14 Print real general matrix (easy-to-use)
X04CBF 14 Print real general matrix (comprehensive)
X04CCF 14 Print real packed triangular matrix (easy-to-use)
X04CDF 14 Print real packed triangular matrix (comprehensive)
X04CEF 14 Print real packed banded matrix (easy-to-use)
X04CFF 14 Print real packed banded matrix (comprehensive)
X04DAF 14 Print complex general matrix (easy-to-use)
X04DBF 14 Print complex general matrix (comprehensive)
X04DCF 14 Print complex packed triangular matrix (easy-to-use)
X04DDF 14 Print complex packed triangular matrix (comprehensive)
X04DEF 14 Print complex packed banded matrix (easy-to-use)
X04DFF 14 Print complex packed banded matrix (comprehensive)
X04EAF 14 Print integer matrix (easy-to-use)
X04EBF 14 Print integer matrix (comprehensive)

X05 – Date and Time Utilities


Routine Name
Mark of
Introduction

Purpose
X05AAF 14 Return date and time as an array of integers
X05ABF 14 Convert array of integers representing date and time to character string
X05ACF 14 Compare two character strings representing date and time
X05BAF 14 Return the CPU time

Mark 21 Library Contents (pdf version)
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2006