Mark 22 Library Contents (PDF version)
NAG Library Manual

NAG Library

Mark 22 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
A00ADF 22 Library identification, details of implementation, major and minor marks

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's method
C02AGF 13 All zeros of real polynomial, modified Laguerre's 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, Brent algorithm
C05AGF 8 Zero of continuous function, Brent 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 Brent algorithm (reverse communication)
C05BAF 22 Real values of Lambert's W function, W(x)
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)
C05PBA 22 Solution of system of nonlinear equations using first derivatives (easy-to-use)
C05PBF 9 Solution of system of nonlinear equations using first derivatives (easy-to-use)
C05PCA 22 Solution of system of nonlinear equations using first derivatives (comprehensive)
C05PCF 9 Solution of system of nonlinear equations using first derivatives (comprehensive)
C05PDA 20 Solution of system of nonlinear equations using first derivatives (reverse communication)
C05PDF 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 storage format for Hermitian sequences
C06PCF 19 Single one-dimensional complex discrete Fourier transform, complex data type
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 storage format for Hermitian sequences
C06PQF 19 Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using complex storage format for Hermitian sequences
C06PRF 19 Multiple one-dimensional complex discrete Fourier transforms using complex data type
C06PSF 19 Multiple one-dimensional complex discrete Fourier transforms using complex data type and sequences stored as columns
C06PUF 19 Two-dimensional complex discrete Fourier transform, complex data type
C06PXF 19 Three-dimensional complex discrete Fourier transform, Complex data type
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)

C09 – Wavelet Transforms

Routine
Name
Mark of
Introduction

Purpose
C09AAF 22 Wavelet filter initialization
C09CAF 22 one-dimensional discrete wavelet transform
C09CBF 22 one-dimensional inverse discrete wavelet transform
C09CCF 22 one-dimensional multi-level discrete wavelet transform
C09CDF 22 one-dimensional inverse multi-level discrete wavelet transform

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 8 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 Ordinary differential equations, boundary value problem, shooting and matching technique, allowing interior matching point, general parameters to be determined
D02BGF 7 Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until a component attains given value (simple driver)
D02BHF 7 Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until function of solution is zero (simple driver)
D02BJF
18 Ordinary differential equations, initial value problem, Runge–Kutta method, until function of solution is zero, integration over range with intermediate output (simple driver)
D02CJF
13 Ordinary differential equations, initial value problem, Adams method, until function of solution is zero, intermediate output (simple driver)
D02EJF
12 Ordinary differential equations, stiff initial value problem, backward diffential formulae method, until function of solution is zero, intermediate output (simple driver)
D02GAF
8 Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem
D02GBF
8 Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, general linear problem
D02HAF
8 Ordinary differential equations, boundary value problem, shooting and matching, boundary values to be determined
D02HBF
8 Ordinary differential equations, boundary value problem, shooting and matching, general parameters to be determined
D02JAF
8 Ordinary differential equations, boundary value problem, collocation and least-squares, single nth-order linear equation
D02JBF
8 Ordinary differential equations, 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 ordinary differential equations, initial value problem, Runge–Kutta–Nystrom method
D02LXF 13 Second-order ordinary differential equations, initial value problem, setup for D02LAF
D02LYF 13 Second-order ordinary differential equations, initial value problem, diagnostics for D02LAF
D02LZF 13 Second-order ordinary differential equations, initial value problem, interpolation for D02LAF
D02MCF 22 Implicit ordinary differential equations/DAEs, initial value problem, DASSL method continuation for D02NEF
D02MVF
14 Ordinary differential equations, initial value problem, DASSL method, setup for D02M–N routines
D02MWF 22 Implicit ordinary differential equations/DAEs, initial value problem, setup for D02NEF
D02MZF 14 Ordinary differential equations, initial value problem, interpolation for D02M–N routines, natural interpolant
D02NBF
12 Explicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
D02NCF
12 Explicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
D02NDF
12 Explicit ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
D02NEF 22 Implicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator
D02NGF
12 Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
D02NHF 12 Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
D02NJF
12 Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
D02NMF
12 Explicit ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
D02NNF 12 Implicit/algebraic ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
D02NPF 22 Implicit ordinary differential equations/DAEs, initial value problem linear algebra setup routine for D02NEF
D02NRF 12 Ordinary differential equations, initial value problem, for use with D02M–N routines, sparse Jacobian, enquiry routine
D02NSF 12 Ordinary differential equations, initial value problem, for use with D02M–N routines, full Jacobian, linear algebra set up
D02NTF 12 Ordinary differential equations, initial value problem, for use with D02M–N routines, banded Jacobian, linear algebra set up
D02NUF 12 Ordinary differential equations, initial value problem, for use with D02M–N routines, sparse Jacobian, linear algebra set up
D02NVF 12 Ordinary differential equations, initial value problem, backward diffential formulae method, setup for D02M–N routines
D02NWF 12 Ordinary differential equations, initial value problem, Blend method, setup for D02M–N routines
D02NXF 12 Ordinary differential equations, initial value problem, sparse Jacobian, linear algebra diagnostics, for use with D02M–N routines
D02NYF 12 Ordinary differential equations, initial value problem, integrator diagnostics, for use with D02M–N routines
D02NZF 12 Ordinary differential equations, initial value problem, setup for continuation calls to integrator, for use with D02M–N routines
D02PCF
16 Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output
D02PDF
16 Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step
D02PVF 16 Ordinary differential equations, initial value problem, setup for D02PCF and D02PDF
D02PWF
16 Ordinary differential equations, initial value problem, resets end of range for D02PDF
D02PXF
16 Ordinary differential equations, initial value problem, interpolation for D02PDF
D02PYF 16 Ordinary differential equations, initial value problem, integration diagnostics for D02PCF and D02PDF
D02PZF
16 Ordinary differential equations, initial value problem, error assessment diagnostics for D02PCF and D02PDF
D02QFF 13 Ordinary differential equations, initial value problem, Adams method with root-finding (forward communication, comprehensive)
D02QGF
13 Ordinary differential equations, initial value problem, Adams method with root-finding (reverse communication, comprehensive)
D02QWF 13 Ordinary differential equations, initial value problem, setup for D02QFF and D02QGF
D02QXF 13 Ordinary differential equations, initial value problem, diagnostics for D02QFF and D02QGF
D02QYF 13 Ordinary differential equations, initial value problem, root-finding diagnostics for D02QFF and D02QGF
D02QZF
13 Ordinary differential equations, initial value problem, interpolation for D02QFF or D02QGF
D02RAF
8 Ordinary differential equations, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility
D02SAF
8 Ordinary differential equations, boundary value problem, shooting and matching technique, subject to extra algebraic equations, general parameters to be determined
D02TGF
8 nth-order linear ordinary differential equations, boundary value problem, collocation and least-squares
D02TKF
17 Ordinary differential equations, general nonlinear boundary value problem, collocation technique
D02TVF
17 Ordinary differential equations, general nonlinear boundary value problem, setup for D02TKF
D02TXF
17 Ordinary differential equations, general nonlinear boundary value problem, continuation facility for D02TKF
D02TYF
17 Ordinary differential equations, general nonlinear boundary value problem, interpolation for D02TKF
D02TZF
17 Ordinary differential equations, general nonlinear boundary value problem, diagnostics for D02TKF
D02XJF 12 Ordinary differential equations, initial value problem, interpolation for D02M–N routines, natural interpolant
D02XKF 12 Ordinary differential equations, initial value problem, interpolation for D02M–N routines, C1 interpolant
D02ZAF 12 Ordinary differential equations, initial value problem, 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 coordinates
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
D03PCA 20 General system of parabolic PDEs, method of lines, finite differences, one space variable
D03PCF
15 General system of parabolic PDEs, method of lines, finite differences, one space variable
D03PDA 20 General system of parabolic PDEs, method of lines, Chebyshev C0 collocation, one space variable
D03PDF
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
D03PHA 20 General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable
D03PHF
15 General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable
D03PJA 20 General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C0 collocation, one space variable
D03PJF
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
D03PPA 20 General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable
D03PPF
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 parallel to one independent coordinate axis
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
E04ABA 20 Minimum, function of one variable using function values only
E04ABF 6 Minimum, function of one variable using function values only
E04BBA 20 Minimum, function of one variable, using first derivative
E04BBF 6 Minimum, function of one variable, using first derivative
E04CBF
22 Unconstrained minimization using simplex algorithm, function of several variables using function values only
E04CCA 20 Unconstrained minimum, simplex algorithm, function of several variables using function values only (comprehensive)
E04CCF 1 Unconstrained minimum, simplex algorithm, function of several variables using function values only (comprehensive)
E04DGA 20 Unconstrained minimum, preconditioned conjugate gradient algorithm, function of several variables using first derivatives (comprehensive)
E04DGF 12 Unconstrained minimum, preconditioned conjugate gradient algorithm, function of several variables using first derivatives (comprehensive)
E04DJA 20 Supply optional parameter values for E04DGF/E04DGA from external file
E04DJF 12 Supply optional parameter values for E04DGF/E04DGA from external file
E04DKA 20 Supply optional parameter values to E04DGF/E04DGA
E04DKF 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)
E04MFA 20 LP problem (dense)
E04MFF 16 LP problem (dense)
E04MGA 20 Supply optional parameter values for E04MFF/E04MFA from external file
E04MGF 16 Supply optional parameter values for E04MFF/E04MFA from external file
E04MHA 20 Supply optional parameter values to E04MFF/E04MFA
E04MHF 16 Supply optional parameter values to E04MFF/E04MFA
E04MZF 18 Converts MPSX data file defining LP or QP problem to format required by E04NKF/E04NKA
E04NCA 20 Convex QP problem or linearly-constrained linear least-squares problem (dense)
E04NCF 12 Convex QP problem or linearly-constrained linear least-squares problem (dense)
E04NDA 20 Supply optional parameter values for E04NCF/E04NCA from external file
E04NDF 12 Supply optional parameter values for E04NCF/E04NCA from external file
E04NEA 20 Supply optional parameter values to E04NCF/E04NCA
E04NEF 12 Supply optional parameter values to E04NCF/E04NCA
E04NFA 20 QP problem (dense)
E04NFF 16 QP problem (dense)
E04NGA 20 Supply optional parameter values for E04NFF/E04NFA from external file
E04NGF 16 Supply optional parameter values for E04NFF/E04NFA from external file
E04NHA 20 Supply optional parameter values to E04NFF/E04NFA
E04NHF 16 Supply optional parameter values to E04NFF/E04NFA
E04NKA 20 LP or QP problem (sparse)
E04NKF 18 LP or QP problem (sparse)
E04NLA 20 Supply optional parameter values for E04NKF/E04NKA from external file
E04NLF 18 Supply optional parameter values for E04NKF/E04NKA from external file
E04NMA 20 Supply optional parameter values to E04NKF/E04NKA
E04NMF 18 Supply optional parameter values to E04NKF/E04NKA
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 real argument
E04NXF 21 Get the setting of an integer valued option of E04NQF
E04NYF 21 Get the setting of a real valued option of E04NQF
E04UCA 20 Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (comprehensive)
E04UCF 12 Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (comprehensive)
E04UDA 20 Supply optional parameter values for E04UCF/E04UCA or E04UFF/E04UFA from external file
E04UDF 12 Supply optional parameter values for E04UCF/E04UCA or E04UFF/E04UFA from external file
E04UEA 20 Supply optional parameter values to E04UCF/E04UCA or E04UFF/E04UFA
E04UEF 12 Supply optional parameter values to E04UCF/E04UCA or E04UFF/E04UFA
E04UFA 20 Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (reverse communication, comprehensive)
E04UFF 18 Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (reverse communication, comprehensive)
E04UGA 20 NLP problem (sparse)
E04UGF 19 NLP problem (sparse)
E04UHA 20 Supply optional parameter values for E04UGF/E04UGA from external file
E04UHF 19 Supply optional parameter values for E04UGF/E04UGA from external file
E04UJA 20 Supply optional parameter values to E04UGF/E04UGA
E04UJF 19 Supply optional parameter values to E04UGF/E04UGA
E04UQA 20 Supply optional parameter values for E04USF/E04USA from external file
E04UQF 14 Supply optional parameter values for E04USF/E04USA from external file
E04URA 20 Supply optional parameter values to E04USF/E04USA
E04URF 14 Supply optional parameter values to E04USF/E04USA
E04USA 20 Minimum of a sum of squares, nonlinear constraints, sequential QP method, using function values and optionally first derivatives (comprehensive)
E04USF 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 real argument
E04VRF 21 Get the setting of an integer valued option of E04VHF
E04VSF 21 Get the setting of a real valued option of E04VHF
E04WBF 20 Initialization routine for E04DGA, E04MFA, E04NCA, E04NFA, E04UFA, E04UGA and 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 real argument
E04WKF 21 Get the setting of an integer valued option of E04WDF
E04WLF 21 Get the setting of a real valued option of E04WDF
E04XAA 20 Estimate (using numerical differentiation) gradient and/or Hessian of a function
E04XAF 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)
E04ZCA 20 Check user's routines for calculating first derivatives of function and constraints
E04ZCF 11 Check user's routines for calculating first derivatives of function and constraints

E05 – Global Optimization of a Function

Routine
Name
Mark of
Introduction

Purpose
E05JAF 22 Initialization routine for E05JBF
E05JBF
22 Global optimization by multi-level coordinate search, simple bounds, using function values only
E05JCF
22 Supply optional parameter values for E05JBF from external file
E05JDF 22 Set a single optional parameter for E05JBF from a character string
E05JEF 22 Set a single optional parameter for E05JBF from an ‘ON’/‘OFF’-valued character argument
E05JFF 22 Set a single optional parameter for E05JBF from an integer argument
E05JGF 22 Set a single optional parameter for E05JBF from a real argument
E05JHF 22 Determine whether an optional parameter for E05JBF has been set by you or not
E05JJF 22 Get the setting of an ‘ON’/‘OFF’-valued character optional parameter of E05JBF
E05JKF 22 Get the setting of an Integer valued optional parameter of E05JBF
E05JLF 22 Get the setting of a real valued optional parameter of E05JBF

F – Linear Algebra

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 realm by n matrix (mn)
F01BRF 7 LU factorization of real sparse matrix
F01BSF 7 LU factorization of real sparse matrix with known sparsity pattern
F01BUF 7 ULDLTUT 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
F01ECF 22 Real matrix exponential
F01LEF 11 LU factorization of real tridiagonal matrix
F01LHF 13 LU factorization of real almost block diagonal matrix
F01MCF 8 LDLT factorization of real symmetric positive-definite variable-bandwidth matrix
F01QGF 14 RQ factorization of realm by n upper trapezoidal matrix (mn)
F01QJF 14 RQ factorization of realm by n matrix (mn)
F01QKF 14 Operations with orthogonal matrices, form rows of Q, after RQ factorization by F01QJF
F01RGF 14 RQ factorization of complex m by n upper trapezoidal matrix (mn)
F01RJF 14 RQ factorization of complex m by n matrix (mn)
F01RKF 14 Operations with unitary matrices, form rows of Q, after RQ 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
F02BJF 6 Computes all eigenvalues and, optionally, eigenvectors of generalized eigenproblem by QZ algorithm, real matrices (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F02EAF 16 All eigenvalues and Schur factorization of real general matrix (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F02EBF 16 All eigenvalues and eigenvectors of real general matrix (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F02ECF 17 Selected eigenvalues and eigenvectors of real nonsymmetric matrix (Black Box)
F02FAF 16 Computes all eigenvalues and, optionally, eigenvectors of real symmetric matrix (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F02FCF 17 Selected eigenvalues and optionally eigenvectors of real symmetric matrix (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F02FDF 16 All eigenvalues and eigenvectors of real symmetric-definite generalized problem (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F02FHF 11 All eigenvalues of generalized banded real symmetric-definite eigenproblem (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F02FJF 11 Selected eigenvalues and eigenvectors of sparse symmetric eigenproblem (Black Box)
F02GAF 16 All eigenvalues and Schur factorization of complex general matrix (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F02GBF 16 Computes all eigenvalues and, optionally, eigenvectors of complex general matrix (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F02GCF 17 Selected eigenvalues and eigenvectors of complex nonsymmetric matrix (Black Box)
F02GJF 8 Computes all eigenvalues and, optionally, eigenvectors of generalized complex eigenproblem by QZ algorithm (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F02HAF 16 All eigenvalues and eigenvectors of complex Hermitian matrix (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F02HCF 17 Selected eigenvalues and eigenvectors of complex Hermitian matrix (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F02HDF 16 All eigenvalues and eigenvectors of complex Hermitian-definite generalized problem (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F02SDF 8 Eigenvector of generalized real banded eigenproblem by inverse iteration
F02WDF 8 QR factorization, possibly followed by SVD
F02WEF 13 SVD of real matrix (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F02WGF 22 Computes leading terms in the singular value decomposition of a real general matrix; also computes corresponding left and right singular vectors
F02WUF 14 SVD of real upper triangular matrix (Black Box)
F02XEF 13 SVD of complex matrix (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
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 LLT factorization and determinant of real symmetric positive-definite matrix
F03AFF 2 LU factorization and determinant of real matrix

F04 – Simultaneous Linear Equations

Routine
Name
Mark of
Introduction

Purpose
F04AAF 2 Solution of real simultaneous linear equations with multiple right-hand sides (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F04ABF 2 Solution of real symmetric positive-definite simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box)
F04ACF 2 Solution of real symmetric positive-definite banded simultaneous linear equations with multiple right-hand sides (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F04ADF 2 Solution of complex simultaneous linear equations with multiple right-hand sides (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
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 mreal equations in n unknowns, rank = n, mn using iterative refinement (Black Box)
F04ARF 4 Solution of real simultaneous linear equations, one right-hand side (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
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.
F04EAF 11 Solution of real tridiagonal simultaneous linear equations, one right-hand side (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F04FAF 11 Solution of real symmetric positive-definite tridiagonal simultaneous linear equations, one right-hand side (Black Box)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
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
F04JAF 8 Minimal least-squares solution of mreal equations in n unknowns, rank n, mn
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F04JDF 8 Minimal least-squares solution of mreal equations in n unknowns, rank m, mn
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F04JGF 8 Least-squares (if rank = n) or minimal least-squares (if rank < n) solution of mreal equations in n unknowns, mn
F04JLF 17 Real general Gauss–Markov linear model (including weighted least-squares)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F04JMF 17 Equality-constrained real linear least-squares problem
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F04KLF 17 Complex general Gauss–Markov linear model (including weighted least-squares)
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
F04KMF 17 Equality-constrained complex linear least-squares problem
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
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, mreal equations in n unknowns
F04YAF 11 Covariance matrix for linear least-squares problems, mreal 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 12 DROTG
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), reala 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 12 DDOT
Dot product of two real vectors
F06ECF 12 DAXPY
Add scalar times real vector to real vector
F06EDF 12 DSCAL
Multiply real vector by scalar
F06EFF 12 DCOPY
Copy real vector
F06EGF 12 DSWAP
Swap two real vectors
F06EJF 12 DNRM2
Compute Euclidean norm of real vector
F06EKF 12 DASUM
Sum absolute values of real vector elements
F06EPF 12 DROT
Apply real plane rotation
F06ERF 14 DDOTI
Dot product of two real sparse vectors
F06ETF 14 DAXPYI
Add scalar times real sparse vector to real sparse vector
F06EUF 14 DGTHR
Gather real sparse vector
F06EVF 14 DGTHRZ
Gather and set to zero real sparse vector
F06EWF 14 DSCTR
Scatter real sparse vector
F06EXF 14 DROTI
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 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 12 ZDOTU
Dot product of two complex vectors, unconjugated
F06GBF 12 ZDOTC
Dot product of two complex vectors, conjugated
F06GCF 12 ZAXPY
Add scalar times complex vector to complex vector
F06GDF 12 ZSCAL
Multiply complex vector by complex scalar
F06GFF 12 ZCOPY
Copy complex vector
F06GGF 12 ZSWAP
Swap two complex vectors
F06GRF 14 ZDOTUI
Dot product of two complex sparse vector, unconjugated
F06GSF 14 ZDOTCI
Dot product of two complex sparse vector, conjugated
F06GTF 14 ZAXPYI
Add scalar times complex sparse vector to complex sparse vector
F06GUF 14 ZGTHR
Gather complex sparse vector
F06GVF 14 ZGTHRZ
Gather and set to zero complex sparse vector
F06GWF 14 ZSCTR
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
F06HMF 21 ZROT
Apply plane rotation with real cosine and complex sine
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 12 ZDSCAL
Multiply complex vector by real scalar
F06JJF 12 DZNRM2
Compute Euclidean norm of complex vector
F06JKF 12 DZASUM
Sum absolute values of complex vector elements
F06JLF 12 IDAMAX
Index, real vector element with largest absolute value
F06JMF 12 IZAMAX
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 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 12 DGEMV
Matrix-vector product, real rectangular matrix
F06PBF 12 DGBMV
Matrix-vector product, real rectangular band matrix
F06PCF 12 DSYMV
Matrix-vector product, real symmetric matrix
F06PDF 12 DSBMV
Matrix-vector product, real symmetric band matrix
F06PEF 12 DSPMV
Matrix-vector product, real symmetric packed matrix
F06PFF 12 DTRMV
Matrix-vector product, real triangular matrix
F06PGF 12 DTBMV
Matrix-vector product, real triangular band matrix
F06PHF 12 DTPMV
Matrix-vector product, real triangular packed matrix
F06PJF 12 DTRSV
System of equations, real triangular matrix
F06PKF 12 DTBSV
System of equations, real triangular band matrix
F06PLF 12 DTPSV
System of equations, real triangular packed matrix
F06PMF 12 DGER
Rank-1 update, real rectangular matrix
F06PPF 12 DSYR
Rank-1 update, real symmetric matrix
F06PQF 12 DSPR
Rank-1 update, real symmetric packed matrix
F06PRF 12 DSYR2
Rank-2 update, real symmetric matrix
F06PSF 12 DSPR2
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 QR factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix
F06QQF 13 QR factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row
F06QRF 13 QR or RQ factorization by sequence of plane rotations, real upper Hessenberg matrix
F06QSF 13 QR or RQ factorization by sequence of plane rotations, real upper spiked matrix
F06QTF 13 QR factorization of UP or RQ factorization of PU, Ureal upper triangular, P 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 12 ZGEMV
Matrix-vector product, complex rectangular matrix
F06SBF 12 ZGBMV
Matrix-vector product, complex rectangular band matrix
F06SCF 12 ZHEMV
Matrix-vector product, complex Hermitian matrix
F06SDF 12 ZHBMV
Matrix-vector product, complex Hermitian band matrix
F06SEF 12 ZHPMV
Matrix-vector product, complex Hermitian packed matrix
F06SFF 12 ZTRMV
Matrix-vector product, complex triangular matrix
F06SGF 12 ZTBMV
Matrix-vector product, complex triangular band matrix
F06SHF 12 ZTPMV
Matrix-vector product, complex triangular packed matrix
F06SJF 12 ZTRSV
System of equations, complex triangular matrix
F06SKF 12 ZTBSV
System of equations, complex triangular band matrix
F06SLF 12 ZTPSV
System of equations, complex triangular packed matrix
F06SMF 12 ZGERU
Rank-1 update, complex rectangular matrix, unconjugated vector
F06SNF 12 ZGERC
Rank-1 update, complex rectangular matrix, conjugated vector
F06SPF 12 ZHER
Rank-1 update, complex Hermitian matrix
F06SQF 12 ZHPR
Rank-1 update, complex Hermitian packed matrix
F06SRF 12 ZHER2
Rank-2 update, complex Hermitian matrix
F06SSF 12 ZHPR2
Rank-2 update, complex Hermitian packed matrix
F06TAF 21 Matrix-vector product, complex symmetric matrix
F06TBF 21 Rank-1 update, complex symmetric matrix
F06TCF 21 Matrix-vector product, complex symmetric packed matrix
F06TDF 21 Rank-1 update, complex symmetric 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 QR factorization by sequence of plane rotations, rank-1 update of complex upper triangular matrix
F06TQF 13 QR × k factorization by sequence of plane rotations, complex upper triangular matrix augmented by a full row
F06TRF 13 QR or RQ factorization by sequence of plane rotations, complex upper Hessenberg matrix
F06TSF 13 QR or RQ factorization by sequence of plane rotations, complex upper spiked matrix
F06TTF 13 QR factorization of UP or RQ factorization of PU, U complex upper triangular, P 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 14 DGEMM
Matrix-matrix product, two real rectangular matrices
F06YCF 14 DSYMM
Matrix-matrix product, one real symmetric matrix, one real rectangular matrix
F06YFF 14 DTRMM
Matrix-matrix product, one real triangular matrix, one real rectangular matrix
F06YJF 14 DTRSM
Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix
F06YPF 14 DSYRK
Rank-k update of a real symmetric matrix
F06YRF 14 DSYR2K
Rank-2k update of a real symmetric matrix
F06ZAF 14 ZGEMM
Matrix-matrix product, two complex rectangular matrices
F06ZCF 14 ZHEMM
Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix
F06ZFF 14 ZTRMM
Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix
F06ZJF 14 ZTRSM
Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix
F06ZPF 14 ZHERK
Rank-k update of a complex Hermitian matrix
F06ZRF 14 ZHER2K
Rank-2k update of a complex Hermitian matrix
F06ZTF 14 ZSYMM
Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix
F06ZUF 14 ZSYRK
Rank-k update of a complex symmetric matrix
F06ZWF 14 ZSYR2K
Rank-2k update of a complex symmetric matrix

F07 – Linear Equations (LAPACK)

Routine
Name
Mark of
Introduction

Purpose
F07AAF 21 DGESV
Computes the solution to a real system of linear equations
F07ABF 21 DGESVX
Uses the LU factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
F07ACF 22 DSGESV
Mixed precision real system solver
F07ADF 15 DGETRF
LU factorization of realm by n matrix
F07AEF 15 DGETRS
Solution of real system of linear equations, multiple right-hand sides, matrix already factorized by F07ADF (DGETRF)
F07AFF 21 DGEEQU
Computes row and column scalings intended to equilibrate a general real matrix and reduce its condition number
F07AGF 15 DGECON
Estimate condition number of real matrix, matrix already factorized by F07ADF (DGETRF)
F07AHF 15 DGERFS
Refined solution with error bounds of real system of linear equations, multiple right-hand sides
F07AJF 15 DGETRI
Inverse of real matrix, matrix already factorized by F07ADF (DGETRF)
F07ANF 21 ZGESV
Computes the solution to a complex system of linear equations
F07APF 21 ZGESVX
Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
F07AQF 22 ZCGESV
Mixed precision complex system solver
F07ARF 15 ZGETRF
LU factorization of complex m by n matrix
F07ASF 15 ZGETRS
Solution of complex system of linear equations, multiple right-hand sides, matrix already factorized by F07ARF (ZGETRF)
F07ATF 21 ZGEEQU
Computes row and column scalings intended to equilibrate a general complex matrix and reduce its condition number
F07AUF 15 ZGECON
Estimate condition number of complex matrix, matrix already factorized by F07ARF (ZGETRF)
F07AVF 15 ZGERFS
Refined solution with error bounds of complex system of linear equations, multiple right-hand sides
F07AWF 15 ZGETRI
Inverse of complex matrix, matrix already factorized by F07ARF (ZGETRF)
F07BAF 21 DGBSV
Computes the solution to a real banded system of linear equations
F07BBF 21 DGBSVX
Uses the LU factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations
F07BDF 15 DGBTRF
LU factorization of realm by n band matrix
F07BEF 15 DGBTRS
Solution of real band system of linear equations, multiple right-hand sides, matrix already factorized by F07BDF (DGBTRF)
F07BFF 21 DGBEQU
Computes row and column scalings intended to equilibrate a real banded matrix and reduce its condition number
F07BGF 15 DGBCON
Estimate condition number of real band matrix, matrix already factorized by F07BDF (DGBTRF)
F07BHF 15 DGBRFS
Refined solution with error bounds of real band system of linear equations, multiple right-hand sides
F07BNF 21 ZGBSV
Computes the solution to a complex banded system of linear equations
F07BPF 21 ZGBSVX
Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations
F07BRF 15 ZGBTRF
LU factorization of complex m by n band matrix
F07BSF 15 ZGBTRS
Solution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by F07BRF (ZGBTRF)
F07BTF 21 ZGBEQU
Computes row and column scalings intended to equilibrate a complex banded matrix and reduce its condition number
F07BUF 15 ZGBCON
Estimate condition number of complex band matrix, matrix already factorized by F07BRF (ZGBTRF)
F07BVF 15 ZGBRFS
Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides
F07CAF 21 DGTSV
Computes the solution to a real tridiagonal system of linear equations
F07CBF 21 DGTSVX
Uses the LU factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations
F07CDF 21 DGTTRF
LU factorization of real tridiagonal matrix
F07CEF 21 DGTTRS
Solves a real tridiagonal system of linear equations using the LU factorization computed by F07CDF (DGTTRF)
F07CGF 21 DGTCON
Estimates the reciprocal of the condition number of a real tridiagonal matrix using the LU factorization computed by F07CDF (DGTTRF)
F07CHF 21 DGTRFS
Refined solution with error bounds of real tridiagonal system of linear equations, multiple right-hand sides
F07CNF 21 ZGTSV
Computes the solution to a complex tridiagonal system of linear equations
F07CPF 21 ZGTSVX
Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex tridiagonal system of linear equations
F07CRF 21 ZGTTRF
LU factorization of complex tridiagonal matrix
F07CSF 21 ZGTTRS
Solves a complex tridiagonal system of linear equations using the LU factorization computed by F07CDF (DGTTRF)
F07CUF 21 ZGTCON
Estimates the reciprocal of the condition number of a complex tridiagonal matrix using the LU factorization computed by F07CDF (DGTTRF)
F07CVF 21 ZGTRFS
Refined solution with error bounds of complex tridiagonal system of linear equations, multiple right-hand sides
F07FAF 21 DPOSV
Computes the solution to a real symmetric positive-definite system of linear equations
F07FBF 21 DPOSVX
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite system of linear equations
F07FDF 15 DPOTRF
Cholesky factorization of real symmetric positive-definite matrix
F07FEF 15 DPOTRS
Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FDF (DPOTRF)
F07FFF 21 DPOEQU
Computes row and column scalings intended to equilibrate a real symmetric positive-definite matrix and reduce its condition number
F07FGF 15 DPOCON
Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by F07FDF (DPOTRF)
F07FHF 15 DPORFS
Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides
F07FJF 15 DPOTRI
Inverse of real symmetric positive-definite matrix, matrix already factorized by F07FDF (DPOTRF)
F07FNF 21 ZPOSV
Computes the solution to a complex Hermitian positive-definite system of linear equations
F07FPF 21 ZPOSVX
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite system of linear equations
F07FRF 15 ZPOTRF
Cholesky factorization of complex Hermitian positive-definite matrix
F07FSF 15 ZPOTRS
Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FRF (ZPOTRF)
F07FTF 21 ZPOEQU
Computes row and column scalings intended to equilibrate a complex Hermitian positive-definite matrix and reduce its condition number
F07FUF 15 ZPOCON
Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by F07FRF (ZPOTRF)
F07FVF 15 ZPORFS
Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides
F07FWF 15 ZPOTRI
Inverse of complex Hermitian positive-definite matrix, matrix already factorized by F07FRF (ZPOTRF)
F07GAF 21 DPPSV
Computes the solution to a real symmetric positive-definite system of linear equations, packed storage
F07GBF 21 DPPSVX
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite system of linear equations, packed storage
F07GDF 15 DPPTRF
Cholesky factorization of real symmetric positive-definite matrix, packed storage
F07GEF 15 DPPTRS
Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GDF (DPPTRF), packed storage
F07GFF 21 DPPEQU
Computes row and column scalings intended to equilibrate a real symmetric positive-definite matrix and reduce its condition number, packed storage
F07GGF 15 DPPCON
Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by F07GDF (DPPTRF), packed storage
F07GHF 15 DPPRFS
Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides, packed storage
F07GJF 15 DPPTRI
Inverse of real symmetric positive-definite matrix, matrix already factorized by F07GDF (DPPTRF), packed storage
F07GNF 21 ZPPSV
Computes the solution to a complex Hermitian positive-definite system of linear equations, packed storage
F07GPF 21 ZPPSVX
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite system of linear equations, packed storage
F07GRF 15 ZPPTRF
Cholesky factorization of complex Hermitian positive-definite matrix, packed storage
F07GSF 15 ZPPTRS
Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GRF (ZPPTRF), packed storage
F07GTF 21 ZPPEQU
Computes row and column scalings intended to equilibrate a complex Hermitian positive-definite matrix and reduce its condition number, packed storage
F07GUF 15 ZPPCON
Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by F07GRF (ZPPTRF), packed storage
F07GVF 15 ZPPRFS
Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, packed storage
F07GWF 15 ZPPTRI
Inverse of complex Hermitian positive-definite matrix, matrix already factorized by F07GRF (ZPPTRF), packed storage
F07HAF 21 DPBSV
Computes the solution to a real symmetric positive-definite banded system of linear equations
F07HBF 21 DPBSVX
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite banded system of linear equations
F07HDF 15 DPBTRF
Cholesky factorization of real symmetric positive-definite band matrix
F07HEF 15 DPBTRS
Solution of real symmetric positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HDF (DPBTRF)
F07HFF 21 DPBEQU
Computes row and column scalings intended to equilibrate a real symmetric positive-definite banded matrix and reduce its condition number
F07HGF 15 DPBCON
Estimate condition number of real symmetric positive-definite band matrix, matrix already factorized by F07HDF (DPBTRF)
F07HHF 15 DPBRFS
Refined solution with error bounds of real symmetric positive-definite band system of linear equations, multiple right-hand sides
F07HNF 21 ZPBSV
Computes the solution to a complex Hermitian positive-definite banded system of linear equations
F07HPF 21 ZPBSVX
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite banded system of linear equations
F07HRF 15 ZPBTRF
Cholesky factorization of complex Hermitian positive-definite band matrix
F07HSF 15 ZPBTRS
Solution of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HRF (ZPBTRF)
F07HTF 21 ZPBEQU
Computes row and column scalings intended to equilibrate a complex Hermitian positive-definite banded matrix and reduce its condition number
F07HUF 15 ZPBCON
Estimate condition number of complex Hermitian positive-definite band matrix, matrix already factorized by F07HRF (ZPBTRF)
F07HVF 15 ZPBRFS
Refined solution with error bounds of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides
F07JAF 21 DPTSV
Computes the solution to a real symmetric positive-definite tridiagonal system of linear equations
F07JBF 21 DPTSVX
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 21 DPTTRF
Computes the modified Cholesky factorization of a real symmetric positive-definite tridiagonal matrix
F07JEF 21 DPTTRS
Solves a real symmetric positive-definite tridiagonal system using the modified Cholesky factorization computed by F07JDF (DPTTRF)
F07JGF 21 DPTCON
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 21 DPTRFS
Refined solution with error bounds of real symmetric positive-definite tridiagonal system of linear equations, multiple right-hand sides
F07JNF 21 ZPTSV
Computes the solution to a complex Hermitian positive-definite tridiagonal system of linear equations
F07JPF 21 ZPTSVX
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 21 ZPTTRF
Computes the modified Cholesky factorization of a complex Hermitian positive-definite tridiagonal matrix
F07JSF 21 ZPTTRS
Solves a complex Hermitian positive-definite tridiagonal system using the modified Cholesky factorization computed by F07JRF (ZPTTRF)
F07JUF 21 ZPTCON
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 21 ZPTRFS
Refined solution with error bounds of complex Hermitian positive-definite tridiagonal system of linear equations, multiple right-hand sides
F07MAF 21 DSYSV
Computes the solution to a real symmetric system of linear equations
F07MBF 21 DSYSVX
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations
F07MDF 15 DSYTRF
Bunch–Kaufman factorization of real symmetric indefinite matrix
F07MEF 15 DSYTRS
Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MDF (DSYTRF)
F07MGF 15 DSYCON
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07MDF (DSYTRF)
F07MHF 15 DSYRFS
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides
F07MJF 15 DSYTRI
Inverse of real symmetric indefinite matrix, matrix already factorized by F07MDF (DSYTRF)
F07MNF 21 ZHESV
Computes the solution to a complex Hermitian system of linear equations
F07MPF 21 ZHESVX
Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations
F07MRF 15 ZHETRF
Bunch–Kaufman factorization of complex Hermitian indefinite matrix
F07MSF 15 ZHETRS
Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MRF (ZHETRF)
F07MUF 15 ZHECON
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07MRF (ZHETRF)
F07MVF 15 ZHERFS
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides
F07MWF 15 ZHETRI
Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07MRF (ZHETRF)
F07NNF 21 ZSYSV
Computes the solution to a complex symmetric system of linear equations
F07NPF 21 ZSYSVX
Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations
F07NRF 15 ZSYTRF
Bunch–Kaufman factorization of complex symmetric matrix
F07NSF 15 ZSYTRS
Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07NRF (ZSYTRF)
F07NUF 15 ZSYCON
Estimate condition number of complex symmetric matrix, matrix already factorized by F07NRF (ZSYTRF)
F07NVF 15 ZSYRFS
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides
F07NWF 15 ZSYTRI
Inverse of complex symmetric matrix, matrix already factorized by F07NRF (ZSYTRF)
F07PAF 21 DSPSV
Computes the solution to a real symmetric system of linear equations, packed storage
F07PBF 21 DSPSVX
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage
F07PDF 15 DSPTRF
Bunch–Kaufman factorization of real symmetric indefinite matrix, packed storage
F07PEF 15 DSPTRS
Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PDF (DSPTRF), packed storage
F07PGF 15 DSPCON
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07PDF (DSPTRF), packed storage
F07PHF 15 DSPRFS
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage
F07PJF 15 DSPTRI
Inverse of real symmetric indefinite matrix, matrix already factorized by F07PDF (DSPTRF), packed storage
F07PNF 21 ZHPSV
Computes the solution to a complex Hermitian system of linear equations, packed storage
F07PPF 21 ZHPSVX
Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations, packed storage
F07PRF 15 ZHPTRF
Bunch–Kaufman factorization of complex Hermitian indefinite matrix, packed storage
F07PSF 15 ZHPTRS
Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PRF (ZHPTRF), packed storage
F07PUF 15 ZHPCON
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07PRF (ZHPTRF), packed storage
F07PVF 15 ZHPRFS
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage
F07PWF 15 ZHPTRI
Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07PRF (ZHPTRF), packed storage
F07QNF 21 ZSPSV
Computes the solution to a complex symmetric system of linear equations, packed storage
F07QPF 21 ZSPSVX
Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations, packed storage
F07QRF 15 ZSPTRF
Bunch–Kaufman factorization of complex symmetric matrix, packed storage
F07QSF 15 ZSPTRS
Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07QRF (ZSPTRF), packed storage
F07QUF 15 ZSPCON
Estimate condition number of complex symmetric matrix, matrix already factorized by F07QRF (ZSPTRF), packed storage
F07QVF 15 ZSPRFS
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage
F07QWF 15 ZSPTRI
Inverse of complex symmetric matrix, matrix already factorized by F07QRF (ZSPTRF), packed storage
F07TEF 15 DTRTRS
Solution of real triangular system of linear equations, multiple right-hand sides
F07TGF 15 DTRCON
Estimate condition number of real triangular matrix
F07THF 15 DTRRFS
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides
F07TJF 15 DTRTRI
Inverse of real triangular matrix
F07TSF 15 ZTRTRS
Solution of complex triangular system of linear equations, multiple right-hand sides
F07TUF 15 ZTRCON
Estimate condition number of complex triangular matrix
F07TVF 15 ZTRRFS
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides
F07TWF 15 ZTRTRI
Inverse of complex triangular matrix
F07UEF 15 DTPTRS
Solution of real triangular system of linear equations, multiple right-hand sides, packed storage
F07UGF 15 DTPCON
Estimate condition number of real triangular matrix, packed storage
F07UHF 15 DTPRFS
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage
F07UJF 15 DTPTRI
Inverse of real triangular matrix, packed storage
F07USF 15 ZTPTRS
Solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
F07UUF 15 ZTPCON
Estimate condition number of complex triangular matrix, packed storage
F07UVF 15 ZTPRFS
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
F07UWF 15 ZTPTRI
Inverse of complex triangular matrix, packed storage
F07VEF 15 DTBTRS
Solution of real band triangular system of linear equations, multiple right-hand sides
F07VGF 15 DTBCON
Estimate condition number of real band triangular matrix
F07VHF 15 DTBRFS
Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides
F07VSF 15 ZTBTRS
Solution of complex band triangular system of linear equations, multiple right-hand sides
F07VUF 15 ZTBCON
Estimate condition number of complex band triangular matrix
F07VVF 15 ZTBRFS
Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides

F08 – Least-squares and Eigenvalue Problems (LAPACK)

Routine
Name
Mark of
Introduction

Purpose
F08AAF 21 DGELS
Solves an overdetermined or underdetermined real linear system
F08AEF 16 DGEQRF
QR factorization of real general rectangular matrix
F08AFF 16 DORGQR
Form all or part of orthogonal Q from QR factorization determined by F08AEF (DGEQRF) or F08BEF (DGEQPF)
F08AGF 16 DORMQR
Apply orthogonal transformation determined by F08AEF (DGEQRF) or F08BEF (DGEQPF)
F08AHF 16 DGELQF
LQ factorization of real general rectangular matrix
F08AJF 16 DORGLQ
Form all or part of orthogonal Q from LQ factorization determined by F08AHF (DGELQF)
F08AKF 16 DORMLQ
Apply orthogonal transformation determined by F08AHF (DGELQF)
F08ANF 21 ZGELS
Solves an overdetermined or underdetermined complex linear system
F08ASF 16 ZGEQRF
QR factorization of complex general rectangular matrix
F08ATF 16 ZUNGQR
Form all or part of unitary Q from QR factorization determined by F08ASF (ZGEQRF) or F08BSF (ZGEQPF)
F08AUF 16 ZUNMQR
Apply unitary transformation determined by F08ASF (ZGEQRF) or F08BSF (ZGEQPF)
F08AVF 16 ZGELQF
LQ factorization of complex general rectangular matrix
F08AWF 16 ZUNGLQ
Form all or part of unitary Q from LQ factorization determined by F08AVF (ZGELQF)
F08AXF 16 ZUNMLQ
Apply unitary transformation determined by F08AVF (ZGELQF)
F08BAF 21 DGELSY
Computes the minimum-norm solution to a real linear least-squares problem
F08BEF 16 DGEQPF
QR factorization of real general rectangular matrix with column pivoting
F08BFF 21 DGEQP3
QR factorization of real general rectangular matrix with column pivoting, using BLAS-3
F08BHF 21 DTZRZF
Reduces a real upper trapezoidal matrix to upper triangular form
F08BKF 21 DORMRZ
Apply orthogonal transformation determined by F08BHF (DTZRZF)
F08BNF 21 ZGELSY
Computes the minimum-norm solution to a complex linear least-squares problem
F08BSF 16 ZGEQPF
QR factorization of complex general rectangular matrix with column pivoting
F08BTF 21 ZGEQP3
QR factorization of complex general rectangular matrix with column pivoting, using BLAS-3
F08BVF 21 ZTZRZF
Reduces a complex upper trapezoidal matrix to upper triangular form
F08BXF 21 ZUNMRZ
Apply unitary transformation determined by F08BVF (ZTZRZF)
F08CEF 21 DGEQLF
QL factorization of real general rectangular matrix
F08CFF 21 DORGQL
Form all or part of orthogonal Q from QL factorization determined by F08CEF (DGEQLF)
F08CGF 21 DORMQL
Apply orthogonal transformation determined by F08CEF (DGEQLF)
F08CHF 21 DGERQF
RQ factorization of real general rectangular matrix
F08CJF 21 DORGRQ
Form all or part of orthogonal Q from RQ factorization determined by F08CHF (DGERQF)
F08CKF 21 DORMRQ
Apply orthogonal transformation determined by F08CHF (DGERQF)
F08CSF 21 ZGEQLF
QL factorization of complex general rectangular matrix
F08CTF 21 ZUNGQL
Form all or part of orthogonal Q from QL factorization determined by F08CSF (ZGEQLF)
F08CUF 21 ZUNMQL
Apply unitary transformation determined by F08CSF (ZGEQLF)
F08CVF 21 ZGERQF
RQ factorization of complex general rectangular matrix
F08CWF 21 ZUNGRQ
Form all or part of orthogonal Q from RQ factorization determined by F08CVF (ZGERQF)
F08CXF 21 ZUNMRQ
Apply unitary transformation determined by F08CVF (ZGERQF)
F08FAF 21 DSYEV
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
F08FBF 21 DSYEVX
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
F08FCF 19 DSYEVD
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
F08FDF 21 DSYEVR
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
F08FEF 16 DSYTRD
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
F08FFF 16 DORGTR
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF (DSYTRD)
F08FGF 16 DORMTR
Apply orthogonal transformation determined by F08FEF (DSYTRD)
F08FLF 21 DDISNA
Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix
F08FNF 21 ZHEEV
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
F08FPF 21 ZHEEVX
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
F08FQF 19 ZHEEVD
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
F08FRF 21 ZHEEVR
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
F08FSF 16 ZHETRD
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
F08FTF 16 ZUNGTR
Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF (ZHETRD)
F08FUF 16 ZUNMTR
Apply unitary transformation matrix determined by F08FSF (ZHETRD)
F08GAF 21 DSPEV
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
F08GBF 21 DSPEVX
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
F08GCF 19 DSPEVD
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer)
F08GEF 16 DSPTRD
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
F08GFF 16 DOPGTR
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF (DSPTRD)
F08GGF 16 DOPMTR
Apply orthogonal transformation determined by F08GEF (DSPTRD)
F08GNF 21 ZHPEV
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
F08GPF 21 ZHPEVX
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
F08GQF 19 ZHPEVD
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer)
F08GSF 16 ZHPTRD
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
F08GTF 16 ZUPGTR
Generate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF (ZHPTRD)
F08GUF 16 ZUPMTR
Apply unitary transformation matrix determined by F08GSF (ZHPTRD)
F08HAF 21 DSBEV
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
F08HBF 21 DSBEVX
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
F08HCF 19 DSBEVD
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer)
F08HEF 16 DSBTRD
Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
F08HNF 21 ZHBEV
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
F08HPF 21 ZHBEVX
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
F08HQF 19 ZHBEVD
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
F08HSF 16 ZHBTRD
Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
F08JAF 21 DSTEV
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
F08JBF 21 DSTEVX
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
F08JCF 19 DSTEVD
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
F08JDF 21 DSTEVR
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
F08JEF 16 DSTEQR
All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit QL or QR algorithm
F08JFF 16 DSTERF
All eigenvalues of real symmetric tridiagonal matrix, root-free variant of the QL or QR algorithm
F08JGF 16 DPTEQR
Computes all eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from real symmetric positive-definite matrix
F08JHF 21 DSTEDC
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
F08JJF 16 DSTEBZ
Selected eigenvalues of real symmetric tridiagonal matrix by bisection
F08JKF 16 DSTEIN
Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
F08JLF 21 DSTEGR
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
F08JSF 16 ZSTEQR
All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit QL or QR algorithm
F08JUF 16 ZPTEQR
Computes all eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from complex Hermitian positive-definite matrix
F08JVF 21 ZSTEDC
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
F08JXF 16 ZSTEIN
Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
F08JYF 21 ZSTEGR
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
F08KAF 21 DGELSS
Computes the minimum-norm solution to a real linear least-squares problem using singular value decomposition
F08KBF 21 DGESVD
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
F08KCF 21 DGELSD
Computes the minimum-norm solution to a real linear least-squares problem using singular value decomposition (divide-and-conquer)
F08KDF 21 DGESDD
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
F08KEF 16 DGEBRD
Orthogonal reduction of real general rectangular matrix to bidiagonal form
F08KFF 16 DORGBR
Generate orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF (DGEBRD)
F08KGF 16 DORMBR
Apply orthogonal transformations from reduction to bidiagonal form determined by F08KEF (DGEBRD)
F08KNF 21 ZGELSS
Computes the minimum-norm solution to a complex linear least-squares problem using singular value decomposition
F08KPF 21 ZGESVD
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
F08KQF 21 ZGELSD
Computes the minimum-norm solution to a complex linear least-squares problem using singular value decomposition (divide-and-conquer)
F08KRF 21 ZGESDD
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
F08KSF 16 ZGEBRD
Unitary reduction of complex general rectangular matrix to bidiagonal form
F08KTF 16 ZUNGBR
Generate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF (ZGEBRD)
F08KUF 16 ZUNMBR
Apply unitary transformations from reduction to bidiagonal form determined by F08KSF (ZGEBRD)
F08LEF 19 DGBBRD
Reduction of real rectangular band matrix to upper bidiagonal form
F08LSF 19 ZGBBRD
Reduction of complex rectangular band matrix to upper bidiagonal form
F08MDF 21 DBDSDC
Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
F08MEF 16 DBDSQR
SVD of real bidiagonal matrix reduced from real general matrix
F08MSF 16 ZBDSQR
SVD of real bidiagonal matrix reduced from complex general matrix
F08NAF 21 DGEEV
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
F08NBF 21 DGEEVX
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
F08NEF 16 DGEHRD
Orthogonal reduction of real general matrix to upper Hessenberg form
F08NFF 16 DORGHR
Generate orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD)
F08NGF 16 DORMHR
Apply orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD)
F08NHF 16 DGEBAL
Balance real general matrix
F08NJF 16 DGEBAK
Transform eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF (DGEBAL)
F08NNF 21 ZGEEV
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
F08NPF 21 ZGEEVX
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
F08NSF 16 ZGEHRD
Unitary reduction of complex general matrix to upper Hessenberg form
F08NTF 16 ZUNGHR
Generate unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD)
F08NUF 16 ZUNMHR
Apply unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD)
F08NVF 16 ZGEBAL
Balance complex general matrix
F08NWF 16 ZGEBAK
Transform eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF (ZGEBAL)
F08PAF 21 DGEES
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
F08PBF 21 DGEESX
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
F08PEF 16 DHSEQR
Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
F08PKF 16 DHSEIN
Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
F08PNF 21 ZGEES
Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
F08PPF 21 ZGEESX
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 16 ZHSEQR
Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
F08PXF 16 ZHSEIN
Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
F08QFF 16 DTREXC
Reorder Schur factorization of real matrix using orthogonal similarity transformation
F08QGF 16 DTRSEN
Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QHF 16 DTRSYL
Solve real Sylvester matrix equation AX + XB = C, A and B are upper quasi-triangular or transposes
F08QKF 16 DTREVC
Left and right eigenvectors of real upper quasi-triangular matrix
F08QLF 16 DTRSNA
Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
F08QTF 16 ZTREXC
Reorder Schur factorization of complex matrix using unitary similarity transformation
F08QUF 16 ZTRSEN
Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QVF 16 ZTRSYL
Solve complex Sylvester matrix equation AX + XB = C, A and B are upper triangular or conjugate-transposes
F08QXF 16 ZTREVC
Left and right eigenvectors of complex upper triangular matrix
F08QYF 16 ZTRSNA
Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
F08SAF 21 DSYGV
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
F08SBF 21 DSYGVX
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
F08SCF 21 DSYGVD
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
F08SEF 16 DSYGST
Reduction to standard form of real symmetric-definite generalized eigenproblem Ax = λBx, ABx = λx or BAx = λx, B factorized by F07FDF (DPOTRF)
F08SNF 21 ZHEGV
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
F08SPF 21 ZHEGVX
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
F08SQF 21 ZHEGVD
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
F08SSF 16 ZHEGST
Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax = λBx, ABx = λx or BAx = λx, B factorized by F07FRF (ZPOTRF)
F08TAF 21 DSPGV
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
F08TBF 21 DSPGVX
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
F08TCF 21 DSPGVD
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
F08TEF 16 DSPGST
Reduction to standard form of real symmetric-definite generalized eigenproblem Ax = λBx, ABx = λx or BAx = λx, packed storage, B factorized by F07GDF (DPPTRF)
F08TNF 21 ZHPGV
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
F08TPF 21 ZHPGVX
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
F08TQF 21 ZHPGVD
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
F08TSF 16 ZHPGST
Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax = λBx, ABx = λx or BAx = λx, packed storage, B factorized by F07GRF (ZPPTRF)
F08UAF 21 DSBGV
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
F08UBF 21 DSBGVX
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
F08UCF 21 DSBGVD
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
F08UEF 19 DSBGST
Reduction of real symmetric-definite banded generalized eigenproblem Ax = λBx to standard form Cy = λy, such that C has the same bandwidth as A
F08UFF 19 DPBSTF
Computes a split Cholesky factorization of real symmetric positive-definite band matrix A
F08UNF 21 ZHBGV
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
F08UPF 21 ZHBGVX
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
F08UQF 21 ZHBGVD
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
F08USF 19 ZHBGST
Reduction of complex Hermitian-definite banded generalized eigenproblem Ax = λBx to standard form Cy = λy, such that C has the same bandwidth as A
F08UTF 19 ZPBSTF
Computes a split Cholesky factorization of complex Hermitian positive-definite band matrix A
F08VAF 21 DGGSVD
Computes the generalized singular value decomposition of a real matrix pair
F08VEF 21 DGGSVP
Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a real matrix pair
F08VNF 21 ZGGSVD
Computes the generalized singular value decomposition of a complex matrix pair
F08VSF 21 ZGGSVP
Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a complex matrix pair
F08WAF 21 DGGEV
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
F08WBF 21 DGGEVX
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
F08WEF 20 DGGHRD
Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
F08WHF 20 DGGBAL
Balance a pair of real general matrices
F08WJF 20 DGGBAK
Transform eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF (DGGBAL)
F08WNF 21 ZGGEV
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
F08WPF 21 ZGGEVX
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
F08WSF 20 ZGGHRD
Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
F08WVF 20 ZGGBAL
Balance a pair of complex general matrices
F08WWF 20 ZGGBAK
Transform eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF (ZGGBAL)
F08XAF 21 DGGES
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
F08XBF 21 DGGESX
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
F08XEF 20 DHGEQZ
Eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
F08XNF 21 ZGGES
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
F08XPF 21 ZGGESX
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
F08XSF 20 ZHGEQZ
Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex general matrices
F08YEF 21 DTGSJA
Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
F08YFF 21 DTGEXC
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
F08YGF 21 DTGSEN
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
F08YHF 21 DTGSYL
Solves the real-valued generalized Sylvester equation
F08YKF 20 DTGEVC
Left and right eigenvectors of a pair of real upper quasi-triangular matrices
F08YLF 21 DTGSNA
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form
F08YSF 21 ZTGSJA
Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
F08YTF 21 ZTGEXC
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
F08YUF 21 ZTGSEN
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
F08YVF 21 ZTGSYL
Solves the complex generalized Sylvester equation
F08YXF 20 ZTGEVC
Left and right eigenvectors of a pair of complex upper triangular matrices
F08YYF 21 ZTGSNA
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form
F08ZAF 21 DGGLSE
Solves the real linear equality-constrained least-squares (LSE) problem
F08ZBF 21 DGGGLM
Solves a real general Gauss–Markov linear model (GLM) problem
F08ZEF 21 DGGQRF
Computes a generalized QR factorization of a real matrix pair
F08ZFF 21 DGGRQF
Computes a generalized RQ factorization of a real matrix pair
F08ZNF 21 ZGGLSE
Solves the complex linear equality-constrained least-squares (LSE) problem
F08ZPF 21 ZGGGLM
Solves a complex general Gauss–Markov linear model (GLM) problem
F08ZSF 21 ZGGQRF
Computes a generalized QR factorization of a complex matrix pair
F08ZTF 21 ZGGRQF
Computes a generalized RQ 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 LU factorization
F11DBF 18 Solution of linear system involving incomplete LU 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 LU factorization
F11DPF 19 Solution of complex linear system involving incomplete LU 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 LU 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 F12APF) 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 F12FBF) 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

F16 – Further Linear Algebra Support Routines

Routine
Name
Mark of
Introduction

Purpose
F16DLF 22 Sum elements of integer vector
F16DNF 22 Maximum value and location, integer vector
F16DPF 22 Minimum value and location, integer vector
F16DQF 22 Maximum absolute value and location, integer vector
F16DRF 22 Minimum absolute value and location, integer vector
F16EHF 22 BLAS_DWAXPBY
Real scaled vector addition preserving input
F16ELF 22 BLAS_DSUM
Sum elements of real vector
F16GHF 22 BLAS_ZWAXPBY
Complex scaled vector addition preserving input
F16GLF 22 BLAS_ZSUM
Sum elements of complex vector
F16JNF 22 BLAS_DMAX_VAL
Maximum value and location, real vector
F16JPF 22 BLAS_DMIN_VAL
Minimum value and location, real vector
F16JQF 22 BLAS_DAMAX_VAL
Maximum absolute value and location, real vector
F16JRF 22 BLAS_DAMIN_VAL
Minimum absolute value and location, real vector
F16JSF 22 BLAS_ZAMAX_VAL
Maximum absolute value and location, complex vector
F16JTF 22 BLAS_ZAMIN_VAL
Minimum absolute value and location, complex vector

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)
G01AMF 22 Find quantiles of an unordered vector, real numbers
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
G02AAF 22 Computes the nearest correlation matrix to a real square matrix, using the method of Qi and Sun
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
G02GPF 22 Computes a predicted value and its associated standard error based on a previously fitted generalized linear model.
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)
G02KAF 22 Ridge regression, optimizing a ridge regression parameter
G02KBF 22 Ridge regression using a number of supplied ridge regression parameters
G02LAF 22 Partial least-squares (PLS) regression using singular value decomposition
G02LBF 22 Partial least-squares (PLS) regression using Wold's iterative method
G02LCF 22 PLS parameter estimates following partial least-squares regression by G02LAF or G02LBF
G02LDF 22 PLS predictions based on parameter estimates from G02LCF

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
G03BDF 22 ProMax 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 coordinate 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 (εt - 1 + γ)2
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05HLF 20 Univariate time series, generate n terms of a GARCH process with asymmetry of the form (|εt - 1| + γεt - 1)2
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05HMF 20 Univariate time series, generate n terms of an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05HNF 20 Univariate time series, generate n terms of an exponential GARCH (EGARCH) process
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05KAF 20 Pseudorandom real numbers, uniform distribution over (0,1), seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05KBF 20 Initialize seeds of a given generator for random number generating routines (that pass seeds explicitly) to give a repeatable sequence
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05KCF 20 Initialize seeds of a given generator for random number generating routines (that pass seeds expicitly) to give non-repeatable sequence
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05KEF 20 Pseudorandom logical (boolean) value, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05KFF 22 Initializes a pseudorandom number generator to give a repeatable sequence
G05KGF 22 Initializes a pseudorandom number generator to give a non-repeatable sequence
G05KHF 22 Primes a pseudorandom number generator for generating multiple streams using leap-frog
G05KJF 22 Primes a pseudorandom number generator for generating multiple streams using skip-ahead
G05LAF 20 Generates a vector of random numbers from a Normal distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05LBF 20 Generates a vector of random numbers from a Student's t-distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05LCF 20 Generates a vector of random numbers from a χ2 distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05LDF 20 Generates a vector of random numbers from an F-distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05LEF 20 Generates a vector of random numbers from a β distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05LFF 20 Generates a vector of random numbers from a γ distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05LGF 20 Generates a vector of random numbers from a uniform distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05LHF 20 Generates a vector of random numbers from a triangular distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05LJF 20 Generates a vector of random numbers from an exponential distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05LKF 20 Generates a vector of random numbers from a log-normal distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05LLF 20 Generates a vector of random numbers from a Cauchy distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05LMF 20 Generates a vector of random numbers from a Weibull distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05LNF 20 Generates a vector of random numbers from a logistic distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05LPF 20 Generates a vector of random numbers from a von Mises distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05LQF 20 Generates a vector of random numbers from an exponential mixture distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05LXF 21 Generates a matrix of random numbers from a multivariate Student's t-distribution, seeds and generator passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05LYF 21 Generates a matrix of random numbers from a multivariate Normal distribution, seeds and generator passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05LZF 20 Generates a vector of random numbers from a multivariate Normal distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05MAF 20 Generates a vector of random integers from a uniform distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05MBF 20 Generates a vector of random integers from a geometric distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05MCF 20 Generates a vector of random integers from a negative binomial distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05MDF 20 Generates a vector of random integers from a logarithmic distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05MEF 20 Generates a vector of random integers from a Poisson distribution with varying mean, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05MJF 20 Generates a vector of random integers from a binomial distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05MKF 20 Generates a vector of random integers from a Poisson distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05MLF 20 Generates a vector of random integers from a hypergeometric distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05MRF 20 Generates a vector of random integers from a multinomial distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05MZF 20 Generates a vector of random integers from a general discrete distribution, seeds and generator number passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05NAF 20 Pseudorandom permutation of an integer vector
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05NBF 20 Pseudorandom sample from an integer vector
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05NCF 22 Pseudorandom permutation of an integer vector
G05NDF 22 Pseudorandom sample from an integer vector
G05PAF 20 Generates a realization of a time series from an ARMA model
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05PCF 20 Generates a realization of a multivariate time series from a VARMA model
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05PDF 22 Generates a realization of a time series from a GARCH process with asymmetry of the form (εt - 1 + γ)2
G05PEF 22 Generates a realization of a time series from a GARCH process with asymmetry of the form (|εt - 1| + γεt - 1)2
G05PFF 22 Generates a realization of a time series from an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
G05PGF 22 Generates a realization of a time series from an exponential GARCH (EGARCH) process
G05PHF 22 Generates a realization of a time series from an ARMA model
G05PJF 22 Generates a realization of a multivariate time series from a VARMA model
G05PMF 22 Generates a realization of a time series from an exponential smoothing model
G05PXF 22 Generates a random orthogonal matrix
G05PYF 22 Generates a random correlation matrix
G05PZF 22 Generates a random two-way table
G05QAF 20 Computes a random orthogonal matrix
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05QBF 20 Computes a random correlation matrix
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05QDF 20 Generates a random table matrix
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05RAF 21 Generates a matrix of random numbers from a Gaussian copula, seeds and generator passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05RBF 21 Generates a matrix of random numbers from a Student's t-copula, seeds and generator passed explicitly
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05RCF 22 Generates a matrix of pseudorandom numbers from a Student's t-copula
G05RDF 22 Generates a matrix of pseudorandom numbers from a Gaussian copula
G05RYF 22 Generates a matrix of pseudorandom numbers from a multivariate Student's t-distribution
G05RZF 22 Generates a matrix of pseudorandom numbers from a multivariate Normal distribution
G05SAF 22 Generates a vector of pseudorandom numbers from a uniform distribution over (0,1]
G05SBF 22 Generates a vector of pseudorandom numbers from a beta distribution
G05SCF 22 Generates a vector of pseudorandom numbers from a Cauchy distribution
G05SDF 22 Generates a vector of pseudorandom numbers from a χ2 distribution
G05SEF 22 Generates a vector of pseudorandom numbers from a Dirichlet distribution
G05SFF 22 Generates a vector of pseudorandom numbers from an exponential distribution
G05SGF 22 Generates a vector of pseudorandom numbers from an exponential mix distribution
G05SHF 22 Generates a vector of pseudorandom numbers from an F-distribution
G05SJF 22 Generates a vector of pseudorandom numbers from a gamma distribution
G05SKF 22 Generates a vector of pseudorandom numbers from a Normal distribution
G05SLF 22 Generates a vector of pseudorandom numbers from a logistic distribution
G05SMF 22 Generates a vector of pseudorandom numbers from a log-normal distribution
G05SNF 22 Generates a vector of pseudorandom numbers from a Student's t-distribution
G05SPF 22 Generates a vector of pseudorandom numbers from a triangular distribution
G05SQF 22 Generates a vector of pseudorandom numbers from a uniform distribution over [a,b]
G05SRF 22 Generates a vector of pseudorandom numbers from a von Mises distribution
G05SSF 22 Generates a vector of pseudorandom numbers from a Weibull distribution
G05TAF 22 Generates a vector of pseudorandom integers from a binomial distribution
G05TBF 22 Generates a vector of pseudorandom logical values
G05TCF 22 Generates a vector of pseudorandom integers from a geometric distribution
G05TDF 22 Generates a vector of pseudorandom integers from a general discrete distribution
G05TEF 22 Generates a vector of pseudorandom integers from a hypergeometric distribution
G05TFF 22 Generates a vector of pseudorandom integers from a logarithmic distribution
G05TGF 22 Generates a vector of pseudorandom integers from a multinomial distribution
G05THF 22 Generates a vector of pseudorandom integers from a negative binomial distribution
G05TJF 22 Generates a vector of pseudorandom integers from a Poisson distribution
G05TKF 22 Generates a vector of pseudorandom integers from a Poisson distribution with varying mean
G05TLF 22 Generates a vector of pseudorandom integers from a uniform distribution
G05YAF 20 Multi-dimensional quasi-random number generator with a uniform probability distribution
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05YBF 20 Multi-dimensional quasi-random number generator with a Gaussian or log-normal probability distribution
Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05YCF 21 Initializes the Faure generator (G05YDF/G05YJF/G05YKF)
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05YDF 21 Generates a sequence of quasi-random numbers using Faure's method
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05YEF 21 Initializes the Sobol generator (G05YFF/G05YJF/G05YKF)
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05YFF 21 Generates a sequence of quasi-random numbers using Sobol's method
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05YGF 21 Initializes the Niederreiter generator (G05YHF/G05YJF/G05YKF)
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05YHF 21 Generates a sequence of quasi-random numbers using Niederreiter's method
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G05YJF 21 Generates a Normal quasi-random number sequence
G05YKF 21 Generates a log-normal quasi-random number sequence
G05YLF 22 Initializes a quasi-random number generator
G05YMF 22 Generates a uniform quasi-random number sequence
G05YNF 22 Initializes a scrambled quasi-random number generator

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
G13AMF 22 Univariate time series, exponential smoothing
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
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
G13DDF 22 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 G13DDF
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 (εt - 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 (εt - 1 + γ)2
G13FCF 20 Univariate time series, parameter estimation for a GARCH process with asymmetry of the form (|εt - 1| + γεt - 1)2
G13FDF 20 Univariate time series, forecast function for a GARCH process with asymmetry of the form (|εt - 1| + γεt - 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), using E04NKF/E04NKA
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 and Searching

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
M01NAF 22 Binary search in set of real numbers
M01NBF 22 Binary search in set of integer numbers
M01NCF 22 Binary search in set of character data
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
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.

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 realx
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
S15AGF 22 Scaled complement of error function, erfcx(x)
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 Yν + a(z), reala0, complex z, ν = 0,1,2,
S17DEF 13 Bessel functions Jν + a(z), reala0, 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 Hν + a(j)(z), j = 1,2, reala0, 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 exK0(x)
S18CDF 10 Scaled modified Bessel function exK1(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 Kν + a(z), reala0, complex z, ν = 0,1,2,
S18DEF 13 Modified Bessel functions Iν + a(z), reala0, complex z, ν = 0,1,2,
S18GKF 21 Bessel function of the 1st kind Jα ± 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)
S21BEF 22 Elliptic integral of 1st kind, Legendre form, F(φ|m)
S21BFF 22 Elliptic integral of 2nd kind, Legendre form, E(φ|m)
S21BGF 22 Elliptic integral of 3rd kind, Legendre form, Π(n ; φ|m)
S21BHF 22 Complete elliptic integral of 1st kind, Legendre form, K(m)
S21BJF 22 Complete elliptic integral of 2nd kind, Legendre form, E(m)
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)
S30AAF 22 Black–Scholes–Merton option pricing formula
S30ABF 22 Black–Scholes–Merton option pricing formula with Greeks
S30BAF 22 Floating-strike lookback option pricing formula
S30BBF 22 Floating-strike lookback option pricing formula with Greeks
S30CAF 22 Binary option: cash-or-nothing pricing formula
S30CBF 22 Binary option: cash-or-nothing pricing formula with Greeks
S30CCF 22 Binary option: asset-or-nothing pricing formula
S30CDF 22 Binary option: asset-or-nothing pricing formula with Greeks
S30FAF 22 Standard barrier option pricing formula
S30JAF 22 Jump-diffusion, Merton's model, option pricing formula
S30JBF 22 Jump-diffusion, Merton's model, option pricing formula with Greeks
S30NAF 22 Heston's model option pricing formula
S30QCF 22 American option: Bjerksund and Stensland pricing formula
S30SAF 22 Asian option: geometric continuous average rate pricing formula
S30SBF 22 Asian option: geometric continuous average rate pricing formula with Greeks

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
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.
X02DJF 12 The floating-point model parameter ROUNDS
Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information.

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 22 Library Contents (PDF version)
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2009