Routine Index

This document lists all the routines in the Fortran Library in order of functionality.

A02 – Complex Arithmetic

Complex numbers,
division	A02ACF
modulus	A02ABF
square root	A02AAF

C02 – Zeros of Polynomials

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

C05 – Roots of One or More Transcendental Equations

Zeros of functions of one variable:
Direct communication:
binary search followed by Bus and Dekker algorithm	C05AGF
Bus and Dekker algorithm	C05ADF
continuation method	C05AJF
Reverse communication:
binary search	C05AVF
Bus and Dekker algorithm	C05AZF
continuation method	C05AXF
Zeros of functions of several variables:
Checking Routine:
Checks user-supplied Jacobian	C05ZAF
Direct communication:
easy-to-use,
derivatives required	C05PBF
no derivatives required	C05NBF
sophisticated	C05NCF
sophisticated, derivatives required	C05PCF
Reverse Communication:
sophisticated	C05NDF
sophisticated,
derivatives required	C05PDF/C05PDA

C06 – Summation of Series

Acceleration of convergence	C06BAF
Complex conjugate,
complex sequence	C06GCF
Hermitian sequence	C06GBF
multiple Hermitian sequences	C06GQF
Complex sequence from Hermitian sequences	C06GSF
Convolution or Correlation,
complex vectors,
time-saving	C06PKF
real vectors,
space-saving	C06EKF
time-saving	C06FKF
Discrete Fourier Transform,
half- and quarter-wave transforms,
multiple Fourier cosine transforms	C06HBF
multiple Fourier cosine transforms,
simple use	C06RBF
multiple Fourier sine transforms	C06HAF
multiple Fourier sine transforms,
simple use	C06RAF
multiple quarter-wave cosine transforms	C06HDF
multiple quarter-wave cosine transforms,
simple use	C06RDF
multiple quarter-wave sine transforms	C06HCF
multiple quarter-wave sine transforms,
simple use	C06RCF
multi-dimensional,
complex sequence,
complex storage	C06PJF
real storage	C06FJF
one-dimensional,
multi-variable,
complex sequence,
complex storage	C06PFF
real storage	C06FFF
multiple transforms,
complex sequence,
complex storage by columns	C06PSF
complex storage by rows	C06PRF
real storage by rows	C06FRF
Hermitian sequence,
real storage by rows	C06FQF
Hermitian/real sequence,
complex storage by columns	C06PQF
complex storage by rows	C06PPF
real sequence,
real storage by rows	C06FPF
single transforms,
complex sequence,
space saving,
real storage	C06ECF
time-saving,
complex storage	C06PCF
real storage	C06FCF
Hermitian sequence,
space-saving,
real storage	C06EBF
time-saving,
real storage	C06FBF
Hermitian/real sequence,
time-saving,
complex storage	C06PAF
real sequence,
space-saving,
real storage	C06EAF
time-saving,
real storage	C06FAF
three-dimensional,
complex sequence,
complex storage	C06PXF
real storage	C06FXF
two-dimensional,
complex sequence,
complex storage	C06PUF
real storage	C06FUF
Inverse Laplace Transform,
Crump's method	C06LAF
Weeks' method,
compute coefficients of solution	C06LBF
evaluate solution	C06LCF
Summation of Chebyshev series	C06DBF

D01 – Quadrature

Korobov optimal coefficients for use in D01GCF and D01GDF:
when number of points is a product of 2 primes	D01GZF
when number of points is prime	D01GYF
Multi-dimensional quadrature:
over a general product region:
Korobov–Conroy number-theoretic method	D01GCF
Sag–Szekeres method (also over n -sphere	D01FDF
variant of D01GCF especially efficient on vector machines	D01GDF
over a hyper-rectangle:
adaptive method	D01FCF
adaptive method,
multiple integrands	D01EAF
Gaussian quadrature rule-evaluation	D01FBF
Monte Carlo method	D01GBF
over an n -simplex	D01PAF
over an n -sphere (n≥4) ,
allowing for badly behaved integrands	D01JAF
One-dimensional quadrature:
adaptive integration of a function over a finite interval:
allowing for singularities at user-specified break-points	D01ALF
method suitable for oscillating functions	D01AKF
strategy due to Patterson,
suitable for well-behaved integrands	D01AHF
strategy due to Piessens and de Doncker,
allowing for badly behaved integrands	D01AJF
variant of D01AJF especially efficient on vector machines	D01ATF
variant of D01AKF especially efficient on vector machines	D01AUF
weight function 1 / (x-c) Cauchy principal value (Hilbert transform)	D01AQF
weight function with end-point singularities of algebraico-logarithmic type	D01APF
weight function cos(ωx) or sin(ωx)	D01ANF
adaptive integration of a function over an infinite interval or semi-infinite interval	D01AMF
adaptive integration of a function over an infinite interval or semi-infinite interval:
weight function cos(ωx) or sin(ωx)	D01ASF
Gaussian quadrature rule-evaluation	D01BAF
integration of a function defined by data values only,
Gill–Miller method	D01GAF
non-adaptive integration over a finite interval	D01BDF
non-adaptive integration over a finite interval:
with provision for indefinite integrals also	D01ARF
Two-dimensional quadrature over a finite region	D01DAF
Weights and abscissae for Gaussian qadrature rules:
more general choice of rule,
calculating the weights and abscissae	D01BCF
restricted choice of rule,
using pre-computed weights and abscissae	D01BBF

D02 – Ordinary Differential Equations

Second-order Sturm–Liouville problems:
regular system, finite range, user-specified break-points:
eigenvalue only	D02KAF
regular/singular system, finite/infinite range:
eigenvalue and eigenfunction	D02KEF
eigenvalue only	D02KDF
System of first-order ordinary differential equations, initial value problems:
C ¹ -interpolant	D02XKF
comprehensive integrator routines for stiff systems:
explicit ODEs (reverse communication):
full Jacobian	D02NMF
explicit ODEs:
banded Jacobian	D02NCF
full Jacobian	D02NBF
sparse Jacobian	D02NDF
implicit ODEs coupled with algebraic equations (reverse communication)	D02NNF
implicit ODEs coupled with algebraic equations:
banded Jacobian	D02NHF
full Jacobian	D02NGF
sparse Jacobian	D02NJF
comprehensive integrator routines using Adams method with root-finding option:
diagnostic routine	D02QXF
diagnostic routine for root-finding	D02QYF
forward communication	D02QFF
interpolant	D02QZF
reverse communication	D02QGF
set-up routine	D02QWF
comprehensive integrator routines using Runge–Kutta methods:
diagnostic routine	D02PYF
diagnostic routine for global error assessment	D02PZF
interpolant	D02PXF
over a range with intermediate output	D02PCF
over a step	D02PDF
reset end of range	D02PWF
set-up routine	D02PVF
compute weighted norm of local error estimate	D02ZAF
enquiry routine for use with sparse Jacobian	D02NRF
integrator diagnostic routine	D02NYF
integrator set-up for BDF method	D02NVF
integrator set-up for Blend method	D02NWF
integrator set-up for DASSL method	D02MVF
linear algebra diagnostic routine for sparse Jacobians	D02NXF
linear algebra set-up for banded Jacobians	D02NTF
linear algebra set-up for full Jacobians	D02NSF
linear algebra set-up for sparse Jacobians	D02NUF
natural interpolant	D02MZF
natural interpolant (for use by MONITR subroutine)	D02XJF
set-up routine for continuation calls to integrator	D02NZF
simple driver routines:
Runge–Kutta–Merson method:
until (optionally) a function of the solution is zero, with optional intermediate output	D02BJF
until a function of the solution is zero	D02BHF
until a specified component attains a given value	D02BGF
variable-order variable-step Adams method:
until (optionally) a function of the solution is zero, with optional intermediate output	D02CJF
variable-order variable-step BDF method for stiff systems:
until (optionally) a function of the solution is zero, with optional intermediate output	D02EJF
System of ordinary differential equations, boundary value problems:
collocation and least-squares:
single n th-order linear equation	D02JAF
system of first-order linear equations	D02JBF
system of n th-order linear equations	D02TGF
comprehensive routines using a collocation technique:
continuation routine	D02TXF
diagnostic routine	D02TZF
general nonlinear problem solver	D02TKF
interpolation routine	D02TYF
set-up routine	D02TVF
finite difference technique with deferred correction:
general linear problem	D02GBF
general nonlinear problem, with continuation facility	D02RAF
simple nonlinear problem	D02GAF
shooting and matching technique:
boundary values to be determined	D02HAF
general parameters to be determined	D02HBF
general parameters to be determined, allowing interior matching-point	D02AGF
general parameters to be determined, subject to extra algebraic equations	D02SAF
System of second-order ordinary differential equations:
Runge–Kutta–Nystrom method:
diagnostic routine	D02LYF
integrator	D02LAF
interpolating solutions	D02LZF
set-up routine	D02LXF

D03 – Partial Differential Equations

Automatic mesh generation,
triangles over a plane domain	D03MAF
Black–Scholes equation,
analytic	D03NDF
finite difference	D03NCF
Convection-diffusion system(s),
nonlinear,
one space dimension,
using upwind difference scheme based on Riemann solvers	D03PFF
using upwind difference scheme based on Riemann solvers,
with coupled differential algebraic system	D03PLF
with remeshing	D03PSF
Elliptic equations,
discretization on rectangular grid (seven-point two-dimensional molecule)	D03EEF
equations on rectangular grid (seven-point two-dimensional molecule)	D03EDF
finite difference equations (five-point two-dimensional molecule)	D03EBF
finite difference equations (seven-point three-dimensional molecule)	D03ECF
Helmholtz's equation in three dimensions	D03FAF
Laplace's equation in two dimensions	D03EAF
First-order system(s),
nonlinear,
one space dimension,
using Keller box scheme	D03PEF
using Keller box scheme,
with coupled differential algebraic system	D03PKF
with remeshing	D03PRF
Partial differential equations (PDEs), elliptic:
PDEs, general system, one space variable, method of lines:
parabolic:
collocation spatial discretization:
coupled DAEs, comprehensive	D03PJF/D03PJA
easy-to-use	D03PDF/D03PDA
finite differences spatial discretization:
coupled DAEs, comprehensive	D03PHF/D03PHA
coupled DAEs, remeshing, comprehensive	D03PPF/D03PPA
easy-to-use	D03PCF/D03PCA
Second order system(s),
nonlinear,
two space dimensions,
in rectangular domain	D03RAF
in rectilinear domain	D03RBF
Utility routine,
average values for D03NDF	D03NEF
basic SIP for five-point two-dimensional molecule	D03UAF
basic SIP for seven-point three-dimensional molecule	D03UBF
check initial grid data for D03RBF	D03RYF
exact Riemann solver for Euler equations	D03PXF
HLL Riemann solver for Euler equations	D03PWF
interpolation routine for collocation scheme	D03PYF
interpolation routine for finite difference,
Keller box and upwind scheme	D03PZF
Osher's Riemann solver for Euler equations	D03PVF
return co-ordinates of grid points for D03RBF	D03RZF
Roe's Riemann solver for Euler equations	D03PUF

D04 – Numerical Differentiation

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

D05 – Integral Equations

Fredholm equation of second kind,
linear,
non-singular discontinuous or ‘split’ kernel:	D05AAF
non-singular smooth kernel:	D05ABF
Volterra equation of first kind,
nonlinear,
weakly-singular,
convolution equation (Abel):	D05BEF
Volterra equation of second kind,
nonlinear,
non-singular,
convolution equation:	D05BAF
weakly-singular,
convolution equation (Abel):	D05BDF
Weight generating routines,
weights for general solution of Volterra equations	D05BWF
weights for general solution of Volterra equations with weakly-singular kernel	D05BYF

D06 – Mesh Generation

Boundary mesh generation,
2 D boundary mesh generation	D06BAF
Interior mesh generation,
2 D mesh generation using a simple incremental method	D06AAF
2 D mesh generation using advancing front method	D06ACF
2 D mesh generation using Delaunay-Voronoi method	D06ABF
Mesh Management and Utility routine,
2 D mesh smoother using a barycentering technique	D06CAF
2 D mesh transformer by an affine transformation	D06DAF
2 D mesh vertex renumbering	D06CCF
finite Element matrix sparsity pattern generation	D06CBF
joins together two given adjacent (possibly overlapping) meshes	D06DBF

E01 – Interpolation

Derivative,
of interpolant,
from E01BEF	E01BGF
from E01SGF	E01SHF
from E01TGF	E01THF
Evaluation,
of interpolant,
from E01BEF	E01BFF
from E01RAF	E01RBF
from E01SAF	E01SBF
from E01SGF	E01SHF
from E01TGF	E01THF
Extrapolation,
one variable	E01AAF
one variable	E01AEF
one variable	E01BEF
one variable	E01RAF
Integration (definite) of interpolant from E01BEF	E01BHF
Interpolated values,
one variable,
from interpolant from E01BEF	E01BFF
from interpolant from E01BEF	E01BGF
from polynomial,
equally spaced data	E01ABF
general data	E01AAF
from rational function	E01RBF
three variables,
from interpolant from E01TGF	E01THF
two variables,
from interpolant from E01SAF	E01SBF
from interpolant from E01SGF	E01SHF
Interpolating function,
one variable,
cubic spline	E01BAF
other piecewise polynomial	E01BEF
polynomial,
data with or without derivatives	E01AEF
rational function	E01RAF
three variables,
modified Shepard method	E01TGF
two variables,
bicubic spline	E01DAF
modified Shepard method	E01SAF
modified Shepard method	E01SGF
other piecewise polynomial	E01SAF

E02 – Curve and Surface Fitting

Automatic fitting,
with bicubic splines	E02DCF
with bicubic splines	E02DDF
with cubic splines	E02BEF
Data on lines	E02CAF
Data on rectangular mesh	E02DCF
Differentiation,
of cubic splines	E02BCF
of polynomials	E02AHF
Evaluation,
of bicubic splines	E02DEF
of bicubic splines	E02DFF
of cubic splines	E02BBF
of cubic splines and derivatives	E02BCF
of definite integral of cubic splines	E02BDF
of polynomials,
in one variable	E02AEF
in one variable	E02AKF
in two variables	E02CBF
of rational functions	E02RBF
Integration,
of cubic splines (definite integral)	E02BDF
of polynomials	E02AJF
l₁ fit,
with constraints	E02GBF
with general linear function	E02GAF
Least-squares curve fit,
with cubic splines	E02BAF
with polynomials,
arbitrary data points	E02ADF
selected data points	E02AFF
with constraints	E02AGF
Least-squares surface fit,
with bicubic splines	E02DAF
with polynomials	E02CAF
Minimax space fit,
with general linear function	E02GCF
with polynomials in one variable	E02ACF
Padé approximants	E02RAF
Sorting	E02ZAF

E04 – Minimizing or Maximizing a Function

Constrained minimum of a sum of squares, nonlinear constraints,
using function values and optionally first derivatives, sequential QP method,
forward communication (dense)	E04USF/E04USA
Convex QP problem or linearly-constrained linear least-squares problem (dense)	E04NCF/E04NCA
Linear programming (LP) problem (dense)	E04MFF/E04MFA
LP or QP problem (sparse)	E04NQF
Minimum, function of one variable,
using first derivative	E04BBF/E04BBA
using function values only	E04ABF/E04ABA
Minimum, function of several variables, nonlinear constraints (comprehensive),
using function values and optionally first derivatives, sequential QP method,
forward communication (dense)	E04WDF
forward communication (sparse)	E04UGF/E04UGA
forward communication (sparse)	E04VHF
reverse communication (dense)	E04UFF/E04UFA
using second derivatives,
combined Gauss–Newton and modified Newton algorithm	E04HYF
Minimum, function of several variables, simple bounds (comprehensive),
using first and second derivatives, modified Newton algorithm	E04LBF
using first derivatives, modified Newton algorithm	E04KDF
Minimum, function of several variables, simple bounds (easy-to-use),
using first and second derivatives, modified Newton algorithm	E04LYF
using first derivatives,
modified Newton algorithm	E04KZF
quasi-Newton algorithm	E04KYF
using function values only, quasi-Newton algorithm	E04JYF
Quadratic programming (QP) problem (dense)	E04NFF/E04NFA
Service routines:
check user's routine for calculating:
first derivatives of function	E04HCF
Hessian of a sum of squares	E04YBF
Jacobian of first derivatives	E04YAF
second derivatives of function	E04HDF
check user's routines calculating first derivatives of function and constraints	E04ZCF/E04ZCA
convert MPSX data file defining LP or QP problem to format required by E04NQF	E04MZF
covariance matrix for nonlinear least-squares problem	E04YCF
determine Jacobian sparsity structure before a call of E04VHF	E04VJF
estimate gradient and/or Hessian of a function	E04XAF/E04XAA
Initialization routine for:
E04NQF	E04NPF
E04VHF	E04VGF
E04DGA, E04MFA, E04NCA, E04NFA, E04UFA, E04UGA and E04USA	E04WBF
E04WDF	E04WCF
retrieve INTEGER optional parameter values used by:
E04NQF	E04NXF
E04NQF	E04NYF
E04VHF	E04VRF
E04VHF	E04VSF
E04WDF	E04WKF
E04WDF	E04WLF
supply INTEGER optional parameter values to:
E04NQF	E04NTF
E04NQF	E04NUF
E04VHF	E04VMF
E04VHF	E04VNF
E04WDF	E04WGF
E04WDF	E04WHF
supply optional parameter values from external file for:
E04DGF/E04DGA	E04DJF/E04DJA
E04MFF/E04MFA	E04MGF/E04MGA
E04NCF/E04NCA	E04NDF/E04NDA
E04NFF/E04NFA	E04NGF/E04NGA
E04NQF	E04NRF
E04UCF/E04UCA	E04UDF/E04UDA
E04UGF/E04UGA	E04UHF/E04UHA
E04USF/E04USA	E04UQF/E04UQA
E04VHF	E04VKF
E04WDF	E04WEF
supply optional parameter values to,
E04UGF/E04UGA	E04UJF/E04UJA
supply optional parameter values to:
E04DGF/E04DGA	E04DKF/E04DKA
E04MFF/E04MFA	E04MHF/E04MHA
E04NCF/E04NCA	E04NEF/E04NEA
E04NFF/E04NFA	E04NHF/E04NHA
E04NQF	E04NSF
E04UCF/E04UCA	E04UEF/E04UEA
E04USF/E04USA	E04URF/E04URA
E04VHF	E04VLF
E04WDF	E04WFF
E04WDF	E04WJF
Unconstrained minimum of a sum of squares (comprehensive):
using first derivatives,
combined Gauss–Newton and modified Newton algorithm	E04GDF
combined Gauss–Newton and quasi-Newton algorithm	E04GBF
using function values only,
combined Gauss–Newton and modified Newton algorithm	E04FCF
using second derivatives,
combined Gauss–Newton and modified Newton algorithm	E04HEF
Unconstrained minimum of a sum of squares (easy-to-use):
using first derivatives,
combined Gauss–Newton and modified Newton algorithm	E04GZF
combined Gauss–Newton and quasi-Newton algorithm	E04GYF
using function values only,
combined Gauss–Newton and modified Newton algorithm	E04FYF
Unconstrained minimum, function of several variables (comprehensive):
using first derivatives, pre-conditioned conjugate gradient algorithm	E04DGF/E04DGA
using function values only, simplex algorithm	E04CCF/E04CCA

F01 – Matrix Operations, Including Inversion

Inversion (also see Chapter F07),
real m by n matrix,
pseudo inverse	F01BLF
real symmetric positive-definite matrix,
accurate inverse	F01ABF
approximate inverse	F01ADF
Matrix Arithmetic and Manipulation,
matrix addition,
complex matrices	F01CWF
real matrices	F01CTF
matrix multiplication	F01CKF
matrix storage conversion,
packed band ↔ rectangular storage,
complex matrices	F01ZDF
real matrices	F01ZCF
packed triangular ↔ square storage,
complex matrices	F01ZBF
eal matrices	F01ZAF
matrix subtraction,
complex matrices	F01CWF
real matrices	F01CTF
matrix transpose	F01CRF
Matrix Transformations,
complex m by n (m≤n) matrix,
RQ factorization	F01RJF
complex matrix, form unitary matrix	F01RKF
complex upper trapezoidal matrix,
RQ factorization	F01RGF
eigenproblem A x = λ B x , A , B banded,
reduction to standard symmetric problem	F01BVF
real almost block-diagonal matrix,
LU factorization	F01LHF
real band symmetric positive-definite matrix,
U L D L^T U^T factorization	F01BUF
variable bandwidth, L D L^T factorization	F01MCF
real m by n (m≤n) matrix,
RQ factorization	F01QJF
real matrix,
form orthogonal matrix	F01QKF
real Sparse matrix,
factorization	F01BRF
factorization, known sparsity pattern	F01BSF
real upper trapezoidal matrix,
RQ factorization	F01QGF
tridiagonal matrix,
LU factorization	F01LEF

F02 – Eigenvalues and Eigenvectors

Black Box routines,
complex eigenproblem,
selected eigenvalues and eigenvectors	F02GCF
complex upper triangular matrix,
singular values and, optionally, left and/or right singular vectors	F02XUF
generalized real sparse symmetric-definite eigenproblem,
selected eigenvalues and eigenvectors	F02FJF
real eigenproblem,
selected eigenvalues and eigenvectors	F02ECF
real sparse symmetric matrix,
selected eigenvalues and eigenvectors	F02FJF
real upper triangular matrix,
singular values and, optionally, left and/or right singular vectors	F02WUF
General Purpose routines (see also Chapter F08),
real band matrix, selected eigenvector, A - λ B	F02SDF
real m by n matrix (m≥n) , Q R factorization and SVD	F02WDF

F03 – Determinants

Black Box routines,
complex matrix	F03ADF
real matrix	F03AAF
real symmetric positive-definite band matrix	F03ACF
real symmetric positive-definite matrix	F03ABF
General Purpose routines,
including the decomposition into triangular factors:
real matrix	F03AFF
real symmetric positive-definite matrix	F03AEF

F04 – Simultaneous Linear Equations

Black Box routines, A x = b ,
complex general band matrix	F04CBF
complex general matrix	F04CAF
complex general tridiagonal matrix	F04CCF
complex Hermitian matrix,
packed matrix format	F04CJF
standard matrix format	F04CHF
complex Hermitian positive-definite band matrix	F04CFF
complex Hermitian positive-definite matrix,
packed matrix format	F04CEF
standard matrix format	F04CDF
complex Hermitian positive-definite tridiagonal matrix	F04CGF
complex symmetric matrix,
packed matrix format	F04DJF
standard matrix format	F04DHF
real general band matrix	F04BBF
Real general matrix
Multiple right-hand sides
Iterative refinement using additional precision	F04AEF
Single right-hand side
Iterative refinement using additional precision	F04ATF
real general matrix,
multiple right-hand sides, standard precision	F04BAF
real general tridiagonal matrix	F04BCF
real symmetric matrix,
packed matrix format	F04BJF
standard matrix format	F04BHF
real symmetric positive-definite band matrix	F04BFF
Real symmetric positive-definite matrix
Multiple right-hand sides
Iterative refinement using additional precision	F04ABF
Single right-hand side
Iterative refinement using additional precision	F04ASF
real symmetric positive-definite matrix,
multiple right-hand sides, standard precision	F04BDF
packed matrix format	F04BEF
Real symmetric positive-definite Toeplitz matrix
General right-hand side	F04FFF
Yule–Walker equations	F04FEF
real symmetric positive-definite tridiagonal matrix	F04BGF
General Purpose routines, A x = b ,
real almost block-diagonal matrix	F04LHF
real band symmetric positive-definite matrix, variable bandwidth	F04MCF
real matrix	F04AJF
real matrix, Iterative refinement	F04AHF
real sparse matrix,
direct method	F04AXF
iterative method	F04QAF
real symmetric positive-definite matrix	F04AGF
real symmetric positive-definite matrix, Iterative refinement	F04AFF
real symmetric positive-definite Toeplitz matrix,
general right-hand side, Update solution	F04MFF
Yule–Walker equations, Update solution	F04MEF
real tridiagonal matrix	F04LEF
Least-squares and Homogeneous Equations,
real m by n matrix,
m ≥ n , Rank = n or minimal solution	F04JGF
rank = n , Iterative refinement	F04AMF
real sparse matrix	F04QAF
Service Routines,
complex matrix,
norm and condition number estimation	F04ZCF
real matrix,
covariance matrix for linear least-squares problems	F04YAF
norm and condition number estimation	F04YCF

F05 – Orthogonalisation

Schmidt orthogonalisation of n vectors of order m

F05AAF

F06 – Linear Algebra Support Routines

Level 0 (Scalar) operations:
Complex numbers:
apply similarity rotation to 2 by 2 Hermitian matrix	F06CHF
generate a plane rotation, storing the tangent, real cosine	F06CAF
generate a plane rotation, storing the tangent, real sine	F06CBF
quotient of two numbers, with overflow flag	F06CLF
recover cosine and sine from given tangent, real cosine	F06CCF
recover cosine and sine from given tangent, real sine	F06CDF
Real numbers:
apply similarity rotation to 2 by 2 symmetric matrix	F06BHF
compute (a2+b2) 1 / 2	F06BNF
compute Euclidean norm from scaled form	F06BMF
eigenvalue of 2 by 2 symmetric matrix	F06BPF
generate a Jacobi plane rotation	F06BEF
generate a plane rotation	F06AAF (DROTG)
generate a plane rotation storing the tangent	F06BAF
quotient of two numbers, with overflow flag	F06BLF
recover cosine and sine from given tangent	F06BCF
Level 1 (Vector) operations:
Complex vector(s),
add scalar times a vector to another vector	F06GCF (ZAXPY)
apply a complex plane rotation	F06HPF
apply a real plane rotation	F06KPF
apply an elementary reflection to a vector	F06HTF
broadcast a scalar into a vector	F06HBF
copy a real vector to a complex vector	F06KFF
copy a vector	F06GFF (ZCOPY)
dot product of two vectors, conjugated	F06GBF (ZDOTC)
dot product of two vectors, unconjugated	F06GAF (ZDOTU)
Euclidean norm of a vector	F06JJF (DZNRM2)
generate a sequence of plane rotations	F06HQF
generate an elementary reflection	F06HRF
index of element of largest absolute value	F06JMF (IZAMAX)
multiply vector by a complex scalar	F06GDF (ZSCAL)
multiply vector by a complex scalar, preserving input vector	F06HDF
multiply vector by a real scalar	F06JDF (ZDSCAL)
multiply vector by a real scalar, preserving input vector	F06KDF
multiply vector by complex diagonal matrix	F06HCF
multiply vector by real diagonal matrix	F06KCF
multiply vector by reciprocal of a real scalar	F06KEF (ZDRSCL)
negate a vector	F06HGF
sum of absolute values of vector-elements	F06JKF (DZASUM)
swap two vectors	F06GGF (ZSWAP)
update Euclidean norm in scaled form	F06KJF
Integer vector(s),
broadcast a scalar into a vector	F06DBF
copy a vector	F06DFF
Real vector(s),
add scalar times a vector to another vector	F06ECF (DAXPY)
apply a symmetric plane rotation to two vectors	F06FPF
apply an elementary reflection to a vector (Linpack style)	F06FUF
apply an elementary reflection to a vector (NAG style)	F06FTF
apply plane rotation	F06EPF (DROT)
broadcast a scalar into a vector	F06FBF
copy a vector	F06EFF (DCOPY)
cosine of angle between two vectors	F06FAF
dot product of two vectors	F06EAF (DDOT)
elements of largest and smallest absolute value	F06FLF
Euclidean norm of a vector	F06EJF (DNRM2)
generate a sequence of plane rotations	F06FQF
generate an elementary reflection (Linpack style)	F06FSF
generate an elementary reflection (NAG style)	F06FRF
index of element of largest absolute value	F06JLF (IDAMAX)
index of last non-negligible element	F06KLF
multiply vector by a scalar	F06EDF (DSCAL)
multiply vector by a scalar, preserving input vector	F06FDF
multiply vector by diagonal matrix	F06FCF
multiply vector by reciprocal of a scalar	F06FEF (DRSCL)
negate a vector	F06FGF
sum of absolute values of vector-elements	F06EKF (DASUM)
swap two vectors	F06EGF (DSWAP)
update Euclidean norm in scaled form	F06FJF
weighted Euclidean norm of a vector	F06FKF
Level 2 (Matrix-vector and matrix) operations:
Complex matrix and vector(s),
apply sequence of plane rotations to a rectangular matrix:
complex cosine, real sine	F06TYF
real cosine and sine	F06VXF
real cosine, complex sine	F06TXF
compute a norm or the element of largest absolute value:
band matrix	F06UBF
general matrix	F06UAF
Hermitian band matrix	F06UEF
Hermitian matrix	F06UCF
Hermitian matrix, packed form	F06UDF
Hermitian tridiagonal matrix	F06UPF
Hessenberg matrix	F06UMF
symmetric band matrix	F06UHF
symmetric matrix	F06UFF
symmetric matrix, packed form	F06UGF
trapezoidal matrix	F06UJF
triangular band matrix	F06ULF
triangular matrix, packed form	F06UKF
tridiagonal matrix	F06UNF
compute upper Hessenberg matrix by applying sequence of plane rotations to an upper triangular matrix	F06TVF
compute upper spiked matrix by applying sequence of plane rotations to an upper triangular matrix	F06TWF
matrix initialization	F06THF
matrix-vector product,
Hermitian band matrix	F06SDF (ZHBMV)
Hermitian matrix	F06SCF (ZHEMV)
Hermitian packed matrix	F06SEF (ZHPMV)
rectangular band matrix	F06SBF (ZGBMV)
rectangular matrix	F06SAF (ZGEMV)
symmetric matrix	F06TAF (ZSYMV)
symmetric packed matrix	F06TCF (ZSPMV)
triangular band matrix	F06SGF (ZTBMV)
triangular matrix	F06SFF (ZTRMV)
triangular packed matrix	F06SHF (ZTPMV)
permute rows or columns of a matrix:
permutations represented by a real array	F06VKF
permutations represented by an integer array	F06VJF
Q R factorization by sequence of plane rotations:
of rank-1 update of upper triangular matrix	F06TPF
of upper triangular matrix augmented by a full row	F06TQF
Q R factorization of U Z or R Q factorization of Z U , where U is upper triangular and Z is a sequence of plane rotations	F06TTF
Q R or R Q factorization by sequence of plane rotations:
of upper Hessenberg matrix	F06TRF
of upper spiked matrix	F06TSF
rank-1 update,
Hermitian matrix	F06SPF (ZHER)
Hermitian packed matrix	F06SQF (ZHPR)
rectangular matrix, conjugated vector	F06SNF (ZGERC)
rectangular matrix, unconjugated vector	F06SMF (ZGERU)
symmetric matrix	F06TBF (ZSYR)
symmetric packed matrix	F06TDF (ZSPR)
rank-2 update,
Hermitian matrix	F06SRF (ZHER2)
Hermitian packed matrix	F06SSF (ZHPR2)
matrix copy, rectangular or trapezoidal	F06TFF
solution of a system of equations:
triangular band matrix	F06SKF (ZTBSV)
triangular matrix	F06SJF (ZTRSV)
triangular packed matrix	F06SLF (ZTPSV)
unitary similarity transformation of a Hermitian matrix,
as sequence of plane rotations	F06TMF
Real matrix and vector(s),
apply sequence of plane rotations to a rectangular matrix	F06QXF
compute a norm or the element of largest absolute value:
band matrix	F06RBF
general matrix	F06RAF
Hessenberg matrix	F06RMF
matrix initialization	F06QHF
symmetric band matrix	F06REF
symmetric matrix	F06RCF
symmetric matrix, packed form	F06RDF
symmetric tridiagonal matrix	F06RPF
trapezoidal matrix	F06RJF
triangular band matrix	F06RLF
triangular matrix, packed form	F06RKF
tridiagonal matrix	F06RNF
compute upper Hessenberg matrix by applying sequence of plane rotations to an upper triangular matrix	F06QVF
compute upper spiked matrix by applying sequence of plane rotations to an upper triangular matrix	F06QWF
matrix-vector product,
rectangular band matrix	F06PBF (DGBMV)
rectangular matrix	F06PAF (DGEMV)
symmetric band matrix	F06PDF (DSBMV)
symmetric matrix	F06PCF (DSYMV)
symmetric packed matrix	F06PEF (DSPMV)
triangular band matrix	F06PGF (DTBMV)
triangular matrix	F06PFF (DTRMV)
triangular packed matrix	F06PHF (DTPMV)
orthogonal similarity transformation of a symmetric matrix,
as sequence of plane rotations	F06QMF
permute rows or columns of a matrix:
permutations represented by a real array	F06QKF
permutations represented by an integer array	F06QJF
Q R factorization by sequence of plane rotations:
of rank-1 update of upper triangular matrix	F06QPF
of upper triangular matrix augmented by a full row	F06QQF
Q R factorization of U Z or R Q factorization of Z U , where U is upper triangular and Z is a sequence of plane rotations	F06QTF
Q R or R Q factorization by sequence of plane rotations:
of upper Hessenberg matrix	F06QRF
of upper spiked matrix	F06QSF
rank-1 update,
rectangular matrix	F06PMF (DGER)
symmetric matrix	F06PPF (DSYR)
symmetric packed matrix	F06PQF (DSPR)
rank-2 update,
matrix copy, rectangular or trapezoidal	F06QFF
symmetric matrix	F06PRF (DSYR2)
symmetric packed matrix	F06PSF (DSPR2)
solution of system of equations,
triangular band matrix	F06PKF (DTBSV)
triangular matrix	F06PJF (DTRSV)
triangular packed matrix	F06PLF (DTPSV)
Level 3 (Matrix-matrix) operations:
Complex matrices:
matrix-matrix product:
one matrix Hermitian	F06ZCF (ZHEMM)
one matrix symmetric	F06ZTF (ZSYMM)
triangular matrix	F06ZFF (ZTRMM)
two rectangular matrices	F06ZAF (ZGEMM)
rank- 2 k update:
of a Hermitian matrix	F06ZRF (ZHER2K)
of a symmetric matrix	F06ZWF (ZSYR2K)
rank- k update:
of a Hermitian matrix	F06ZPF (ZHERK)
of a symmetric matrix	F06ZUF (ZSYRK)
solution of triangular systems of equations	F06ZJF (ZTRSM)
Real matrices:
matrix-matrix product:
one matrix symmetric	F06YCF (DSYMM)
one matrix triangular	F06YFF (DTRMM)
rectangular matrices	F06YAF (DGEMM)
rank- 2 k update of a symmetric matrix	F06YRF (DSYR2K)
rank- k update of a symmetric matrix	F06YPF (DSYRK)
solution of triangular systems of equations	F06YJF (DTRSM)
Sparse level 1 (vector) operations:
Complex vectors:
add scalar times sparse vector to another sparse vector	F06GTF (ZAXPYI)
dot product of two sparse vectors (conjugated)	F06GSF (ZDOTCI)
dot product of two sparse vectors (unconjugated)	F06GRF (ZDOTUI)
gather and set to zero a sparse vector	F06GVF (ZGTHRZ)
gather sparse vector	F06GUF (ZGTHR)
scatter sparse vector	F06GWF (ZSCTR)
Real vectors:
add scalar times sparse vector to another sparse vector	F06ETF (DAXPYI)
apply plane rotation to two sparse vectors	F06EXF (DROTI)
dot product of two sparse vectors	F06ERF (DDOTI)
gather and set to zero a sparse vector	F06EVF (DGTHRZ)
gather sparse vector	F06EUF (DGTHR)
scatter sparse vector	F06EWF (DSCTR)

F07 – Linear Equations (LAPACK)

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

F08 – Least-squares and Eigenvalue Problems (LAPACK)

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

F11 – Large Scale Linear Systems

Apply iterative refinement to the solution and compute error estimates, after factorizing the matrix of coefficients,
real sparse nonsymmetric matrix in CCS format	F11MHF
Basic routines for real sparse nonsymmetric linear systems
Matrix-matrix multiplier for real sparse nonsymmetric matrices in CCS format	F11MKF
Basic routines for complex Hermitian linear systems,
diagnostic routine	F11GTF
setup routine	F11GRF
Basic routines for complex non-Hermitian linear systems,
diagnostic routine	F11BTF
reverse communication RGMRES, CGS, Bi-CGSTAB (ℓ) or TFQMR solver routine	F11BSF
setup routine	F11BRF
Basic routines for real nonsymmetric linear systems,
diagnostic routine	F11BFF
reverse communication RGMRES, CGS, Bi-CGSTAB (ℓ) or TFQMR solver routine	F11BEF
setup routine	F11BDF
Basic routines for real symmetric linear systems,
diagnostic routine	F11GFF
reverse communication CG or SYMMLQ solver	F11GEF
setup routine	F11GDF
Black Box routines for complex Hermitian linear systems,
CG or SYMMLQ solver
with incomplete Cholesky preconditioning	F11JQF
with no preconditioning, Jacobi or SSOR preconditioning	F11JSF
Black Box routines for complex non-Hermitian linear systems,
RGMRES, CGS, Bi-CGSTAB (ℓ) or TFQMR solver
with incomplete L U preconditioning	F11DQF
with no preconditioning, Jacobi, or SSOR preconditioning	F11DSF
Black Box routines for real nonsymmetric linear systems,
RGMRES, CGS, Bi-CGSTAB (ℓ) or TFQMR solver
with incomplete L U preconditioning	F11DCF
with no preconditioning, Jacobi, or SSOR preconditioning	F11DEF
Black Box routines for real symmetric linear systems,
CG or SYMMLQ solver
with incomplete Cholesky preconditioning	F11JCF
with no preconditioning, Jacobi, or SSOR preconditioning	F11JEF
Compute a norm or the element of largest absolute value,
real sparse nonsymmetric matrix in CCS format	F11MLF
Condition number estimation, after factorizing the matrix of coefficients,
real sparse nonsymmetric matrix in CCS format	F11MGF
L U factorization,
diagnostic routine,
real sparse nonsymmetric matrix in CCS format	F11MMF
real sparse nonsymmetric matrix in CCS format	F11MEF
setup routine,
real sparse nonsymmetric matrices in CCS format	F11MDF
matrix-vector multiplier for complex Hermitian matrices in SCS format	F11XSF
reverse communication CG or SYMMLQ solver routine	F11GSF
Solution of simultaneous linear equations, after factorizing the matrix of coefficients,
real sparse nonsymmetric matrix in CCS format	F11MFF
Utility routine for complex Hermitian linear systems,
incomplete Cholesky factorization	F11JNF
solver for linear systems involving preconditioning matrix from F11JNF	F11JPF
solver for linear systems involving SSOR preconditioning matrix	F11JRF
sort routine for complex Hermitian matrices in SCS format	F11ZPF
Utility routine for complex non-Hermitian linear systems,
incomplete L U factorization	F11DNF
matrix-vector multiplier for complex non-Hermitian matrices in CS format	F11XNF
solver for linear systems involving iterated Jacobi method	F11DXF
solver for linear systems involving preconditioning matrix from F11DNF	F11DPF
solver for linear systems involving SSOR preconditioning matrix	F11DRF
sort routine for complex non-Hermitian matrices in CS format	F11ZNF
Utility routine for real nonsymmetric linear systems,
incomplete L U factorization	F11DAF
matrix-vector multiplier for real nonsymmetric matrices in CS format	F11XAF
solver for linear systems involving iterated Jacobi method	F11DKF
solver for linear systems involving preconditioning matrix from F11DAF	F11DBF
solver for linear systems involving SSOR preconditioning matrix	F11DDF
sort routine for real nonsymmetric matrices in CS format	F11ZAF
Utility routine for real symmetric linear systems,
incomplete Cholesky factorization	F11JAF
matrix-vector multiplier for real symmetric matrices in SCS format	F11XEF
solver for linear systems involving preconditioning matrix from F11JAF	F11JBF
solver for linear systems involving SSOR preconditioning matrix	F11JDF
sort routine for real symmetric matrices in SCS format	F11ZBF

F12 – Large Scale Eigenproblems

Standard or generalized eigenvalue problems for complex matrices:
general matrices,
initialize problem and method	F12ANF
option setting	F12ARF
reverse communication implicitly restarted Arnoldi method	F12APF
reverse communication monitoring	F12ASF
selected eigenvalues, eigenvectors and/or Schur vectors of original problem	F12AQF
Standard or generalized eigenvalue problems for real nonsymmetric matrices:
banded matrices,
initialize problem and method	F12AFF
selected eigenvalues, eigenvectors and/or Schur vectors	F12AGF
general matrices,
initialize problem and method	F12AAF
option setting	F12ADF
reverse communication implicitly restarted Arnoldi method	F12ABF
reverse communication monitoring	F12AEF
selected eigenvalues, eigenvectors and/or Schur vectors of original problem	F12ACF
Standard or generalized eigenvalue problems for real symmetric matrices:
banded matrices,
initialize problem and method	F12FFF
option setting	F12FDF
selected eigenvalues, eigenvectors and/or Schur vectors	F12FGF
general matrices,
initialize problem and method	F12FAF
reverse communication implicitly restarted Arnoldi(Lanczos) method	F12FBF
reverse communication monitoring	F12FEF
selected eigenvalues and eigenvectors and/or Schur vectors of original problem	F12FCF

G01 – Simple Calculations on Statistical Data

Descriptive statistics / Exploratory analysis:
plots:
box and whisker	G01ASF
histogram	G01AJF
Normal probability ( Q - Q ) plot	G01AHF
scatter plot	G01AGF
stem and leaf	G01ARF
summaries:
frequency / contigency table,
one variable	G01AEF
two variables, with χ² and Fisher's exact test	G01AFF
mean, variance, skewness, kurtosis (one variable),
from frequency table	G01ADF
mean, variance, sums of squares and products (two variables)	G01ABF
median, hinges / quartiles, minimum, maximum	G01ALF
Descriptive statistics / Exporatory analysis:
summaries:
mean, variance, skewness, kurtosis (one variable),
from raw data	G01AAF
Distributions:
Beta:
central:
deviates	G01FEF
probabilities and probability density function	G01EEF
non-central:
probabilities	G01GEF
Binomial:
distribution function	G01BJF
Durbin–Watson statistic:
probabilities	G01EPF
Energy loss distributions:
Landau:
density	G01MTF
derivative of density	G01RTF
distribution	G01ETF
first moment	G01PTF
inverse distribution	G01FTF
second moment	G01QTF
Vavilov:
density	G01MUF
distribution	G01EUF
initialization	G01ZUF
F :
central:
deviates	G01FDF
probabilities	G01EDF
non-central:
probabilities	G01GDF
Gamma:
deviates	G01FFF
probabilities	G01EFF
Hypergeometeric:
distribution function	G01BLF
Kolomogorov–Smirnov:
probabilities:
one-sample	G01EYF
two-sample	G01EZF
Normal:
bivariate:
probabilities	G01HAF
multivariate:
probabilities	G01HBF
quadratic forms:
cumulants and moments	G01NAF
moments of ratios	G01NBF
univariate:
deviates	G01FAF
probabilities	G01EAF
reciprocal of Mill's Ratio	G01MBF
Shapiro and Wilks test for Normality	G01DDF
Poisson:
distribution function	G01BKF
Student's t :
central:
deviates	G01FBF
probabilities	G01EBF
non-central:
probabilities	G01GBF
Studentized range statistic:
deviates	G01FMF
probabilities	G01EMF
von Mises:
probabilities	G01ERF
χ² :
central:
deviates	G01FCF
probabilities	G01ECF
probability of linear combination	G01JDF
non-central:
probabilities	G01GCF
probability of linear combination	G01JCF
Scores:
Normal scores, ranks or exponential (Savage) scores	G01DHF
Normal scores:
accurate	G01DAF
approximate	G01DBF
variance-covariance matrix	G01DCF

G02 – Correlation and Regression Analysis

Correlation-like coefficients:
all variables
casewise treatment of missing values	G02BEF
no missing values	G02BDF
pairwise treatment of missing values	G02BFF
subset of variables
casewise treatment of missing values	G02BLF
no missing values	G02BKF
pairwise treatment of missing values	G02BMF
Generalized linear models:
Binomial errors	G02GBF
computes estimable function	G02GNF
Gamma errors	G02GDF
Normal errors	G02GAF
Poisson errors	G02GCF
transform model parameters	G02GKF
Linear mixed effects regression:
via maximum likelihood (ML)	G02JBF
via restricted maximum likelihood (REML)	G02JAF
Multiple linear regression/General linear model:
add independent variable to model	G02DEF
add/delete observation from model	G02DCF
computes estimable function	G02DNF
delete independent variable from model	G02DFF
general linear regression model	G02DAF
regression for new dependent variable	G02DGF
regression parameters from updated model	G02DDF
transform model parameters	G02DKF
Multiple linear regression:
from correlation coefficients	G02CGF
from correlation-like coefficients	G02CHF
Non-parametric rank correlation (Kendall and/or Spearman):
missing values
casewise treatment of missing values
overwriting input data	G02BPF
preserving input data	G02BRF
pairwise treatment of missing values	G02BSF
no missing values
overwriting input data	G02BNF
preserving input data	G02BQF
Product moment correlation:
correlation coefficients, all variables
casewise treatment of missing values	G02BBF
no missing values	G02BAF
pairwise treatment of missing values	G02BCF
correlation coefficients, subset of variables
casewise treatment of missing values	G02BHF
no missing values	G02BGF
pairwise treatment of missing values	G02BJF
correlation matrix
compute correlation and covariance matrices	G02BXF
compute from sum of squares matrix	G02BWF
compute partial correlation and covariance matrices	G02BYF
sum of squares matrix
compute	G02BUF
update	G02BTF
Residuals:
Durbin–Watson test	G02FCF
standardized residuals and influence statistics	G02FAF
Robust correlation:
Huber's method	G02HKF
user-supplied weight function only	G02HMF
user-supplied weight function plus derivatives	G02HLF
Robust regression:
compute weights for use with G02HDF	G02HBF
standard M -estimates	G02HAF
user supplies weight functions	G02HDF
variance-covariance matrix following G02HDF	G02HFF
Selecting regression model:
all possible regressions	G02EAF
forward selection	G02EEF
R² and C_p statistics	G02ECF
Service routines:
for multiple linear regression
reorder elements from vectors and matrices	G02CFF
select elements from vectors and matrices	G02CEF
Simple linear regression:
simple linear regression	G02CAF
simple linear regression,
no intercept	G02CBF
no intercept with missing values	G02CDF
with missing values	G02CCF
Stepwise linear regression:
Clarke's sweep algorithm	G02EFF

G03 – Multivariate Methods

Canonical correlation analysis	G03ADF
Canonical variate analysis	G03ACF
Cluster Analysis:
compute distance matrix	G03EAF
construct clusters following G03ECF	G03EJF
construct dendrogram following G03ECF	G03EHF
hierarchical	G03ECF
K-means	G03EFF
Discriminant Analysis:
allocation of observations to groups, following G03DAF	G03DCF
Mahalanobis squared distances, following G03DAF	G03DBF
test for equality of within-group covariance matrices	G03DAF
Factor Analysis:
maximum likelihood estimates of parameters	G03CAF
factor score coefficients, following G03CAF	G03CCF
Principal component analysis	G03AAF
Rotations:
orthogonal rotations for loading matrix	G03BAF
Procustes rotations	G03BCF
Scaling Methods:
multidimensional scaling	G03FCF
principal co-ordinate analysis	G03FAF
Standardize values of a data matrix	G03ZAF

G04 – Analysis of Variance

Analysis of variance for:
complete factorial design	G04CAF
general block design or completely randomized design	G04BBF
general block design or completely randomized design,
row and column design	G04BCF
two-way hierarchical classification, subgroups of unequal size	G04AGF
General linear model:
generate dummy variables and orthogonal polynomials	G04EAF
Inferences on means:
simultaneous confidence intervals	G04DBF
sum of squares for contrast between means	G04DAF

G05 – Random Number Generators

Generating samples, matrices and tables,
random correlation matrix	G05QBF
random orthogonal matrix	G05QAF
random permutation of an integer vector	G05NAF
random sample from an integer vector	G05NBF
random table	G05QDF
Generation of time series,
asymmetric GARCH Type II	G05HLF
asymmetric GJR GARCH	G05HMF
EGARCH	G05HNF
symmetric GARCH or asymmetric GARCH Type I	G05HKF
univariate ARMA model,
Normal errors	G05PAF
vector ARMA model,
Normal errors	G05PCF
Pseudo-random numbers,
array of variates from multivariate distributions,
multinomial distribution	G05MRF
Normal distribution	G05LXF
Student's t distribution	G05LYF
Copulas
Gaussian Copula	G05RAF
Student's t Copula	G05RBF
initialize generator,
nonrepeatable sequence	G05KCF
repeatable sequence	G05KBF
single variate from multivariate distributions,
Normal distribution	G05LZF
single variate, from a univariate disribution
logical value .TRUE. or .FALSE.	G05KEF
real number from the continuous uniform distribution	G05KAF
vector of variates from discrete univariate distributions,
binomial distribution	G05MJF
geometric distribution	G05MBF
hypergeometric distribution	G05MLF
logarithmic distribution	G05MDF
negative binomial distribution	G05MCF
Poisson distribution	G05MKF
uniform distribution	G05MAF
user-supplied distribution	G05MZF
variate array from discrete distributions with array of parameters,
Poisson distribution with varying mean	G05MEF
vectors of variates from continuous univariate distributions,
beta distribution	G05LEF
Cauchy distribution	G05LLF
chi-square distribution	G05LCF
exponential mix distribution	G05LQF
F -distribution	G05LDF
gamma distribution	G05LFF
logistic distribution	G05LNF
lognormal distribution	G05LKF
negative exponential distribution	G05LJF
Normal distribution	G05LAF
Student's t -distribution	G05LBF
triangular distribution	G05LHF
uniform distribution	G05LGF
von Mises distribution	G05LPF
Weibull distribution	G05LMF
Quasi-random numbers,
array of variates from univariate distributions,
Faure generator	G05YDF
Log normal distribution	G05YKF
Neiderreiter generator	G05YHF
Normal distribution	G05YJF
Sobol generator	G05YFF
initialize generator,
Faure generators	G05YCF
Neiderreiter generators	G05YGF
Sobol generators	G05YEF

G07 – Univariate Estimation

2 sample t -test	G07CAF
Confidence intervals for parameters:
binomial distribution	G07AAF
Poisson distribution	G07ABF
Maximum likelihood estimation of parameters:
Normal distribution, grouped and/or censored data	G07BBF
Weibull distribution	G07BEF
Robust estimation:
confidence intervals:
one sample	G07EAF
two samples	G07EBF
M -estimates for location and scale parameters:
standard weight functions	G07DBF
trimmed and winsorized means and estimates of their variance	G07DDF
user-defined weight functions	G07DCF
median, median absolute deviation and robust standard deviation	G07DAF

G08 – Nonparametric Statistics

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

G10 – Smoothing in Statistics

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

G11 – Contingency Table Analysis

Conditional logistic model for stratified data	G11CAF
Frequency count for G11SAF	G11SBF
Latent variable model for dichotomous data	G11SAF
Multiway tables from set of classification factors:
marginal table from G11BAF or G11BBF	G11BCF
using given percentile/quantile	G11BBF
using selected statistic	G11BAF
χ² statistics for two-way contingency table	G11AAF

G12 – Survival Analysis

Cox's proportional hazard model:
create the risk sets	G12ZAF
parameter estimates and other statistics	G12BAF
Survivor function	G12AAF

G13 – Time Series Analysis

ARMA modelling,
ACF	G13ABF
diagnostic checking	G13ASF
differencing	G13AAF
estimation (comprehensive)	G13AEF
estimation (easy-to-use)	G13AFF
forecasting from fully specified model	G13AJF
forecasting from state set	G13AHF
mean/range	G13AUF
PACF	G13ACF
preliminary estimation	G13ADF
update state set	G13AGF
Bivariate spectral analysis,
Bartlett, Tukey, Parzen windows	G13CCF
direct smoothing	G13CDF
other representations	G13CEF
other representations	G13CFF
other representations	G13CGF
GARCH,
asymmetric ARCH/GARCH,
fitting	G13FAF
fitting	G13FCF
fitting	G13FEF
forecasting	G13FBF
forecasting	G13FDF
forecasting	G13FFF
EGARCH,
fitting	G13FGF
forecasting	G13FHF
symmetric ARCH/GARCH,
fitting	G13FAF
forecasting	G13FBF
Kalman filter,
Time invariant,
square root covariance	G13EBF
Time varying,
square root covariance	G13EAF
Transfer function modelling,
cross-correlations	G13BCF
filtering	G13BBF
fitting	G13BEF
forecasting from fully specified model	G13BJF
forecasting from state set	G13BHF
pre-whitening	G13BAF
preliminary estimation	G13BDF
update state set	G13BGF
Univariate spectral analysis,
Bartlett, Tukey, Parzen windows	G13CAF
direct smoothing	G13CBF
Vector ARMA,
cross-correlations	G13DMF
diagnostic checks	G13DSF
differencing	G13DLF
fitting	G13DCF
forecasting	G13DJF
partial-correlations/autoregressions	G13DBF
partial-correlations/autoregressions	G13DNF
partial-correlations/autoregressions	G13DPF
update forecast	G13DKF
zeros of ARIMA operator	G13DXF

H – Operations Research

Convert data to arrays for use with H02BBF or E04MFF/E04MFA	H02BUF
Integer programming problem (dense):
print solution with specified names	H02BVF
solve LP problem using branch and bound method	H02BBF
solve QP problem using branch and bound method	H02CBF
supply further information on the solution obtained from H02BBF	H02BZF
Integer programming problem (sparse):
solve LP or QP problem using branch and bound method	H02CEF
MPSX data input, defining IP or LP problem:
interpret data, optimize and print solution	H02BFF
Read optional parameter values from external file for H02CBF	H02CCF
Read optional parameter values from external file for H02CEF	H02CFF
Shortest path, through directed or undirected network	H03ADF
Supply optional parameter values to H02CBF	H02CDF
Supply optional parameter values to H02CEF	H02CGF
Transportation problem	H03ABF

M01 – Sorting

Ranking:
arbitrary data	M01DZF
columns of a matrix,
integer numbers	M01DKF
real numbers	M01DJF
rows of a matrix,
integer numbers	M01DFF
real numbers	M01DEF
vector,
character data	M01DCF
integer numbers	M01DBF
real numbers	M01DAF
Rearranging (according to pre-determined ranks):
vector,
character data	M01ECF
complex numbers	M01EDF
integer numbers	M01EBF
real numbers	M01EAF
Service routines:
check validity of a permutation	M01ZBF
decompose a permutation into cycles	M01ZCF
invert a permutation (ranks to indices or vice versa)	M01ZAF
Sorting (i.e., rearranging into sorted order):
quick sort,
vector,
real numbers	M01CAF
vector,
character data	M01CCF
integer numbers	M01CBF

P01 – Error Trapping

Return value of error indicator/terminate with error message

P01ABF

S – Approximations of Special Functions

Airy function,
Ai or Ai ′ , complex argument, optionally scaled	S17DGF
Ai , real argument	S17AGF
Ai ′ , real argument	S17AJF
Bi or Bi ′ , complex argument, optionally scaled	S17DHF
Bi , real argument	S17AHF
Bi ′ , real argument	S17AKF
Arccos,
inverse circular cosine	S09ABF
Arccosh,
inverse hyperbolic cosine	S11ACF
Arcsin,
inverse circular sine	S09AAF
Arcsinh,
inverse hyperbolic sine	S11ABF
Arctanh,
inverse hyperbolic tangent	S11AAF
Bessel function,
J₀ , real argument	S17AEF
J₁ , real argument	S17AFF
J_α ± n (z) , real argument	S18GKF
J_ν , complex argument, optionally scaled	S17DEF
Y₀ , real argument	S17ACF
Y₁ , real argument	S17ADF
Y_ν , complex argument, optionally scaled	S17DCF
Complement of the Cumulative Normal distribution	S15ACF
Complement of the Error function,
complex argument, scaled	S15DDF
real argument	S15ADF
Cosine Integral	S13ACF
Cosine,
hyperbolic	S10ACF
Cumulative Normal distribution function	S15ABF
Dawson's Integral	S15AFF
Digamma function, scaled	S14ADF
Elliptic functions, Jacobian, sn, cn, dn
complex argument	S21CBF
real argument	S21CAF
Elliptic integral,
general,
of 2nd kind, F (z, k ′ ,a,b)	S21DAF
symmetrised,
degenerate of 1st kind, R_C	S21BAF
of 1st kind, R_F	S21BBF
of 2nd kind, R_D	S21BCF
of 3rd kind, R_J	S21BDF
Erf,
real argument	S15AEF
Erfc,
complex argument, scaled	S15DDF
real argument	S15ADF
Error function,
real argument	S15AEF
Exponential Integral	S13AAF
Exponential,
complex	S01EAF
Fresnel Integral,
C	S20ADF
S	S20ACF
Gamma function	S14AAF
Gamma function,
incomplete	S14BAF
Generalized Factorial function	S14AAF
Hankel function H_ν⁽¹⁾ or H_ν⁽²⁾ ,
complex argument, optionally scaled	S17DLF
Jacobian elliptic functions, sn, cn, dn,
complex argument	S21CBF
real argument	S21CAF
Jacobian theta functions θ_k (x,q) ,
real argument	S21CCF
Kelvin function,
berx	S19AAF
beix	S19ABF
kerx	S19ACF
keix	S19ADF
Legendre functions of 1st kind P_n^m (x) , P_n^m (x)	S22AAF
Logarithm of 1 + x	S01BAF
Logarithm of Gamma function,
complex	S14AGF
real	S14ABF
Modified Bessel function(s),
I₀ , real argument	S18AEF
I₁ , real argument	S18AFF
I_ν , complex argument, optionally scaled	S18DEF
K₀ , real argument	S18ACF
K₁ , real argument	S18ADF
K_ν , complex argument, optionally scaled	S18DCF
Polygamma function,
ψ⁽ⁿ⁾ (x) , real x	S14AEF
ψ⁽ⁿ⁾ (z) , complex z	S14AFF
Psi function	S14ACF
Psi function and derivatives, scaled	S14ADF
Scaled modified Bessel function(s),
e^- \|x\| I₀ (x) , real argument	S18CEF
e^- \|x\| I₁ (x) , real argument	S18CFF
e^x K₀ (x) , real argument	S18CCF
e^x K₁ (x) , real argument	S18CDF
Sine Integral	S13ADF
Sine,
hyperbolic	S10ABF
Tangent,
circular	S07AAF
hyperbolic	S10AAF
Trigamma function, scaled	S14ADF
Zeros of Bessel functions J_α (x) , J_α ′ (x) , Y_α (x) , Y_α ′ (x)	S17ALF

X01 – Mathematical Constants

Euler's constant, γ	X01ABF
π	X01AAF

X02 – Machine Constants

Derived parameters of model of floating-point arithmetic:
largest positive model number	X02ALF
machine precision	X02AJF
safe range	X02AMF
safe range of complex floating point arithmetic	X02ANF
smallest positive model number	X02AKF
Largest permissible argument for SIN and COS	X02AHF
Largest representable integer	X02BBF
Maximum number of decimal digits that can be represented	X02BEF
Parameters of model of floating-point arithmetic:
b	X02BHF
emax	X02BLF
emin	X02BKF
p	X02BJF
ROUNDS	X02DJF
Switch for taking precautions to avoid underflow	X02DAF

X03 – Inner Products

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

X04 – Input/Output Utilities

Accessing external formatted file:
reading a record	X04BBF
writing a record	X04BAF
Accessing unit number:
of advisory message unit	X04ABF
of error message unit	X04AAF
Disconnecting an external file	X04ADF
Connecting an external file	X04ACF
Printing matrices:
Comprehensive routines:
general complex matrix	X04DBF
general integer matrix	X04EBF
general real matrix	X04CBF
packed complex band matrix	X04DFF
packed complex triangular matrix	X04DDF
packed real band matrix	X04CFF
packed real triangular matrix	X04CDF
Easy-to-use routines:
general complex matrix	X04DAF
general integer matrix	X04EAF
general real matrix	X04CAF
packed complex band matrix	X04DEF
packed complex triangular matrix	X04DCF
packed real band matrix	X04CEF
packed real triangular matrix	X04CCF

X05 – Date and Time Utilities

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

NAG Fortran Library