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Linear programming (LP),

dense,

active-set method/primal simplex,

alternative 1

e04mfc

alternative 2

e04ncc

sparse,

active-set method/primal simplex,

recommended (see Section 4.3 in the E04 Chapter Introduction)

e04nqc

alternative

e04nkc

Airy function,

$\mathrm{Ai}$, real argument,

scalar

s17agc

$\mathrm{Ai}$ or ${\mathrm{Ai}}^{\prime }$, complex argument, optionally scaled

s17dgc

${\mathrm{Ai}}^{\prime }$, real argument,

scalar

s17ajc

$\mathrm{Bi}$, real argument,

scalar

s17ahc

$\mathrm{Bi}$ or ${\mathrm{Bi}}^{\prime }$, complex argument, optionally scaled

s17dhc

${\mathrm{Bi}}^{\prime }$, real argument,

scalar

s17akc

Arccosh,

inverse hyperbolic cosine

s11acc

Arcsinh,

inverse hyperbolic sine

s11abc

Arctanh,

inverse hyperbolic tangent

s11aac

ARMA modelling,

ACF

g13abc

diagnostic checking

g13asc

differencing

g13aac

mean/range

g13auc

PACF

g13acc

Quadratic programming (QP),

dense,

active-set method for (possibly nonconvex) QP problem

e04nfc

active-set method for convex QP problem

e04ncc

sparse,

active-set method sparse convex QP problem,

recommended (see Section 4.3 in the E04 Chapter Introduction)

e04nqc

alternative

e04nkc

Bessel function,

$I_0$, real argument,

scalar

s18aec

$I_1$, real argument,

scalar

s18afc

$J_0$, real argument,

scalar

s17aec

$J_1$, real argument,

scalar

s17afc

$K_0$, real argument,

scalar

s18acc

$K_1$, real argument,

scalar

s18adc

$Y_0$, real argument,

scalar

s17acc

$Y_1$, real argument,

scalar

s17adc

Complement of the Cumulative Normal distribution,

scalar

s15acc

vectorized

s15aqc

Complement of the Error function,

real argument,

scalar

s15adc

vectorized

s15arc

real argument, scaled,

scalar

s15agc

vectorized

s15auc

Complex conjugate,

multiple Hermitian sequences

c06gqc

Complex sequence from Hermitian sequences

c06gsc

Compute error estimates,

real triangular matrix

f07thc

Cosine,

hyperbolic

s10acc

Cosine Integral

s13acc

Cumulative Normal distribution function,

scalar

s15abc

vectorized

s15apc

Nonlinear programming (NLP),

dense,

active-set sequential quadratic programming (SQP),

direct communication,

recommended (see Section 4.3 in the E04 Chapter Introduction)

e04ucc

alternative

e04wdc

reverse communication

e04ufc

sparse,

active-set sequential quadratic programming (SQP),

alternative

e04vhc

alternative

e04ugc

Dawson's Integral,

scalar

s15afc

vectorized

s15atc

Derivative,

of interpolant,

from e01bec

e01bgc

Descriptive statistics / Exploratory analysis,

summaries,

frequency / contingency table,

one variable

g01aec

mean, variance, skewness, kurtosis (one variable),

from frequency table

g01adc

median, hinges / quartiles, minimum, maximum

g01alc

quantiles,

unordered vector

unweighted

g01amc

Digamma function, scaled

s14adc

Discrete Fourier Transform,

one-dimensional,

multiple transforms,

Hermitian sequence,

real storage by rows

c06fqc

real sequence,

real storage by rows

c06fpc

Distributions,

Beta,

central,

deviates,

scalar

g01fec

probabilities and probability density function,

scalar

g01eec

non-central,

probabilities

g01gec

binomial,

distribution function,

scalar

g01bjc

Durbin–Watson statistic,

probabilities

g01epc

energy loss distributions,

Landau,

density

g01mtc

derivative of density

g01rtc

distribution

g01etc

first moment

g01ptc

inverse distribution

g01ftc

second moment

g01qtc

Vavilov,

density

g01muc

distribution

g01euc

initialization

g01zuc

$F$:

central,

deviates,

scalar

g01fdc

probabilities,

scalar

g01edc

non-central,

probabilities

g01gdc

gamma,

deviates,

scalar

g01ffc

probabilities,

scalar

g01efc

Hypergeometric,

distribution function,

scalar

g01blc

Kolomogorov–Smirnov,

probabilities,

one-sample

g01eyc

two-sample

g01ezc

Normal,

bivariate,

probabilities

g01hac

multivariate,

probabilities

g01hbc

quadratic forms,

cumulants and moments

g01nac

moments of ratios

g01nbc

univariate,

deviates,

scalar

g01fac

probabilities,

scalar

g01eac

reciprocal of Mill's Ratio

g01mbc

Shapiro and Wilk's test for Normality

g01ddc

Poisson,

distribution function,

scalar

g01bkc

Student's $t$:

central,

univariate,

deviates,

scalar

g01fbc

probabilities,

scalar

g01ebc

non-central,

probabilities

g01gbc

Studentized range statistic,

deviates

g01fmc

probabilities

g01emc

von Mises,

probabilities

g01erc

${\chi }^2$:

central,

deviates

g01fcc

probabilities

g01ecc

probability of linear combination

g01jdc

non-central,

probabilities

g01gcc

probability of linear combination

g01jcc

Nonlinear programming (NLP) – derivative-free optimization (DFO),

model-based method for bound-constrained optimization

e04jcc

model-based method for bound-constrained optimization,

reverse communication

e04jec

direct communication

e04jdc

Nelder–Mead simplex method for unconstrained optimization

e04cbc

Eigenvalue problems for condensed forms of matrices,

complex Hermitian matrix,

eigenvalues and eigenvectors,

general matrix,

all/selected eigenvalues and eigenvectors by root-free $QR$ algorithm

f08fpc

all eigenvalues and eigenvectors by a divide-and-conquer algorithm

f08fqc

eigenvalues only,

general matrix,

all/selected eigenvalues by the Pal–Walker–Kahan variant of the $QL$ or $QR$ algorithm

f08fpc

real symmetric matrix,

eigenvalues and eigenvectors,

general matrix,

all/selected eigenvalues and eigenvectors by root-free $QR$ algorithm

f08fbc

all eigenvalues and eigenvectors by a divide-and-conquer algorithm

f08fcc

all eigenvalues and eigenvectors by root-free $QR$ algorithm

f08fac

eigenvalues only,

general matrix,

all/selected eigenvalues by the Pal–Walker–Kahan variant of the $QL$ or $QR$ algorithm

f08fbc

all eigenvalues by the Pal–Walker–Kahan variant of the $QL$ or $QR$ algorithm

f08fac

Eigenvalue problems for nonsymmetric matrices,

complex matrix,

all eigenvalues and left/right eigenvectors, plus balancing transformation and reciprocal condition numbers

f08npc

real matrix,

all eigenvalues and left/right eigenvectors, plus balancing transformation and reciprocal condition numbers

f08nbc

Elliptic functions, Jacobian, sn, cn, dn,

complex argument

s21cbc

real argument

s21cac

Elliptic integral,

Legendre form,

complete of 1st kind, $K\left(m\right)$

s21bhc

complete of 2nd kind, $E\left(m\right)$

s21bjc

of 1st kind, $F\left(\varphi \right|m)$

s21bec

of 2nd kind, $E\left(\varphi \mid m\right)$

s21bfc

of 3rd kind, $\Pi \left(n;\varphi \mid m\right)$

s21bgc

symmetrised,

degenerate of 1st kind, $R_C$

s21bac

of 1st kind, $R_F$

s21bbc

of 2nd kind, $R_D$

s21bcc

of 3rd kind, $R_J$

s21bdc

Erf,

real argument,

scalar

s15aec

vectorized

s15asc

Erfc,

real argument,

scalar

s15adc

vectorized

s15arc

erfcx,

real argument,

scalar

s15agc

vectorized

s15auc

Evaluation,

at a point,

of cubic splines

e02bbc

of cubic splines and derivatives

e02bcc

at vector of points,

of bicubic splines at vector of points

e02dec

of interpolant,

from e01bec

e01bfc

from triangulation from e01eac

e01ebc

on mesh,

of bicubic splines

e02dfc

Exponential Integral

s13aac

Exponential smoothing

g13amc

Extrapolation,

one variable,

piecewise cubic

e01bec

polynomial,

general data

e01aac

Nonlinear programming (NLP) – special cases,

unidimensional optimization (one-dimensional) with bound constraints,

method based on quadratic interpolation, no derivatives

e04abc

method based on cubic interpolation

e04bbc

unconstrained,

preconditioned conjugate gradient method

e04dgc

bound-constrained,

modified Newton algorithm, first and second derivatives

e04lbc

Fresnel integral,

$C$,

scalar

s20adc

$S$,

scalar

s20acc

Nonlinear programming (NLP) – global optimization,

bound constrained,

branching algorithm, multi-level coordinate search

e05kbc

branching algorithm, multi-level coordinate search (D)

e05jbc

generic, including nonlinearly constrained,

multi-start

e05ucc

Gamma function,

incomplete,

scalar

s14bac

vectorized

s14bnc

scalar

s14aac

vectorized

s14anc

GARCH,

GJR GARCH,

fitting

g13fec

forecasting

g13ffc

symmetric or type I AGARCH,

fitting

g13fac

forecasting

g13fbc

type II AGARCH,

fitting

g13fcc

forecasting

g13fdc

Generalized eigenvalue problems for nonsymmetric matrix pairs,

complex nonsymmetric matrix pairs,

all eigenvalues and left/right eigenvectors, plus the balancing transformation and reciprocal condition numbers

f08wpc

real nonsymmetric matrix pairs,

all eigenvalues and left/right eigenvectors, plus the balancing transformation and reciprocal condition numbers

f08wbc

Generalized factorial function,

scalar

s14aac

vectorized

s14anc

Generalized linear models,

binomial errors

g02gbc

computes estimable function

g02gnc

gamma errors

g02gdc

Normal errors

g02gac

Poisson errors

g02gcc

prediction

g02gpc

transform model parameters

g02gkc

Generating samples, matrices and tables,

random correlation matrix

g05pyc

random orthogonal matrix

g05pxc

random permutation of an integer vector

g05ncc

random sample from an integer vector,

unequal weights, without replacement

g05nec

unweighted, without replacement

g05ndc

random table

g05pzc

resample from an integer vector,

unequal weights

g05nfc

Generation of time series,

asymmetric GARCH Type II

g05pec

asymmetric GJR GARCH

g05pfc

EGARCH

g05pgc

exponential smoothing

g05pmc

type I AGARCH

g05pdc

univariate ARMA

g05phc

vector ARMA

g05pjc

Linear least squares, linear regression, data fitting,

constrained,

bound-constrained least squares problem

e04pcc

linearly-constrained active-set method

e04ncc

Data fitting,

general loss functions (for sum of squares, see nonlinear least squares)

e04gnc

Nonlinear least squares, data fitting,

unconstrained,

combined Gauss–Newton and modified Newton algorithm,

no derivatives

e04fcc

combined Gauss–Newton and quasi-Newton algorithm,

first derivatives

e04gbc

bound constrained,

model-based derivative-free algorithm,

direct communication

e04ffc

reverse communication

e04fgc

trust region algorithm,

first derivatives, optionally second derivatives

e04ggc

Nonlinear least squares, data fitting – global optimization,

generic, including nonlinearly constrained,

multi-start

e05usc

Mixed integer linear programming (MILP),

dense,

branch and bound method

h02bbc

Integration (definite) of interpolant from e01bec

e01bhc

Interpolated values,

one variable,

from interpolant from e01bec

e01bfc

from interpolant from e01bec (including derivative)

e01bgc

from polynomial,

general data

e01aac

two variables,

barycentric, from triangulation from e01eac

e01ebc

Interpolating function,

one variable,

cubic spline

e01bac

other piecewise polynomial

e01bec

two variables,

bicubic spline

e01dac

NAG optimization modelling suite,

solvers,

constrained nonlinear data fitting (NLDF)

e04gnc

derivative-free optimisation (DFO) for nonlinear least squares problems,

direct communication

e04ffc

reverse communication

e04fgc

trust region optimisation for nonlinear least squares problems (BXNL)

e04ggc

model-based method for bound-constrained optimization,

direct communication

e04jdc

reverse communication

e04jec

Jacobian theta functions ${\theta }_k(x,q)$,

real argument

s21ccc

Service functions,

derivative check and approximation,

check user's function for calculating first derivatives of function

e04hcc

check user's function for calculating second derivatives of function

e04hdc

check user's function for calculating Jacobian of first derivatives

e04yac

estimate (using numerical differentiation) gradient and/or Hessian of a function

e04xac

determine the pattern of nonzeros in the Jacobian matrix for e04vhc

e04vjc

Kelvin function,

$\mathrm{bei}x$,

scalar

s19abc

$\mathrm{ber}x$,

scalar

s19aac

$\mathrm{kei}x$,

scalar

s19adc

$\ker x$,

scalar

s19acc

Korobov optimal coefficients for use in d01gdc:

when number of points is a product of $2$ primes

d01gzc

when number of points is prime

d01gyc

least squares problems,

real matrices,

minimum norm solution using a complete orthogonal factorization

f08bac

minimum norm solution using the singular value decomposition (divide-and-conquer)

f08kcc

Least squares surface fit,

with bicubic splines

e02dac

Legendre functions of 1st kind $P_n^m\left(x\right)$, $\overline{P_n^m}\left(x\right)$

s22aac

Linear mixed effects regression,

via maximum likelihood (ML)

g02jbc

via restricted maximum likelihood (REML)

g02jac

$L{L}^{\mathrm{T}}$ or $U^{\mathrm{T}}U$ factorization,

real symmetric positive definite band matrix

f07hdc

real symmetric positive definite matrix

f07fdc

Logarithm of $1+x$

s01bac

Logarithm of gamma function,

real,

scalar

s14abc

vectorized

s14apc

$LU$ factorization,

complex matrix

f07arc

real matrix

f07adc

real tridiagonal matrix

f07cdc

Matrix Arithmetic and Manipulation,

matrix storage conversion,

full to packed triangular storage,

complex matrices

f01vbc

real matrices

f01vac

full to Rectangular Full Packed storage,

complex matrix

f01vfc

real matrix

f01vec

packed triangular to full storage,

complex matrices

f01vdc

real matrices

f01vcc

packed triangular to Rectangular Full Packed storage,

complex matrices

f01vkc

real matrices

f01vjc

Rectangular Full Packed to full storage,

complex matrices

f01vhc

real matrices

f01vgc

Rectangular Full Packed to packed triangular storage,

complex matrices

f01vmc

real matrices

f01vlc

Matrix function,

complex Hermitian $n\times n$ matrix,

matrix exponential

f01fdc

matrix function

f01ffc

complex $n\times n$ matrix,

matrix exponential

f01fcc

real symmetric $n\times n$ matrix,

matrix exponential

f01edc

matrix function

f01efc

Matrix inversion,

after factorizing the matrix of coefficients,

real matrix

f07ajc

real symmetric positive definite matrix

f07fjc

real triangular matrix

f07tjc

Multidimensional quadrature,

over a finite two-dimensional region

d01dac

over a general product region,

Korobov–Conroy number-theoretic method

d01gdc

over a hyper-rectangle,

Gaussian quadrature rule-evaluation

d01fbc

over an $n$-simplex

d01pac

Multiple linear regression/General linear model,

add/delete observation from model

g02dcc

add independent variable to model

g02dec

computes estimable function

g02dnc

delete independent variable from model

g02dfc

general linear regression model

g02dac

regression for new dependent variable

g02dgc

regression parameters from updated model

g02ddc

transform model parameters

g02dkc

Nearest correlation matrix,

$k$-factor structure

g02aec

method of Qi and Sun,

unweighted, unbounded

g02aac

weighted norm

g02abc

Non-parametric rank correlation (Kendall and/or Spearman):

missing values,

casewise treatment of missing values,

preserving input data

g02brc

One-dimensional quadrature,

adaptive integration of a function over a finite interval,

strategy due to Gonnet,

suitable for badly behaved integrals,

vectorized interface

d01rgc

strategy due to Piessens and de Doncker,

allowing for singularities at user-specified break-points

d01rlc

suitable for badly behaved integrands

d01rjc

suitable for highly oscillatory integrals

d01rkc

integration of a function defined by data values only,

Gill–Miller method

d01gac

non-adaptive integration over a finite interval

d01bdc

Operations on eigenvectors of a real symmetric or complex Hermitian matrix, or singular vectors of a general matrix,

estimate condition numbers

f08flc

Option Pricing,

American option, Bjerksund and Stensland option price

s30qcc

Asian option, geometric continuous average rate price

s30sac

Asian option, geometric continuous average rate price with Greeks

s30sbc

binary asset-or-nothing option price

s30ccc

binary asset-or-nothing option price with Greeks

s30cdc

binary cash-or-nothing option price

s30cac

binary cash-or-nothing option price with Greeks

s30cbc

Black–Scholes implied volatility

s30acc

Black–Scholes–Merton option price

s30aac

Black–Scholes–Merton option price with Greeks

s30abc

European option, option prices, using Merton jump-diffusion model

s30jac

European option, option price with Greeks, using Merton jump-diffusion model

s30jbc

floating-strike lookback option price

s30bac

floating-strike lookback option price with Greeks

s30bbc

Heston's model option price

s30nac

Heston's model option price with Greeks

s30nbc

Heston's model option price with Greeks, sensitivities of model parameters and negative rates

s30ndc

Heston's model with term structure

s30ncc

standard barrier option price

s30fac

Outlier detection,

Peirce,

raw data or single variance supplied

g07gac

two variances supplied

g07gbc

Overdetermined and underdetermined linear systems,

complex matrices,

solves an overdetermined or undetermined complex linear system

f08anc

real matrices,

solves an overdetermined or undetermined real linear system

f08aac

Partial least squares,

calculates predictions given an estimated PLS model

g02ldc

fits a PLS model for a given number of factors

g02lcc

orthogonal scores using SVD

g02lac

orthogonal scores using Wold's method

g02lbc

Polygamma function,

${\psi }^{\left(n\right)}\left(x\right)$, real $x$

s14aec

Principal component analysis

g03aac

Product-moment correlation,

correlation matrix,

compute correlation and covariance matrices

g02bxc

compute from sum of squares matrix

g02bwc

compute partial correlation and covariance matrices

g02byc

sum of squares matrix,

compute

g02buc

update

g02btc

Pseudorandom numbers,

array of variates from multivariate distributions,

Dirichlet distribution

g05sec

multinomial distribution

g05tgc

Normal distribution

g05rzc

Student's $t$ distribution

g05ryc

copulas,

Gaussian copula

g05rdc

Student's $t$ copula

g05rcc

initialize generator,

multiple streams,

leap-frog

g05khc

skip-ahead

g05kjc

skip-ahead (power of 2)

g05kkc

vector of variates from discrete univariate distributions,

binomial distribution

g05tac

geometric distribution

g05tcc

hypergeometric distribution

g05tec

logarithmic distribution

g05tfc

logical value Nag_TRUE or Nag_FALSE

g05tbc

negative binomial distribution

g05thc

Poisson distribution

g05tjc

uniform distribution

g05tlc

user-supplied distribution

g05tdc

variate array from discrete distributions with array of parameters,

Poisson distribution with varying mean

g05tkc

vectors of variates from continuous univariate distributions,

beta distribution

g05sbc

Cauchy distribution

g05scc

exponential mix distribution

g05sgc

$F$-distribution

g05shc

gamma distribution

g05sjc

logistic distribution

g05slc

log-normal distribution

g05smc

negative exponential distribution

g05sfc

Normal distribution

g05skc

real number from the continuous uniform distribution

g05sac

Student's $t$-distribution

g05snc

triangular distribution

g05spc

uniform distribution

g05sqc

von Mises distribution

g05src

Weibull distribution

g05ssc

${\chi }^2$ square distribution

g05sdc

psi function

s14acc

psi function derivatives, scaled

s14adc

$QR$ factorization and related operations,

real matrices,

general matrices,

apply orthogonal matrix

f08agc

factorization,

with column pivoting, using BLAS-3

f08bfc

factorization, orthogonal matrix

f08aec

factorization, with column pivoting, deprecated

f08bec

Quantile regression,

linear,

comprehensive

g02qgc

simple

g02qfc

Quasi-random numbers,

array of variates from univariate distributions,

uniform distribution

g05ymc

initialize generator,

scrambled Sobol or Niederreiter

g05ync

Sobol, Niederreiter or Faure

g05ylc

Residuals,

Durbin–Watson test

g02fcc

standardized residuals and influence statistics

g02fac

Ridge regression,

ridge parameter(s) supplied

g02kbc

ridge parameter optimized

g02kac

Robust correlation,

Huber's method

g02hkc

user-supplied weight function only

g02hmc

user-supplied weight function plus derivatives

g02hlc

Robust regression,

compute weights for use with g02hdc

g02hbc

standard $M$-estimates

g02hac

user-supplied weight functions

g02hdc

variance-covariance matrix following g02hdc

g02hfc

Scaled modified Bessel function(s),

$e^{-\left|x\right|}{I}_0\left(x\right)$, real argument,

scalar

s18cec

$e^{-\left|x\right|}{I}_1\left(x\right)$, real argument,

scalar

s18cfc

$e^x{K}_0\left(x\right)$, real argument,

scalar

s18ccc

$e^x{K}_1\left(x\right)$, real argument,

scalar

s18cdc

Scores,

Normal scores,

accurate

g01dac

variance-covariance matrix

g01dcc

Normal scores, ranks or exponential (Savage) scores

g01dhc

Simple linear regression,

no intercept

g02cbc

with intercept

g02cac

Sine,

hyperbolic

s10abc

Sine Integral

s13adc

Singular value decomposition,

complex matrix,

using bidiagonal $QR$ iteration

f08kpc

real matrix,

using a divide-and-conquer algorithm

f08kdc

using bidiagonal $QR$ iteration

f08kbc

Solution of simultaneous linear equations,

after factorizing the matrix of coefficients,

complex matrix

f07asc

real symmetric positive definite band matrix

f07hec

real symmetric positive definite matrix

f07fec

real tridiagonal matrix

f07cec

expert drivers (with condition and error estimation):

complex Hermitian positive definite matrix

f07fpc

complex matrix

f07apc

real matrix

f07abc

real symmetric positive definite matrix

f07fbc

simple drivers,

real matrix

f07aac

real symmetric positive definite matrix

f07fac

real triangular matrix

f07tec

real tridiagonal matrix

f07cac

Spectral analysis

Bivariate,

Bartlett, Tukey, Parzen windows

g13ccc

cross amplitude spectrum

g13cec

direct smoothing

g13cdc

gain and phase

g13cfc

noise spectrum

g13cgc

Univariate,

Bartlett, Tukey, Parzen windows

g13cac

direct smoothing

g13cbc

Stepwise linear regression,

Clarke's sweep algorithm

g02efc

Tangent,

hyperbolic

s10aac

Transfer function modelling,

cross-correlations

g13bcc

filtering

g13bbc

fitting

g13bec

forecasting from fully specified model

g13bjc

preliminary estimation

g13bdc

pre-whitening

g13bac

update state set

g13bgc

Trigamma function, scaled

s14adc

Vector ARMA,

differencing

g13dlc

fitting

g13ddc

forecasting

g13djc

update forecast

g13dkc

zeros of ARIMA operator

g13dxc

Weights and abscissae for Gaussian quadrature rules,

more general choice of rule,

calculating the weights and abscissae

d01tcc

Zeros of Bessel functions $J_{\alpha }\left(x\right)$, $J_{\alpha }^{\prime }\left(x\right)$, $Y_{\alpha }\left(x\right)$, $Y_{\alpha }^{\prime }\left(x\right)$,

scalar

s17alc

Zeros of functions of one variable,

direct communication,

binary search followed by Brent algorithm

c05auc

Brent algorithm

c05ayc

continuation method

c05awc

reverse communication,

binary search

c05avc

Brent algorithm

c05azc

continuation method

c05axc

Zeros of functions of several variables,

checking function,

checks user-supplied Jacobian

c05zdc

direct communication,

easy-to-use,

derivatives required

c05rbc

no derivatives required

c05qbc

sophisticated,

derivatives required

c05rcc

no derivatives required

c05qcc

reverse communication,

sophisticated,

derivatives required

c05rdc

no derivatives required

c05qdc