Nag Library for .NET Release 2

Table of Contents

• Introduction
  • Overview
  • Introduction
  • NAG F# Examples
  • C++ Example
  • NAG Fortran Library Interfaces
• Utility Classes
  • Complex — Complex Numbers
  • PrintManager — Control output from the library
  • DataReader — Auxiliary functions used in example programs to read the supplied data files
• A00 — Library Identification
  • a00aa — Library identification, details of implementation and mark
  • a00ac — Check availability of a valid licence key
• C05 — Roots of One or More Transcendental Equations
  • c05au — Zero of continuous function, Brent algorithm, from a given starting value, binary search for interval
  • c05av — Binary search for interval containing zero of continuous function (reverse communication)
  • c05aw — Zero of continuous function, continuation method, from a given starting value
  • c05ax — Zero of continuous function, continuation method, from a given starting value (reverse communication)
  • c05ay — Zero of continuous function in a given interval, Brent algorithm
  • c05az — Zero of continuous function in a given interval, Brent algorithm (reverse communication)
  • c05qb — Solution of a system of nonlinear equations using function values only (easy-to-use)
  • c05qc — Solution of a system of nonlinear equations using function values only (comprehensive)
  • c05qd — Solution of a system of nonlinear equations using function values only (reverse communication)
  • c05rb — Solution of a system of nonlinear equations using first derivatives (easy-to-use)
  • c05rc — Solution of a system of nonlinear equations using first derivatives (comprehensive)
  • c05rd — Solution of a system of nonlinear equations using first derivatives (reverse communication)
  • c05zd — Check user's function for calculating first derivatives of a set of nonlinear functions of several variables
• C06 — Summation of Series
  • c06ea — Single one-dimensional real discrete Fourier transform, no extra workspace
  • c06eb — Single one-dimensional Hermitian discrete Fourier transform, no extra workspace
  • c06fp — Multiple one-dimensional real discrete Fourier transforms
  • c06fq — Multiple one-dimensional Hermitian discrete Fourier transforms
  • c06gb — Complex conjugate of Hermitian sequence
  • c06gq — Complex conjugate of multiple Hermitian sequences
  • c06gs — Convert Hermitian sequences to general complex sequences
• C09 — Wavelet Transforms
  • c09ca — One-dimensional discrete wavelet transform
  • c09cb — One-dimensional inverse discrete wavelet transform
  • c09cc — One-dimensional multi-level discrete wavelet transform
  • c09cd — One-dimensional inverse multi-level discrete wavelet transform
• D01 — Quadrature
  • d01ah — One-dimensional quadrature, adaptive, finite interval, strategy due to Patterson, suitable for well-behaved integrands
  • d01aj — One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands
  • d01ak — One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions
  • d01al — One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points
  • d01am — One-dimensional quadrature, adaptive, infinite or semi-infinite interval
  • d01an — One-dimensional quadrature, adaptive, finite interval, weight function cos((ωx)) or sin((ωx))
  • d01ap — One-dimensional quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type
  • d01aq — One-dimensional quadrature, adaptive, finite interval, weight function 1/(x−c), Cauchy principal value (Hilbert transform)
  • d01ar — One-dimensional quadrature, non-adaptive, finite interval with provision for indefinite integrals
  • d01as — One-dimensional quadrature, adaptive, semi-infinite interval, weight function cos((ωx)) or sin((ωx))
  • d01bc — Calculation of weights and abscissae for Gaussian quadrature rules, general choice of rule
  • d01bd — One-dimensional quadrature, non-adaptive, finite interval
  • d01da — Two-dimensional quadrature, finite region
  • d01fc — Multidimensional adaptive quadrature over hyper-rectangle
  • d01gd — Multidimensional quadrature, general product region, number-theoretic method, variant of d01gc efficient on vector machines
  • d01gy — Korobov optimal coefficients for use in d01gc or d01gd, when number of points is prime
  • d01gz — Korobov optimal coefficients for use in d01gc or d01gd, when number of points is product of two primes
  • d01ja — Multidimensional quadrature over an n-sphere, allowing for badly behaved integrands
  • d01pa — Multidimensional quadrature over an n-simplex
• E01 — Interpolation
  • e01ba — Interpolating functions, cubic spline interpolant, one variable
  • e01be — Interpolating functions, monotonicity-preserving, piecewise cubic Hermite, one variable
  • e01bf — Interpolated values, interpolant computed by e01be, function only, one variable
  • e01da — Interpolating functions, fitting bicubic spline, data on rectangular grid
• E02 — Curve and Surface Fitting
  • e02bb — Evaluation of fitted cubic spline, function only
  • e02de — Evaluation of fitted bicubic spline at a vector of points
  • e02df — Evaluation of fitted bicubic spline at a mesh of points
• E04 — Minimizing or Maximizing a Function
  • e04ab — Minimum, function of one variable using function values only
  • e04bb — Minimum, function of one variable, using first derivative
  • e04cb — Unconstrained minimization using simplex algorithm, function of several variables using function values only
  • e04dg — Unconstrained minimum, preconditioned conjugate gradient algorithm, function of several variables using first derivatives (comprehensive)
  • e04fc — Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using function values only (comprehensive)
  • e04fy — Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using function values only (easy-to-use)
  • e04gd — Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using first derivatives (comprehensive)
  • e04gy — Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use)
  • e04gz — Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using first derivatives (easy-to-use)
  • e04hc — Check user's function for calculating first derivatives of function
  • e04hd — Check user's function for calculating second derivatives of function
  • e04he — Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (comprehensive)
  • e04hy — Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (easy-to-use)
  • e04jc — Minimum by quadratic approximation, function of several variables, simple bounds, using function values only
  • e04jy — Minimum, function of several variables, quasi-Newton algorithm, simple bounds, using function values only (easy-to-use)
  • e04kd — Minimum, function of several variables, modified Newton algorithm, simple bounds, using first derivatives (comprehensive)
  • e04ky — Minimum, function of several variables, quasi-Newton algorithm, simple bounds, using first derivatives (easy-to-use)
  • e04kz — Minimum, function of several variables, modified Newton algorithm, simple bounds, using first derivatives (easy-to-use)
  • e04lb — Minimum, function of several variables, modified Newton algorithm, simple bounds, using first and second derivatives (comprehensive)
  • e04ly — Minimum, function of several variables, modified Newton algorithm, simple bounds, using first and second derivatives (easy-to-use)
  • e04mf — LP problem (dense)
  • e04nc — Convex QP problem or linearly-constrained linear least squares problem (dense)
  • e04nf — QP problem (dense)
  • e04nk — LP or QP problem (sparse)
  • e04nq — LP or QP problem (suitable for sparse problems)
  • e04pc — Computes the least squares solution to a set of linear equations subject to fixed upper and lower bounds on the variables. An option is provided to return a minimal length solution if a solution is not unique
  • e04uc — Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (comprehensive)
  • e04uf — Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (reverse communication, comprehensive)
  • e04ug — NLP problem (sparse)
  • e04us — Minimum of a sum of squares, nonlinear constraints, sequential QP method, using function values and optionally first derivatives (comprehensive)
  • e04vh — General sparse nonlinear optimizer
  • e04vj — Determine the pattern of nonzeros in the Jacobian matrix for e04vh
  • e04wd — Solves the nonlinear programming (NLP) problem
  • e04xa — Estimate (using numerical differentiation) gradient and/or Hessian of a function
  • e04ya — Check user's function for calculating Jacobian of first derivatives
  • e04yb — Check user's function for calculating Hessian of a sum of squares
• E05 — Global Optimization of a Function
  • e05jb — Global optimization by multi-level coordinate search, simple bounds, using function values only
  • e05uc — Global optimization using multi-start, nonlinear constraints
  • e05us — Global optimization of a sum of squares problem using multi-start, nonlinear constraints
• F01 — Matrix Operations, Including Inversion
  • f01ed — Real symmetric matrix exponential
  • f01ef — Function of a real symmetric matrix
  • f01fc — Complex matrix exponential
  • f01fd — Complex Hermitian matrix exponential
  • f01ff — Function of a complex Hermitian matrix
  • f01va — Copies a real triangular matrix from full format to packed format scheme
  • f01vb — Copies a complex triangular matrix from full format to packed format scheme
  • f01vc — Copies a real triangular matrix from packed format to full format scheme
  • f01vd — Copies a complex triangular matrix from packed format to full format scheme
  • f01ve — Copies a real triangular matrix from full format to Rectangular Full Packed format scheme
  • f01vf — Copies a complex triangular matrix from full format to Rectangular Full Packed format scheme
  • f01vg — Copies a real triangular matrix from Rectangular Full Packed format to full format scheme
  • f01vh — Copies a complex triangular matrix from Rectangular Full Packed format to full format scheme
  • f01vj — Copies a real triangular matrix from packed format to Rectangular Full Packed format scheme
  • f01vk — Copies a complex triangular matrix from packed format to Rectangular Full Packed format scheme
  • f01vl — Copies a real triangular matrix from Rectangular Full Packed format to packed format scheme
  • f01vm — Copies a complex triangular matrix from Rectangular Full Packed format to packed format scheme
• F06 — Linear Algebra Support Routines
  • f06bn — Compute square root of (a²+b²), real a and b
  • f06db — Broadcast scalar into integer vector
  • f06ea — Dot product of two real vectors
  • f06ef — Copy real vector
  • f06ej — Compute Euclidean norm of real vector
  • f06fd — Multiply real vector by scalar, preserving input vector
  • f06jj — Compute Euclidean norm of complex vector
  • f06pa — Matrix-vector product, real rectangular matrix
  • f06pj — System of equations, real triangular matrix
  • f06qf — Matrix copy, real rectangular or trapezoidal matrix
  • f06qh — Matrix initialization, real rectangular matrix
  • f06ya — Matrix-matrix product, two real rectangular matrices
  • f06yj — Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix
• F07 — Linear Equations (LAPACK)
  • f07ab — Uses the LU factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
  • f07ap — Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
  • f07ar — LU factorization of complex m by n matrix
  • f07as — Solution of complex system of linear equations, multiple right-hand sides, matrix already factorized by f07ar
  • f07fb — Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations
  • f07fp — Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations
  • f07hd — Cholesky factorization of real symmetric positive definite band matrix
  • f07he — Solution of real symmetric positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by f07hd
  • f07te — Solution of real triangular system of linear equations, multiple right-hand sides
  • f07th — Error bounds for solution of real triangular system of linear equations, multiple right-hand sides
  • f07tj — Inverse of real triangular matrix
• F08 — Least Squares and Eigenvalue Problems (LAPACK)
  • f08aa — Solves a real linear least problem of full rank
  • f08ag — Applies an orthogonal transformation determined by f08ae, f08be, f08bf
  • f08an — Solves a complex linear least problem of full rank
  • f08be — QR factorization, with column pivoting, of real general rectangular matrix
  • f08bf — QR factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
  • f08fa — Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
  • f08fb — Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
  • f08fl — Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix
  • f08fp — Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
  • f08kb — Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
  • f08kp — Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
  • f08nb — Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
  • f08np — Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
  • f08wb — Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
  • f08wp — Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
• G01 — Simple Calculations on Statistical Data
  • g01aa — Mean, variance, skewness, kurtosis, etc., one variable, from raw data
  • g01ad — Mean, variance, skewness, kurtosis, etc., one variable, from frequency table
  • g01ae — Frequency table from raw data
  • g01af — Two-way contingency table analysis, with χ²/Fisher's exact test
  • g01al — Computes a five-point summary (median, hinges and extremes)
  • g01am — Find quantiles of an unordered vector, real numbers
  • g01bj — Binomial distribution function
  • g01bk — Poisson distribution function
  • g01bl — Hypergeometric distribution function
  • g01da — Normal scores, accurate values
  • g01db — Normal scores, approximate values
  • g01dc — Normal scores, approximate variance-covariance matrix
  • g01dd — Shapiro and Wilk's W test for Normality
  • g01dh — Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores
  • g01ea — Computes probabilities for the standard Normal distribution
  • g01eb — Computes probabilities for Student's t-distribution
  • g01ec — Computes probabilities for χ² distribution
  • g01ed — Computes probabilities for F-distribution
  • g01ee — Computes upper and lower tail probabilities and probability density function for the beta distribution
  • g01ef — Computes probabilities for the gamma distribution
  • g01em — Computes probability for the Studentized range statistic
  • g01ep — Computes bounds for the significance of a Durbin–Watson statistic
  • g01er — Computes probability for von Mises distribution
  • g01et — Landau distribution function
  • g01eu — Vavilov distribution function
  • g01ey — Computes probabilities for the one-sample Kolmogorov–Smirnov distribution
  • g01ez — Computes probabilities for the two-sample Kolmogorov–Smirnov distribution
  • g01fa — Computes deviates for the standard Normal distribution
  • g01fb — Computes deviates for Student's t-distribution
  • g01fc — Computes deviates for the χ² distribution
  • g01fd — Computes deviates for the F-distribution
  • g01fe — Computes deviates for the beta distribution
  • g01ff — Computes deviates for the gamma distribution
  • g01fm — Computes deviates for the Studentized range statistic
  • g01ft — Landau inverse function Ψ(x)
  • g01gb — Computes probabilities for the non-central Student's t-distribution
  • g01gc — Computes probabilities for the non-central χ² distribution
  • g01gd — Computes probabilities for the non-central F-distribution
  • g01ge — Computes probabilities for the non-central beta distribution
  • g01ha — Computes probability for the bivariate Normal distribution
  • g01hb — Computes probabilities for the multivariate Normal distribution
  • g01jc — Computes probability for a positive linear combination of χ² variables
  • g01jd — Computes lower tail probability for a linear combination of (central) χ² variables
  • g01mb — Computes reciprocal of Mills' Ratio
  • g01mt — Landau density function ϕ(λ)
  • g01mu — Vavilov density function ϕ_V(λ;κβ²)
  • g01na — Cumulants and moments of quadratic forms in Normal variables
  • g01nb — Moments of ratios of quadratic forms in Normal variables, and related statistics
  • g01pt — Landau first moment function Φ₁(x)
  • g01qt — Landau second moment function Φ₂(x)
  • g01rt — Landau derivative function ϕ'(λ)
  • g01zu — Initialization function for g01mu and g01eu
• G02 — Correlation and Regression Analysis
  • g02aa — Computes the nearest correlation matrix to a real square matrix, using the method of Qi and Sun
  • g02ab — Computes the nearest correlation matrix to a real square matrix, augmented g02aa to incorporate weights and bounds
  • g02ae — Computes the nearest correlation matrix with k-factor structure to a real square matrix
  • g02ba — Pearson product-moment correlation coefficients, all variables, no missing values
  • g02bb — Pearson product-moment correlation coefficients, all variables, casewise treatment of missing values
  • g02bc — Pearson product-moment correlation coefficients, all variables, pairwise treatment of missing values
  • g02bd — Correlation-like coefficients (about zero), all variables, no missing values
  • g02be — Correlation-like coefficients (about zero), all variables, casewise treatment of missing values
  • g02bf — Correlation-like coefficients (about zero), all variables, pairwise treatment of missing values
  • g02bg — Pearson product-moment correlation coefficients, subset of variables, no missing values
  • g02bh — Pearson product-moment correlation coefficients, subset of variables, casewise treatment of missing values
  • g02bj — Pearson product-moment correlation coefficients, subset of variables, pairwise treatment of missing values
  • g02bk — Correlation-like coefficients (about zero), subset of variables, no missing values
  • g02bl — Correlation-like coefficients (about zero), subset of variables, casewise treatment of missing values
  • g02bm — Correlation-like coefficients (about zero), subset of variables, pairwise treatment of missing values
  • g02bn — Kendall/Spearman non-parametric rank correlation coefficients, no missing values, overwriting input data
  • g02bp — Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, overwriting input data
  • g02bq — Kendall/Spearman non-parametric rank correlation coefficients, no missing values, preserving input data
  • g02br — Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, preserving input data
  • g02bs — Kendall/Spearman non-parametric rank correlation coefficients, pairwise treatment of missing values
  • g02bt — Update a weighted sum of squares matrix with a new observation
  • g02bu — Computes a weighted sum of squares matrix
  • g02bw — Computes a correlation matrix from a sum of squares matrix
  • g02bx — Computes (optionally weighted) correlation and covariance matrices
  • g02by — Computes partial correlation/variance-covariance matrix from correlation/variance-covariance matrix computed by g02bx
  • g02ca — Simple linear regression with constant term, no missing values
  • g02cb — Simple linear regression without constant term, no missing values
  • g02cc — Simple linear regression with constant term, missing values
  • g02cd — Simple linear regression without constant term, missing values
  • g02ce — Service function for multiple linear regression, select elements from vectors and matrices
  • g02cf — Service function for multiple linear regression, reorder elements of vectors and matrices
  • g02cg — Multiple linear regression, from correlation coefficients, with constant term
  • g02ch — Multiple linear regression, from correlation-like coefficients, without constant term
  • g02da — Fits a general (multiple) linear regression model
  • g02dc — Add/delete an observation to/from a general linear regression model
  • g02dd — Estimates of linear parameters and general linear regression model from updated model
  • g02de — Add a new independent variable to a general linear regression model
  • g02df — Delete an independent variable from a general linear regression model
  • g02dg — Fits a general linear regression model to new dependent variable
  • g02dk — Estimates and standard errors of parameters of a general linear regression model for given constraints
  • g02dn — Computes estimable function of a general linear regression model and its standard error
  • g02ef — Stepwise linear regression
  • g02fa — Calculates standardized residuals and influence statistics
  • g02fc — Computes Durbin–Watson test statistic
  • g02ga — Fits a generalized linear model with Normal errors
  • g02gb — Fits a generalized linear model with binomial errors
  • g02gc — Fits a generalized linear model with Poisson errors
  • g02gd — Fits a generalized linear model with gamma errors
  • g02gk — Estimates and standard errors of parameters of a general linear model for given constraints
  • g02gn — Computes estimable function of a generalized linear model and its standard error
  • g02gp — Computes a predicted value and its associated standard error based on a previously fitted generalized linear model
  • g02ha — Robust regression, standard M-estimates
  • g02hb — Robust regression, compute weights for use with g02hd
  • g02hd — Robust regression, compute regression with user-supplied functions and weights
  • g02hf — Robust regression, variance-covariance matrix following g02hd
  • g02hk — Calculates a robust estimation of a correlation matrix, Huber's weight function
  • g02hl — Calculates a robust estimation of a correlation matrix, user-supplied weight function plus derivatives
  • g02hm — Calculates a robust estimation of a correlation matrix, user-supplied weight function
  • g02ja — Linear mixed effects regression using Restricted Maximum Likelihood (REML)
  • g02jb — Linear mixed effects regression using Maximum Likelihood (ML)
  • g02ka — Ridge regression, optimizing a ridge regression parameter
  • g02kb — Ridge regression using a number of supplied ridge regression parameters
  • g02la — Partial least squares (PLS) regression using singular value decomposition
  • g02lb — Partial least squares (PLS) regression using Wold's iterative method
  • g02lc — PLS parameter estimates following partial least squares regression by g02la, g02lb
  • g02ld — PLS predictions based on parameter estimates from g02lc
  • g02qf — Linear quantile regression, simple interface, independent, identically distributed (IID) errors
  • g02qg — Linear quantile regression, comprehensive interface
• G03 — Multivariate Methods
  • g03aa — Performs principal component analysis
• G05 — Random Number Generators
  • g05kh — Primes a pseudorandom number generator for generating multiple streams using leap-frog
  • g05kj — Primes a pseudorandom number generator for generating multiple streams using skip-ahead
  • g05kk — Primes a pseudorandom number generator for generating multiple streams using skip-ahead, skipping ahead a power of 2
  • g05nc — Pseudorandom permutation of an integer vector
  • g05nd — Pseudorandom sample from an integer vector
  • g05pd — Generates a realization of a time series from a GARCH process with asymmetry of the form (ε_t−1+γ)²
  • g05pe — Generates a realization of a time series from a GARCH process with asymmetry of the form (|ε_t−1|+γε_t−1)²
  • g05pf — Generates a realization of a time series from an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
  • g05pg — Generates a realization of a time series from an exponential GARCH (EGARCH) process
  • g05ph — Generates a realization of a time series from an ARMA model
  • g05pj — Generates a realization of a multivariate time series from a VARMA model
  • g05pm — Generates a realization of a time series from an exponential smoothing model
  • g05px — Generates a random orthogonal matrix
  • g05py — Generates a random correlation matrix
  • g05pz — Generates a random two-way table
  • g05rc — Generates a matrix of pseudorandom numbers from a Student's t-copula
  • g05rd — Generates a matrix of pseudorandom numbers from a Gaussian copula
  • g05ry — Generates a matrix of pseudorandom numbers from a multivariate Student's t-distribution
  • g05rz — Generates a matrix of pseudorandom numbers from a multivariate Normal distribution
  • g05sa — Generates a vector of pseudorandom numbers from a uniform distribution over (01)
  • g05sb — Generates a vector of pseudorandom numbers from a beta distribution
  • g05sc — Generates a vector of pseudorandom numbers from a Cauchy distribution
  • g05sd — Generates a vector of pseudorandom numbers from a χ² distribution
  • g05se — Generates a vector of pseudorandom numbers from a Dirichlet distribution
  • g05sf — Generates a vector of pseudorandom numbers from an exponential distribution
  • g05sg — Generates a vector of pseudorandom numbers from an exponential mix distribution
  • g05sh — Generates a vector of pseudorandom numbers from an F-distribution
  • g05sj — Generates a vector of pseudorandom numbers from a gamma distribution
  • g05sk — Generates a vector of pseudorandom numbers from a Normal distribution
  • g05sl — Generates a vector of pseudorandom numbers from a logistic distribution
  • g05sm — Generates a vector of pseudorandom numbers from a log-normal distribution
  • g05sn — Generates a vector of pseudorandom numbers from a Student's t-distribution
  • g05sp — Generates a vector of pseudorandom numbers from a triangular distribution
  • g05sq — Generates a vector of pseudorandom numbers from a uniform distribution over (ab)
  • g05sr — Generates a vector of pseudorandom numbers from a von Mises distribution
  • g05ss — Generates a vector of pseudorandom numbers from a Weibull distribution
  • g05ta — Generates a vector of pseudorandom integers from a binomial distribution
  • g05tb — Generates a vector of pseudorandom logical values
  • g05tc — Generates a vector of pseudorandom integers from a geometric distribution
  • g05td — Generates a vector of pseudorandom integers from a general discrete distribution
  • g05te — Generates a vector of pseudorandom integers from a hypergeometric distribution
  • g05tf — Generates a vector of pseudorandom integers from a logarithmic distribution
  • g05tg — Generates a vector of pseudorandom integers from a multinomial distribution
  • g05th — Generates a vector of pseudorandom integers from a negative binomial distribution
  • g05tj — Generates a vector of pseudorandom integers from a Poisson distribution
  • g05tk — Generates a vector of pseudorandom integers from a Poisson distribution with varying mean
  • g05tl — Generates a vector of pseudorandom integers from a uniform distribution
  • g05yl — Initializes a quasi-random number generator
  • g05ym — Generates a uniform quasi-random number sequence
  • g05yn — Initializes a scrambled quasi-random number generator
• G07 — Univariate Estimation
  • g07ga — Outlier detection using method of Peirce, raw data or single variance supplied
  • g07gb — Outlier detection using method of Peirce, two variances supplied
• G13 — Time Series Analysis
  • g13aa — Univariate time series, seasonal and non-seasonal differencing
  • g13ab — Univariate time series, sample autocorrelation function
  • g13ac — Univariate time series, partial autocorrelations from autocorrelations
  • g13ad — Univariate time series, preliminary estimation, seasonal ARIMA model
  • g13af — Univariate time series, estimation, seasonal ARIMA model (easy-to-use)
  • g13ag — Univariate time series, update state set for forecasting
  • g13ah — Univariate time series, forecasting from state set
  • g13aj — Univariate time series, state set and forecasts, from fully specified seasonal ARIMA model
  • g13am — Univariate time series, exponential smoothing
  • g13as — Univariate time series, diagnostic checking of residuals, following g13ae or g13af
  • g13au — Computes quantities needed for range-mean or standard deviation-mean plot
  • g13ba — Multivariate time series, filtering (pre-whitening) by an ARIMA model
  • g13bb — Multivariate time series, filtering by a transfer function model
  • g13bc — Multivariate time series, cross-correlations
  • g13bd — Multivariate time series, preliminary estimation of transfer function model
  • g13be — Multivariate time series, estimation of multi-input model
  • g13bg — Multivariate time series, update state set for forecasting from multi-input model
  • g13bj — Multivariate time series, state set and forecasts from fully specified multi-input model
  • g13ca — Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window
  • g13cb — Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window
  • g13cc — Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window
  • g13cd — Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window
  • g13ce — Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra
  • g13cf — Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra
  • g13cg — Multivariate time series, noise spectrum, bounds, impulse response function and its standard error
  • g13dd — Multivariate time series, estimation of VARMA model
  • g13dj — Multivariate time series, forecasts and their standard errors
  • g13dk — Multivariate time series, updates forecasts and their standard errors
  • g13dl — Multivariate time series, differences and/or transforms
  • g13dx — Calculates the zeros of a vector autoregressive (or moving average) operator
  • g13fa — Univariate time series, parameter estimation for either a symmetric GARCH process or a GARCH process with asymmetry of the form (ε_t−1+γ)²
  • g13fb — Univariate time series, forecast function for either a symmetric GARCH process or a GARCH process with asymmetry of the form (ε_t−1+γ)²
  • g13fc — Univariate time series, parameter estimation for a GARCH process with asymmetry of the form (|ε_t−1|+γε_t−1)²
  • g13fd — Univariate time series, forecast function for a GARCH process with asymmetry of the form (|ε_t−1|+γε_t−1)²
  • g13fe — Univariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
  • g13ff — Univariate time series, forecast function for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
  • g13fg — Univariate time series, parameter estimation for an exponential GARCH (EGARCH) process
  • g13fh — Univariate time series, forecast function for an exponential GARCH (EGARCH) process
• H — Operations Research
  • h02bb — Integer LP problem (dense)
  • h02cb — Integer QP problem (dense)
  • h02ce — Integer LP or QP problem (sparse), using e04nk
• S — Approximations of Special Functions
  • s01ba — ln((1+x))
  • s07aa — tan(x)
  • s09aa — arcsin(x)
  • s09ab — arccos(x)
  • s10aa — tanh(x)
  • s10ab — sinh(x)
  • s10ac — cosh(x)
  • s11aa — arctanh(x)
  • s11ab — arcsinh(x)
  • s11ac — arccosh(x)
  • s13aa — Exponential integral E₁(x)
  • s13ac — Cosine integral Ci((x))
  • s13ad — Sine integral Si((x))
  • s14aa — Gamma function
  • s14ab — Log gamma function, real argument
  • s14ac — *(x)−ln(x) where *(x) is the psi function
  • s14ad — Scaled derivatives of ψ(x)
  • s14ae — Polygamma function ψ⁽ⁿ⁾(x) for real x
  • s14ba — Incomplete gamma functions P(ax) and Q(ax)
  • s15ab — Cumulative Normal distribution function P(x)
  • s15ac — Complement of cumulative Normal distribution function Q(x)
  • s15ad — Complement of error function erfc((x))
  • s15ae — Error function erf((x))
  • s15af — Dawson's integral
  • s15ag — Scaled complement of error function, erfcx((x))
  • s17ac — Bessel function Y₀(x)
  • s17ad — Bessel function Y₁(x)
  • s17ae — Bessel function J₀(x)
  • s17af — Bessel function J₁(x)
  • s17ag — Airy function Ai((x))
  • s17ah — Airy function Bi((x))
  • s17aj — Airy function Ai'((x))
  • s17ak — Airy function Bi'((x))
  • s17al — Zeros of Bessel functions J_α(x), J'_α(x), Y_α(x) or Y'_α(x)
  • s17dg — Airy functions Ai((z)) and Ai'((z)), complex z
  • s17dh — Airy functions Bi((z)) and Bi'((z)), complex z
  • s18ac — Modified Bessel function K₀(x)
  • s18ad — Modified Bessel function K₁(x)
  • s18ae — Modified Bessel function I₀(x)
  • s18af — Modified Bessel function I₁(x)
  • s18cc — Scaled modified Bessel function e^xK₀(x)
  • s18cd — Scaled modified Bessel function e^xK₁(x)
  • s18ce — Scaled modified Bessel function e^−|x|I₀(x)
  • s18cf — Scaled modified Bessel function e^−|x|I₁(x)
  • s19aa — Kelvin function ber(x)
  • s19ab — Kelvin function bei(x)
  • s19ac — Kelvin function ker(x)
  • s19ad — Kelvin function kei(x)
  • s20ac — Fresnel integral S(x)
  • s20ad — Fresnel integral C(x)
  • s21ba — Degenerate symmetrised elliptic integral of 1st kind R_C(xy)
  • s21bb — Symmetrised elliptic integral of 1st kind R_F(xyz)
  • s21bc — Symmetrised elliptic integral of 2nd kind R_D(xyz)
  • s21bd — Symmetrised elliptic integral of 3rd kind R_J(xyzr)
  • s21be — Elliptic integral of 1st kind, Legendre form, F(ϕ∣m)
  • s21bf — Elliptic integral of 2nd kind, Legendre form, E(ϕ∣m)
  • s21bg — Elliptic integral of 3rd kind, Legendre form, Π(n;ϕ∣m)
  • s21bh — Complete elliptic integral of 1st kind, Legendre form, K(m)
  • s21bj — Complete elliptic integral of 2nd kind, Legendre form, E(m)
  • s21ca — Jacobian elliptic functions sn, cn and dn of real argument
  • s21cb — Jacobian elliptic functions sn, cn and dn of complex argument
  • s21cc — Jacobian theta functions θ_k(xq) of real argument
  • s22aa — Legendre functions of 1st kind P_n^m(x) or (P_n^m)^—(x)
• X01 — Mathematical Constants
  • x01aa — Provides the mathematical constant π
  • x01ab — Provides the mathematical constant γ (Euler's constant)
• X02 — Machine Constants
  • x02aj — The machine precision
  • x02ak — The smallest positive model number
  • x02al — The largest positive model number
  • x02am — The safe range parameter
  • x02bb — The largest representable integer
  • x02be — The maximum number of decimal digits that can be represented
  • x02bh — The floating-point model parameter, b
• X04 — Input/Output Utilities
  • x04ca — Print real general matrix (easy-to-use)
  • x04cb — Print real general matrix (comprehensive)
  • x04cc — Print real packed triangular matrix (easy-to-use)
  • x04ce — Print real packed banded matrix (easy-to-use)
  • x04da — Print complex general matrix (easy-to-use)
  • x04db — Print complex general matrix (comprehensive)