Numerical Algorithms Group

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a00 - Library Identification

a00aac

nag_implementation_details
Library identification, details of implementation and mark

a02 - Complex Arithmetic

a02bac	nag_complex Complex number from real and imaginary parts
a02bbc	nag_complex_real Real part of a complex number
a02bcc	nag_complex_imag Imaginary part of a complex number
a02cac	nag_complex_add Addition of two complex numbers
a02cbc	nag_complex_subtract Subtraction of two complex numbers
a02ccc	nag_complex_multiply Multiplication of two complex numbers
a02cdc	nag_complex_divide Quotient of two complex numbers
a02cec	nag_complex_negate Negation of a complex number
a02cfc	nag_complex_conjg Conjugate of a complex number
a02cgc	nag_complex_equal Equality of two complex numbers
a02chc	nag_complex_not_equal Inequality of two complex numbers
a02dac	nag_complex_arg Argument of a complex number
a02dbc	nag_complex_abs Modulus of a complex number
a02dcc	nag_complex_sqrt Square root of a complex number
a02ddc	nag_complex_i_power Complex number raised to integer power
a02dec	nag_complex_r_power Complex number raised to real power
a02dfc	nag_complex_c_power Complex number raised to complex power
a02dgc	nag_complex_log Complex logarithm
a02dhc	nag_complex_exp Complex exponential
a02djc	nag_complex_sin Complex sine
a02dkc	nag_complex_cos Complex cosine
a02dlc	nag_complex_tan Complex tangent

c02 - Zeros of Polynomials

c02afc	nag_zeros_complex_poly Zeros of a polynomial with complex coefficients
c02agc	nag_zeros_real_poly Zeros of a polynomial with real coefficients
c02akc	nag_cubic_roots Zeros of a cubic polynomial with real coefficients
c02alc	nag_quartic_roots Zeros of a quartic polynomial with real coefficients

c05 - Roots of One or More Transcendental Equations

c05adc	nag_zero_cont_func_bd Zero of a continuous function of one variable
c05nbc	nag_zero_nonlin_eqns Solution of a system of nonlinear equations (function values only)
c05pbc	nag_zero_nonlin_eqns_deriv Solution of a system of nonlinear equations (using first derivatives)
c05sdc	nag_zero_cont_func_bd_1 Zero of a continuous function of one variable, thread-safe
c05tbc	nag_zero_nonlin_eqns_1 Solution of a system of nonlinear equations (function values only), thread-safe
c05ubc	nag_zero_nonlin_eqns_deriv_1 Solution of a system of nonlinear equations (using first derivatives), thread-safe
c05zbc	nag_check_deriv Derivative checker for nag_zero_nonlin_eqns_deriv (c05pbc)
c05zcc	nag_check_deriv_1 Derivative checker for nag_zero_nonlin_eqns_deriv_1 (c05ubc), thread-safe

c06 - Fourier Transforms

c06eac	nag_fft_real Single 1-D real discrete Fourier transform
c06ebc	nag_fft_hermitian Single 1-D Hermitian discrete Fourier transform
c06ecc	nag_fft_complex Single 1-D complex discrete Fourier transform
c06ekc	nag_convolution_real Circular convolution or correlation of two real vectors
c06fpc	nag_fft_multiple_real Multiple 1-D real discrete Fourier transforms
c06fqc	nag_fft_multiple_hermitian Multiple 1-D Hermitian discrete Fourier transforms
c06frc	nag_fft_multiple_complex Multiple 1-D complex discrete Fourier transforms
c06fuc	nag_fft_2d_complex 2-D complex discrete Fourier transform
c06gbc	nag_conjugate_hermitian Complex conjugate of Hermitian sequence
c06gcc	nag_conjugate_complex Complex conjugate of complex sequence
c06gqc	nag_multiple_conjugate_hermitian Complex conjugate of multiple Hermitian sequences
c06gsc	nag_multiple_hermitian_to_complex Convert Hermitian sequences to general complex sequences
c06gzc	nag_fft_init_trig Initialisation function for other c06 functions
c06hac	nag_fft_multiple_sine Discrete sine transform
c06hbc	nag_fft_multiple_cosine Discrete cosine transform
c06hcc	nag_fft_multiple_qtr_sine Discrete quarter-wave sine transform
c06hdc	nag_fft_multiple_qtr_cosine Discrete quarter-wave cosine transform

d01 - Quadrature

d01ajc	nag_1d_quad_gen 1-D adaptive quadrature, allowing for badly-behaved integrands
d01akc	nag_1d_quad_osc 1-D adaptive quadrature, suitable for oscillating functions
d01alc	nag_1d_quad_brkpts 1-D adaptive quadrature, allowing for singularities at specified points
d01amc	nag_1d_quad_inf 1-D adaptive quadrature over infinite or semi-infinite interval
d01anc	nag_1d_quad_wt_trig 1-D adaptive quadrature, finite interval, sine or cosine weight functions
d01apc	nag_1d_quad_wt_alglog 1-D adaptive quadrature, weight function with end-point singularities of algebraic-logarithmic type
d01aqc	nag_1d_quad_wt_cauchy 1-D adaptive quadrature, weight function 1/(x-c), Cauchy principal value
d01asc	nag_1d_quad_inf_wt_trig 1-D adaptive quadrature, semi-infinite interval, sine or cosine weight function
d01bac	nag_1d_quad_gauss 1-D Gaussian quadrature rule evaluation
d01fcc	nag_multid_quad_adapt Multi-dimensional adaptive quadrature
d01gac	nag_1d_quad_vals 1-D integration of a function defined by data values only
d01gbc	nag_multid_quad_monte_carlo Multi-dimensional quadrature, using Monte Carlo method
d01sjc	nag_1d_quad_gen_1 1-D adaptive quadrature, allowing for badly-behaved integrands, thread-safe
d01skc	nag_1d_quad_osc_1 1-D adaptive quadrature, suitable for oscillating functions, thread-safe
d01slc	nag_1d_quad_brkpts_1 1-D adaptive quadrature, allowing for singularities at specified points, thread-safe
d01smc	nag_1d_quad_inf_1 1-D adaptive quadrature over infinite or semi-infinite interval, thread-safe
d01snc	nag_1d_quad_wt_trig_1 1-D adaptive quadrature, finite interval, sine or cosine weight functions, thread-safe
d01spc	nag_1d_quad_wt_alglog_1 1-D adaptive quadrature, weight function with end-point singularities of algebraic-logarithmic type, thread-safe
d01sqc	nag_1d_quad_wt_cauchy_1 1-D adaptive quadrature, weight function 1/(x-c), Cauchy principal value, thread-safe
d01ssc	nag_1d_quad_inf_wt_trig_1 1-D adaptive quadrature, semi-infinite interval, sine or cosine weight function, thread-safe
d01tac	nag_1d_quad_gauss_1 1-D Gaussian quadrature rule evaluation, thread-safe
d01wcc	nag_multid_quad_adapt_1 Multi-dimensional adaptive quadrature, thread-safe
d01xbc	nag_multid_quad_monte_carlo_1 Multi-dimensional quadrature, using Monte Carlo method, thread-safe

d02 - Ordinary Differential Equations

d02cjc	nag_ode_ivp_adams_gen Ordinary differential equation solver using a variable-order variable-step Adams method (black box)
d02ejc	nag_ode_ivp_bdf_gen Ordinary differential equations solver, stiff, initial value problems using the Backward Differentiation Formulae
d02gac	nag_ode_bvp_fd_nonlin_fixedbc Ordinary differential equations solver, for simple nonlinear 2-point boundary value problems, using a finite difference technique with deferred correction
d02gbc	nag_ode_bvp_fd_lin_gen Ordinary differential equations solver, for general linear two-point boundary value problems, using a finite difference technique with deferred correction
d02pcc	nag_ode_ivp_rk_range Ordinary differential equations solver, initial value problems over a range using Runge-Kutta methods
d02pdc	nag_ode_ivp_rk_onestep Ordinary differential equations solver, initial value problems, one time step using Runge-Kutta methods
d02ppc	nag_ode_ivp_rk_free Freeing function for use with the Runge-Kutta suite (d02p functions)
d02pvc	nag_ode_ivp_rk_setup Set-up function for use with nag_ode_ivp_rk_range (d02pcc) and/or nag_ode_ivp_rk_onestep (d02pdc)
d02pwc	nag_ode_ivp_rk_reset_tend A function to re-set the end point following a call to nag_ode_ivp_rk_onestep (d02pdc)
d02pxc	nag_ode_ivp_rk_interp Ordinary differential equations solver, computes the solution by interpolation anywhere on an integration step taken by nag_ode_ivp_rk_onestep (d02pdc)
d02pzc	nag_ode_ivp_rk_errass A function to provide global error assessment during an integration with either nag_ode_ivp_rk_range (d02pcc) or nag_ode_ivp_rk_onestep (d02pdc)
d02qfc	nag_ode_ivp_adams_roots Ordinary differential equation solver using Adams method (sophisticated use)
d02qwc	nag_ode_ivp_adams_setup Set-up function for nag_ode_ivp_adams_roots (d02qfc)
d02qyc	nag_ode_ivp_adams_free Freeing function for use with nag_ode_ivp_adams_roots (d02qfc)
d02qzc	nag_ode_ivp_adams_interp Interpolation function for use with nag_ode_ivp_adams_roots (d02qfc)
d02rac	nag_ode_bvp_fd_nonlin_gen Ordinary differential equations solver, for general non-linear two-point boundary value problems, using a finite difference technique with deferred correction

e01 - Interpolation

e01bac	nag_1d_spline_interpolant Interpolating function, cubic spline interpolant, one variable
e01bec	nag_monotonic_interpolant Interpolating function, monotonicity-preserving, piecewise cubic Hermite, one variable
e01bfc	nag_monotonic_evaluate Evaluation of interpolant computed by nag_monotonic_interpolant (e01bec), function only
e01bgc	nag_monotonic_deriv Evaluation of interpolant computed by nag_monotonic_interpolant (e01bec), function and first derivative
e01bhc	nag_monotonic_intg Evaluation of interpolant computed by nag_monotonic_interpolant (e01bec), definite integral
e01dac	nag_2d_spline_interpolant Interpolating function, bicubic spline interpolant, two variables
e01sac	nag_2d_scat_interpolant A function to generate a two-dimensional surface interpolating a set of data points, using either the method of Renka and Cline or using the modified Shepard's method
e01sbc	nag_2d_scat_eval A function to evaluate at a set of points, the two-dimensional interpolant function generated by nag_2d_scat_interpolant (e01sac)
e01szc	nag_2d_scat_free Freeing function for use with nag_2d_scat_eval (e01sbc)

e02 - Curve and Surface Fitting

e02adc	nag_1d_cheb_fit Computes the coefficients of a Chebyshev series polynomial for arbitrary data
e02aec	nag_1d_cheb_eval Evaluates the coefficients of a Chebyshev series polynomial
e02afc	nag_1d_cheb_interp_fit Computes the coefficients of a Chebyshev series polynomial for interpolated data
e02bac	nag_1d_spline_fit_knots Least-squares curve cubic spline fit (including interpolation), one variable
e02bbc	nag_1d_spline_evaluate Evaluation of fitted cubic spline, function only
e02bcc	nag_1d_spline_deriv Evaluation of fitted cubic spline, function and derivatives
e02bdc	nag_1d_spline_intg Evaluation of fitted cubic spline, definite integral
e02bec	nag_1d_spline_fit Least-squares cubic spline curve fit, automatic knot placement, one variable
e02dcc	nag_2d_spline_fit_grid Least-squares bicubic spline fit with automatic knot placement, two variables (rectangular grid)
e02ddc	nag_2d_spline_fit_scat Least-squares bicubic spline fit with automatic knot placement, two variables (scattered data)
e02dec	nag_2d_spline_eval Evaluation of bicubic spline, at a set of points
e02dfc	nag_2d_spline_eval_rect Evaluation of bicubic spline, at a mesh of points

e04 - Minimizing or Maximizing a Function

e04abc	nag_opt_one_var_no_deriv Minimizes a function of one variable, using function values only
e04bbc	nag_opt_one_var_deriv Minimizes a function of one variable, requires first derivatives
e04ccc	nag_opt_simplex Unconstrained minimization using simplex algorithm
e04dgc	nag_opt_conj_grad Unconstrained minimization using conjugate gradients
e04fcc	nag_opt_lsq_no_deriv Unconstrained nonlinear least squares (no derivatives required)
e04gbc	nag_opt_lsq_deriv Unconstrained nonlinear least squares (first derivatives required)
e04hcc	nag_opt_check_deriv Derivative checker for use with nag_opt_bounds_deriv (e04kbc)
e04hdc	nag_opt_check_2nd_deriv Checks 2nd derivatives of a user-defined function
e04jbc	nag_opt_bounds_no_deriv Bound constrained nonlinear minimization (no derivatives required)
e04kbc	nag_opt_bounds_deriv Bound constrained nonlinear minimization (first derivatives required)
e04lbc	nag_opt_bounds_2nd_deriv Solves bound constrained problems. 1st and 2nd derivatives are required.
e04mfc	nag_opt_lp Linear programming
e04myc	nag_opt_sparse_mps_free Free memory allocated by nag_opt_sparse_mps_read (e04mzc)
e04mzc	nag_opt_sparse_mps_read Read MPSX data for sparse LP or QP problem from a file
e04ncc	nag_opt_lin_lsq Solves linear least-squares and convex quadratic programming problems (non-sparse)
e04nfc	nag_opt_qp Quadratic programming
e04nkc	nag_opt_sparse_convex_qp Solves sparse linear programming or convex quadratic programming problems
e04ucc	nag_opt_nlp Minimization with nonlinear constraints using a sequential QP method
e04ugc	nag_opt_nlp_sparse NLP problem (sparse)
e04unc	nag_opt_nlin_lsq Solves nonlinear least-squares problems using the sequential QP method
e04xac	nag_opt_estimate_deriv Computes an approximation to the gradient vector and/or the Hessian matrix for use with nag_opt_nlp (e04ucc) and other nonlinear optimization functions
e04xxc	nag_opt_init Initialisation function for option setting
e04xyc	nag_opt_read Read options from a textfile
e04xzc	nag_opt_free NAG memory freeing function for use with option setting
e04yac	nag_opt_lsq_check_deriv Least-squares derivative checker for use with nag_opt_lsq_deriv (e04gbc)
e04ycc	nag_opt_lsq_covariance Covariance matrix for nonlinear least-squares

f - Linear Algebra

f01bnc	nag_complex_cholesky UU^H factorization of complex Hermitian positive-definite matrix
f01mcc	nag_real_cholesky_skyline LDL^T factorization of real symmetric positive-definite variable-bandwidth (skyline) matrix
f01qcc	nag_real_qr QR factorization of real m by n matrix (m >= n)
f01qdc	nag_real_apply_q Compute QB or Q^T B after factorization by nag_real_qr (f01qcc)
f01qec	nag_real_form_q Form columns of Q after factorization by nag_real_qr (f01qcc)
f01rcc	nag_complex_qr QR factorization of complex m by n matrix (m >= n)
f01rdc	nag_complex_apply_q Compute QB or Q^H B after factorization by nag_complex_qr (f01rcc)
f01rec	nag_complex_form_q Form columns of Q after factorization bynag_complex_qr (f01rcc)
f02aac	nag_real_symm_eigenvalues All eigenvalues of real symmetric matrix
f02abc	nag_real_symm_eigensystem All eigenvalues and eigenvectors of real symmetric matrix
f02adc	nag_real_symm_general_eigenvalues All eigenvalues of generalized real symmetric-definite eigenproblem
f02aec	nag_real_symm_general_eigensystem All eigenvalues and eigenvectors of generalized real symmetric-definite eigenproblem
f02afc	nag_real_eigenvalues All eigenvalues of real matrix
f02agc	nag_real_eigensystem All eigenvalues and eigenvectors of real matrix
f02awc	nag_hermitian_eigenvalues All eigenvalues of complex Hermitian matrix
f02axc	nag_hermitian_eigensystem All eigenvalues and eigenvectors of complex Hermitian matrix
f02bjc	nag_real_general_eigensystem All eigenvalues and optionally eigenvectors of real generalized eigenproblem, by QZ algorithm
f02ecc	nag_real_eigensystem_sel Computes selected eigenvalues and eigenvectors of a real general matrix
f02gcc	nag_complex_eigensystem_sel Computes selected eigenvalues and eigenvectors of a complex general matrix
f02wec	nag_real_svd SVD of real matrix
f02xec	nag_complex_svd SVD of complex matrix
f03aec	nag_real_cholesky LL^T factorization and determinant of real symmetric positive-definite matrix
f03afc	nag_real_lu LU factorization and determinant of real matrix
f03ahc	nag_complex_lu LU factorization and determinant of complex matrix
f04adc	nag_complex_lin_eqn_mult_rhs Approximate solution of complex simultaneous linear equations with multiple right-hand sides
f04agc	nag_real_cholesky_solve_mult_rhs Approximate solution of real symmetric positive-definite simultaneous linear equations (coefficient matrix already factorized by nag_real_cholesky (f03aec))
f04ajc	nag_real_lu_solve_mult_rhs Approximate solution of real simultaneous linear equations (coefficient matrix already factorized by nag_real_lu (f03afc))
f04akc	nag_complex_lu_solve_mult_rhs Approximate solution of complex simultaneous linear equations (coefficient matrix already factorized by nag_complex_lu (f03ahc))
f04arc	nag_real_lin_eqn Approximate solution of real simultaneous linear equations, one right-hand side
f04awc	nag_hermitian_lin_eqn_mult_rhs Approximate solution of complex Hermitian positive-definite simultaneous linear equations (coefficient matrix already factorized by nag_complex_cholesky (f01bnc))
f04mcc	nag_real_cholesky_skyline_solve Approximate solution of real symmetric positive-definite variable-bandwidth simultaneous linear equations (coefficient matrix already factorized by nag_real_cholesky_skyline (f01mcc))

f06 - Linear Algebra Support Functions

f06pac	dgemv Matrix-vector product, real rectangular matrix
f06pbc	dgbmv Matrix-vector product, real rectangular band matrix
f06pcc	dsymv Matrix-vector product, real symmetric matrix
f06pdc	dsbmv Matrix-vector product, real symmetric band matrix
f06pec	dspmv Matrix-vector product, real symmetric packed matrix
f06pfc	dtrmv Matrix-vector product, real triangular matrix
f06pgc	dtbmv Matrix-vector product, real triangular band matrix
f06phc	dtpmv Matrix-vector product, real triangular packed matrix
f06pjc	dtrsv System of equations, real triangular matrix
f06pkc	dtbsv System of equations, real triangular band matrix
f06plc	dtpsv System of equations, real triangular packed matrix
f06pmc	dger Rank-1 update, real rectangular matrix
f06ppc	dsyr Rank-1 update, real symmetric matrix
f06pqc	dspr Rank-1 update, real symmetric packed matrix
f06prc	dsyr2 Rank-2 update, real symmetric matrix
f06psc	dspr2 Rank-2 update, real symmetric packed matrix
f06sac	zgemv Matrix-vector product, complex rectangular matrix
f06sbc	zgbmv Matrix-vector product, complex rectangular band matrix
f06scc	zhemv Matrix-vector product, complex Hermitian matrix
f06sdc	zhbmv Matrix-vector product, complex Hermitian band matrix
f06sec	zhpmv Matrix-vector product, complex Hermitian packed matrix
f06sfc	ztrmv Matrix-vector product, complex triangular matrix
f06sgc	ztbmv Matrix-vector product, complex triangular band matrix
f06shc	ztpmv Matrix-vector product, complex triangular packed matrix
f06sjc	ztrsv System of equations, complex triangular matrix
f06skc	ztbsv System of equations, complex triangular band matrix
f06slc	ztpsv System of equations, complex triangular packed matrix
f06smc	zgeru Rank-1 update, complex rectangular matrix, unconjugated vector
f06snc	zgerc Rank-1 update, complex rectangular matrix, conjugated vector
f06spc	zher Rank-1 update, complex Hermitian matrix
f06sqc	zhpr Rank-1 update, complex Hermitian packed matrix
f06src	zher2 Rank-2 update, complex Hermitian matrix
f06ssc	zhpr2 Rank-2 update, complex Hermitian packed matrix
f06yac	dgemm Matrix-matrix product, two real rectangular matrices
f06ycc	dsymm Matrix-matrix product, one real symmetric matrix, one real rectangular matrix
f06yfc	dtrmm Matrix-matrix product, one real triangular matrix, one real rectangular matrix
f06yjc	dtrsm Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix
f06ypc	dsyrk Rank-k update of a real symmetric matrix
f06yrc	dsyr2k Rank-2k update of a real symmetric matrix
f06zac	zgemm Matrix-matrix product, two complex rectangular matrices
f06zcc	zhemm Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix
f06zfc	ztrmm Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix
f06zjc	ztrsm Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix
f06zpc	zherk Rank-k update of a complex Hermitian matrix
f06zrc	zher2k Rank-2k update of a complex Hermitian matrix
f06ztc	zsymm Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix
f06zuc	zsyrk Rank-k update of a complex symmetric matrix
f06zwc	zsyr2k Rank-2k update of a complex symmetric matrix

f11 - Sparse Linear Algebra

f11dac	nag_sparse_nsym_fac Incomplete LU factorization (nonsymmetric)
f11dcc	nag_sparse_nsym_fac_sol Solver with incomplete LU preconditioning (nonsymmetric)
f11dec	nag_sparse_nsym_sol Solver with no/Jacobi/SSOR/preconditioning (nonsymmetric)
f11jac	nag_sparse_sym_chol_fac Incomplete Cholesky factorization (symmetric)
f11jcc	nag_sparse_sym_chol_sol Solver with incomplete Cholesky preconditioning (symmetric)
f11jec	nag_sparse_sym_sol Solver with Jacobi, SSOR, or no preconditioning (symmetric)
f11zac	nag_sparse_nsym_sort Sparse sort (nonsymmetric)
f11zbc	nag_sparse_sym_sort Sparse sort (symmetric)

g01 - Simple Calculations on Statistical Data

g01aac	nag_summary_stats_1var Mean, variance, skewness, kurtosis etc, one variable, from raw data
g01aec	nag_frequency_table Frequency table from raw data
g01alc	nag_5pt_summary_stats Five-point summary (median, hinges and extremes)
g01bjc	nag_binomial_dist Binomial distribution function
g01bkc	nag_poisson_dist Poisson distribution function
g01blc	nag_hypergeom_dist Hypergeometric distribution function
g01cec	nag_deviates_normal_dist Deviate of Normal distribution function
g01ddc	nag_shapiro_wilk_test Shapiro and Wilk's W test for Normality
g01dhc	nag_ranks_and_scores Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores
g01eac	nag_prob_normal Probabilities for the standard Normal distribution
g01ebc	nag_prob_students_t Probabilities for Student's t-distribution
g01ecc	nag_prob_chi_sq Probabilities for chi² distribution
g01edc	nag_prob_f_dist Probabilities for F-distribution
g01eec	nag_prob_beta_dist Upper and lower tail probabilities and probability density function for the beta distribution
g01efc	nag_gamma_dist Probabilities for the gamma distribution
g01fac	nag_deviates_normal Deviates for the Normal distribution
g01fbc	nag_deviates_students_t Deviates for Student's t-distribution
g01fcc	nag_deviates_chi_sq Deviates for the chi² distribution
g01fdc	nag_deviates_f_dist Deviates for the F-distribution
g01fec	nag_deviates_beta Deviates for the beta distribution
g01ffc	nag_deviates_gamma_dist Deviates for the gamma distribution
g01gbc	nag_prob_non_central_students_t Computes probabilities for the non-central Student's t-distribution
g01gcc	nag_prob_non_central_chi_sq Computes probabilities for the non-central chi² distribution
g01gdc	nag_prob_non_central_f_dist Computes probabilities for the non-central F-distribution
g01gec	nag_prob_non_central_beta_dist Computes probabilities for the non-central beta distribution
g01hac	nag_bivariate_normal_dist Probability for the bivariate Normal distribution
g01hbc	nag_multi_normal Computes probabilities for the multivariate Normal distribution

g02 - Regression Analysis

g02brc	nag_ken_spe_corr_coeff Kendall and/or Spearman non-parametric rank correlation coefficients, allows variables and observations to be selectively disregarded
g02bxc	nag_corr_cov Product-moment correlation, unweighted/weighted correlation and covariance matrix, allows variables to be disregarded
g02byc	nag_partial_corr Computes partial correlation/variance-covariance matrix from correlation/variance-covariance matrix computed by nag_corr_cov (g02bxc)
g02cac	nag_simple_linear_regression Simple linear regression with or without a constant term, data may be weighted
g02cbc	nag_regress_confid_interval Simple linear regression confidence intervals for the regression line and individual points
g02dac	nag_regsn_mult_linear Fits a general (multiple) linear regression model
g02dcc	nag_regsn_mult_linear_addrem_obs Add/delete an observation to/from a general linear regression model
g02ddc	nag_regsn_mult_linear_upd_model Estimates of regression parameters from an updated model
g02dec	nag_regsn_mult_linear_add_var Add a new independent variable to a general linear regression model
g02dfc	nag_regsn_mult_linear_delete_var Delete an independent variable from a general linear regression model
g02dgc	nag_regsn_mult_linear_newyvar Fits a general linear regression model to new dependent variable
g02dkc	nag_regsn_mult_linear_tran_model Estimates of parameters of a general linear regression model for given constraints
g02dnc	nag_regsn_mult_linear_est_func Estimate of an estimable function for a general linear regression model
g02fac	nag_regsn_std_resid_influence Calculate standardized residuals and influence statistics
g02gac	nag_glm_normal Fits a Generalised linear model with Normal errors
g02gbc	nag_glm_binomial Fits a generalised linear model with binomial errors
g02gcc	nag_glm_poisson Fits a generalised linear model with Poisson errors
g02gdc	nag_glm_gamma Fits a generalised linear model with gamma errors
g02gkc	nag_glm_tran_model Estimates and standard errors of the parameters of a general linear model for given constraints
g02gnc	nag_glm_est_func Estimatable function and the standard error of a generalized linear model
g02hac	nag_robust_m_regsn_estim Robust regression, standard M-estimates
g02hkc	nag_robust_corr_estim Robust estimation of a correlation matrix, Huber's weight function

g03 - Multivariate Methods

g03aac	nag_mv_prin_comp Principal component analysis
g03acc	nag_mv_canon_var Canonical variate analysis
g03adc	nag_mv_canon_corr Canonical correlation analysis
g03bac	nag_mv_orthomax Orthogonal rotations for loading matrix
g03bcc	nag_mv_procustes Procrustes rotations
g03cac	nag_mv_factor Maximum likelihood estimates of parameters
g03ccc	nag_mv_fac_score Factor score coefficients, following nag_mv_factor (g03cac)
g03dac	nag_mv_discrim Test for equality of wthin-group covariance matrices
g03dbc	nag_mv_discrim_mahaldist Mahalanobis squared distances, following nag_mv_discrim (g03dac)
g03dcc	nag_mv_discrim_group Allocation of observations to groups, following nag_mv_discrim (g03dac)
g03eac	nag_mv_distance_mat Compute distance (dissimilarity) matrix
g03ecc	nag_mv_hierar_cluster_analysis Performs hierarchical cluster analysis
g03efc	nag_mv_kmeans_cluster_analysis K-means
g03ehc	nag_mv_dendrogram Construct dendogram following nag_mv_hierar_cluster_analysis (g03ecc)
g03ejc	nag_mv_cluster_indicator Construct clusters following nag_mv_hierar_cluster_analysis (g03ecc)
g03fac	nag_mv_prin_coord_analysis Principal co-ordinate analysis
g03fcc	nag_mv_ordinal_multidimscale Multidimensional scaling
g03xzc	nag_mv_dend_free Frees memory allocated to the dendrogram array in nag_mv_dendrogram (g03ehc)
g03zac	nag_mv_z_scores Standardize values of a data matrix

g04 - Analysis of Variance

g04bbc	nag_anova_random General block design or completely randomized design
g04bcc	nag_anova_row_col Analysis of variance, general row and column design, treatment means and standard errors
g04cac	nag_anova_factorial Complete factorial design
g04czc	nag_anova_factorial_free Complete factorial design
g04dbc	nag_anova_confid_interval Computes confidence intervals for differences between means computed by nag_anova_random (g04bbc) or nag_anova_row_col (g04bcc)
g04eac	nag_dummy_vars Computes orthogonal polynomials or dummy variables for factor/classification variable

g05 - Random Number Generators

g05cac	nag_random_continuous_uniform Pseudo-random real number, uniform distribution over (0,1)
g05cbc	nag_random_init_repeatable Initialise random number generating functions to give repeatable sequence
g05ccc	nag_random_init_nonrepeatable Initialise random number generating functions to give non-repeatable sequence
g05cfc	nag_save_random_state Save state of random number generating functions
g05cgc	nag_restore_random_state Restore state of random number generating functions
g05dac	nag_random_continuous_uniform_ab Pseudo-random real number, uniform distribution over (a,b)
g05dbc	nag_random_exp Pseudo-random real number, (negative) exponential distribution
g05ddc	nag_random_normal Pseudo-random real number, Normal distribution
g05dyc	nag_random_discrete_uniform Pseudo-random integer from uniform distribution
g05eac	nag_ref_vec_multi_normal Set up reference vector for multivariate Normal distribution
g05ecc	nag_ref_vec_poisson Set up reference vector for generating pseudo-random integers, Poisson distribution
g05edc	nag_ref_vec_binomial Set up reference vector for generating pseudo-random integers, binomial distribution
g05ehc	nag_ran_permut_vec Pseudo-random permutation of a vector of integers
g05ejc	nag_ran_sample_vec Pseudo-random sample without replacement from an integer vector
g05exc	nag_ref_vec_discrete_pdf_cdf Set up reference vector from supplied cumulative distribution function or probability distribution function
g05eyc	nag_return_discrete Pseudo-random integer from reference vector
g05ezc	nag_return_multi_normal Pseudo-random multivariate Normal vector from reference vector
g05fec	nag_random_beta Pseudo-random real numbers from the beta distribution
g05ffc	nag_random_gamma Pseudo-random real numbers from the gamma distribution
g05hac	nag_arma_time_series ARMA time series of n terms
g05hkc	nag_generate_agarchI Univariate time series, generate n terms of either a symmetric GARCH process or a GARCH process with asymmetry of the form (epsilon_t-1 + gamma)²
g05hlc	nag_generate_agarchII Univariate time series, generate n terms of a GARCH process with asymmetry of the form (\|epsilon_t-1\| + gamma epsilon_t-1)²
g05hmc	nag_generate_garchGJR Univariate time series, generate n terms of an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process

g07 - Univariate Estimation

g07cac	nag_2_sample_t_test t-test statistic, for a difference in means between two Normal populations, confidence interval
g07dac	nag_median_1var Robust estimation, median, median absolute deviation, robust standard deviation
g07dbc	nag_robust_m_estim_1var Robust estimation, M-estimate of location and scale parameters, standard weight function
g07ddc	nag_robust_trimmed_1var Trimmed and winsorized mean of a sample with estimates of the variances of the two means

g08 - Nonparametric Statistics

g08aac	nag_sign_test Sign test on two paired samples
g08acc	nag_median_test Median test on two samples of unequal size
g08aec	nag_friedman_test Friedman two-way analysis of variance on k matched samples
g08afc	nag_kruskal_wallis_test Kruskal–Wallis one-way analysis of variance on k samples of unequal size
g08agc	nag_wilcoxon_test Performs the Wilcoxon one-sample (matched pairs) signed rank test
g08amc	nag_mann_whitney Performs the Mann–Whitney U test on two independent samples
g08cbc	nag_1_sample_ks_test Performs the one-sample Kolmogorov–Smirnov test for standard distributions
g08cdc	nag_2_sample_ks_test Performs the two-sample Kolmogorov–Smirnov test
g08cgc	nag_chi_sq_goodness_of_fit_test Performs the chi² goodness of fit test, for standard continuous distributions
g08eac	nag_runs_test Performs the runs up or runs down test for randomness
g08ebc	nag_pairs_test Performs the pairs (serial) test for randomness
g08ecc	nag_triplets_test Performs the triplets test for randomness
g08edc	nag_gaps_test Performs the gaps test for randomness

g10 - Smoothing in Statistics

g10abc	nag_smooth_spline_fit Fit cubic smoothing spline, smoothing parameter given
g10acc	nag_smooth_spline_estim Fit cubic smoothing spline, smoothing parameter estimated
g10bac	nag_kernel_density_estim Kernel density estimate using Gaussian kernel
g10cac	nag_running_median_smoother Smoothed data sequence using running median smoother
g10zac	nag_order_data Reorder data to give ordered distinct observations

g11 - Contingency Table Analysis

g11aac	nag_chi_sq_2_way_table chi² statistic for two-way contingency table
g11bac	nag_tabulate_stats Computes multiway table from set of classification factors using selected statistic
g11bbc	nag_tabulate_percentile Computes multiway table from set of classification factors using given percentile/quantile

g12 - Survival Analysis

g12aac	nag_prod_limit_surviv_fn Kaplan-Meier (product-limit) estimates of survival probabilities
g12bac	nag_surviv_cox_model Fits Cox's proportional hazard model

g13 - Time Series Analysis

g13abc	nag_tsa_auto_corr Sample autocorrelation function
g13acc	nag_tsa_auto_corr_part Partial autocorrelation function
g13asc	nag_tsa_resid_corr Univariate time series, diagnostic checking of residuals, following nag_tsa_multi_inp_model_estim (g13bec)
g13bec	nag_tsa_multi_inp_model_estim Estimation for time series models
g13bjc	nag_tsa_multi_inp_model_forecast Forecasting function
g13bxc	nag_tsa_options_init Initialisation function for option setting
g13byc	nag_tsa_transf_orders Function to allocate memory to transfer function model orders
g13bzc	nag_tsa_trans_free Freeing function for the structure holding the transfer function model orders
g13cbc	nag_tsa_spectrum_univar Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window
g13cdc	nag_tsa_spectrum_bivar Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window
g13cec	nag_tsa_cross_spectrum_bivar Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra
g13cfc	nag_tsa_gain_phase_bivar Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra
g13cgc	nag_tsa_noise_spectrum_bivar Multivariate time series, noise spectrum, bounds, impulse response function and its standard error
g13eac	nag_kalman_sqrt_filt_cov_var One iteration step of the time-varying Kalman filter recursion using the square root covariance implementation
g13ebc	nag_kalman_sqrt_filt_cov_invar One iteration step of the time-invariant Kalman filter recursion using the square root covariance implementation with (A,C) in lower observer Hessenberg form
g13ecc	nag_kalman_sqrt_filt_info_var One iteration step of the time-varying Kalman filter recursion using the square root information implementation
g13edc	nag_kalman_sqrt_filt_info_invar One iteration step of the time-invariant Kalman filter recursion using the square root information implementation with (A^-1, A^-1 B) in upper controller Hessenberg form
g13ewc	nag_trans_hessenberg_observer Unitary state-space transformation to reduce (A,C) to lower or upper observer Hessenberg form
g13exc	nag_trans_hessenberg_controller Unitary state-space transformation to reduce (B,A) to lower or upper controller Hessenberg form
g13fac	nag_estimate_agarchI Univariate time series, parameter estimation for either a symmetric GARCH process or a GARCH process with asymmetry of the form (epsilon_t-1 + gamma)²
g13fbc	nag_forecast_agarchI Univariate time series, forecast function for either a symmetric GARCH process or a GARCH process with asymmetry of the form (epsilon_t-1 + gamma)²
g13fcc	nag_estimate_agarchII Univariate time series, parameter estimation for a GARCH process with asymmetry of the form (\|epsilon_t-1\| + gamma epsilon_t-1)²
g13fdc	nag_forecast_agarchII Univariate time series, forecast function for a GARCH process with asymmetry of the form (\|epsilon_t-1\| + gamma epsilon_t-1)²
g13fec	nag_estimate_garchGJR Univariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
g13ffc	nag_forecast_garchGJR Univariate time series, forecast function for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
g13xzc	nag_tsa_free Freeing function for use with g13 option setting

h - Operations Research

h02bbc	nag_ip_bb Solves integer programming problems using a branch and bound method
h02buc	nag_ip_mps_read Read MPSX data for IP, LP or QP problem from a file
h02bvc	nag_ip_mps_free Free memory allocated by nag_ip_mps_read (h02buc)
h02xxc	nag_ip_init Initialize option structure to null values
h02xyc	nag_ip_read Read optional parameter values from a file
h02xzc	nag_ip_free Free NAG allocated memory from option structures
h03abc	nag_transport Classical transportation algorithm

m01 - Sorting

m01cac	nag_double_sort Quicksort of set of values of data type double
m01csc	nag_quicksort Quicksort of set of values of arbitrary data type
m01ctc	nag_stable_sort Stable sort of set of values of arbitrary data type
m01cuc	nag_chain_sort Chain sort of linked list
m01dsc	nag_rank_sort Rank sort of set of values of arbitrary data type
m01esc	nag_reorder_vector Reorders set of values of arbitrary data type into the order specified by a set of indices
m01fsc	nag_search_vector Searches a vector for either the first or last match to a given value
m01zac	nag_make_indices Inverts a permutation converting a rank vector to an index vector or vice versa

s - Approximations of Special Functions

s10aac	nag_tanh Hyperbolic tangent, tanh x
s10abc	nag_sinh Hyperbolic sine, sinh x
s10acc	nag_cosh Hyperbolic cosine, cosh x
s11aac	nag_arctanh Inverse hyperbolic tangent, arctanh x
s11abc	nag_arcsinh Inverse hyperbolic sine, arcsinh x
s11acc	nag_arccosh Inverse hyperbolic cosine, arccosh x
s13aac	nag_exp_integral Exponential integral E₁ (x)
s13acc	nag_cos_integral Cosine integral Ci(x)
s13adc	nag_sin_integral Sine integral Si(x)
s14aac	nag_gamma Gamma function gamma(x)
s14abc	nag_log_gamma Log Gamma function ln(gamma(x))
s14aec	nag_real_polygamma Derivative of the psi function psi(x)
s14afc	nag_complex_polygamma Derivative of the psi function psi(z)
s14bac	nag_incomplete_gamma Incomplete gamma functions P(a,x) and Q(a,x)
s15abc	nag_cumul_normal Cumulative normal distribution function, P(x)
s15acc	nag_cumul_normal_complem Complement of cumulative normal distribution function, Q(x)
s15adc	nag_erfc Complement of error function, erfc x
s15aec	nag_erf Error function, erf x
s17acc	nag_bessel_y0 Bessel function Y₀ (x)
s17adc	nag_bessel_y1 Bessel function Y₁ (x)
s17aec	nag_bessel_j0 Bessel function J₀ (x)
s17afc	nag_bessel_j1 Bessel function J₁ (x)
s17agc	nag_airy_ai Airy function Ai(x)
s17ahc	nag_airy_bi Airy function Bi(x)
s17ajc	nag_airy_ai_deriv Airy function Ai'(x)
s17akc	nag_airy_bi_deriv Airy function Bi'(x)
s17alc	nag_bessel_zeros Zeros of Bessel functions J_alpha(x), J'_alpha(x), Y_alpha(x) or Y'_alpha(x)
s18acc	nag_bessel_k0 Modified Bessel function K₀ (x)
s18adc	nag_bessel_k1 Modified Bessel function K₁ (x)
s18aec	nag_bessel_i0 Modified Bessel function I₀ (x)
s18afc	nag_bessel_i1 Modified Bessel function I₁ (x)
s18ccc	nag_bessel_k0_scaled Scaled modified Bessel function e^x K₀ (x)
s18cdc	nag_bessel_k1_scaled Scaled modified Bessel function e^x K₁ (x)
s18cec	nag_bessel_i0_scaled Scaled modified Bessel function e^-\|x\| I₀ (x)
s18cfc	nag_bessel_i1_scaled Scaled modified Bessel function e^-\|x\| I₁ (x)
s18ecc	nag_bessel_i_nu_scaled Scaled modified Bessel function e^-x I_nu/4(x)
s18edc	nag_bessel_k_nu_scaled Scaled modified Bessel function e^x K_nu/4(x)
s18eec	nag_bessel_i_nu Modified Bessel function I_nu/4(x)
s18efc	nag_bessel_k_nu Modified Bessel function K_nu/4(x)
s18egc	nag_bessel_k_alpha Modified Bessel functions K_alpha+n(x) for real x > 0, selected values of alpha ≥ 0 and n = 0,1,...,N
s18ehc	nag_bessel_k_alpha_scaled Scaled modified Bessel functions functions K_alpha+n(x) for real x > 0, selected values of alpha ≥ 0 and n = 0,1,...,N
s18ejc	nag_bessel_i_alpha Modified Bessel functions I_alpha+n-1(x) or I_alpha-n+1(x) for real x ≠ 0, non-negative alpha < 1 and n = 1,2,...,\|N\|+1
s18ekc	nag_bessel_j_alpha Bessel functions J_alpha+n-1(x) or J_alpha-n+1(x) for real x ≠ 0, non-negative alpha < 1 and n = 1,2,...,\|N\|+1
s19aac	nag_kelvin_ber Kelvin function ber x
s19abc	nag_kelvin_bei Kelvin function bei x
s19acc	nag_kelvin_ker Kelvin function ker x
s19adc	nag_kelvin_kei Kelvin function kei x
s20acc	nag_fresnel_s Fresnel integral S(x)
s20adc	nag_fresnel_c Fresnel integral C(x)
s21bac	nag_elliptic_integral_rc Degenerate symmetrised elliptic integral of 1st kind R_C (x,y)
s21bbc	nag_elliptic_integral_rf Symmetrised elliptic integral of 1st kind R_F (x,y,z)
s21bcc	nag_elliptic_integral_rd Symmetrised elliptic integral of 2nd kind R_D (x,y,z)
s21bdc	nag_elliptic_integral_rj Symmetrised elliptic integral of 3rd kind R_J (x,y,z,r)
s21cbc	nag_jacobian_elliptic Jacobian elliptic functions sn, cn and dn with complex arguments
s21ccc	nag_jacobian_theta Jacobian theta functions with real arguments
s21dac	nag_elliptic_integral_f Elliptic integrals of the second kind with complex arguments
s22aac	nag_legendre_p Legendre and associated Legendre functions of the first kind with real arguments

x01 - Mathematical Constants

X01AAC	nag_pi pi
X01ABC	nag_euler_constant Euler's constant, gamma

x02 - Machine Constants

X02AHC	nag_max_sine_argument Largest permissible argument for sin and cos functions
X02AJC	nag_machine_precision Machine precision
X02AKC	nag_real_smallest_number Smallest positive model number
X02ALC	nag_real_largest_number Largest positive model number
X02AMC	nag_real_safe_small_number Safe range of floating-point arithmetic
X02BBC	nag_max_integer Largest representable integer
X02BEC	nag_decimal_digits Maximum number of decimal digits that can be represented
X02BHC	nag_real_base Parameter b of model of floating-point arithmetic
X02BJC	nag_real_base_digits Parameter p of model of floating-point arithmetic
X02BKC	nag_real_min_exponent Parameter e_min of model of floating-point arithmetic
X02BLC	nag_real_max_exponent Parameter e_max of model of floating-point arithmetic
X02DAC	nag_underflow_flag Switch for taking precautions to avoid underflow
X02DJC	nag_real_arithmetic_rounds Parameter ROUNDS of model of floating-point arithmetic

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