C Library Mark 5 Documentation

Introduction

• Essential Introduction
• NAG C Library Mark 5 News

Chapter a00 - Library Identification

• a00aac (nag_implementation_details) - Library identification, details of implementation and mark

Chapter a02 - Complex Number Functions

• a02bac (nag_complex) - Complex number from real and imaginary parts
• a02bbc (nag_complex_real) - Real part of complex number
• a02bcc (nag_complex_imag) - Imaginary part of complex number
• a02cac (nag_complex_add) - Addition of two complex numbers
• a02cbc (nag_complex_subtract) - Subtraction of 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

Chapter 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

Chapter 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

Chapter 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

Chapter 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 with end-point singularities of algebraic-logarithmic type
• d01aqc (nag_1d_quad_wt_cauchy) - 1-D adaptive quadrature, Hilbert transform weight function
• 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

Chapter 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 two-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

Chapter 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)

Chapter 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

Chapter 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 sequential QP method
• 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) - Reads 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 e04gbc
• e04ycc (nag_opt_lsq_covariance) - Covariance matrix for nonlinear least-squares

Chapter 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 by nag_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))

Chapter f06 - Linear Algebra

• 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

Chapter 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 facroization (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)

Chapter g01 - Simple Calculations on Statistical Data

• g01aac (nag_summary_stats_1var) - Mean, variance, skewness, kurtosis etc, one variable, 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 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 chi-square 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 chi-square 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
• g01hac (nag_bivariate_normal_dist) - Probability for the bivariate Normal distribution

Chapter 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
• 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) - Fit 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 for 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 of 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

Chapter 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

Chapter g04 - Analysis of Variance

• g04bbc (nag_anova_random) - General block design or completely randomized design
• g04cac (nag_anova_factorial) - Complete factorial design
• g04czc (nag_anova_factorial_free) - Complete factorial design

Chapter 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 routines
• g05cgc (nag_restore_random_state) - Restore state of random number generating routines
• 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,
• 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

Chapter 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

Chapter g10 - Smoothing in Statistics

• g10cac (nag_running_median_smoother) - Smoothed data sequence using running median smoother

Chapter g11 - Contingency Table Analysis

• g11aac (nag_chi_sq_2_way_table) - chi-square statistic for two-way contingency table

Chapter g12 - Survival Analysis

• g12aac (nag_prod_limit_surviv_fn) - Kaplan-Meier (product-limit) estimates of survival probabilities

Chapter g13 - Time Series Analysis

• g13abc (nag_tsa_auto_corr) - Sample autocorrelation function
• g13acc (nag_tsa_auto_corr_part) - Partial autocorrelation function
• 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_transf_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
• g13xzc (nag_tsa_free) - Freeing function for use with g13 option setting

Chapter 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

Chapter 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

Chapter 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 E_1(x)
• s13acc (nag_cos_integral) - Cosine integral Ci(x)
• s13adc (nag_sin_integral) - Sine integral Si(x)
• s14aac (nag_gamma) - Gamma function
• s14abc (nag_log_gamma) - Log Gamma function
• 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 Y_0(x)
• s17adc (nag_bessel_y1) - Bessel function Y_1(x)
• s17aec (nag_bessel_j0) - Bessel function J_0(x)
• s17afc (nag_bessel_j1) - Bessel function J_1(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)
• s18acc (nag_bessel_k0) - Modified Bessel function K_0(x)
• s18adc (nag_bessel_k1) - Modified Bessel function K_1(x)
• s18aec (nag_bessel_i0) - Modified Bessel function I_0(x)
• s18afc (nag_bessel_i1) - Modified Bessel function I_1(x)
• s18ccc (nag_bessel_k0_scaled) - Scaled modified Bessel function e**x K_0(x)
• s18cdc (nag_bessel_k1_scaled) - Scaled modified Bessel function e**x K_1(x)
• s18cec (nag_bessel_i0_scaled) - Scaled modified Bessel function e**-|x| I_0(x)
• s18cfc (nag_bessel_i1_scaled) - Scaled modified Bessel function e**-|x| I_1(x)
• 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)

Chapter x01 - Mathematical Constants

• X01AAC (nag_pi) - pi
• X01ABC (nag_euler_constant) - Euler's constant, gamma

Chapter 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