### List of Contents, Release 4

Chapter 1: Utilities
 Chapter Introduction Module 1.1: nag_lib_support - Library Support Facilities nag_lib_ident Prints details of the Library implementation nag_deallocate Deallocates storage from structures with types defined by the Library Module 1.2: nag_error_handling - Error Handling nag_set_error Controls how errors are to be handled by the Library nag_error Communicates information about error-handling between a user's program and the Library (type) Module 1.3: nag_write_mat - Matrix Printing nag_write_gen_mat Writes a real, complex or integer general matrix nag_write_tri_mat Writes a real or complex triangular matrix nag_write_bnd_mat Writes a real or complex band matrix Module 1.4: nag_sort - Sorting nag_sort_vec Sorts a vector of numeric or character data into ascending or descending order nag_rank_vec Ranks a vector of numeric or character data in ascending or descending order nag_reorder_vec Reorders a vector of numeric or character data into the order specified by a vector of ranks nag_rank_mat Ranks the rows or columns of a matrix of integer or real numbers in ascending or descending order nag_rank_arb_data Ranks arbitrary data according to a user-supplied comparison procedure nag_invert_perm Inverts a permutation, thus converts a rank vector to an index vector, or vice versa nag_check_perm Checks the validity of a permutation nag_decomp_perm Decomposes a permutation into cycles, as an aid to reordering ranked data Module 1.5: nag_math_constants - Mathematical Constants nag_pi Returns an approximation to π nag_euler_constant Returns an approximation to γ (Euler's constant)

Chapter 3: Special Functions
 Chapter Introduction Module 3.1: nag_inv_hyp_fun - Inverse Hyperbolic Functions nag_arctanh Inverse hyperbolic tangent, arctanh x nag_arcsinh Inverse hyperbolic sine, arcsinh x nag_arccosh Inverse hyperbolic cosine, arccosh x Module 3.2: nag_gamma_fun - Gamma Functions nag_gamma Gamma function nag_log_gamma Log gamma function nag_polygamma Polygamma functions nag_incompl_gamma Incomplete gamma functions Module 3.3: nag_err_fun - Error Functions nag_erf Error function erf x nag_erfc Complementary error function erfc x nag_dawson Dawson's integral F(x) Module 3.4: nag_bessel_fun - Bessel Functions nag_bessel_j0 Bessel function J0(x) nag_bessel_j1 Bessel function J1(x) nag_bessel_j Bessel function Jν(z) nag_bessel_y0 Bessel function Y0(x) nag_bessel_y1 Bessel function Y1(x) nag_bessel_y Bessel function Yν(z) nag_bessel_i0 Modified Bessel function I0(x) nag_bessel_i1 Modified Bessel function I1(x) nag_bessel_i Modified Bessel function Iν(z) nag_bessel_k0 Modified Bessel function K0(x) nag_bessel_k1 Modified Bessel function K1(x) nag_bessel_k Modified Bessel function Kν(z) Module 3.5: nag_fresnel_intg - Fresnel Integrals nag_fresnel_s Fresnel integral S(x) nag_fresnel_c Fresnel integral C(x) Module 3.6: nag_ell_intg - Elliptic Integrals nag_ell_rf Symmetrised elliptic integral of the first kind nag_ell_rc Degenerate form of elliptic integral of the first kind nag_ell_rd Symmetrised elliptic integral of the second kind nag_ell_rj Symmetrised elliptic integral of the third kind Module 3.7: nag_ell_fun - Elliptic Functions nag_ell_jac Jacobian elliptic functions sn, cn and dn Module 3.8: nag_airy_fun - Airy Functions nag_airy_ai Airy function Ai(z) nag_airy_bi Airy function Bi(z) Module 3.9: nag_kelvin_fun - Kelvin Functions nag_kelvin_ber Kelvin function ber x nag_kelvin_bei Kelvin function bei x nag_kelvin_ker Kelvin function ker x nag_kelvin_kei Kelvin function kei x

Chapter 4: Matrix and Vector Operations
 Chapter Introduction Module 4.1: nag_mat_norm - Norms of a Matrix nag_gen_mat_norm Computes a norm, or the element of largest absolute value, of a general real or complex matrix nag_gen_bnd_mat_norm Computes a norm, or the element of largest absolute value, of a real or complex square banded matrix nag_sym_mat_norm Computes a norm, or the element of largest absolute value, of a real or complex, symmetric or Hermitian matrix, stored in conventional or packed storage nag_sym_bnd_mat_norm Computes a norm, or the element of largest absolute value, of a real or complex, symmetric or Hermitian band matrix nag_trap_mat_norm Computes a norm, or the element of largest absolute value, of a real or complex trapezoidal matrix nag_tri_mat_norm Computes a norm, or the element of largest absolute value, of a real or complex triangular matrix, stored in conventional or packed storage nag_tri_bnd_mat_norm Computes a norm, or the element of largest absolute value, of a real or complex triangular band matrix nag_hessen_mat_norm Computes a norm, or the element of largest absolute value, of a real or complex upper Hessenberg matrix Module 4.2: nag_mat_inv - Matrix Inversion nag_gen_mat_inv Computes the inverse of a general real or complex matrix nag_gen_mat_inv_fac Computes the inverse of a general real or complex matrix, with the matrix previously factorized using nag_gen_lin_fac nag_sym_mat_inv Computes the inverse of a real or complex, symmetric or Hermitian matrix nag_sym_mat_inv_fac Computes the inverse of a real or complex, symmetric or Hermitian matrix, with the matrix previously factorized using nag_sym_lin_fac nag_tri_mat_inv Computes the inverse of a real or complex triangular matrix Module 4.3: nag_sparse_mat - Sparse Matrix Utilities nag_sparse_mat_init_coo Initializes a sparse matrix data structure from COO format nag_sparse_mat_init_csc Initializes a sparse matrix data structure from CSC format nag_sparse_mat_init_csr Initializes a sparse matrix data structure from CSR format nag_sparse_mat_init_dia Initializes a sparse matrix data structure from DIA format nag_sparse_mat_extract Extracts details of a sparse matrix from a structure of type nag_sparse_mat_real_wp or nag_sparse_mat_cmplx_wp nag_sparse_mat_real_wp Represents a real sparse matrix nag_sparse_mat_cmplx_wp Represents a complex sparse matrix

Chapter 5: Linear Equations
 Chapter Introduction Module 5.1: nag_gen_lin_sys - General Systems of Linear Equations nag_gen_lin_sol Solves a general real or complex system of linear equations with one or many right-hand sides nag_gen_lin_fac Performs an LU factorization of a general real or complex matrix nag_gen_lin_sol_fac Solves a general real or complex system of linear equations, with coefficient matrix previously factorized by nag_gen_lin_fac Module 5.2: nag_sym_lin_sys - Symmetric Systems of Linear Equations nag_sym_lin_sol Solves a real or complex, symmetric or Hermitian system of linear equations with one or many right-hand sides nag_sym_lin_fac Performs a Cholesky or Bunch-Kaufman factorization of a real or complex, symmetric or Hermitian matrix nag_sym_lin_sol_fac Solves a real or complex, symmetric or Hermitian system of linear equations, with coefficient matrix previously factorized by nag_sym_lin_fac Module 5.3: nag_tri_lin_sys - Triangular Systems of Linear Equations nag_tri_lin_sol Solves a real or complex triangular system of linear equations nag_tri_lin_cond Estimates the condition number of a real or complex triangular matrix nag_tri_mat_det Evaluates the determinant of a real or complex triangular matrix Module 5.4: nag_gen_bnd_lin_sys - General Banded Systems of Linear Equations nag_gen_bnd_lin_sol Solves a general real or complex banded system of linear equations, with one or many right-hand sides nag_gen_bnd_lin_fac Performs an LU factorization of a general real or complex band matrix nag_gen_bnd_lin_sol_fac Solves a general real or complex banded system of linear equations, with coefficient matrix previously factorized by nag_gen_bnd_lin_fac Module 5.5: nag_sym_bnd_lin_sys - Symmetric Banded Systems of Linear Equations nag_sym_bnd_lin_sol Solves a real symmetric or complex Hermitian positive definite banded system of linear equations, with one or many right-hand sides nag_sym_bnd_lin_fac Performs a Cholesky factorization of a real symmetric or complex Hermitian positive definite band matrix nag_sym_bnd_lin_sol_fac Solves a real symmetric or complex Hermitian positive definite banded system of linear equations, with coefficient matrix previously factorized by nag_sym_bnd_lin_fac Module 5.6: nag_sparse_prec - Sparse Matrix Preconditioner Set-up and Solve nag_sparse_prec_init_jac Initializes sparse Jacobi preconditioner nag_sparse_prec_init_ssor Initializes sparse SSOR preconditioner nag_sparse_prec_init_ilu Initializes sparse ILU preconditioner for real non-symmetric or complex non-Hermitian matrices nag_sparse_prec_sol Sparse matrix preconditioned system solver Module 5.7: nag_sparse_lin_sys - Sparse Linear System Iterative Solvers nag_sparse_gen_lin_sol General sparse linear system solver

Chapter 6: Eigenvalue and Least-squares Problems
 Chapter Introduction Module 6.1: nag_sym_eig - Standard Symmetric Eigenvalue Problems nag_sym_eig_all All eigenvalues, and optionally eigenvectors, of a real symmetric or complex Hermitian matrix nag_sym_eig_sel Selected eigenvalues, and optionally the corresponding eigenvectors, of a real symmetric or complex Hermitian matrix nag_sym_tridiag_reduc Reduction of a real symmetric or complex Hermitian matrix to real symmetric tridiagonal form nag_sym_tridiag_orth Form or apply the transformation matrix determined by nag_sym_tridiag_reduc nag_sym_tridiag_eig_all All eigenvalues, and optionally eigenvectors, of a real symmetric tridiagonal matrix nag_sym_tridiag_eig_val Selected eigenvalues of a real symmetric tridiagonal matrix nag_sym_tridiag_eig_vec Selected eigenvectors of a real symmetric tridiagonal matrix Module 6.2: nag_nsym_eig - Standard Nonsymmetric Eigenvalue Problems nag_nsym_eig_all All eigenvalues, and optionally eigenvectors, of a general real or complex matrix nag_schur_fac Schur factorization of a general real or complex matrix Module 6.3: nag_svd - Singular Value Decomposition (SVD) nag_gen_svd Singular value decomposition of a general real or complex matrix nag_gen_bidiag_reduc Reduction of a general real or complex matrix to real bidiagonal form nag_bidiag_svd Singular value decomposition of a real bidiagonal matrix Module 6.4: nag_lin_lsq - Linear Least-squares problems nag_lin_lsq_sol Solves a real or complex linear least-squares problem nag_lin_lsq_sol_svd Solves a real or complex linear least-squares problem, assuming that a singular value decomposition of the coefficient matrix has already been computed nag_qr_fac QR factorization of a general real or complex matrix nag_qr_orth Form or apply the matrix determined by nag_qr_fac nag_lin_lsq_sol_qr Solves a real or complex linear least-squares problem, assuming that the factorization of the coefficient matrix has already been computed nag_lin_lsq_sol_qr_svd Solves a real or complex linear least-squares problem using the SVD, assuming that the QR factorization of the coefficient matrix has already been computed Module 6.5: nag_sym_gen_eig - Symmetric-definite Generalized Eigenvalue Problems nag_sym_gen_eig_all All eigenvalues, and optionally eigenvectors, of a real symmetric-definite or complex Hermitian-definite generalized eigenvalue problem nag_sym_gen_eig_sel Selected eigenvalues, and optionally the corresponding eigenvectors, of a real symmetric-definite or complex Hermitian-definite generalized eigenvalue problem Module 6.6: nag_nsym_gen_eig - Nonsymmetric Generalized Eigenvalue Problems nag_nsym_gen_eig_all All eigenvalues, and optionally eigenvectors, of a real or complex nonsymmetric generalized eigenvalue problem nag_gen_schur_fac Generalized Schur factorization of a real or complex matrix pencil

Chapter 7: Transforms
 Chapter Introduction Module 7.1: nag_fft - Discrete Fourier Transforms nag_fft_1d Single or multiple 1-d complex discrete Fourier transform, or its inverse nag_fft_1d_real Single or multiple 1-d real or Hermitian discrete Fourier transform, or its inverse nag_fft_1d_basic Single or multiple 1-d real, Hermitian or complex discrete Fourier transform, which is overwritten on the input data nag_fft_2d 2-d complex discrete Fourier transform, or its inverse nag_fft_2d_basic 2-d complex discrete Fourier transform, which is overwritten on the input data nag_fft_3d 3-d complex discrete Fourier transform, or its inverse nag_fft_3d_basic 3-d complex discrete Fourier transform, which is overwritten on the input data nag_fft_trig Trigonometric coefficients for computing discrete Fourier transforms nag_herm_to_cmplx Convert Hermitian sequences to general complex sequences nag_cmplx_to_herm Convert Hermitian complex sequences to their compact real form nag_conj_herm Complex conjugates of Hermitian sequences Module 7.2: nag_sym_fft - Symmetric Discrete Fourier Transforms nag_fft_sin Single or multiple 1-d discrete Fourier sine transform nag_fft_cos Single or multiple 1-d discrete Fourier cosine transform nag_fft_qtr_sin Single or multiple 1-d discrete quarter-wave Fourier sine transform, or its inverse nag_fft_qtr_cos Single or multiple 1-d discrete quarter-wave Fourier cosine transform, or its inverse Module 7.3: nag_conv - Convolution and Correlation nag_fft_conv Computes the convolution or correlation of two real or complex vectors

Chapter 8: Curve and Surface Fitting
 Chapter Introduction Module 8.1: nag_pch_interp - Piecewise Cubic Hermite Interpolation nag_pch_monot_interp Generates a monotonicity-preserving piecewise cubic Hermite interpolant nag_pch_eval Computes values and optionally derivatives of a piecewise cubic Hermite interpolant nag_pch_intg Computes the definite integral of a piecewise cubic Hermite interpolant nag_pch_extract Extracts details of a piecewise cubic Hermite interpolant from a structure of type nag_pch_comm_wp nag_pch_comm_wp Represents a piecewise cubic Hermite interpolant (type) Module 8.2: nag_spline_1d - One-dimensional Spline Fitting nag_spline_1d_auto_fit Generates a cubic spline approximation to an arbitrary 1-d data set, with automatic knot selection nag_spline_1d_lsq_fit Generates a weighted least-squares cubic spline fit to an arbitrary 1-d data set, with given interior knots nag_spline_1d_interp Generates a cubic spline interpolant to an arbitrary 1-d data set nag_spline_1d_eval Computes values of a cubic spline and optionally its first three derivatives nag_spline_1d_intg Computes the definite integral of a cubic spline nag_spline_1d_set Initializes a cubic spline with given interior knots and B-spline coefficients nag_spline_1d_extract Extracts details of a cubic spline from a structure of type nag_spline_1d_comm_wp nag_spline_1d_comm_wp Represents a 1-d cubic spline in B-spline series form (type) Module 8.3: nag_spline_2d - Two-dimensional Spline Fitting nag_spline_2d_auto_fit Generates a bicubic spline approximation to a 2-d data set, with automatic knot selection nag_spline_2d_lsq_fit Generates a minimal, weighted least-squares bicubic spline surface fit to a given set of data points, with given interior knots nag_spline_2d_interp Generates a bicubic spline interpolating surface through a set of data values, given on a rectangular grid of the xy plane nag_spline_2d_eval Computes values of a bicubic spline nag_spline_2d_intg Computes the definite integral of a bicubic spline nag_spline_2d_set Initializes a bicubic spline with given interior knots and B-spline coefficients nag_spline_2d_extract Extracts details of a bicubic spline from a structure of type nag_spline_2d_comm_wp nag_spline_2d_comm_wp Represents a 2-d bicubic spline in B-spline series form (type) Module 8.4: nag_scat_interp - Interpolation of Scattered Data nag_scat_2d_interp Generates a 2-d interpolating function using a modified Shepard method nag_scat_2d_eval Computes values of the interpolant generated by nag_scat_2d_interp and its partial derivatives nag_scat_3d_interp Generates a 3-d interpolating function using a modified Shepard method nag_scat_3d_eval Computes values of the interpolant generated by nag_scat_3d_interp and its partial derivatives nag_scat_2d_set Initializes a structure of type nag_scat_comm_wp to represent a 2-d scattered data interpolant nag_scat_3d_set Initializes a structure of type nag_scat_comm_wp to represent a 3-d scattered data interpolant nag_scat_extract Extracts details of a scattered data interpolant from a structure of derived type nag_scat_comm_wp nag_scat_comm_wp Represents a scattered data interpolant generated either by nag_scat_2d_interp or nag_scat_3d_interp (type) Module 8.5: nag_cheb_1d - Chebyshev Series nag_cheb_1d_fit Finds the least-squares fit using arbitrary data points nag_cheb_1d_interp Generates the coefficients of the Chebyshev polynomial which interpolates (passes exactly through) data at a special set of points nag_cheb_1d_fit_con Finds the least-squares fit using arbitrary data points with constraints on some data points nag_cheb_1d_eval Evaluation of fitted polynomial in one variable, from Chebyshev series form nag_cheb_1d_deriv Derivatives of fitted polynomial in Chebyshev series form nag_cheb_1d_intg Integral of fitted polynomial in Chebyshev series form

Chapter 9: Optimization
 Chapter Introduction Module 9.1: nag_qp - Linear and Quadratic Programming nag_qp_sol Solves a linear or quadratic programming problem nag_qp_cntrl_init Initialization procedure for nag_qp_cntrl_wp nag_qp_cntrl_wp Control parameters for nag_qp_sol (type) Module 9.2: nag_nlin_lsq - Unconstrained Nonlinear Least-squares nag_nlin_lsq_sol Finds an unconstrained minimum of a sum of squares nag_nlin_lsq_cov Computes the variance-covariance matrix for a nonlinear least-squares problem nag_nlin_lsq_cntrl_init Initialization procedure for nag_nlin_lsq_cntrl_wp nag_nlin_lsq_cntrl_wp Control parameters for nag_nlin_lsq_sol (type) Module 9.3: nag_nlp - Nonlinear Programming nag_nlp_sol Solves a dense nonlinear programming problem nag_nlp_cntrl_init Initialization procedure for nag_nlp_cntrl_wp nag_nlp_cntrl_wp Control parameters for nag_nlp_sol (type) Module 9.4: nag_con_nlin_lsq - Constrained Nonlinear Least-squares nag_con_nlin_lsq_sol Please note that this procedure is scheduled for withdrawal from the Library at a future release.Finds a constrained minimum of a sum of squares nag_con_nlin_lsq_sol_1 Finds a constrained minimum of a sum of squares nag_con_nlin_lsq_cntrl_init Initialization procedure for nag_con_nlin_lsq_cntrl_wp nag_con_nlin_lsq_cntrl_wp Control parameters for nag_con_nlin_lsq_sol and nag_con_nlin_lsq_sol_1(type) Module 9.5: nag_uv_min - Univariate Minimization nag_uv_min_sol Finds the minimum of a continuous function of a single variable in a given finite interval Module 9.6: nag_nlp_sparse - Sparse Nonlinear Programming nag_nlp_sparse_sol Solves a sparse nonlinear programming problem nag_nlp_sparse_cntrl_init Initialization procedure for nag_nlp_sparse_cntrl_wp nag_nlp_sparse_cntrl_wp Control parameters for nag_nlp_sparse_sol

Chapter 10: Nonlinear Equations
 Chapter Introduction Module 10.1: nag_polynom_eqn - Roots of Polynomials nag_polynom_roots Calculates the roots of a polynomial Module 10.2: nag_nlin_eqn - Roots of a Single Nonlinear equation nag_nlin_eqn_sol Finds a solution of a single nonlinear equation Module 10.3: nag_nlin_sys - Roots of a System of Nonlinear equations nag_nlin_sys_sol Finds a solution of a system of nonlinear equations

Chapter 12: Ordinary Differential Equations (ODE's)
 Chapter Introduction Module 12.1: nag_ivp_ode_rk - Solution of Initial Value Problems for ODE's by Runge-Kutta Methods nag_rk_setup Sets up the integration nag_rk_interval Integrates across an interval and provides the solution at user-specified points nag_rk_info Provides statistics about the integration nag_rk_global_err Provides information about global error assessment nag_rk_step Integrates one step at a time nag_rk_interp Interpolates the solution nag_rk_reset_end Resets the end point of integration nag_rk_comm_wp Communicating structure for nag_ivp_ode_rk (type)

Chapter 13: Partial Differential Equations (PDE's)
 Chapter Introduction Module 13.1: nag_pde_helm - Helmholtz Equations nag_pde_helm_3d Solves the 3-d Helmholtz equation using a standard seven-point finite difference scheme and a fast Fourier transform method Module 13.2: nag_pde_ell_mg - Multigrid Solution of Elliptic PDE's nag_pde_ell_rect Generates a seven-diagonal system of linear equations which arises from the discretization of a two-dimensional elliptic PDE's on a rectangle nag_pde_ell_mg_sol Solves a seven-diagonal system of linear equations using a multigrid iteration Module 13.3: nag_pde_parab_1d - Parabolic PDE's in One Space Variable nag_pde_parab_1d_fd Integrates a system of parabolic PDE's in one space variable, coupled with ODE's; using finite differences for the spatial discretisation with optional automatic adaptive spatial remeshing nag_pde_interp_1d_fd Interpolates the solution and first derivative of a system of PDE's solved using finite differences, at a set of user-specified points nag_pde_parab_1d_coll Integrates a system of parabolic PDE's in one space variable, coupled with ODE's; using a Chebyshev C0 collocation method for the spatial discretisation nag_pde_interp_1d_coll Interpolates the solution and first derivative of a system of PDE's solved using a Chebyshev C0 collocation method, at a set of user-specified points nag_pde_parab_1d_cntrl_wp Control parameters for procedures nag_pde_parab_1d_fd and nag_pde_parab_1d_coll nag_pde_parab_1d_cntrl_init Initialization procedure for type nag_pde_parab_1d_cntrl_wp nag_pde_parab_1d_comm_wp Communicates arrays for the underlying ODE solver between calls to the procedures in nag_pde_parab_1d

Chapter 19: Operations Research
 Chapter Introduction Module 19.1: nag_ip - Integer Programming nag_ip_sol Solves 'zero-one', 'general', 'mixed' or 'all' integer linear programming problems nag_ip_cntrl_wp Control parameters for nag_ip_sol nag_ip_cntrl_init Initialization procedure for nag_ip_cntrl_wp Module 19.2: nag_short_path - Shortest Path Problems nag_short_path_find Finds the shortest path through a directed or undirected acyclic network

Chapter 20: Statistical Distribution Functions
 Chapter Introduction Module 20.1: nag_normal_dist - Probabilities and Deviate for a Normal Distribution nag_normal_prob Computes probabilities for various parts of a univariate Normal distribution nag_normal_deviate Computes the deviate associated with a given probability of a standard Normal distribution nag_bivar_normal_prob Computes the lower tail probability for a bivariate Normal distribution nag_mv_normal_prob Computes probabilities for various parts of a multivariate Normal distribution Module 20.2: nag_t_dist - Probabilities and Deviate for a Student's t-distribution nag_t_prob Computes probabilities for various parts of a Student's t-distribution with ν degrees of freedom nag_t_deviate Computes the deviate associated with a given probability of a Student's t-distribution Module 20.3: nag_chisq_dist - Probabilities and Deviate for a χ2 Distribution nag_chisq_prob Computes lower or upper tail probability for a χ2 distribution with ν degrees of freedom nag_chisq_deviate Computes the deviate associated with a given lower tail probability of a χ2 distribution with ν degrees of freedom Module 20.4: nag_f_dist - Probabilities and Deviate for an F-distribution nag_f_prob Computes lower or upper tail probability for an F-distribution with ν1 and ν2 degrees of freedom nag_f_deviate Computes the deviate associated with a given lower tail probability of an F-distribution with ν1 and ν2 degrees of freedom Module 20.5: nag_beta_dist - Probabilities and Deviate for a Beta Distribution nag_beta_prob Computes lower or upper tail probability for a beta distribution with parameters a and b nag_beta_deviate Computes the deviate associated with a given lower tail probability of a beta distribution with parameters a and b Module 20.6: nag_gamma_dist - Probabilities and Deviate for a Gamma Distribution nag_gamma_prob Computes lower or upper tail probability for a gamma distribution with shape parameter a and scale parameter b nag_gamma_deviate Computes the deviate associated with a given lower tail probability of a gamma distribution with shape parameter a and scale parameter b Module 20.7: nag_discrete_dist - Probabilities for Discrete Distributions nag_binom_prob Computes lower tail, upper tail or point probability for a binomial distribution with parameters n and p nag_poisson_prob Computes lower tail, upper tail or point probability for a Poisson distribution with parameter λ nag_hypergeo_prob Computes lower tail, upper tail or point probability for a hypergeometric distribution with parameters n, l and m

Chapter 21: Random Number Generation
 Chapter Introduction Module 21.1: nag_rand_util - Utilities for Random Number Generation nag_rand_seed_set Sets the seed used by random number generating procedures to give a repeatable or non-repeatable sequence of random numbers nag_seed_wp Stores data required to generate successive random numbers from a given stream (type) Module 21.2: nag_rand_contin - Random Numbers from Continuous Distributions nag_rand_uniform Generates random numbers from a uniform distribution over (a,b) nag_rand_normal Generates random numbers from a Normal distribution with mean a and standard deviation b nag_rand_mv_normal Generates a vector of random numbers from a multivariate Normal distribution with mean vector a and covariance matrix C nag_rand_beta Generates random numbers from a beta distribution with parameters a and b nag_rand_neg_exp Generates random numbers from a (negative) exponential distribution with mean a nag_rand_gamma Generates random numbers from a gamma distribution with parameters a and b Module 21.3: nag_rand_discrete - Random Numbers from Discrete Distributions nag_rand_binom Generates random integers from a binomial distribution and/or returns a reference vector for the distribution nag_rand_neg_binom Generates random integers from a negative binomial distribution and/or returns a reference vector for the distribution nag_rand_hypergeo Generates random integers from an hypergeometric distribution and/or returns a reference vector for the distribution nag_rand_user_dist Generates random integers and/or returns a reference vector from a discrete distribution defined in terms of its PDF or CDF nag_rand_ref_vec Generates random integers from a discrete distribution, using a reference vector nag_ref_vec_wp Stores a reference vector which is used to generate random integers from a discrete distribution (type)

Chapter 22: Basic Descriptive Statistics
 Chapter Introduction Module 22.1: nag_basic_stats - Basic Descriptive Statistics for Univariate Data nag_summary_stats_1v Computes basic descriptive statistics for univariate data

Chapter 25: Correlation and Regression Analysis
 Chapter Introduction Module 25.1: nag_lin_reg - Regression Analysis nag_simple_lin_reg Performs a simple linear regression analysis for a pair of related variables nag_mult_lin_reg Performs a general multiple linear regression analysis for any given predictor variables and a response variable Module 25.2: nag_correl - Correlation Analysis nag_prod_mom_correl Calculates the variance-covariance matrix and the Pearson product-moment correlation coefficients for a set of data nag_part_correl Calculates the partial variance-covariance matrix and the partial correlation matrix from a correlation or variance covariance matrix

Chapter 28: Multivariate Analysis
 Chapter Introduction Module 28.1: nag_fac_analysis - Factor Analysis and Principal Component nag_prin_comp Performs principal component analysis Module 28.2: nag_canon_analysis - Canonical Analysis nag_canon_var Performs canonical variate analysis Module 28.3: nag_mv_rotation - Rotations nag_orthomax Computes orthogonal rotation, using a generalized orthomax rotations

Chapter 29: Time Series Analysis
 Chapter Introduction Module 29.1: nag_tsa_identify - Time Series Analysis - Identification nag_tsa_acf Calculates the sample autocorrelation function of a univariate time series nag_tsa_pacf Calculates the sample partial autocorrelation function of a univariate time series Module 29.2: nag_tsa_kalman - Kalman Filtering nag_kalman_init Provides an initial estimate of the Kalman filter state covariance matrix nag_kalman_predict Calculates a one step prediction for the square root covariance Kalman filter nag_kalman_sqrt_cov_var Calculates a time-varying square root covariance Kalman filter nag_kalman_sqrt_cov_invar Calculates a time-invariant square root covariance Kalman filter Module 29.3: nag_tsa_spectral - Time Series Spectral Analysis nag_spectral_data Calculates the smoothed sample spectrum of a univariate time series nag_spectral_cov Calculates the smoothed sample spectrum of a univariate time series using autocovariances data nag_bivar_spectral_data Calculates the smoothed sample cross spectrum of a bivariate time series nag_bivar_spectral_cov Calculates the smoothed sample cross spectrum of a bivariate time series using autocovariances data nag_bivar_spectral_coh Calculates the squared coherency, the cross amplitude, the gain and the phase spectra nag_bivar_spectral_lin_sys Calculates the noise spectrum and the impulse response function from a linear system

© The Numerical Algorithms Group Ltd, Oxford, UK. 2000