NAG fl90 Library, Release 4: List of Contents

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 J_ν(z)
`nag_bessel_y0`	Bessel function Y₀(x)
`nag_bessel_y1`	Bessel function Y₁(x)
`nag_bessel_y`	Bessel function Y_ν(z)
`nag_bessel_i0`	Modified Bessel function I₀(x)
`nag_bessel_i1`	Modified Bessel function I₁(x)
`nag_bessel_i`	Modified Bessel function I_ν(z)
`nag_bessel_k0`	Modified Bessel function K₀(x)
`nag_bessel_k1`	Modified Bessel function K₁(x)
`nag_bessel_k`	Modified Bessel function K_ν(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 11: Quadrature

Chapter Introduction
Module 11.1: `nag_quad_1d` - Numerical Integration over a Finite Interval
`nag_quad_1d_gen`	1-d quadrature, adaptive, finite interval, allowing for badly behaved integrand, allowing for singularities at user-specified break-points, suitable for oscillatory integrands
`nag_quad_1d_wt_trig`	1-d quadrature, adaptive, finite interval, weight function cos(ω x) or sin(ω x)
`nag_quad_1d_wt_end_sing`	1-d quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type
`nag_quad_1d_wt_hilb`	1-d quadrature, adaptive, finite interval, weight function 1/(x−c), Cauchy principal value (Hilbert transform)
`nag_quad_1d_data`	1-d quadrature, integration of function defined by data values, Gill-Miller method
Module 11.2: `nag_quad_1d_inf` - Numerical Integration over an Infinite Interval
`nag_quad_1d_inf_gen`	1-d quadrature, adaptive, semi-infinite or infinite interval
`nag_quad_1d_inf_wt_trig`	1-d quadrature, adaptive, semi-infinite interval, weight function cos(ω x) or sin(ω x)
Module 11.3: `nag_quad_md` - Multi-dimensional Integrals
`nag_quad_md_rect`	Multi-dimensional adaptive quadrature over a hyper-rectangle
`nag_quad_md_rect_mintg`	Multi-dimensional adaptive quadrature over a hyper-rectangle, multiple integrands
`nag_quad_2d`	2-d quadrature, finite region
`nag_quad_monte_carlo`	Multi-dimensional quadrature over hyper-rectangle, Monte-Carlo method
Module 11.4: `nag_quad_util` - Numerical Integration Utilities
`nag_quad_gs_wt_absc`	Calculation of weights and abscissae for Gaussian quadrature rules, general choice of rule

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