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New Functions

The 149 new user-callable functions included in the NAG Toolbox at Mark 23 are as follows.
Function
Name

Purpose
nag_roots_contfn_brent_interval (c05au) Zero of continuous function, Brent algorithm, from a given starting value, binary search for interval
nag_roots_contfn_cntin (c05aw) Zero of continuous function, continuation method, from a given starting value
nag_roots_contfn_brent (c05ay) Zero of continuous function in a given interval, Brent algorithm
nag_roots_lambertw_complex (c05bb) Values of Lambert's W function, W(z)
nag_roots_sys_func_easy (c05qb) Solution of a system of nonlinear equations using function values only (easy-to-use)
nag_roots_sys_func_expert (c05qc) Solution of a system of nonlinear equations using function values only (comprehensive)
nag_roots_sys_func_rcomm (c05qd) Solution of a system of nonlinear equations using function values only (reverse communication)
nag_roots_sparsys_func_expert (c05qs) Solution of a sparse system of nonlinear equations using function values only (easy-to-use)
nag_roots_sys_deriv_easy (c05rb) Solution of a system of nonlinear equations using first derivatives (easy-to-use)
nag_roots_sys_deriv_expert (c05rc) Solution of a system of nonlinear equations using first derivatives (comprehensive)
nag_roots_sys_deriv_rcomm (c05rd) Solution of a system of nonlinear equations using first derivatives (reverse communication)
nag_roots_sys_deriv_check (c05zd) Check user's function for calculating first derivatives of a set of nonlinear functions of several variables
nag_sum_chebyshev (c06dc) Sum of a Chebyshev series at a set of points
nag_wav_2d_init (c09ab) Two-dimensional wavelet filter initialization
nag_wav_1d_cont (c09ba) One-dimensional real continuous wavelet transform
nag_wav_2d_sngl_fwd (c09ea) Two-dimensional discrete wavelet transform
nag_wav_2d_sngl_inv (c09eb) Two-dimensional inverse discrete wavelet transform
nag_wav_2d_multi_fwd (c09ec) Two-dimensional multi-level discrete wavelet transform
nag_wav_2d_multi_inv (c09ed) Two-dimensional inverse multi-level discrete wavelet transform
nag_ode_bvp_ps_lin_coeffs (d02ua) Coefficients of Chebyshev interpolating polynomial from function values on Chebyshev grid
nag_ode_bvp_ps_lin_cgl_vals (d02ub) Function or low-order-derivative values on Chebyshev grid from coefficients of Chebyshev interpolating polynomial
nag_ode_bvp_ps_lin_cgl_grid (d02uc) Chebyshev Gauss–Lobatto grid generation
nag_ode_bvp_ps_lin_cgl_deriv (d02ud) Differentiate a function by the FFT using function values on Chebyshev grid
nag_ode_bvp_ps_lin_solve (d02ue) Solve linear constant coefficient boundary value problem on Chebyshev grid, Integral formulation
nag_ode_bvp_ps_lin_grid_vals (d02uw) Interpolate a function from Chebyshev grid to uniform grid using barycentric Lagrange interpolation
nag_ode_bvp_ps_lin_quad_weights (d02uy) Clenshaw–Curtis quadrature weights for integration using computed Chebyshev coefficients
nag_ode_bvp_ps_lin_cheb_eval (d02uz) Chebyshev polynomial evaluation, Tk(x)
nag_numdiff_rcomm (d04ba) Numerical differentiation, user-supplied function values, derivatives up to order 14, derivatives with respect to one real variable
nag_numdiff_sample (d04bb) Generates sample points for function evaluations by nag_numdiff_rcomm (d04ba)
nag_interp_4d_scat_shep (e01tk) Interpolating functions, modified Shepard's method, four variables
nag_interp_4d_scat_shep_eval (e01tl) Interpolated values, evaluate interpolant computed by nag_interp_4d_scat_shep (e01tk), function and first derivatives, four variables
nag_interp_5d_scat_shep (e01tm) Interpolating functions, modified Shepard's method, five variables
nag_interp_5d_scat_shep_eval (e01tn) Interpolated values, evaluate interpolant computed by nag_interp_5d_scat_shep (e01tm), function and first derivatives, five variables
nag_fit_2dspline_derivm (e02dh) Evaluation of spline surface at mesh of points with derivatives
nag_opt_bounds_bobyqa_func (e04jc) Minimum by quadratic approximation, function of several variables, simple bounds, using function values only
nag_glopt_bnd_pso (e05sa) Global optimization using particle swarm algorithm (PSO), bound constraints only
nag_glopt_nlp_pso (e05sb) Global optimization using particle swarm algorithm (PSO), comprehensive
nag_glopt_nlp_multistart_sqp (e05uc) Global optimization using multi-start, nonlinear constraints
nag_glopt_nlp_multistart_sqp_lsq (e05us) Global optimization of a sum of squares problem using multi-start, nonlinear constraints
nag_glopt_optset (e05zk) Option setting routine for nag_glopt_bnd_pso (e05sa) and nag_glopt_nlp_pso (e05sb)
nag_glopt_optget (e05zl) Option getting routine for nag_glopt_bnd_pso (e05sa) and nag_glopt_nlp_pso (e05sb)
nag_matop_real_symm_matrix_exp (f01ed) Real symmetric matrix exponential
nag_matop_real_symm_matrix_fun (f01ef) Function of a real symmetric matrix
nag_matop_complex_gen_matrix_exp (f01fc) Complex matrix exponential
nag_matop_complex_herm_matrix_exp (f01fd) Complex Hermitian matrix exponential
nag_matop_complex_herm_matrix_fun (f01ff) Function of a complex Hermitian matrix
nag_matop_dtrttp (f01va) Copies a real triangular matrix from full format to packed format scheme
nag_matop_ztrttp (f01vb) Copies a complex triangular matrix from full format to packed format scheme
nag_matop_dtpttr (f01vc) Copies a real triangular matrix from packed format to full format scheme
nag_matop_ztpttr (f01vd) Copies a complex triangular matrix from packed format to full format scheme
nag_matop_dtrttf (f01ve) Copies a real triangular matrix from full format to Rectangular Full Packed format scheme
nag_matop_ztrttf (f01vf) Copies a complex triangular matrix from full format to Rectangular Full Packed format scheme
nag_matop_dtfttr (f01vg) Copies a real triangular matrix from Rectangular Full Packed format to full format scheme
nag_matop_ztfttr (f01vh) Copies a complex triangular matrix from Rectangular Full Packed format to full format scheme
nag_matop_dtpttf (f01vj) Copies a real triangular matrix from packed format to Rectangular Full Packed format scheme
nag_matop_ztpttf (f01vk) Copies a complex triangular matrix from packed format to Rectangular Full Packed format scheme
nag_matop_dtfttp (f01vl) Copies a real triangular matrix from Rectangular Full Packed format to packed format scheme
nag_matop_ztfttp (f01vm) Copies a complex triangular matrix from Rectangular Full Packed format to packed format scheme
nag_det_real_gen (f03ba) Determinant of real matrix, matrix already factorized by nag_lapack_dgetrf (f07ad)
nag_det_real_sym (f03bf) Determinant of real symmetric positive definite matrix
nag_det_real_band_sym (f03bh) Determinant of real symmetric positive definite banded matrix
nag_det_complex_gen (f03bn) Determinant of complex matrix
nag_lapack_dsposv (f07fc) Uses the Cholesky factorization to compute the solution for a real symmetric positive definite system of linear equations
nag_lapack_zcposv (f07fq) Uses the Cholesky factorization to compute the solution for a complex Hermitian positive definite system of linear equations
nag_lapack_dpstrf (f07kd) Cholesky factorization of real symmetric positive semidefinite matrix
nag_lapack_zpstrf (f07kr) Cholesky factorization of complex Hermitian positive semidefinite matrix
nag_lapack_dpftrf (f07wd) Cholesky factorization of real symmetric positive definite matrix, Rectangular Full Packed format
nag_lapack_dpftrs (f07we) Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by nag_lapack_dpftrf (f07wd), Rectangular Full Packed format
nag_lapack_dpftri (f07wj) Inverse of real symmetric positive definite matrix, matrix already factorized by nag_lapack_dpftrf (f07wd), Rectangular Full Packed format
nag_lapack_dtftri (f07wk) Inverse of real triangular matrix, Rectangular Full Packed format, expert driver
nag_lapack_zpftrf (f07wr) Cholesky factorization of complex Hermitian positive definite matrix, Rectangular Full Packed format
nag_lapack_zpftrs (f07ws) Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by nag_lapack_zpftrf (f07wr), Rectangular Full Packed format
nag_lapack_zpftri (f07ww) Inverse of complex Hermitian positive definite matrix, matrix already factorized by nag_lapack_zpftrf (f07wr), Rectangular Full Packed format
nag_lapack_ztftri (f07wx) Inverse of complex triangular matrix, Rectangular Full Packed format
nag_lapack_dgejsv (f08kh) Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
nag_lapack_dgesvj (f08kj) Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
nag_blast_dgb_norm (f16rb) 1-norm, -norm, Frobenius norm, largest absolute element, real band matrix
nag_blast_zgb_norm (f16ub) 1-norm, -norm, Frobenius norm, largest absolute element, complex band matrix
nag_stat_quantiles_stream_fixed (g01an) Calculates approximate quantiles from a data stream of known size
nag_stat_quantiles_stream_arbitrary (g01ap) Calculates approximate quantiles from a data stream of unknown size
nag_stat_prob_bivariate_students_t (g01hc) Computes probabilities for the bivariate Student's t-distribution
nag_stat_pdf_normal (g01ka) Calculates the value for the probability density function of the Normal distribution at a chosen point
nag_stat_pdf_gamma (g01kf) Calculates the value for the probability density function of the gamma distribution at a chosen point
nag_stat_pdf_gamma_vector (g01kk) Calculates a vector of values for the probability density function of the gamma distribution at chosen points
nag_stat_pdf_normal_vector (g01kq) Calculates a vector of values for the probability density function of the Normal distribution at chosen points
nag_stat_prob_normal_vector (g01sa) Computes a vector of probabilities for the standard Normal distribution
nag_stat_prob_students_t_vector (g01sb) Computes a vector of probabilities for Student's t-distribution
nag_stat_prob_chisq_vector (g01sc) Computes a vector of probabilities for χ2 distribution
nag_stat_prob_f_vector (g01sd) Computes a vector of probabilities for F-distribution
nag_stat_prob_beta_vector (g01se) Computes a vector of probabilities for the beta distribution
nag_stat_prob_gamma_vector (g01sf) Computes a vector of probabilities for the gamma distribution
nag_stat_prob_binomial_vector (g01sj) Computes a vector of the binomial distribution
nag_stat_prob_poisson_vector (g01sk) Computes a vector of the Poisson distribution
nag_stat_prob_hypergeom_vector (g01sl) Computes a vector of the hypergeometeric distribution
nag_stat_inv_cdf_normal_vector (g01ta) Computes a vector of deviates for the standard Normal distribution
nag_stat_inv_cdf_students_t_vector (g01tb) Computes a vector of deviates for Student's t-distribution
nag_stat_inv_cdf_chisq_vector (g01tc) Computes a vector of deviates for χ2 distribution
nag_stat_inv_cdf_f_vector (g01td) Computes deviates for F-distribution
nag_stat_inv_cdf_beta_vector (g01te) Computes a vector of deviates for the beta distribution
nag_stat_inv_cdf_gamma_vector (g01tf) Computes a vector of deviates for the gamma distribution
nag_correg_corrmat_nearest_bounded (g02ab) Computes the nearest correlation matrix to a real square matrix, augmented nag_correg_corrmat_nearest (g02aa) to incorporate weights and bounds
nag_correg_corrmat_nearest_kfactor (g02ae) Computes the nearest correlation matrix with k-factor structure to a real square matrix
nag_correg_mixeff_hier_init (g02jc) Hierarchical mixed effects regression, initialization function for nag_correg_mixeff_hier_reml (g02jd) and nag_correg_mixeff_hier_ml (g02je)
nag_correg_mixeff_hier_reml (g02jd) Hierarchical mixed effects regression using Restricted Maximum Likelihood (REML)
nag_correg_mixeff_hier_ml (g02je) Hierarchical mixed effects regression using Maximum Likelihood (ML)
nag_correg_quantile_linreg_easy (g02qf) Quantile linear regression, simple interface, independent, identically distributed (IID) errors
nag_correg_quantile_linreg (g02qg) Quantile linear regression, comprehensive interface
nag_correg_optset (g02zk) Option setting function for nag_correg_quantile_linreg (g02qg)
nag_correg_optget (g02zl) Option getting function for nag_correg_quantile_linreg (g02qg)
nag_rand_init_skipahead_power2 (g05kk) Primes a pseudorandom number generator for generating multiple streams using skip-ahead, skipping ahead a power of 2
nag_rand_sample_wgt (g05ne) Pseudorandom sample, without replacement, unequal weights
nag_rand_copula_clayton_bivar (g05re) Generates a matrix of pseudorandom numbers from a bivariate Clayton/Cook–Johnson copula
nag_rand_copula_frank_bivar (g05rf) Generates a matrix of pseudorandom numbers from a bivariate Frank copula
nag_rand_copula_plackett_bivar (g05rg) Generates a matrix of pseudorandom numbers from a bivariate Plackett copula
nag_rand_copula_clayton (g05rh) Generates a matrix of pseudorandom numbers from a multivariate Clayton/Cook–Johnson copula
nag_rand_copula_frank (g05rj) Generates a matrix of pseudorandom numbers from a multivariate Frank copula
nag_rand_copula_gumbel (g05rk) Generates a matrix of pseudorandom numbers from a Gumbel–Hougaard copula
nag_univar_estim_genpareto (g07bf) Estimates parameter values of the generalized Pareto distribution
nag_univar_outlier_peirce_1var (g07ga) Outlier detection using method of Peirce, raw data or single variance supplied
nag_univar_outlier_peirce_2var (g07gb) Outlier detection using method of Peirce, two variances supplied
nag_nonpar_gofstat_anddar (g08ch) Calculates the Anderson–Darling goodness-of-fit test statistic
nag_nonpar_gofstat_anddar_unif (g08cj) Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of uniformly distributed data
nag_nonpar_gofstat_anddar_normal (g08ck) Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of a fully-unspecified Normal distribution
nag_nonpar_gofstat_anddar_exp (g08cl) Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of an unspecified exponential distribution
nag_surviv_logrank (g12ab) Computes rank statistics for comparing survival curves
nag_specfun_gamma_log_scaled_real (s14ah) Scaled log gamma function
nag_specfun_bessel_y0_real_vector (s17aq) Bessel function vectorized Y0(x)
nag_specfun_bessel_y1_real_vector (s17ar) Bessel function vectorized Y1(x)
nag_specfun_bessel_j0_real_vector (s17as) Bessel function vectorized J0(x)
nag_specfun_bessel_j1_real_vector (s17at) Bessel function vectorized J1(x)
nag_specfun_airy_ai_real_vector (s17au) Airy function vectorized Ai(x)
nag_specfun_airy_bi_real_vector (s17av) Airy function vectorized Bi(x)
nag_specfun_airy_ai_deriv_vector (s17aw) Airy function vectorized Ai(x)
nag_specfun_airy_bi_deriv_vector (s17ax) Airy function vectorized Bi(x)
nag_specfun_bessel_k0_real_vector (s18aq) Modified Bessel function vectorized K0(x)
nag_specfun_bessel_k1_real_vector (s18ar) Modified Bessel function vectorized K1(x)
nag_specfun_bessel_i0_real_vector (s18as) Modified Bessel function vectorized I0(x)
nag_specfun_bessel_i1_real_vector (s18at) Modified Bessel function vectorized I1(x)
nag_specfun_bessel_k0_scaled_vector (s18cq) Scaled modified Bessel function vectorized exK0(x)
nag_specfun_bessel_k1_scaled_vector (s18cr) Scaled modified Bessel function vectorized exK1(x)
nag_specfun_bessel_i0_scaled_vector (s18cs) Scaled modified Bessel function vectorized e − |x|I0(x)
nag_specfun_bessel_i1_scaled_vector (s18ct) Scaled modified Bessel function vectorized e − |x|I1(x)
nag_specfun_kelvin_ber_vector (s19an) Kelvin function vectorized berx
nag_specfun_kelvin_bei_vector (s19ap) Kelvin function vectorized beix
nag_specfun_kelvin_ker_vector (s19aq) Kelvin function vectorized kerx
nag_specfun_kelvin_kei_vector (s19ar) Kelvin function vectorized keix
nag_specfun_fresnel_s_vector (s20aq) Fresnel integral vectorized S(x)
nag_specfun_fresnel_c_vector (s20ar) Fresnel integral vectorized C(x)
nag_specfun_opt_heston_greeks (s30nb) Heston's model option pricing formula with Greeks

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