Chapter Contents
NAG Toolbox
NAG Toolbox News

# New Functions

The new user-callable functions included in the NAG Toolbox at Mark 24 are as follows.
 FunctionName Purpose nag_sum_fft_real_2d (c06pv) Two-dimensional real-to-complex discrete Fourier transform nag_sum_fft_hermitian_2d (c06pw) Two-dimensional complex-to-real discrete Fourier transform nag_sum_fft_real_3d (c06py) Three-dimensional real-to-complex discrete Fourier transform nag_sum_fft_hermitian_3d (c06pz) Three-dimensional complex-to-real discrete Fourier transform nag_wav_3d_init (c09ac) Three-dimensional wavelet filter initialization nag_wav_3d_sngl_fwd (c09fa) Three-dimensional discrete wavelet transform nag_wav_3d_sngl_inv (c09fb) Three-dimensional inverse discrete wavelet transform nag_wav_3d_multi_fwd (c09fc) Three-dimensional multi-level discrete wavelet transform nag_wav_3d_mxolap_multi_inv (c09fd) Three-dimensional inverse multi-level discrete wavelet transform nag_quad_1d_gen_vec_multi_rcomm (d01ra) One-dimensional quadrature, adaptive, finite interval, multiple integrands, vectorized abscissae, reverse communication nag_quad_1d_gen_vec_multi_dimreq (d01rc) Determine required array dimensions for nag_quad_1d_gen_vec_multi_rcomm (d01ra) nag_quad_1d_fin_gonnet_vec (d01rg) One-dimensional quadrature, adaptive, finite interval, strategy due to Gonnet, allowing for badly behaved integrands nag_quad_1d_gauss_wres (d01tb) Pre-computed weights and abscissae for Gaussian quadrature rules, restricted choice of rule nag_quad_1d_gauss_vec (d01ua) One-dimensional Gaussian quadrature, choice of weight functions nag_quad_opt_set (d01zk) Option setting function nag_quad_opt_get (d01zl) Option getting function nag_ode_ivp_rkts_range (d02pe) Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output nag_ode_ivp_rkts_onestep (d02pf) Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step nag_ode_ivp_rkts_setup (d02pq) Ordinary differential equations, initial value problem, setup for nag_ode_ivp_rkts_range (d02pe) and nag_ode_ivp_rkts_onestep (d02pf) nag_ode_ivp_rkts_reset_tend (d02pr) Ordinary differential equations, initial value problem, resets end of range for nag_ode_ivp_rkts_onestep (d02pf) nag_ode_ivp_rkts_interp (d02ps) Ordinary differential equations, initial value problem, interpolation for nag_ode_ivp_rkts_onestep (d02pf) nag_ode_ivp_rkts_diag (d02pt) Ordinary differential equations, initial value problem, integration diagnostics for nag_ode_ivp_rkts_range (d02pe) and nag_ode_ivp_rkts_onestep (d02pf) nag_ode_ivp_rkts_errass (d02pu) Ordinary differential equations, initial value problem, error assessment diagnostics for nag_ode_ivp_rkts_range (d02pe) and nag_ode_ivp_rkts_onestep (d02pf) nag_interp_nd_scat_shep (e01zm) Interpolating function, modified Shepard's method, d$d$ dimensions nag_interp_nd_scat_shep_eval (e01zn) Interpolated values, evaluate interpolant computed by nag_interp_nd_scat_shep (e01zm), function and first derivatives, d$d$ dimensions nag_fit_1dspline_deriv_vector (e02bf) Evaluation of fitted cubic spline, function and optionally derivatives at a vector of points nag_fit_2dspline_ts_sctr (e02jd) Spline approximation to a set of scattered data using a two-stage approximation method nag_fit_2dspline_ts_evalv (e02je) Evaluation at a vector of points of a spline computed by nag_fit_2dspline_ts_sctr (e02jd) nag_fit_2dspline_ts_evalm (e02jf) Evaluation at a mesh of points of a spline computed by nag_fit_2dspline_ts_sctr (e02jd) nag_fit_opt_set (e02zk) Option setting routine nag_fit_opt_get (e02zl) Option getting routine nag_opt_miqp_mps_read (e04mx) Reads MPS data file defining LP, QP, MILP or MIQP problem nag_bnd_lin_lsq (e04pc) Computes the least squares solution to a set of linear equations subject to fixed upper and lower bounds on the variables. An option is provided to return a minimal length solution if a solution is not unique nag_matop_real_gen_matrix_log (f01ej) Real matrix logarithm nag_matop_real_gen_matrix_fun_std (f01ek) Exponential, sine, cosine, sinh or cosh of a real matrix (Schur–Parlett algorithm) nag_matop_real_gen_matrix_fun_num (f01el) Function of a real matrix (using numerical differentiation) nag_matop_real_gen_matrix_fun_usd (f01em) Function of a real matrix (using user-supplied derivatives) nag_matop_complex_gen_matrix_log (f01fj) Complex matrix logarithm nag_matop_complex_gen_matrix_fun_std (f01fk) Exponential, sine, cosine, sinh or cosh of a complex matrix (Schur–Parlett algorithm) nag_matop_complex_gen_matrix_fun_num (f01fl) Function of a complex matrix (using numerical differentiation) nag_matop_complex_gen_matrix_fun_usd (f01fm) Function of a complex matrix (using user-supplied derivatives) nag_matop_real_gen_matrix_actexp (f01ga) Action of a real matrix exponential on a real matrix nag_matop_real_gen_matrix_actexp_rcomm (f01gb) Action of a real matrix exponential on a real matrix (reverse communication) nag_matop_complex_gen_matrix_actexp (f01ha) Action of a complex matrix exponential on a complex matrix nag_matop_complex_gen_matrix_actexp_rcomm (f01hb) Action of a complex matrix exponential on a complex matrix (reverse communication) nag_matop_real_gen_matrix_cond_std (f01ja) Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a real matrix nag_matop_real_gen_matrix_cond_num (f01jb) Condition number for a function of a real matrix (using numerical differentiation) nag_matop_real_gen_matrix_cond_usd (f01jc) Condition number for a function of a real matrix (using user-supplied derivatives) nag_matop_complex_gen_matrix_cond_std (f01ka) Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a complex matrix nag_matop_complex_gen_matrix_cond_num (f01kb) Condition number for a function of a complex matrix (using numerical differentiation) nag_matop_complex_gen_matrix_cond_usd (f01kc) Condition number for a function of a complex matrix (using user-supplied derivatives) nag_eigen_real_gen_sparse_arnoldi (f02ek) Selected eigenvalues and eigenvectors of a real sparse general matrix nag_linsys_real_gen_norm_rcomm (f04yd) Norm estimation (for use in condition estimation), real rectangular matrix nag_linsys_complex_gen_norm_rcomm (f04zd) Norm estimation (for use in condition estimation), complex rectangular matrix nag_sparse_real_gen_precon_bdilu (f11df) Real sparse nonsymmetric linear system, incomplete LU$LU$ factorization of local or overlapping diagonal blocks nag_sparse_real_gen_solve_bdilu (f11dg) Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete LU$LU$ block diagonal preconditioner computed by nag_sparse_real_gen_precon_bdilu (f11df) nag_sparse_complex_gen_precon_bdilu (f11dt) Complex sparse nonsymmetric linear system, incomplete LU$LU$ factorization of local or overlapping diagonal blocks nag_sparse_complex_gen_solve_bdilu (f11du) Solution of complex sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete LU$LU$ block diagonal preconditioner computed by nag_sparse_complex_gen_precon_bdilu (f11dt) nag_sparseig_complex_band_init (f12at) Initialization function for (nag_sparseig_complex_band_solve (f12au)) computing selected eigenvalues and, optionally, eigenvectors of a complex banded (standard or generalized) eigenproblem. nag_sparseig_complex_band_solve (f12au) Selected eigenvalues and, optionally, eigenvectors of complex non-Hermitian banded eigenproblem, driver nag_blast_daxpby (f16ec) Real weighted vector addition nag_blast_zaxpby (f16gc) Complex weighted vector addition nag_stat_summary_onevar (g01at) Computes univariate summary information: mean, variance, skewness, kurtosis nag_stat_summary_onevar_combine (g01au) Combines multiple sets of summary information, for use after nag_stat_summary_onevar (g01at) nag_multi_students_t (g01hd) Computes the probability for the multivariate Student's t$t$-distribution nag_stat_pdf_gamma_vector (g01kk) Computes a vector of values for the probability density function of the gamma distribution nag_stat_pdf_normal_vector (g01kq) Computes a vector of values for the probability density function of the Normal distribution nag_stat_pdf_multi_normal_vector (g01lb) Computes a vector of values for the probability density function of the multivariate Normal distribution 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 the Student's t$t$-distribution nag_stat_prob_chisq_vector (g01sc) Computes a vector of probabilities for χ2${\chi }^{2}$ distribution nag_stat_prob_f_vector (g01sd) Computes a vector of probabilities for F$F$-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 probabilities for the binomial distribution nag_stat_prob_poisson_vector (g01sk) Computes a vector of probabilities for the Poisson distribution nag_stat_prob_hypergeom_vector (g01sl) Computes a vector of probabilities for the hypergeometric 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$t$-distribution nag_stat_inv_cdf_chisq_vector (g01tc) Computes a vector of deviates for χ2${\chi }^{2}$ distribution nag_stat_inv_cdf_f_vector (g01td) Computes a vector of deviates for F$F$-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_stat_moving_average (g01wa) Computes the mean and standard deviation using a rolling window nag_nearest_correlation_h_weight (g02aj) Computes the nearest correlation matrix to a real square matrix, using element-wise weighting nag_correg_ssqmat_combine (g02bz) Combines two sums of squares matrices, for use after nag_correg_ssqmat (g02bu) nag_mv_gaussian_mixture (g03ga) Fits a Gaussian mixture model nag_rand_bb_init (g05xa) Initializes the Brownian bridge generator nag_rand_bb (g05xb) Generate paths for a free or non-free Wiener process using the Brownian bridge algorithm nag_rand_bb_inc_init (g05xc) Initializes the generator which backs out the increments of sample paths generated by a Brownian bridge algorithm nag_rand_bb_inc (g05xd) Backs out the increments from sample paths generated by a Brownian bridge algorithm nag_rand_bb_make_bridge_order (g05xe) Creates a Brownian bridge construction order out of a set of input times nag_rand_field_1d_user_setup (g05zm) Setup for simulating one-dimensional random fields, user-defined variogram nag_rand_field_1d_predef_setup (g05zn) Setup for simulating one-dimensional random fields nag_rand_field_1d_generate (g05zp) Generates realisations of a one-dimensional random field nag_rand_field_2d_user_setup (g05zq) Setup for simulating two-dimensional random fields, user-defined variogram nag_rand_field_2d_predef_setup (g05zr) Setup for simulating two-dimensional random fields, preset variogram nag_rand_field_2d_generate (g05zs) Generates realisations of a two-dimensional random field nag_rand_field_fracbm_generate (g05zt) Generates realisations of fractional Brownian motion nag_tsa_inhom_iema (g13me) Computes the iterated exponential moving average for a univariate inhomogeneous time series nag_tsa_inhom_iema_all (g13mf) Computes the iterated exponential moving average for a univariate inhomogeneous time series, intermediate results are also returned nag_tsa_inhom_ma (g13mg) Computes the exponential moving average for a univariate inhomogeneous time series nag_best_subset_given_size_revcomm (h05aa) Best n$n$ subsets of size p$p$ (reverse communication) nag_best_subset_given_size (h05ab) Best n$n$ subsets of size p$p$ (direct communication) nag_specfun_beta_log_real (s14cb) Logarithm of the beta function ln(B,a,b)$\mathrm{ln}\left(B,a,b\right)$ nag_specfun_beta_incomplete (s14cc) Incomplete beta function Ix(a,b)${I}_{x}\left(a,b\right)$ and its complement 1 − Ix$1-{I}_{x}$ nag_specfun_bessel_y0_real_vector (s17aq) Bessel function vectorized Y0(x)${Y}_{0}\left(x\right)$ nag_specfun_bessel_y1_real_vector (s17ar) Bessel function vectorized Y1(x)${Y}_{1}\left(x\right)$ nag_specfun_bessel_j0_real_vector (s17as) Bessel function vectorized J0(x)${J}_{0}\left(x\right)$ nag_specfun_bessel_j1_real_vector (s17at) Bessel function vectorized J1(x)${J}_{1}\left(x\right)$ nag_specfun_airy_ai_real_vector (s17au) Airy function vectorized Ai(x)$\mathrm{Ai}\left(x\right)$ nag_specfun_airy_bi_real_vector (s17av) Airy function vectorized Bi(x)$\mathrm{Bi}\left(x\right)$ nag_specfun_airy_ai_deriv_vector (s17aw) Derivatives of the Airy function, vectorized Ai′(x)${\mathrm{Ai}}^{\prime }\left(x\right)$ nag_specfun_airy_bi_deriv_vector (s17ax) Derivatives of the Airy function, vectorized Bi′(x)${\mathrm{Bi}}^{\prime }\left(x\right)$ nag_specfun_bessel_k0_real_vector (s18aq) Modified Bessel function vectorized K0(x)${K}_{0}\left(x\right)$ nag_specfun_bessel_k1_real_vector (s18ar) Modified Bessel function vectorized K1(x)${K}_{1}\left(x\right)$ nag_specfun_bessel_i0_real_vector (s18as) Modified Bessel function vectorized I0(x)${I}_{0}\left(x\right)$ nag_specfun_bessel_i1_real_vector (s18at) Modified Bessel function vectorized I1(x)${I}_{1}\left(x\right)$ nag_specfun_bessel_k0_scaled_vector (s18cq) Scaled modified Bessel function vectorized exK0(x)${e}^{x}{K}_{0}\left(x\right)$ nag_specfun_bessel_k1_scaled_vector (s18cr) Scaled modified Bessel function vectorized exK1(x)${e}^{x}{K}_{1}\left(x\right)$ nag_specfun_bessel_i0_scaled_vector (s18cs) Scaled modified Bessel function vectorized e − |x|I0(x)${e}^{-|x|}{I}_{0}\left(x\right)$ nag_specfun_bessel_i1_scaled_vector (s18ct) Scaled modified Bessel function vectorized e − |x|I1(x)${e}^{-|x|}{I}_{1}\left(x\right)$ nag_specfun_kelvin_ber_vector (s19an) Kelvin function vectorized berx$\mathrm{ber}x$ nag_specfun_kelvin_bei_vector (s19ap) Kelvin function vectorized beix$\mathrm{bei}x$ nag_specfun_kelvin_ker_vector (s19aq) Kelvin function vectorized kerx$\mathrm{ker}x$ nag_specfun_kelvin_kei_vector (s19ar) Kelvin function vectorized keix$\mathrm{kei}x$ nag_specfun_fresnel_s_vector (s20aq) Fresnel integral vectorized S(x)$S\left(x\right)$ nag_specfun_fresnel_c_vector (s20ar) Fresnel integral vectorized C(x)$C\left(x\right)$ nag_specfun_1f1_real (s22ba) Real confluent hypergeometric function 1F1 (a ; b ; x) ${}_{1}F_{1}\left(a;b;x\right)$ nag_specfun_1f1_real_scaled (s22bb) Real confluent hypergeometric function 1F1 (a ; b ; x) ${}_{1}F_{1}\left(a;b;x\right)$ in scaled form

NAG Toolbox

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