# NAG Library Chapter Contents

## D01 (quad)Quadrature

D01 (quad) Chapter Introduction – a description of the Chapter and an overview of the algorithms available

 RoutineName Mark ofIntroduction Purpose d01ahf Example Text Example Data 8 nagf_quad_1d_fin_well One-dimensional quadrature, adaptive, finite interval, strategy due to Patterson, suitable for well-behaved integrands d01ajf Example Text 8 nagf_quad_1d_fin_bad One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands d01akf Example Text 8 nagf_quad_1d_fin_osc One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions d01alf Example Text 8 nagf_quad_1d_fin_sing One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points d01amf Example Text 8 nagf_quad_1d_inf One-dimensional quadrature, adaptive, infinite or semi-infinite interval d01anf Example Text 8 nagf_quad_1d_fin_wtrig One-dimensional quadrature, adaptive, finite interval, weight function $\mathrm{cos}\left(\omega x\right)$ or $\mathrm{sin}\left(\omega x\right)$ d01apf Example Text 8 nagf_quad_1d_fin_wsing One-dimensional quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type d01aqf Example Text 8 nagf_quad_1d_fin_wcauchy One-dimensional quadrature, adaptive, finite interval, weight function $1/\left(x-c\right)$, Cauchy principal value (Hilbert transform) d01arf Example Text 10 nagf_quad_1d_indef One-dimensional quadrature, non-adaptive, finite interval with provision for indefinite integrals d01asf Example Text 13 nagf_quad_1d_inf_wtrig One-dimensional quadrature, adaptive, semi-infinite interval, weight function $\mathrm{cos}\left(\omega x\right)$ or $\mathrm{sin}\left(\omega x\right)$ d01atf Example Text 13 nagf_quad_1d_fin_bad_vec One-dimensional quadrature, adaptive, finite interval, variant of d01ajf efficient on vector machines d01auf Example Text 13 nagf_quad_1d_fin_osc_vec One-dimensional quadrature, adaptive, finite interval, variant of d01akf efficient on vector machines d01bcf Example TextExample Plot 8 nagf_quad_1d_gauss_wgen Calculation of weights and abscissae for Gaussian quadrature rules, general choice of rule d01bdf Example Text 8 nagf_quad_1d_fin_smooth One-dimensional quadrature, non-adaptive, finite interval d01daf Example Text 5 nagf_quad_2d_fin Two-dimensional quadrature, finite region d01eaf Example TextExample Plot 12 nagf_quad_md_adapt_multi Multidimensional adaptive quadrature over hyper-rectangle, multiple integrands d01esf Example Text 25 nagf_quad_md_sgq_multi_vec Multi-dimensional quadrature using sparse grids d01fbf Example Text 8 nagf_quad_md_gauss Multidimensional Gaussian quadrature over hyper-rectangle d01fcf Example Text 8 nagf_quad_md_adapt Multidimensional adaptive quadrature over hyper-rectangle d01fdf Example Text 10 nagf_quad_md_sphere Multidimensional quadrature, Sag–Szekeres method, general product region or $n$-sphere d01gaf Example Text Example Data 5 nagf_quad_1d_data One-dimensional quadrature, integration of function defined by data values, Gill–Miller method d01gbf Example Text 10 nagf_quad_md_mcarlo Multidimensional quadrature over hyper-rectangle, Monte–Carlo method d01gcf Example Text 10 nagf_quad_md_numth Multidimensional quadrature, general product region, number-theoretic method d01gdf Example Text 14 nagf_quad_md_numth_vec Multidimensional quadrature, general product region, number-theoretic method, variant of d01gcf efficient on vector machines d01gyf Example Text 10 nagf_quad_md_numth_coeff_prime Korobov optimal coefficients for use in d01gcf or d01gdf, when number of points is prime d01gzf Example Text 10 nagf_quad_md_numth_coeff_2prime Korobov optimal coefficients for use in d01gcf or d01gdf, when number of points is product of two primes d01jaf Example Text 10 nagf_quad_md_sphere_bad Multidimensional quadrature over an $n$-sphere, allowing for badly behaved integrands d01paf Example Text 10 nagf_quad_md_simplex Multidimensional quadrature over an $n$-simplex d01raf Example Text 24 nagf_quad_1d_gen_vec_multi_rcomm One-dimensional quadrature, adaptive, finite interval, multiple integrands, vectorized abscissae, reverse communication d01rbf 24 nagf_quad_withdraw_1d_gen_vec_multi_diagnostic Diagnostic routine for d01rafNote: this routine is scheduled for withdrawal at Mark 28, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. d01rcf 24 nagf_quad_1d_gen_vec_multi_dimreq Determine required array dimensions for d01raf d01rgf Example Text 24 nagf_quad_1d_fin_gonnet_vec One-dimensional quadrature, adaptive, finite interval, strategy due to Gonnet, allowing for badly behaved integrands d01tbf Example Text 24 nagf_quad_1d_gauss_wres Pre-computed weights and abscissae for Gaussian quadrature rules, restricted choice of rule d01tdf Example Text 26.0 nagf_quad_1d_gauss_wrec Calculation of weights and abscissae for Gaussian quadrature rules, method of Golub and Welsch d01tef Example Text 26.0 nagf_quad_1d_gauss_recm Generates recursion coefficients needed by d01tdf to calculate a Gaussian quadrature rule d01uaf Example Text 24 nagf_quad_1d_gauss_vec One-dimensional Gaussian quadrature, choice of weight functions (vectorized) d01ubf Example Text 26.0 nagf_quad_1d_inf_exp_wt Non-automatic routine to evaluate d01zkf 24 nagf_quad_opt_set Option setting routine d01zlf 24 nagf_quad_opt_get Option getting routine
© The Numerical Algorithms Group Ltd, Oxford, UK. 2017