D01 Chapter Contents (PDF version)
D01 Chapter Introduction
NAG Library Manual

# NAG Library Chapter ContentsD01 – Quadrature

### D01 Chapter Introduction

 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 D01BAF Example Text 7 nagf_quad_withdraw_1d_gauss One-dimensional Gaussian quadratureNote: this routine is scheduled for withdrawal at Mark 26, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. D01BBF Example Text 7 nagf_quad_1d_gauss_wset Pre-computed weights and abscissae for Gaussian quadrature rules, restricted choice of rule (deprecated)Note: this routine is scheduled for withdrawal at Mark 26, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 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 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_1d_gen_vec_multi_diagnostic Diagnostic routine for D01RAF 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 D01UAF Example Text 24 nagf_quad_1d_gauss_vec One-dimensional Gaussian quadrature, choice of weight functions D01ZKF 24 nagf_quad_opt_set Option setting routine D01ZLF 24 nagf_quad_opt_get Option getting routine

D01 Chapter Contents (PDF version)
D01 Chapter Introduction
NAG Library Manual