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

NAG Library Chapter Contents

D01 – Quadrature


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

Routine
Name
Mark of
Introduction

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 cosωx or sinωx
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/x-c, 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 cosωx or sinωx
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 Text
Example 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 Text
Example 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 D01RAF
Note: this routine is scheduled for withdrawal at Mark 27, 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 nagf_quad_1d_gauss_wrec
Calculation of weights and abscissae for Gaussian quadrature rules, method of Golub and Welsch
D01TEF
Example Text
26 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 nagf_quad_1d_inf_exp_wt
Non-automatic routine to evaluate 0exp-x2fx dx
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

© The Numerical Algorithms Group Ltd, Oxford, UK. 2016