# NAG FL InterfaceD01 (Quad)Quadrature

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D01 (Quad) Chapter Introduction – A description of the Chapter and an overview of the algorithms available.

Routine
Mark of
Introduction

Purpose
d01ahf 8 nagf_quad_dim1_fin_well
One-dimensional quadrature, adaptive, finite interval, strategy due to Patterson, suitable for well-behaved integrands
d01anf 8 nagf_quad_dim1_fin_wtrig
One-dimensional quadrature, adaptive, finite interval, weight function $\mathrm{cos}\left(\omega x\right)$ or $\mathrm{sin}\left(\omega x\right)$
d01apf 8 nagf_quad_dim1_fin_wsing
One-dimensional quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type
d01aqf 8 nagf_quad_dim1_fin_wcauchy
One-dimensional quadrature, adaptive, finite interval, weight function $1/\left(x-c\right)$, Cauchy principal value (Hilbert transform)
d01arf 10 nagf_quad_dim1_indef
One-dimensional quadrature, non-adaptive, finite interval with provision for indefinite integrals
d01asf 13 nagf_quad_dim1_inf_wtrig
One-dimensional quadrature, adaptive, semi-infinite interval, weight function $\mathrm{cos}\left(\omega x\right)$ or $\mathrm{sin}\left(\omega x\right)$
d01bdf 8 nagf_quad_dim1_fin_smooth
One-dimensional quadrature, non-adaptive, finite interval
d01daf 5 nagf_quad_dim2_fin
Two-dimensional quadrature, finite region
d01eaf 12 nagf_quad_md_adapt_multi
Multidimensional adaptive quadrature over hyper-rectangle, multiple integrands
d01esf 25 nagf_quad_md_sgq_multi_vec
Multi-dimensional quadrature using sparse grids
d01fbf 8 nagf_quad_md_gauss
Multidimensional Gaussian quadrature over hyper-rectangle
d01fcf 8 nagf_quad_md_adapt
Multidimensional adaptive quadrature over hyper-rectangle
d01fdf 10 nagf_quad_md_sphere
Multidimensional quadrature, Sag–Szekeres method, general product region or $n$-sphere
d01gaf 5 nagf_quad_dim1_data
One-dimensional quadrature, integration of function defined by data values, Gill–Miller method
d01gbf 10 nagf_quad_md_mcarlo
Multidimensional quadrature over hyper-rectangle, Monte Carlo method
d01gcf 10 nagf_quad_md_numth
Multidimensional quadrature, general product region, number-theoretic method
d01gdf 14 nagf_quad_md_numth_vec
Multidimensional quadrature, general product region, number-theoretic method, variant of d01gcf efficient on vector machines
d01gyf 10 nagf_quad_md_numth_coeff_prime
Korobov optimal coefficients for use in d01gcf or d01gdf, when number of points is prime
d01gzf 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 10 nagf_quad_md_sphere_bad
Multidimensional quadrature over an $n$-sphere, allowing for badly behaved integrands
d01paf 10 nagf_quad_md_simplex
Multidimensional quadrature over an $n$-simplex
d01raf 24 nagf_quad_dim1_gen_vec_multi_rcomm
One-dimensional quadrature, adaptive, finite interval, multiple integrands, vectorized abscissae, reverse communication
d01rcf 24 nagf_quad_dim1_gen_vec_multi_dimreq
Determine required array dimensions for d01raf
d01rgf 24 nagf_quad_dim1_fin_gonnet_vec
One-dimensional quadrature, adaptive, finite interval, strategy due to Gonnet, allowing for badly behaved integrands
d01rjf 27.1 nagf_quad_dim1_fin_general
One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands
d01rkf 27.1 nagf_quad_dim1_fin_osc_fn
One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions
d01rlf 27.1 nagf_quad_dim1_fin_brkpts
One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points
d01rmf 27.1 nagf_quad_dim1_inf_general
One-dimensional quadrature, adaptive, infinite or semi-infinite interval, strategy due to Piessens and de Doncker
d01tbf 24 nagf_quad_dim1_gauss_wres
Pre-computed weights and abscissae for Gaussian quadrature rules, restricted choice of rule
d01tcf 27.1 nagf_quad_dim1_gauss_wgen
Calculation of weights and abscissae for Gaussian quadrature rules, general choice of rule
d01tdf 26 nagf_quad_dim1_gauss_wrec
Calculation of weights and abscissae for Gaussian quadrature rules, method of Golub and Welsch
d01tef 26 nagf_quad_dim1_gauss_recm
Generates recursion coefficients needed by d01tdf to calculate a Gaussian quadrature rule
d01uaf 24 nagf_quad_dim1_gauss_vec
One-dimensional Gaussian quadrature, choice of weight functions (vectorized)
d01ubf 26 nagf_quad_dim1_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
d01ajf 8
(Deprecated)
nagf_quad_dim1_fin_bad
One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands (single abscissa interface)
d01akf 8
(Deprecated)
nagf_quad_dim1_fin_osc
One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions (single abscissa interface)
d01alf 8
(Deprecated)
nagf_quad_dim1_fin_sing
One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points (single abscissa interface)
d01amf 8
(Deprecated)
nagf_quad_dim1_inf
One-dimensional quadrature, adaptive, infinite or semi-infinite interval
d01atf 13
(Deprecated)
nagf_quad_dim1_fin_bad_vec
One-dimensional quadrature, adaptive, finite interval, variant of d01ajf efficient on vector machines
d01auf 13
(Deprecated)
nagf_quad_dim1_fin_osc_vec
One-dimensional quadrature, adaptive, finite interval, variant of d01akf efficient on vector machines
d01bcf 8
(Deprecated)
nagf_quad_withdraw_dim1_gauss_wgen
Old routine for calculating weights and abscissae for Gaussian quadrature rules, replaced by d01tcf
d01rbf 24
(Deprecated)
nagf_quad_withdraw_1d_gen_vec_multi_diagnostic
Diagnostic routine for d01raf