quadrature.hpp File Reference

#include <algorithm>
#include <cmath>
#include <concepts>
#include <complex>
#include <limits>
#include <numbers>
#include <stdexcept>
#include <type_traits>
#include <utility>
#include <vector>

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Classes
struct	randlib::math::detail::Segment< Real >

Namespaces
namespace	randlib
namespace	randlib::math
	Beta-related functions.
namespace	randlib::math::detail

Functions
template<std::floating_point Real>
std::pair< std::complex< Real >, Real >	randlib::math::detail::accelerateOscillatorySums (const std::vector< std::complex< Real > > &partialSums)
template<std::floating_point Real, class F >
Segment< Real >	randlib::math::detail::gaussKronrod21 (const F &f, Real a, Real b, Real &absEstimate)
	21-point Gauss-Kronrod rule with its embedded 10-point Gauss rule (QUADPACK qk21)
template<std::floating_point Real, class F >
Real	randlib::math::detail::integrateFinite (const F &f, Real a, Real b, Real tolerance, int maxSubdivisions)
	Global adaptive scheme (QUADPACK QAG) on a finite interval.
template<std::floating_point Real, class F >
Real	randlib::math::detail::evaluateTanhSinh (const F &f, Real x, Real endpointDistance)
template<std::floating_point Real, class F >
std::pair< Real, Real >	randlib::math::detail::tanhSinhLevel (const F &f, Real a, Real b, Real step)
template<std::floating_point Real = double, class F >
Real	randlib::math::integrate (const F &f, std::type_identity_t< Real > a, std::type_identity_t< Real > b, std::type_identity_t< Real > tolerance=1e-11, int maxSubdivisions=512)
	Global adaptive Gauss-Kronrod quadrature (QUADPACK QAG).
template<std::floating_point Real = double, class F >
Real	randlib::math::integrateTanhSinh (const F &f, std::type_identity_t< Real > a, std::type_identity_t< Real > b, std::type_identity_t< Real > tolerance=1e-11, int maxRefinements=12)
	Double-exponential tanh-sinh quadrature on a finite interval.
template<std::floating_point Real, class F , class TailMass >
std::complex< Real >	randlib::math::detail::integrateHalfPeriods (const F &amplitude, Real frequency, Real lower, Real tolerance, int maxCycles, const TailMass &tailMass)
template<std::floating_point Real = double, class F >
std::complex< Real >	randlib::math::integrateOscillatory (const F &amplitude, std::type_identity_t< Real > frequency, std::type_identity_t< Real > lower=0, std::type_identity_t< Real > tolerance=1e-10, int maxCycles=512)
	QAWF-style Fourier integral on a semi-infinite interval.
template<std::floating_point Real = double, class F , class TailMass > requires std::invocable<const TailMass &, Real>
std::complex< Real >	randlib::math::integrateOscillatory (const F &amplitude, std::type_identity_t< Real > frequency, std::type_identity_t< Real > lower, const TailMass &tailMass, std::type_identity_t< Real > tolerance=1e-10, int maxCycles=512)
	QAWF-style Fourier integral of an amplitude with a known tail bound: the half-period walk stops once the remaining mass is below the tolerance, and is accelerated only beyond half of the mass.