roots.hpp File Reference

#include <randlib/math/constants.hpp>
#include <algorithm>
#include <cmath>
#include <concepts>
#include <functional>
#include <limits>
#include <stdexcept>
#include <tuple>
#include <type_traits>
#include <utility>

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

Functions
template<std::floating_point Real>
bool	randlib::math::detail::bracketResolved (Real a, Real b)
	|b - a| no longer resolvable at the relative precision of Real
template<std::floating_point Real>
Real	randlib::math::detail::safeDivide (Real numerator, Real denominator, Real fallback)
template<std::floating_point Real>
Real	randlib::math::detail::secantStep (Real a, Real b, Real fa, Real fb)
template<std::floating_point Real>
Real	randlib::math::detail::newtonQuadraticStep (Real a, Real b, Real d, Real fa, Real fb, Real fd, int steps)
template<std::floating_point Real>
Real	randlib::math::detail::inverseCubicStep (Real a, Real b, Real d, Real e, Real fa, Real fb, Real fd, Real fe)
template<std::floating_point Real, class F >
std::pair< Real, Real >	randlib::math::toms748 (const F &f, Real a, Real b, Real fa, Real fb, int maxIterations=200)
	Bracketing root finder of Alefeld, Potra and Shi (ACM TOMS algorithm 748): inverse cubic and Newton-quadratic interpolation steps, a double-length secant step and bisection whenever the bracket does not shrink by half; it converges like Brent's method at worst and faster on smooth functions.
template<std::floating_point Real = double, class F >
Real	randlib::math::findRoot (const F &f, std::type_identity_t< Real > a, std::type_identity_t< Real > b, int maxIterations=200)
template<typename RealType >
bool	randlib::math::findRootNewtonFirstOrder (const std::function< DoublePair(RealType)> &funPtr, RealType &root, long double funTol=1e-10, long double stepTol=1e-6)
	Newton's root-finding procedure, using first derivative.
template<typename RealType >
bool	randlib::math::findRootNewtonSecondOrder (const std::function< DoubleTriplet(RealType)> &funPtr, RealType &root, long double funTol=1e-10, long double stepTol=1e-6)
	Newton's root-finding procedure, using first and second derivatives.
bool	randlib::math::findRootNewtonFirstOrder2d (const std::function< DoublePair(DoublePair)> &funPtr, const std::function< std::tuple< DoublePair, DoublePair >(DoublePair)> &gradPtr, DoublePair &root, long double funTol=1e-10, long double stepTol=1e-6)
	Newton's root-finding procedure for 2 functions of 2 parameters, using Jacobian matrix.