Detailed Description

template<typename SubType, typename Function>
class MathLib::Nonlinear::RegulaFalsi< SubType, Function >

Use the regula falsi method to find the root of some scalar function of one variable.

Definition at line 48 of file Root1D.h.

#include <Root1D.h>

Public Member Functions
	RegulaFalsi (Function &&f, double a, double b)

void	step (const unsigned num_steps)
	Do `num_steps` iteration of regula falsi.

double	getResult () const
	Returns the current estimate of the root.

double	getRange () const
	Returns the size of the current search interval.

Private Attributes
Function	f_

double	a_

double	b_

double	fa_

double	fb_

Constructor & Destructor Documentation

◆ RegulaFalsi()

template<typename SubType , typename Function >

MathLib::Nonlinear::RegulaFalsi< SubType, Function >::RegulaFalsi	(	Function &&	f,
		double	a,
		double	b )

inline

Initializes finding a root of the Function f in the interval [a, b].

Definition at line 53 of file Root1D.h.

        : f_(f), a_(a), b_(b), fa_(f(a)), fb_(f(b))
    {
        static_assert(std::is_same_v<double, decltype(f(0.0))>,
                      "Using this class for functions that do not return double"
                      " involves a lot of casts. Hence it is disabled.");
 
        if (detail::almost_zero(fa_))
        {
            b_ = a_;
        }
        else if (detail::almost_zero(fb_))
        {
            a_ = b_;
        }
        else if (detail::same_sign(fa_, fb_))
        {
            OGS_FATAL("Regula falsi cannot be done, because the function values"
                " at the interval ends have the same sign.");
        }
    }

References MathLib::Nonlinear::RegulaFalsi< SubType, Function >::a_, MathLib::Nonlinear::detail::almost_zero(), MathLib::Nonlinear::RegulaFalsi< SubType, Function >::b_, MathLib::Nonlinear::RegulaFalsi< SubType, Function >::fa_, MathLib::Nonlinear::RegulaFalsi< SubType, Function >::fb_, OGS_FATAL, and MathLib::Nonlinear::detail::same_sign().

Member Function Documentation

◆ getRange()

template<typename SubType , typename Function >

double MathLib::Nonlinear::RegulaFalsi< SubType, Function >::getRange ( ) const

inline

Returns the size of the current search interval.

Definition at line 123 of file Root1D.h.

123{ return std::abs(a_ - b_); }

References MathLib::Nonlinear::RegulaFalsi< SubType, Function >::a_, and MathLib::Nonlinear::RegulaFalsi< SubType, Function >::b_.

◆ getResult()

template<typename SubType , typename Function >

double MathLib::Nonlinear::RegulaFalsi< SubType, Function >::getResult ( ) const

inline

Returns the current estimate of the root.

Definition at line 109 of file Root1D.h.

    {
        if (a_ == b_)
        {
            return a_;
        }
 
        const double s = (fb_ - fa_) / (b_ - a_);
        const double c = a_ - fa_ / s;
 
        return c;
    }

References MathLib::Nonlinear::RegulaFalsi< SubType, Function >::a_, MathLib::Nonlinear::RegulaFalsi< SubType, Function >::b_, MathLib::Nonlinear::RegulaFalsi< SubType, Function >::fa_, MathLib::Nonlinear::RegulaFalsi< SubType, Function >::fb_, and MathLib::s.

◆ step()

template<typename SubType , typename Function >

void MathLib::Nonlinear::RegulaFalsi< SubType, Function >::step ( const unsigned num_steps )

inline

Do num_steps iteration of regula falsi.

Definition at line 76 of file Root1D.h.

    {
        for (unsigned i=0; i<num_steps; ++i)
        {
            if (a_ == b_)
            {
                return;
            }
 
            const double s = (fb_ - fa_) / (b_ - a_);
            const double c = a_ - fa_ / s;
            const double fc = f_(c);
 
            if (detail::almost_zero(fc)) {
                a_ = b_ = c;
                return;
            }
            if (!detail::same_sign(fc, fb_))
            {
                a_ = b_;
                fa_ = fb_;
                b_ = c;
                fb_ = fc;
            } else {
                const double m = SubType::get_m(fa_, fb_, fc);
                fa_ *= m;
                b_ = c;
                fb_ = fc;
            }
        }
    }