stator::numeric Namespace Reference

Numerical routines, such as root-finding, etc.

Namespaces
	detail

Functions
template<class F , class Real >
bool	bisection (const F &f, Real &x, Real low_bound, Real high_bound, size_t iterations=0, int digits=std::numeric_limits< Real >::digits/2)
template<class F , size_t Derivatives, class Real >
int	bisection_step (const F &f, std::array< Real, Derivatives > &curr_state, Real &x, Real &low_bound, Real &high_bound, Real x_precision)
	A single bisection step. More...
template<class F , size_t Derivatives, class Real >
int	halley_step (const F &f, std::array< Real, Derivatives > &curr_state, Real &x, Real &low_bound, Real &high_bound, Real x_precision)
	A single step of Halley's method for finding roots. More...
template<class F , class Real >
bool	halleys_method (const F &f, Real &x, Real low_bound=-HUGE_VAL, Real high_bound=+HUGE_VAL, size_t iterations=0, int digits=std::numeric_limits< Real >::digits/2)
	Safeguarded Halley's method for detecting a root. More...
template<class F , class Real >
bool	newton_raphson (const F &f, Real &x, Real low_bound=-HUGE_VAL, Real high_bound=+HUGE_VAL, size_t iterations=0, int digits=std::numeric_limits< Real >::digits/2)
	Safeguarded newton_raphson method for detecting a root. More...
template<class F , size_t Derivatives, class Real >
int	newton_raphson_step (const F &f, std::array< Real, Derivatives > &curr_state, Real &x, Real &low_bound, Real &high_bound, Real x_precision)
	A single step of the Newton-Raphson method for finding roots. More...
template<class F , size_t Derivatives, class Real >
int	schroeder_step (const F &f, std::array< Real, Derivatives > &curr_state, Real &x, Real &low_bound, Real &high_bound, Real x_precision)
	A single step of Schroeder's method for finding roots. More...

Function Documentation

bisection()

template<class F , class Real >

bool stator::numeric::bisection	(	const F &	f,
		Real &	x,
		Real	low_bound,
		Real	high_bound,
		size_t	iterations = 0,
		int	digits = std::numeric_limits<Real>::digits / 2
	)

Definition at line 272 of file numeric.hpp.

bisection_step()

template<class F , size_t Derivatives, class Real >

int stator::numeric::bisection_step ( const F &  f, std::array< Real, Derivatives > &  curr_state, Real &  x, Real &  low_bound, Real &  high_bound, Real  x_precision  )

inline

Definition at line 149 of file numeric.hpp.

halley_step()

template<class F , size_t Derivatives, class Real >

int stator::numeric::halley_step ( const F &  f, std::array< Real, Derivatives > &  curr_state, Real &  x, Real &  low_bound, Real &  high_bound, Real  x_precision  )

inline

Definition at line 102 of file numeric.hpp.

halleys_method()

template<class F , class Real >

bool stator::numeric::halleys_method	(	const F &	f,
		Real &	x,
		Real	low_bound = -HUGE_VAL,
		Real	high_bound = +HUGE_VAL,
		size_t	iterations = 0,
		int	digits = std::numeric_limits<Real>::digits / 2
	)

This returns false if the method is not converging or if the number of iterations was exceeded.

Definition at line 240 of file numeric.hpp.

newton_raphson()

template<class F , class Real >

bool stator::numeric::newton_raphson	(	const F &	f,
		Real &	x,
		Real	low_bound = -HUGE_VAL,
		Real	high_bound = +HUGE_VAL,
		size_t	iterations = 0,
		int	digits = std::numeric_limits<Real>::digits / 2
	)

This returns false if the method is not converging or if the number of iterations was exceeded.

Definition at line 207 of file numeric.hpp.

newton_raphson_step()

template<class F , size_t Derivatives, class Real >

int stator::numeric::newton_raphson_step ( const F &  f, std::array< Real, Derivatives > &  curr_state, Real &  x, Real &  low_bound, Real &  high_bound, Real  x_precision  )

inline

Definition at line 85 of file numeric.hpp.

schroeder_step()

template<class F , size_t Derivatives, class Real >

int stator::numeric::schroeder_step ( const F &  f, std::array< Real, Derivatives > &  curr_state, Real &  x, Real &  low_bound, Real &  high_bound, Real  x_precision  )

inline

Definition at line 136 of file numeric.hpp.