math_NewtonFunctionRoot Class Reference

This class implements the calculation of a root of a function of a single variable starting from an initial near guess using the Newton algorithm. Knowledge of the derivative is required. More...

#include <math_NewtonFunctionRoot.hxx>

Public Member Functions
	math_NewtonFunctionRoot (math_FunctionWithDerivative &F, const Standard_Real Guess, const Standard_Real EpsX, const Standard_Real EpsF, const Standard_Integer NbIterations=100)
	The Newton method is done to find the root of the function F from the initial guess Guess. The tolerance required on the root is given by Tolerance. The solution is found when : abs(Xi - Xi-1) <= EpsX and abs(F(Xi))<= EpsF The maximum number of iterations allowed is given by NbIterations.
	math_NewtonFunctionRoot (math_FunctionWithDerivative &F, const Standard_Real Guess, const Standard_Real EpsX, const Standard_Real EpsF, const Standard_Real A, const Standard_Real B, const Standard_Integer NbIterations=100)
	The Newton method is done to find the root of the function F from the initial guess Guess. The solution must be inside the interval [A, B]. The tolerance required on the root is given by Tolerance. The solution is found when : abs(Xi - Xi-1) <= EpsX and abs(F(Xi))<= EpsF The maximum number of iterations allowed is given by NbIterations.
	math_NewtonFunctionRoot (const Standard_Real A, const Standard_Real B, const Standard_Real EpsX, const Standard_Real EpsF, const Standard_Integer NbIterations=100)
	is used in a sub-class to initialize correctly all the fields of this class.
void	Perform (math_FunctionWithDerivative &F, const Standard_Real Guess)
	is used internally by the constructors.
Standard_Boolean	IsDone () const
	Returns true if the computations are successful, otherwise returns false.
Standard_Real	Root () const
	Returns the value of the root of function <F>. Exception NotDone is raised if the root was not found.
Standard_Real	Derivative () const
	returns the value of the derivative at the root. Exception NotDone is raised if the root was not found.
Standard_Real	Value () const
	returns the value of the function at the root. Exception NotDone is raised if the root was not found.
Standard_Integer	NbIterations () const
	Returns the number of iterations really done on the computation of the Root. Exception NotDone is raised if the root was not found.
void	Dump (Standard_OStream &o) const
	Prints information on the current state of the object.

Detailed Description

This class implements the calculation of a root of a function of a single variable starting from an initial near guess using the Newton algorithm. Knowledge of the derivative is required.

Constructor & Destructor Documentation

math_NewtonFunctionRoot() [1/3]

math_NewtonFunctionRoot::math_NewtonFunctionRoot	(	math_FunctionWithDerivative &	F,
		const Standard_Real	Guess,
		const Standard_Real	EpsX,
		const Standard_Real	EpsF,
		const Standard_Integer	NbIterations = 100
	)

The Newton method is done to find the root of the function F from the initial guess Guess. The tolerance required on the root is given by Tolerance. The solution is found when : abs(Xi - Xi-1) <= EpsX and abs(F(Xi))<= EpsF The maximum number of iterations allowed is given by NbIterations.

math_NewtonFunctionRoot() [2/3]

math_NewtonFunctionRoot::math_NewtonFunctionRoot	(	math_FunctionWithDerivative &	F,
		const Standard_Real	Guess,
		const Standard_Real	EpsX,
		const Standard_Real	EpsF,
		const Standard_Real	A,
		const Standard_Real	B,
		const Standard_Integer	NbIterations = 100
	)

The Newton method is done to find the root of the function F from the initial guess Guess. The solution must be inside the interval [A, B]. The tolerance required on the root is given by Tolerance. The solution is found when : abs(Xi - Xi-1) <= EpsX and abs(F(Xi))<= EpsF The maximum number of iterations allowed is given by NbIterations.

math_NewtonFunctionRoot() [3/3]

math_NewtonFunctionRoot::math_NewtonFunctionRoot	(	const Standard_Real	A,
		const Standard_Real	B,
		const Standard_Real	EpsX,
		const Standard_Real	EpsF,
		const Standard_Integer	NbIterations = 100
	)

is used in a sub-class to initialize correctly all the fields of this class.

Member Function Documentation

Derivative()

Standard_Real math_NewtonFunctionRoot::Derivative

(

)

const

returns the value of the derivative at the root. Exception NotDone is raised if the root was not found.

Dump()

void math_NewtonFunctionRoot::Dump

(

Standard_OStream &

o

)

const

Prints information on the current state of the object.

IsDone()

Standard_Boolean math_NewtonFunctionRoot::IsDone

(

)

const

Returns true if the computations are successful, otherwise returns false.

NbIterations()

Standard_Integer math_NewtonFunctionRoot::NbIterations

(

)

const

Returns the number of iterations really done on the computation of the Root. Exception NotDone is raised if the root was not found.

Perform()

void math_NewtonFunctionRoot::Perform	(	math_FunctionWithDerivative &	F,
		const Standard_Real	Guess
	)

is used internally by the constructors.

Root()

Standard_Real math_NewtonFunctionRoot::Root

(

)

const

Returns the value of the root of function <F>. Exception NotDone is raised if the root was not found.

Value()

Standard_Real math_NewtonFunctionRoot::Value

(

)

const

returns the value of the function at the root. Exception NotDone is raised if the root was not found.

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The documentation for this class was generated from the following file:

• math_NewtonFunctionRoot.hxx