math_NewtonFunctionSetRoot Class Reference

This class computes the root of a set of N functions of N variables, knowing an initial guess at the solution and using the Newton Raphson algorithm. Knowledge of all the partial derivatives (Jacobian) is required. More...

#include <math_NewtonFunctionSetRoot.hxx>

Public Member Functions
	math_NewtonFunctionSetRoot (math_FunctionSetWithDerivatives &theFunction, const math_Vector &theXTolerance, const Standard_Real theFTolerance, const Standard_Integer tehNbIterations=100)
	Initialize correctly all the fields of this class. The range (1, F.NbVariables()) must be especially respected for all vectors and matrix declarations.
	math_NewtonFunctionSetRoot (math_FunctionSetWithDerivatives &theFunction, const Standard_Real theFTolerance, const Standard_Integer theNbIterations=100)
	This constructor should be used in a sub-class to initialize correctly all the fields of this class. The range (1, F.NbVariables()) must be especially respected for all vectors and matrix declarations. The method SetTolerance must be called before performing the algorithm.
virtual	~math_NewtonFunctionSetRoot ()
	Destructor.
void	SetTolerance (const math_Vector &XTol)
	Initializes the tolerance values for the unknowns.
void	Perform (math_FunctionSetWithDerivatives &theFunction, const math_Vector &theStartingPoint)
	The Newton method is done to improve the root of the function from the initial guess point. The solution is found when: abs(Xj - Xj-1)(i) <= XTol(i) and abs(Fi) <= FTol for all i;.
void	Perform (math_FunctionSetWithDerivatives &theFunction, const math_Vector &theStartingPoint, const math_Vector &theInfBound, const math_Vector &theSupBound)
	The Newton method is done to improve the root of the function from the initial guess point. Bounds may be given, to constrain the solution. The solution is found when: abs(Xj - Xj-1)(i) <= XTol(i) and abs(Fi) <= FTol for all i;.
virtual Standard_Boolean	IsSolutionReached (math_FunctionSetWithDerivatives &F)
	This method is called at the end of each iteration to check if the solution is found. Vectors DeltaX, Fvalues and Jacobian Matrix are consistent with the possible solution Vector Sol and can be inspected to decide whether the solution is reached or not.
Standard_Boolean	IsDone () const
	Returns true if the computations are successful, otherwise returns false.
const math_Vector &	Root () const
	Returns the value of the root of function F. Exceptions StdFail_NotDone if the algorithm fails (and IsDone returns false).
void	Root (math_Vector &Root) const
	outputs the root vector in Root. Exception NotDone is raised if the root was not found. Exception DimensionError is raised if the range of Root is not equal to the range of the StartingPoint.
Standard_Integer	StateNumber () const
	Outputs the state number associated with the solution vector root.
const math_Matrix &	Derivative () const
	Returns the matrix value of the derivative at the root. Exception NotDone is raised if the root was not found.
void	Derivative (math_Matrix &Der) const
	Outputs the matrix value of the derivative at the root in Der. Exception NotDone is raised if the root was not found. Exception DimensionError is raised if the range of Der is not equal to the range of the StartingPoint.
const math_Vector &	FunctionSetErrors () const
	Returns the vector value of the error done on the functions at the root. Exception NotDone is raised if the root was not found.
void	FunctionSetErrors (math_Vector &Err) const
	Outputs the vector value of the error done on the functions at the root in Err. Exception NotDone is raised if the root was not found. Exception DimensionError is raised if the range of Err is not equal to the range of the StartingPoint.
Standard_Integer	NbIterations () const
	Returns the number of iterations really done during 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. Is used to redefine the operator <<.

Protected Attributes
math_Vector	TolX
Standard_Real	TolF
math_IntegerVector	Indx
math_Vector	Scratch
math_Vector	Sol
math_Vector	DeltaX
math_Vector	FValues
math_Matrix	Jacobian

Detailed Description

This class computes the root of a set of N functions of N variables, knowing an initial guess at the solution and using the Newton Raphson algorithm. Knowledge of all the partial derivatives (Jacobian) is required.

Constructor & Destructor Documentation

math_NewtonFunctionSetRoot() [1/2]

math_NewtonFunctionSetRoot::math_NewtonFunctionSetRoot	(	math_FunctionSetWithDerivatives &	theFunction,
		const math_Vector &	theXTolerance,
		const Standard_Real	theFTolerance,
		const Standard_Integer	tehNbIterations = 100
	)

Initialize correctly all the fields of this class. The range (1, F.NbVariables()) must be especially respected for all vectors and matrix declarations.

math_NewtonFunctionSetRoot() [2/2]

math_NewtonFunctionSetRoot::math_NewtonFunctionSetRoot	(	math_FunctionSetWithDerivatives &	theFunction,
		const Standard_Real	theFTolerance,
		const Standard_Integer	theNbIterations = 100
	)

This constructor should be used in a sub-class to initialize correctly all the fields of this class. The range (1, F.NbVariables()) must be especially respected for all vectors and matrix declarations. The method SetTolerance must be called before performing the algorithm.

~math_NewtonFunctionSetRoot()

virtual math_NewtonFunctionSetRoot::~math_NewtonFunctionSetRoot ( )

virtual

Destructor.

Member Function Documentation

Derivative() [1/2]

const math_Matrix & math_NewtonFunctionSetRoot::Derivative

(

)

const

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

Derivative() [2/2]

void math_NewtonFunctionSetRoot::Derivative

(

math_Matrix &

Der

)

const

Outputs the matrix value of the derivative at the root in Der. Exception NotDone is raised if the root was not found. Exception DimensionError is raised if the range of Der is not equal to the range of the StartingPoint.

Dump()

void math_NewtonFunctionSetRoot::Dump

(

Standard_OStream &

o

)

const

Prints information on the current state of the object. Is used to redefine the operator <<.

FunctionSetErrors() [1/2]

const math_Vector & math_NewtonFunctionSetRoot::FunctionSetErrors

(

)

const

Returns the vector value of the error done on the functions at the root. Exception NotDone is raised if the root was not found.

FunctionSetErrors() [2/2]

void math_NewtonFunctionSetRoot::FunctionSetErrors

(

math_Vector &

Err

)

const

Outputs the vector value of the error done on the functions at the root in Err. Exception NotDone is raised if the root was not found. Exception DimensionError is raised if the range of Err is not equal to the range of the StartingPoint.

IsDone()

Standard_Boolean math_NewtonFunctionSetRoot::IsDone

(

)

const

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

IsSolutionReached()

virtual Standard_Boolean math_NewtonFunctionSetRoot::IsSolutionReached ( math_FunctionSetWithDerivatives &  F )

virtual

This method is called at the end of each iteration to check if the solution is found. Vectors DeltaX, Fvalues and Jacobian Matrix are consistent with the possible solution Vector Sol and can be inspected to decide whether the solution is reached or not.

NbIterations()

Standard_Integer math_NewtonFunctionSetRoot::NbIterations

(

)

const

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

Perform() [1/2]

void math_NewtonFunctionSetRoot::Perform	(	math_FunctionSetWithDerivatives &	theFunction,
		const math_Vector &	theStartingPoint
	)

The Newton method is done to improve the root of the function from the initial guess point. The solution is found when: abs(Xj - Xj-1)(i) <= XTol(i) and abs(Fi) <= FTol for all i;.

Perform() [2/2]

void math_NewtonFunctionSetRoot::Perform	(	math_FunctionSetWithDerivatives &	theFunction,
		const math_Vector &	theStartingPoint,
		const math_Vector &	theInfBound,
		const math_Vector &	theSupBound
	)

The Newton method is done to improve the root of the function from the initial guess point. Bounds may be given, to constrain the solution. The solution is found when: abs(Xj - Xj-1)(i) <= XTol(i) and abs(Fi) <= FTol for all i;.

Root() [1/2]

const math_Vector & math_NewtonFunctionSetRoot::Root

(

)

const

Returns the value of the root of function F. Exceptions StdFail_NotDone if the algorithm fails (and IsDone returns false).

Root() [2/2]

void math_NewtonFunctionSetRoot::Root

(

math_Vector &

Root

)

const

outputs the root vector in Root. Exception NotDone is raised if the root was not found. Exception DimensionError is raised if the range of Root is not equal to the range of the StartingPoint.

SetTolerance()

void math_NewtonFunctionSetRoot::SetTolerance

(

const math_Vector &

XTol

)

Initializes the tolerance values for the unknowns.

StateNumber()

Standard_Integer math_NewtonFunctionSetRoot::StateNumber

(

)

const

Outputs the state number associated with the solution vector root.

Field Documentation

DeltaX

math_Vector math_NewtonFunctionSetRoot::DeltaX

protected

FValues

math_Vector math_NewtonFunctionSetRoot::FValues

protected

Indx

math_IntegerVector math_NewtonFunctionSetRoot::Indx

protected

Jacobian

math_Matrix math_NewtonFunctionSetRoot::Jacobian

protected

Scratch

math_Vector math_NewtonFunctionSetRoot::Scratch

protected

Sol

math_Vector math_NewtonFunctionSetRoot::Sol

protected

TolF

Standard_Real math_NewtonFunctionSetRoot::TolF

protected

TolX

math_Vector math_NewtonFunctionSetRoot::TolX

protected

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

• math_NewtonFunctionSetRoot.hxx