math_BFGS Class Reference

This class implements the Broyden-Fletcher-Goldfarb-Shanno variant of
Davidson-Fletcher-Powell minimization algorithm of a function of
multiple variables.Knowledge of the function's gradient is required.
More...

#include <math_BFGS.hxx>

Inheritance diagram for math_BFGS:

Public Member Functions
	math_BFGS (math_MultipleVarFunctionWithGradient &F, const math_Vector &StartingPoint, const Standard_Real Tolerance=1.0e-8, const Standard_Integer NbIterations=200, const Standard_Real ZEPS=1.0e-12)
	Given the starting point StartingPoint, the Broyden-Fletcher-Goldfarb-Shanno variant of Davidson-Fletcher-Powell minimization is done on the function F. The tolerance required on F is given by Tolerance. The solution F = Fi is found when : 2.0 * abs(Fi - Fi-1) <= Tolerance * (abs(Fi) + abs(Fi-1) + ZEPS). The maximum number of iterations allowed is given by NbIterations. More...
	math_BFGS (math_MultipleVarFunctionWithGradient &F, const Standard_Real Tolerance=1.0e-8, const Standard_Integer NbIterations=200, const Standard_Real ZEPS=1.0e-12)
	Initializes the computation of the minimum of F. <br> Warning A call to the Perform method must be made after this initialization to effectively compute the minimum of the function F. More...
virtual void	Delete ()
virtual	~math_BFGS ()
void	Perform (math_MultipleVarFunctionWithGradient &F, const math_Vector &StartingPoint)
	Is used internally by the constructors. More...
virtual Standard_Boolean	IsSolutionReached (math_MultipleVarFunctionWithGradient &F) const
	This method is called at the end of each iteration to check if the solution is found. It can be redefined in a sub-class to implement a specific test to stop the iterations. More...
Standard_Boolean	IsDone () const
	Returns true if the computations are successful, otherwise returns false. More...
const math_Vector &	Location () const
	returns the location vector of the minimum. <br> Exception NotDone is raised if the minimum was not found. More...
void	Location (math_Vector &Loc) const
	outputs the location vector of the minimum in Loc. <br> Exception NotDone is raised if the minimum was not found. Exception DimensionError is raised if the range of Loc is not equal to the range of the StartingPoint. More...
Standard_Real	Minimum () const
	returns the value of the minimum. <br> Exception NotDone is raised if the minimum was not found. More...
const math_Vector &	Gradient () const
	Returns the gradient vector at the minimum. <br> Exception NotDone is raised if the minimum was not found. More...
void	Gradient (math_Vector &Grad) const
	Returns the value of the gradient vector at the minimum in Grad. <br> Exception NotDone is raised if the minimum was not found. Exception DimensionError is raised if the range of Grad is not equal to the range of the StartingPoint. More...
Standard_Integer	NbIterations () const
	Returns the number of iterations really done in the <br> calculation of the minimum. <br> The exception NotDone is raised if the minimum was not found. More...
void	Dump (Standard_OStream &o) const
	Prints on the stream o information on the current state of the object. Is used to redefine the operator <<. More...

Protected Attributes
math_Status	TheStatus
math_Vector	TheLocation
math_Vector	TheGradient
Standard_Real	PreviousMinimum
Standard_Real	TheMinimum
Standard_Real	XTol
Standard_Real	EPSZ
Standard_Integer	nbiter

Detailed Description

This class implements the Broyden-Fletcher-Goldfarb-Shanno variant of
Davidson-Fletcher-Powell minimization algorithm of a function of
multiple variables.Knowledge of the function's gradient is required.

Constructor & Destructor Documentation

math_BFGS::math_BFGS	(	math_MultipleVarFunctionWithGradient &	F,
		const math_Vector &	StartingPoint,
		const Standard_Real	Tolerance = 1.0e-8,
		const Standard_Integer	NbIterations = 200,
		const Standard_Real	ZEPS = 1.0e-12
	)

Given the starting point StartingPoint,
the Broyden-Fletcher-Goldfarb-Shanno variant of Davidson-Fletcher-Powell
minimization is done on the function F.
The tolerance required on F is given by Tolerance.
The solution F = Fi is found when :
2.0 * abs(Fi - Fi-1) <= Tolerance * (abs(Fi) + abs(Fi-1) + ZEPS).
The maximum number of iterations allowed is given by NbIterations.

math_BFGS::math_BFGS	(	math_MultipleVarFunctionWithGradient &	F,
		const Standard_Real	Tolerance = 1.0e-8,
		const Standard_Integer	NbIterations = 200,
		const Standard_Real	ZEPS = 1.0e-12
	)

 Initializes the computation of the minimum of F. <br>

Warning
A call to the Perform method must be made after this
initialization to effectively compute the minimum of the
function F.

virtual math_BFGS::~math_BFGS ( )

inlinevirtual

Member Function Documentation

virtual void math_BFGS::Delete ( )

virtual

void math_BFGS::Dump

(

Standard_OStream &

o

)

const

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

const math_Vector& math_BFGS::Gradient

(

)

const

 Returns the gradient vector at the minimum. <br>

Exception NotDone is raised if the minimum was not found.

void math_BFGS::Gradient

(

math_Vector &

Grad

)

const

 Returns the value of the gradient vector at the minimum in Grad. <br>

Exception NotDone is raised if the minimum was not found.
Exception DimensionError is raised if the range of Grad is not
equal to the range of the StartingPoint.

Standard_Boolean math_BFGS::IsDone

(

)

const

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

virtual Standard_Boolean math_BFGS::IsSolutionReached ( math_MultipleVarFunctionWithGradient &  F ) const

virtual

This method is called at the end of each iteration to check if the
solution is found.
It can be redefined in a sub-class to implement a specific test to
stop the iterations.

Reimplemented in GeomInt_Gradient_BFGSOfMyGradientbisOfTheComputeLineOfWLApprox, GeomInt_Gradient_BFGSOfMyGradientOfTheComputeLineBezierOfWLApprox, AppDef_Gradient_BFGSOfMyGradientbisOfBSplineCompute, AppDef_Gradient_BFGSOfMyGradientOfCompute, AppDef_Gradient_BFGSOfTheGradient, BRepApprox_Gradient_BFGSOfMyGradientbisOfTheComputeLineOfApprox, BRepApprox_Gradient_BFGSOfMyGradientOfTheComputeLineBezierOfApprox, GeomInt_BSpGradient_BFGSOfMyBSplGradientOfTheComputeLineOfWLApprox, AppDef_BSpGradient_BFGSOfMyBSplGradientOfBSplineCompute, and BRepApprox_BSpGradient_BFGSOfMyBSplGradientOfTheComputeLineOfApprox.

const math_Vector& math_BFGS::Location

(

)

const

 returns the location vector of the minimum. <br>

Exception NotDone is raised if the minimum was not found.

void math_BFGS::Location

(

math_Vector &

Loc

)

const

 outputs the location vector of the minimum in Loc. <br>

Exception NotDone is raised if the minimum was not found.
Exception DimensionError is raised if the range of Loc is not
equal to the range of the StartingPoint.

Standard_Real math_BFGS::Minimum

(

)

const

 returns the value of the minimum. <br>

Exception NotDone is raised if the minimum was not found.

Standard_Integer math_BFGS::NbIterations

(

)

const

 Returns the number of iterations really done in the <br>
     calculation of the minimum. <br>

The exception NotDone is raised if the minimum was not found.

void math_BFGS::Perform	(	math_MultipleVarFunctionWithGradient &	F,
		const math_Vector &	StartingPoint
	)

Is used internally by the constructors.

Field Documentation

Standard_Real math_BFGS::EPSZ

protected

Standard_Integer math_BFGS::nbiter

protected

Standard_Real math_BFGS::PreviousMinimum

protected

math_Vector math_BFGS::TheGradient

protected

math_Vector math_BFGS::TheLocation

protected

Standard_Real math_BFGS::TheMinimum

protected

math_Status math_BFGS::TheStatus

protected

Standard_Real math_BFGS::XTol

protected

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

• math_BFGS.hxx