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 (const int NbVariables, const double Tolerance=1.0e-8, const int NbIterations=200, const double ZEPS=1.0e-12)
	Initializes the computation of the minimum of a function with NbVariables. Tolerance, ZEPS and NbIterations are described in the method Perform. 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 ()
void	SetBoundary (const math_Vector &theLeftBorder, const math_Vector &theRightBorder)
	Set boundaries for conditional optimization. The expected indices range of vectors is [1, NbVariables].
void	Perform (math_MultipleVarFunctionWithGradient &F, const math_Vector &StartingPoint)
	Given the starting point StartingPoint, minimization is done on the function F. The solution F = Fi is found when : 2.0 * abs(Fi - Fi-1) <= Tolerance * (abs(Fi) + abs(Fi-1) + ZEPS). Tolerance, ZEPS and maximum number of iterations are given in the constructor.
virtual bool	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.
bool	IsDone () const
	Returns true if the computations are successful, otherwise returns false.
const math_Vector &	Location () const
	returns the location vector of the minimum. Exception NotDone is raised if the minimum was not found.
void	Location (math_Vector &Loc) const
	outputs the location vector of the minimum in Loc. 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.
double	Minimum () const
	returns the value of the minimum. Exception NotDone is raised if the minimum was not found.
const math_Vector &	Gradient () const
	Returns the gradient vector at the minimum. Exception NotDone is raised if the minimum was not found.
void	Gradient (math_Vector &Grad) const
	Returns the value of the gradient vector at the minimum in Grad. 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.
int	NbIterations () const
	Returns the number of iterations really done in the calculation of the minimum. The exception NotDone is raised if the minimum was not found.
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 <<.

Protected Attributes
math_Status	TheStatus
math_Vector	TheLocation
math_Vector	TheGradient
double	PreviousMinimum
double	TheMinimum
double	XTol
double	EPSZ
int	nbiter
bool	myIsBoundsDefined
math_Vector	myLeft
math_Vector	myRight

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.

It is possible to solve conditional optimization problem on hyperparallelepiped. Method SetBoundary is used to define hyperparallelepiped borders. With boundaries defined, the algorithm will not make evaluations of the function outside of the borders.

Constructor & Destructor Documentation

math_BFGS()

math_BFGS::math_BFGS	(	const int	NbVariables,
		const double	Tolerance = 1.0e-8,
		const int	NbIterations = 200,
		const double	ZEPS = 1.0e-12 )

Initializes the computation of the minimum of a function with NbVariables. Tolerance, ZEPS and NbIterations are described in the method Perform. Warning: A call to the Perform method must be made after this initialization to effectively compute the minimum of the function F.

~math_BFGS()

virtual math_BFGS::~math_BFGS ( )

virtual

Member Function Documentation

Dump()

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 <<.

Gradient() [1/2]

const math_Vector & math_BFGS::Gradient

(

)

const

Returns the gradient vector at the minimum. Exception NotDone is raised if the minimum was not found.

Gradient() [2/2]

void math_BFGS::Gradient

(

math_Vector &

Grad

)

const

Returns the value of the gradient vector at the minimum in Grad. 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.

IsDone()

bool math_BFGS::IsDone

(

)

const

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

IsSolutionReached()

virtual bool 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 AppDef_BSpGradient_BFGSOfMyBSplGradientOfBSplineCompute, AppDef_Gradient_BFGSOfMyGradientbisOfBSplineCompute, AppDef_Gradient_BFGSOfMyGradientOfCompute, AppDef_Gradient_BFGSOfTheGradient, BRepApprox_BSpGradient_BFGSOfMyBSplGradientOfTheComputeLineOfApprox, BRepApprox_Gradient_BFGSOfMyGradientbisOfTheComputeLineOfApprox, BRepApprox_Gradient_BFGSOfMyGradientOfTheComputeLineBezierOfApprox, GeomInt_BSpGradient_BFGSOfMyBSplGradientOfTheComputeLineOfWLApprox, GeomInt_Gradient_BFGSOfMyGradientbisOfTheComputeLineOfWLApprox, and GeomInt_Gradient_BFGSOfMyGradientOfTheComputeLineBezierOfWLApprox.

Location() [1/2]

const math_Vector & math_BFGS::Location

(

)

const

returns the location vector of the minimum. Exception NotDone is raised if the minimum was not found.

Location() [2/2]

void math_BFGS::Location

(

math_Vector &

Loc

)

const

outputs the location vector of the minimum in Loc. 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.

Minimum()

double math_BFGS::Minimum

(

)

const

returns the value of the minimum. Exception NotDone is raised if the minimum was not found.

NbIterations()

int math_BFGS::NbIterations

(

)

const

Returns the number of iterations really done in the calculation of the minimum. The exception NotDone is raised if the minimum was not found.

Perform()

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

Given the starting point StartingPoint, minimization is done on the function F. The solution F = Fi is found when : 2.0 * abs(Fi - Fi-1) <= Tolerance * (abs(Fi) + abs(Fi-1) + ZEPS). Tolerance, ZEPS and maximum number of iterations are given in the constructor.

SetBoundary()

void math_BFGS::SetBoundary	(	const math_Vector &	theLeftBorder,
		const math_Vector &	theRightBorder )

Set boundaries for conditional optimization. The expected indices range of vectors is [1, NbVariables].

Field Documentation

EPSZ

double math_BFGS::EPSZ

protected

myIsBoundsDefined

bool math_BFGS::myIsBoundsDefined

protected

myLeft

math_Vector math_BFGS::myLeft

protected

myRight

math_Vector math_BFGS::myRight

protected

nbiter

int math_BFGS::nbiter

protected

PreviousMinimum

double math_BFGS::PreviousMinimum

protected

TheGradient

math_Vector math_BFGS::TheGradient

protected

TheLocation

math_Vector math_BFGS::TheLocation

protected

TheMinimum

double math_BFGS::TheMinimum

protected

TheStatus

math_Status math_BFGS::TheStatus

protected

XTol

double math_BFGS::XTol

protected

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

• math_BFGS.hxx