math_FunctionSetRoot Class Reference

The math_FunctionSetRoot class calculates the root of a set of N functions of M variables (N<M, N=M or N>M). Knowing an initial guess of the solution and using a minimization algorithm, a search is made in the Newton direction and then in the Gradient direction if there is no success in the Newton direction. This algorithm can also be used for functions minimization. Knowledge of all the partial derivatives (the Jacobian) is required. More...

`#include <math_FunctionSetRoot.hxx>`

## Public Member Functions

math_FunctionSetRoot (math_FunctionSetWithDerivatives &F, const math_Vector &Tolerance, const Standard_Integer NbIterations=100)
is 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. More...

math_FunctionSetRoot (math_FunctionSetWithDerivatives &F, const Standard_Integer NbIterations=100)
is 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 after this constructor. More...

virtual ~math_FunctionSetRoot ()
Destructor. More...

void SetTolerance (const math_Vector &Tolerance)
Initializes the tolerance values. More...

virtual Standard_Boolean IsSolutionReached (math_FunctionSetWithDerivatives &F)
This routine is called at the end of each iteration to check if the solution was found. It can be redefined in a sub-class to implement a specific test to stop the iterations. In this case, the solution is found when: abs(Xi - Xi-1) <= Tolerance for all unknowns. More...

void Perform (math_FunctionSetWithDerivatives &theFunction, const math_Vector &theStartingPoint, const Standard_Boolean theStopOnDivergent=Standard_False)
Improves the root of function from the initial guess point. The infinum and supremum may be given to constrain the solution. In this case, the solution is found when: abs(Xi - Xi-1)(j) <= Tolerance(j) for all unknowns. More...

void Perform (math_FunctionSetWithDerivatives &theFunction, const math_Vector &theStartingPoint, const math_Vector &theInfBound, const math_Vector &theSupBound, const Standard_Boolean theStopOnDivergent=Standard_False)
Improves the root of function from the initial guess point. The infinum and supremum may be given to constrain the solution. In this case, the solution is found when: abs(Xi - Xi-1) <= Tolerance for all unknowns. More...

Standard_Boolean IsDone () const
Returns true if the computations are successful, otherwise returns false. More...

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. More...

Standard_Integer StateNumber () const
returns the stateNumber (as returned by F.GetStateNumber()) associated to the root found. More...

const math_VectorRoot () const
Returns the value of the root of function F. Exception NotDone is raised if the root was not found. More...

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. More...

const math_MatrixDerivative () const
Returns the matrix value of the derivative at the root. Exception NotDone is raised if the root was not found. More...

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 column range of <Der> is not equal to the range of the startingPoint. More...

const math_VectorFunctionSetErrors () 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. More...

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. 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...

Standard_Boolean IsDivergent () const

## Protected Attributes

math_Vector Delta

math_Vector Sol

math_Matrix DF

math_Vector Tol

## Detailed Description

The math_FunctionSetRoot class calculates the root of a set of N functions of M variables (N<M, N=M or N>M). Knowing an initial guess of the solution and using a minimization algorithm, a search is made in the Newton direction and then in the Gradient direction if there is no success in the Newton direction. This algorithm can also be used for functions minimization. Knowledge of all the partial derivatives (the Jacobian) is required.

## Constructor & Destructor Documentation

 math_FunctionSetRoot::math_FunctionSetRoot ( math_FunctionSetWithDerivatives & F, const math_Vector & Tolerance, const Standard_Integer NbIterations = `100` )

is 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.

 math_FunctionSetRoot::math_FunctionSetRoot ( math_FunctionSetWithDerivatives & F, const Standard_Integer NbIterations = `100` )

is 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 after this constructor.

 virtual math_FunctionSetRoot::~math_FunctionSetRoot ( )
virtual

Destructor.

## Member Function Documentation

 const math_Matrix& math_FunctionSetRoot::Derivative ( ) const

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

 void math_FunctionSetRoot::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 column range of <Der> is not equal to the range of the startingPoint.

 void math_FunctionSetRoot::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_FunctionSetRoot::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 math_FunctionSetRoot::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_Boolean math_FunctionSetRoot::IsDivergent ( ) const
 Standard_Boolean math_FunctionSetRoot::IsDone ( ) const

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

 virtual Standard_Boolean math_FunctionSetRoot::IsSolutionReached ( math_FunctionSetWithDerivatives & F )
virtual

This routine is called at the end of each iteration to check if the solution was found. It can be redefined in a sub-class to implement a specific test to stop the iterations. In this case, the solution is found when: abs(Xi - Xi-1) <= Tolerance for all unknowns.

 Standard_Integer math_FunctionSetRoot::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 math_FunctionSetRoot::Perform ( math_FunctionSetWithDerivatives & theFunction, const math_Vector & theStartingPoint, const Standard_Boolean theStopOnDivergent = `Standard_False` )

Improves the root of function from the initial guess point. The infinum and supremum may be given to constrain the solution. In this case, the solution is found when: abs(Xi - Xi-1)(j) <= Tolerance(j) for all unknowns.

 void math_FunctionSetRoot::Perform ( math_FunctionSetWithDerivatives & theFunction, const math_Vector & theStartingPoint, const math_Vector & theInfBound, const math_Vector & theSupBound, const Standard_Boolean theStopOnDivergent = `Standard_False` )

Improves the root of function from the initial guess point. The infinum and supremum may be given to constrain the solution. In this case, the solution is found when: abs(Xi - Xi-1) <= Tolerance for all unknowns.

 const math_Vector& math_FunctionSetRoot::Root ( ) const

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

 void math_FunctionSetRoot::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.

 void math_FunctionSetRoot::SetTolerance ( const math_Vector & Tolerance )

Initializes the tolerance values.

 Standard_Integer math_FunctionSetRoot::StateNumber ( ) const

returns the stateNumber (as returned by F.GetStateNumber()) associated to the root found.

## Field Documentation

 math_Vector math_FunctionSetRoot::Delta
protected
 math_Matrix math_FunctionSetRoot::DF
protected
 math_Vector math_FunctionSetRoot::Sol
protected
 math_Vector math_FunctionSetRoot::Tol
protected

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