# math_Uzawa Class Reference

This class implements a system resolution C*X = B with an approach solution X0. There are no conditions on the number of equations. The algorithm used is the Uzawa algorithm. It is possible to have equal or inequal (<) equations to solve. The resolution is done with a minimization of Norm(X-X0). If there are only equal equations, the resolution is directly done and is similar to Gauss resolution with an optimisation because the matrix is a symmetric matrix. (The resolution is done with Crout algorithm) More...

`#include <math_Uzawa.hxx>`

## Public Member Functions

math_Uzawa (const math_Matrix &Cont, const math_Vector &Secont, const math_Vector &StartingPoint, const Standard_Real EpsLix=1.0e-06, const Standard_Real EpsLic=1.0e-06, const Standard_Integer NbIterations=500)
Given an input matrix Cont, two input vectors Secont and StartingPoint, it solves Cont*X = Secont (only = equations) with a minimization of Norme(X-X0). The maximum iterations number allowed is fixed to NbIterations. The tolerance EpsLic is fixed for the dual variable convergence. The tolerance EpsLix is used for the convergence of X. Exception ConstructionError is raised if the line number of Cont is different from the length of Secont. More...

math_Uzawa (const math_Matrix &Cont, const math_Vector &Secont, const math_Vector &StartingPoint, const Standard_Integer Nci, const Standard_Integer Nce, const Standard_Real EpsLix=1.0e-06, const Standard_Real EpsLic=1.0e-06, const Standard_Integer NbIterations=500)
Given an input matrix Cont, two input vectors Secont and StartingPoint, it solves Cont*X = Secont (the Nce first equations are equal equations and the Nci last equations are inequalities <) with a minimization of Norme(X-X0). The maximum iterations number allowed is fixed to NbIterations. The tolerance EpsLic is fixed for the dual variable convergence. The tolerance EpsLix is used for the convergence of X. There are no conditions on Nce and Nci. Exception ConstructionError is raised if the line number of Cont is different from the length of Secont and from Nce + Nci. More...

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

const math_VectorValue () const
Returns the vector solution of the system above. An exception is raised if NotDone. More...

const math_VectorInitialError () const
Returns the initial error Cont*StartingPoint-Secont. An exception is raised if NotDone. More...

void Duale (math_Vector &V) const
returns the duale variables V of the systeme. More...

const math_VectorError () const
Returns the difference between X solution and the StartingPoint. An exception is raised if NotDone. More...

Standard_Integer NbIterations () const
returns the number of iterations really done. An exception is raised if NotDone. More...

const math_MatrixInverseCont () const
returns the inverse matrix of (C * Transposed(C)). This result is needed for the computation of the gradient when approximating a curve. More...

void Dump (Standard_OStream &o) const
Prints information on the current state of the object. More...

## Protected Member Functions

void Perform (const math_Matrix &Cont, const math_Vector &Secont, const math_Vector &StartingPoint, const Standard_Integer Nci, const Standard_Integer Nce, const Standard_Real EpsLix=1.0e-06, const Standard_Real EpsLic=1.0e-06, const Standard_Integer NbIterations=500)
Is used internally by the two constructors above. More...

## Detailed Description

This class implements a system resolution C*X = B with an approach solution X0. There are no conditions on the number of equations. The algorithm used is the Uzawa algorithm. It is possible to have equal or inequal (<) equations to solve. The resolution is done with a minimization of Norm(X-X0). If there are only equal equations, the resolution is directly done and is similar to Gauss resolution with an optimisation because the matrix is a symmetric matrix. (The resolution is done with Crout algorithm)

## ◆ math_Uzawa() [1/2]

 math_Uzawa::math_Uzawa ( const math_Matrix & Cont, const math_Vector & Secont, const math_Vector & StartingPoint, const Standard_Real EpsLix = `1.0e-06`, const Standard_Real EpsLic = `1.0e-06`, const Standard_Integer NbIterations = `500` )

Given an input matrix Cont, two input vectors Secont and StartingPoint, it solves Cont*X = Secont (only = equations) with a minimization of Norme(X-X0). The maximum iterations number allowed is fixed to NbIterations. The tolerance EpsLic is fixed for the dual variable convergence. The tolerance EpsLix is used for the convergence of X. Exception ConstructionError is raised if the line number of Cont is different from the length of Secont.

## ◆ math_Uzawa() [2/2]

 math_Uzawa::math_Uzawa ( const math_Matrix & Cont, const math_Vector & Secont, const math_Vector & StartingPoint, const Standard_Integer Nci, const Standard_Integer Nce, const Standard_Real EpsLix = `1.0e-06`, const Standard_Real EpsLic = `1.0e-06`, const Standard_Integer NbIterations = `500` )

Given an input matrix Cont, two input vectors Secont and StartingPoint, it solves Cont*X = Secont (the Nce first equations are equal equations and the Nci last equations are inequalities <) with a minimization of Norme(X-X0). The maximum iterations number allowed is fixed to NbIterations. The tolerance EpsLic is fixed for the dual variable convergence. The tolerance EpsLix is used for the convergence of X. There are no conditions on Nce and Nci. Exception ConstructionError is raised if the line number of Cont is different from the length of Secont and from Nce + Nci.

## ◆ Duale()

 void math_Uzawa::Duale ( math_Vector & V ) const

returns the duale variables V of the systeme.

## ◆ Dump()

 void math_Uzawa::Dump ( Standard_OStream & o ) const

Prints information on the current state of the object.

## ◆ Error()

 const math_Vector& math_Uzawa::Error ( ) const

Returns the difference between X solution and the StartingPoint. An exception is raised if NotDone.

## ◆ InitialError()

 const math_Vector& math_Uzawa::InitialError ( ) const

Returns the initial error Cont*StartingPoint-Secont. An exception is raised if NotDone.

## ◆ InverseCont()

 const math_Matrix& math_Uzawa::InverseCont ( ) const

returns the inverse matrix of (C * Transposed(C)). This result is needed for the computation of the gradient when approximating a curve.

## ◆ IsDone()

 Standard_Boolean math_Uzawa::IsDone ( ) const

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

## ◆ NbIterations()

 Standard_Integer math_Uzawa::NbIterations ( ) const

returns the number of iterations really done. An exception is raised if NotDone.

## ◆ Perform()

 void math_Uzawa::Perform ( const math_Matrix & Cont, const math_Vector & Secont, const math_Vector & StartingPoint, const Standard_Integer Nci, const Standard_Integer Nce, const Standard_Real EpsLix = `1.0e-06`, const Standard_Real EpsLic = `1.0e-06`, const Standard_Integer NbIterations = `500` )
protected

Is used internally by the two constructors above.

## ◆ Value()

 const math_Vector& math_Uzawa::Value ( ) const

Returns the vector solution of the system above. An exception is raised if NotDone.

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