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TKMath
math


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)
.

#include <math_Uzawa.hxx>


Public Member Functions

void * operator new (size_t, void *anAddress)
void * operator new (size_t size)
void operator delete (void *anAddress)
Standard_EXPORT 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 maximun 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 ConstuctionError is raised if the line number
of Cont is different from the length of Secont.
.
Standard_EXPORT 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 maximun 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 ConstuctionError is raised if the line number
of Cont is different from the length of Secont and from
Nce + Nci.
.
Standard_Boolean IsDone () const
 Returns true if the computations are successful, otherwise returns false.
.
const math_VectorValue () const
 Returns the vector solution of the system above.
An exception is raised if NotDone.
.
const math_VectorInitialError () const
 Returns the initial error Cont*StartingPoint-Secont.
An exception is raised if NotDone.
.
Standard_EXPORT void Duale (math_Vector &V) const
 returns the duale variables V of the systeme.

const math_VectorError () const
 Returns the difference between X solution and the
StartingPoint.
An exception is raised if NotDone.
.
Standard_Integer NbIterations () const
 returns the number of iterations really done.
An exception is raised if NotDone.

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.

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

Protected Member Functions

Standard_EXPORT 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.
.

Private Attributes

math_Vector Resul
math_Vector Erruza
math_Vector Errinit
math_Vector Vardua
math_Matrix CTCinv
Standard_Integer NbIter
Standard_Boolean Done


Constructor & Destructor Documentation

Standard_EXPORT 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
 

Standard_EXPORT 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
 


Member Function Documentation

Standard_EXPORT void math_Uzawa::Duale math_Vector V  )  const
 

Standard_EXPORT void math_Uzawa::Dump Standard_OStream o  )  const
 

const math_Vector & math_Uzawa::Error  )  const [inline]
 

const math_Vector & math_Uzawa::InitialError  )  const [inline]
 

const math_Matrix & math_Uzawa::InverseCont  )  const [inline]
 

Standard_Boolean math_Uzawa::IsDone  )  const [inline]
 

Standard_Integer math_Uzawa::NbIterations  )  const [inline]
 

void math_Uzawa::operator delete void *  anAddress  )  [inline]
 

void* math_Uzawa::operator new size_t  size  )  [inline]
 

void* math_Uzawa::operator new size_t  ,
void *  anAddress
[inline]
 

Standard_EXPORT 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]
 

const math_Vector & math_Uzawa::Value  )  const [inline]
 


Field Documentation

math_Matrix math_Uzawa::CTCinv [private]
 

Standard_Boolean math_Uzawa::Done [private]
 

math_Vector math_Uzawa::Errinit [private]
 

math_Vector math_Uzawa::Erruza [private]
 

Standard_Integer math_Uzawa::NbIter [private]
 

math_Vector math_Uzawa::Resul [private]
 

math_Vector math_Uzawa::Vardua [private]
 


The documentation for this class was generated from the following files:
Generated on Mon Aug 25 13:12:47 2008 for OpenCASCADE by  doxygen 1.4.1