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TKMath
math


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.
.

#include <math_FunctionSetRoot.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_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.

Standard_EXPORT 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.

Standard_EXPORT math_FunctionSetRoot (math_FunctionSetWithDerivatives &F, const math_Vector &StartingPoint, const math_Vector &Tolerance, const Standard_Integer NbIterations=100)
 is used to improve the root of the function F
from the initial guess StartingPoint.
The maximum number of iterations allowed is given by
NbIterations.
In this case, the solution is found when:
abs(Xi - Xi-1)(j) <= Tolerance(j) for all unknowns.

Standard_EXPORT math_FunctionSetRoot (math_FunctionSetWithDerivatives &F, const math_Vector &StartingPoint, const math_Vector &Tolerance, const math_Vector &infBound, const math_Vector &supBound, const Standard_Integer NbIterations=100)
 is used to improve the root of the function F
from the initial guess StartingPoint.
The maximum number of iterations allowed is given
by NbIterations.
In this case, the solution is found when:
abs(Xi - Xi-1) <= Tolerance for all unknowns.

virtual Standard_EXPORT void Delete ()
virtual Standard_EXPORT ~math_FunctionSetRoot ()
Standard_EXPORT void SetTolerance (const math_Vector &Tolerance)
 Initializes the tolerance values.
.
Standard_EXPORT void Perform (math_FunctionSetWithDerivatives &F, const math_Vector &StartingPoint, const math_Vector &infBound, const math_Vector &supBound)
 Improves the root of function F from the initial guess
StartingPoint. infBound and supBound may be given to constrain the solution.
Warning
This method is called when computation of the solution is
not performed by the constructors.
.
virtual Standard_EXPORT 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.
.
Standard_Boolean IsDone () const
 Returns true if the computations are successful, otherwise returns false.
.
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.
.
Standard_Integer StateNumber () const
 returns the stateNumber (as returned by
F.GetStateNumber()) associated to the root found.

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

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.

Standard_EXPORT 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.

Standard_EXPORT 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_Vector Delta
math_Vector Sol
math_Matrix DF
math_Vector Tol

Private Attributes

Standard_Boolean Done
Standard_Integer Kount
Standard_Integer State
Standard_Integer Itermax
math_Vector InfBound
math_Vector SupBound
math_Vector SolSave
math_Vector GH
math_Vector DH
math_Vector DHSave
math_Vector FF
math_Vector PreviousSolution
math_Vector Save
math_IntegerVector Constraints
math_Vector Temp1
math_Vector Temp2
math_Vector Temp3
math_Vector Temp4


Constructor & Destructor Documentation

Standard_EXPORT math_FunctionSetRoot::math_FunctionSetRoot math_FunctionSetWithDerivatives F,
const math_Vector Tolerance,
const Standard_Integer  NbIterations = 100
 

Standard_EXPORT math_FunctionSetRoot::math_FunctionSetRoot math_FunctionSetWithDerivatives F,
const Standard_Integer  NbIterations = 100
 

Standard_EXPORT math_FunctionSetRoot::math_FunctionSetRoot math_FunctionSetWithDerivatives F,
const math_Vector StartingPoint,
const math_Vector Tolerance,
const Standard_Integer  NbIterations = 100
 

Standard_EXPORT math_FunctionSetRoot::math_FunctionSetRoot math_FunctionSetWithDerivatives F,
const math_Vector StartingPoint,
const math_Vector Tolerance,
const math_Vector infBound,
const math_Vector supBound,
const Standard_Integer  NbIterations = 100
 

virtual Standard_EXPORT math_FunctionSetRoot::~math_FunctionSetRoot  )  [inline, virtual]
 


Member Function Documentation

virtual Standard_EXPORT void math_FunctionSetRoot::Delete  )  [virtual]
 

void math_FunctionSetRoot::Derivative math_Matrix Der  )  const [inline]
 

const math_Matrix & math_FunctionSetRoot::Derivative  )  const [inline]
 

Standard_EXPORT void math_FunctionSetRoot::Dump Standard_OStream o  )  const
 

Standard_EXPORT void math_FunctionSetRoot::FunctionSetErrors math_Vector Err  )  const
 

const math_Vector & math_FunctionSetRoot::FunctionSetErrors  )  const [inline]
 

Standard_Boolean math_FunctionSetRoot::IsDone  )  const [inline]
 

virtual Standard_EXPORT Standard_Boolean math_FunctionSetRoot::IsSolutionReached math_FunctionSetWithDerivatives F  )  [virtual]
 

Standard_Integer math_FunctionSetRoot::NbIterations  )  const [inline]
 

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

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

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

Standard_EXPORT void math_FunctionSetRoot::Perform math_FunctionSetWithDerivatives F,
const math_Vector StartingPoint,
const math_Vector infBound,
const math_Vector supBound
 

Standard_EXPORT void math_FunctionSetRoot::Root math_Vector Root  )  const
 

const math_Vector & math_FunctionSetRoot::Root  )  const [inline]
 

Standard_EXPORT void math_FunctionSetRoot::SetTolerance const math_Vector Tolerance  ) 
 

Standard_Integer math_FunctionSetRoot::StateNumber  )  const [inline]
 


Field Documentation

math_IntegerVector math_FunctionSetRoot::Constraints [private]
 

math_Vector math_FunctionSetRoot::Delta [protected]
 

math_Matrix math_FunctionSetRoot::DF [protected]
 

math_Vector math_FunctionSetRoot::DH [private]
 

math_Vector math_FunctionSetRoot::DHSave [private]
 

Standard_Boolean math_FunctionSetRoot::Done [private]
 

math_Vector math_FunctionSetRoot::FF [private]
 

math_Vector math_FunctionSetRoot::GH [private]
 

math_Vector math_FunctionSetRoot::InfBound [private]
 

Standard_Integer math_FunctionSetRoot::Itermax [private]
 

Standard_Integer math_FunctionSetRoot::Kount [private]
 

math_Vector math_FunctionSetRoot::PreviousSolution [private]
 

math_Vector math_FunctionSetRoot::Save [private]
 

math_Vector math_FunctionSetRoot::Sol [protected]
 

math_Vector math_FunctionSetRoot::SolSave [private]
 

Standard_Integer math_FunctionSetRoot::State [private]
 

math_Vector math_FunctionSetRoot::SupBound [private]
 

math_Vector math_FunctionSetRoot::Temp1 [private]
 

math_Vector math_FunctionSetRoot::Temp2 [private]
 

math_Vector math_FunctionSetRoot::Temp3 [private]
 

math_Vector math_FunctionSetRoot::Temp4 [private]
 

math_Vector math_FunctionSetRoot::Tol [protected]
 


The documentation for this class was generated from the following files:
Generated on Mon Aug 25 13:12:45 2008 for OpenCASCADE by  doxygen 1.4.1