Open CASCADE Technology
7.1.0.beta

This class computes the root of a set of N functions of N variables, knowing an initial guess at the solution and using the Newton Raphson algorithm. Knowledge of all the partial derivatives (Jacobian) is required. More...
#include <math_NewtonFunctionSetRoot.hxx>
Public Member Functions  
math_NewtonFunctionSetRoot (math_FunctionSetWithDerivatives &theFunction, const math_Vector &theXTolerance, const Standard_Real theFTolerance, const Standard_Integer tehNbIterations=100)  
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_NewtonFunctionSetRoot (math_FunctionSetWithDerivatives &theFunction, const Standard_Real theFTolerance, const Standard_Integer theNbIterations=100)  
This constructor should be used in a subclass 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 before performing the algorithm. More...  
virtual  ~math_NewtonFunctionSetRoot () 
Destructor. More...  
void  SetTolerance (const math_Vector &XTol) 
Initializes the tolerance values for the unknowns. More...  
void  Perform (math_FunctionSetWithDerivatives &theFunction, const math_Vector &theStartingPoint) 
The Newton method is done to improve the root of the function from the initial guess point. The solution is found when: abs(Xj  Xj1)(i) <= XTol(i) and abs(Fi) <= FTol for all i;. More...  
void  Perform (math_FunctionSetWithDerivatives &theFunction, const math_Vector &theStartingPoint, const math_Vector &theInfBound, const math_Vector &theSupBound) 
The Newton method is done to improve the root of the function from the initial guess point. Bounds may be given, to constrain the solution. The solution is found when: abs(Xj  Xj1)(i) <= XTol(i) and abs(Fi) <= FTol for all i;. More...  
virtual Standard_Boolean  IsSolutionReached (math_FunctionSetWithDerivatives &F) 
This method is called at the end of each iteration to check if the solution is found. Vectors DeltaX, Fvalues and Jacobian Matrix are consistent with the possible solution Vector Sol and can be inspected to decide whether the solution is reached or not. More...  
Standard_Boolean  IsDone () const 
Returns true if the computations are successful, otherwise returns false. More...  
const math_Vector &  Root () const 
Returns the value of the root of function F. Exceptions StdFail_NotDone if the algorithm fails (and IsDone returns false). 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...  
Standard_Integer  StateNumber () const 
Outputs the state number associated with the solution vector root. More...  
const math_Matrix &  Derivative () 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 range of Der is not equal to the range of the StartingPoint. More...  
const math_Vector &  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. 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...  
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...  
void  Dump (Standard_OStream &o) const 
Prints information on the current state of the object. Is used to redefine the operator <<. More...  
Protected Attributes  
math_Vector  TolX 
Standard_Real  TolF 
math_IntegerVector  Indx 
math_Vector  Scratch 
math_Vector  Sol 
math_Vector  DeltaX 
math_Vector  FValues 
math_Matrix  Jacobian 
This class computes the root of a set of N functions of N variables, knowing an initial guess at the solution and using the Newton Raphson algorithm. Knowledge of all the partial derivatives (Jacobian) is required.
math_NewtonFunctionSetRoot::math_NewtonFunctionSetRoot  (  math_FunctionSetWithDerivatives &  theFunction, 
const math_Vector &  theXTolerance,  
const Standard_Real  theFTolerance,  
const Standard_Integer  tehNbIterations = 100 

) 
Initialize correctly all the fields of this class. The range (1, F.NbVariables()) must be especially respected for all vectors and matrix declarations.
math_NewtonFunctionSetRoot::math_NewtonFunctionSetRoot  (  math_FunctionSetWithDerivatives &  theFunction, 
const Standard_Real  theFTolerance,  
const Standard_Integer  theNbIterations = 100 

) 
This constructor should be used in a subclass 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 before performing the algorithm.

virtual 
Destructor.
const math_Matrix& math_NewtonFunctionSetRoot::Derivative  (  )  const 
Returns the matrix value of the derivative at the root. Exception NotDone is raised if the root was not found.
void math_NewtonFunctionSetRoot::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 range of Der is not equal to the range of the StartingPoint.
void math_NewtonFunctionSetRoot::Dump  (  Standard_OStream &  o  )  const 
Prints information on the current state of the object. Is used to redefine the operator <<.
const math_Vector& math_NewtonFunctionSetRoot::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_NewtonFunctionSetRoot::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_NewtonFunctionSetRoot::IsDone  (  )  const 
Returns true if the computations are successful, otherwise returns false.

virtual 
This method is called at the end of each iteration to check if the solution is found. Vectors DeltaX, Fvalues and Jacobian Matrix are consistent with the possible solution Vector Sol and can be inspected to decide whether the solution is reached or not.
Standard_Integer math_NewtonFunctionSetRoot::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_NewtonFunctionSetRoot::Perform  (  math_FunctionSetWithDerivatives &  theFunction, 
const math_Vector &  theStartingPoint  
) 
The Newton method is done to improve the root of the function from the initial guess point. The solution is found when: abs(Xj  Xj1)(i) <= XTol(i) and abs(Fi) <= FTol for all i;.
void math_NewtonFunctionSetRoot::Perform  (  math_FunctionSetWithDerivatives &  theFunction, 
const math_Vector &  theStartingPoint,  
const math_Vector &  theInfBound,  
const math_Vector &  theSupBound  
) 
The Newton method is done to improve the root of the function from the initial guess point. Bounds may be given, to constrain the solution. The solution is found when: abs(Xj  Xj1)(i) <= XTol(i) and abs(Fi) <= FTol for all i;.
const math_Vector& math_NewtonFunctionSetRoot::Root  (  )  const 
Returns the value of the root of function F. Exceptions StdFail_NotDone if the algorithm fails (and IsDone returns false).
void math_NewtonFunctionSetRoot::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_NewtonFunctionSetRoot::SetTolerance  (  const math_Vector &  XTol  ) 
Initializes the tolerance values for the unknowns.
Standard_Integer math_NewtonFunctionSetRoot::StateNumber  (  )  const 
Outputs the state number associated with the solution vector root.

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