Open CASCADE Technology
7.6.0

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 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. More...  
math_FunctionSetRoot (math_FunctionSetWithDerivatives &F, const Standard_Integer NbIterations=100)  
is 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 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 subclass to implement a specific test to stop the iterations. In this case, the solution is found when: abs(Xi  Xi1) <= 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  Xi1)(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  Xi1) <= 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_Vector &  Root () 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_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 column 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...  
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 
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.
math_FunctionSetRoot::math_FunctionSetRoot  (  math_FunctionSetWithDerivatives &  F, 
const math_Vector &  Tolerance,  
const Standard_Integer  NbIterations = 100 

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

) 
is 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 after this constructor.

virtual 
Destructor.
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 
This routine is called at the end of each iteration to check if the solution was found. It can be redefined in a subclass to implement a specific test to stop the iterations. In this case, the solution is found when: abs(Xi  Xi1) <= 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 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  Xi1) <= Tolerance for all unknowns.
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  Xi1)(j) <= Tolerance(j) 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.

protected 

protected 

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protected 