Open CASCADE Technology
7.7.0
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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 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. More... | |
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. More... | |
virtual | ~math_FunctionSetRoot () |
Destructor. More... | |
void | SetTolerance (const math_Vector &Tolerance) |
Initializes the tolerance values. More... | |
virtual Standard_Boolean | IsSolutionReached (math_FunctionSetWithDerivatives &) |
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. 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 - Xi-1)(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 - Xi-1) <= 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 |
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) |
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.
math_FunctionSetRoot::math_FunctionSetRoot | ( | math_FunctionSetWithDerivatives & | F, |
const Standard_Integer | NbIterations = 100 |
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) |
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.
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virtual |
Destructor.
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inline |
Returns the matrix value of the derivative at the root. Exception NotDone is raised if the root was not found.
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inline |
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 <<.
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inline |
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.
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inline |
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inline |
Returns true if the computations are successful, otherwise returns false.
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inlinevirtual |
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.
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inline |
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 Standard_Boolean | theStopOnDivergent = Standard_False |
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) |
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 - Xi-1)(j) <= Tolerance(j) for all unknowns.
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 |
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) |
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 - Xi-1) <= Tolerance for all unknowns.
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inline |
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.
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inline |
returns the stateNumber (as returned by F.GetStateNumber()) associated to the root found.
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