# FoundationClasses
TKMath
math

# math_NewtonFunctionSetRoot Class Reference

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.
.

`#include <math_NewtonFunctionSetRoot.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_NewtonFunctionSetRoot (math_FunctionSetWithDerivatives &F, const math_Vector &XTol, const Standard_Real FTol, const Standard_Integer NbIterations=100)
| This constructor should be 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_NewtonFunctionSetRoot (math_FunctionSetWithDerivatives &F, const Standard_Real FTol, const Standard_Integer NbIterations=100)
| This constructor should be 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 before performing the algorithm. .
Standard_EXPORT | math_NewtonFunctionSetRoot (math_FunctionSetWithDerivatives &F, const math_Vector &StartingPoint, const math_Vector &XTol, const Standard_Real FTol, const Standard_Integer NbIterations=100)
| The Newton method is done to improve the root of the function F from the initial guess StartingPoint. The tolerance required on the root is given by Tolerance. The solution is found when : abs(Xj - Xj-1)(i) <= XTol(i) and abs(Fi) <= FTol for all i; The maximum number of iterations allowed is given by NbIterations. .
Standard_EXPORT | math_NewtonFunctionSetRoot (math_FunctionSetWithDerivatives &F, const math_Vector &StartingPoint, const math_Vector &InfBound, const math_Vector &SupBound, const math_Vector &XTol, const Standard_Real FTol, const Standard_Integer NbIterations=100)
| The Newton method is done to improve the root of the function F from the initial guess StartingPoint. The tolerance required on the root is given by Tolerance. The solution is found when : abs(Xj - Xj-1)(i) <= XTol(i) and abs(Fi) <= FTol for all i; The maximum number of iterations allowed is given by NbIterations. .
virtual Standard_EXPORT void | Delete ()
virtual Standard_EXPORT | ~math_NewtonFunctionSetRoot ()
Standard_EXPORT void | SetTolerance (const math_Vector &XTol)
| Initializes the tolerance values for the unknowns. .
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 must be called when the solution is not computed by the constructors. .
virtual Standard_EXPORT 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. .
Standard_Boolean | IsDone () const
| Returns true if the computations are successful, otherwise returns false. .
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). .
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.
Standard_Integer | StateNumber () const
| Outputs the state number associated with the solution vector root. .
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. .
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. .
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. .
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_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_EXPORT void | Dump (Standard_OStream &o) const
| Prints information on the current state of the object. Is used to redefine the operator <<. .

## 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

## Private Attributes

Standard_Boolean | Done
Standard_Integer | State
Standard_Integer | Iter
Standard_Integer | Itermax

## Constructor & Destructor Documentation

Standard_EXPORT math_NewtonFunctionSetRoot::math_NewtonFunctionSetRoot | ( | math_FunctionSetWithDerivatives & | F,
|  | const math_Vector & | XTol,
|  | const Standard_Real | FTol,
|  | const Standard_Integer | NbIterations = `100`
| ) |

Standard_EXPORT math_NewtonFunctionSetRoot::math_NewtonFunctionSetRoot | ( | math_FunctionSetWithDerivatives & | F,
|  | const Standard_Real | FTol,
|  | const Standard_Integer | NbIterations = `100`
| ) |

Standard_EXPORT math_NewtonFunctionSetRoot::math_NewtonFunctionSetRoot | ( | math_FunctionSetWithDerivatives & | F,
|  | const math_Vector & | StartingPoint,
|  | const math_Vector & | XTol,
|  | const Standard_Real | FTol,
|  | const Standard_Integer | NbIterations = `100`
| ) |

Standard_EXPORT math_NewtonFunctionSetRoot::math_NewtonFunctionSetRoot | ( | math_FunctionSetWithDerivatives & | F,
|  | const math_Vector & | StartingPoint,
|  | const math_Vector & | InfBound,
|  | const math_Vector & | SupBound,
|  | const math_Vector & | XTol,
|  | const Standard_Real | FTol,
|  | const Standard_Integer | NbIterations = `100`
| ) |

virtual Standard_EXPORT math_NewtonFunctionSetRoot::~math_NewtonFunctionSetRoot | ( |  | ) | `[inline, virtual]`

## Member Function Documentation

virtual Standard_EXPORT void math_NewtonFunctionSetRoot::Delete | ( |  | ) | `[virtual]`

void math_NewtonFunctionSetRoot::Derivative | ( | math_Matrix & | Der | ) | const`[inline]`

const math_Matrix & math_NewtonFunctionSetRoot::Derivative | ( |  | ) | const`[inline]`

Standard_EXPORT void math_NewtonFunctionSetRoot::Dump | ( | Standard_OStream & | o | ) | const

void math_NewtonFunctionSetRoot::FunctionSetErrors | ( | math_Vector & | Err | ) | const`[inline]`

const math_Vector & math_NewtonFunctionSetRoot::FunctionSetErrors | ( |  | ) | const`[inline]`

Standard_Boolean math_NewtonFunctionSetRoot::IsDone | ( |  | ) | const`[inline]`

virtual Standard_EXPORT Standard_Boolean math_NewtonFunctionSetRoot::IsSolutionReached | ( | math_FunctionSetWithDerivatives & | F | ) | `[virtual]`

Standard_Integer math_NewtonFunctionSetRoot::NbIterations | ( |  | ) | const`[inline]`

void math_NewtonFunctionSetRoot::operator delete | ( | void * | anAddress | ) | `[inline]`

void* math_NewtonFunctionSetRoot::operator new | ( | size_t | size | ) | `[inline]`

void* math_NewtonFunctionSetRoot::operator new | ( | size_t | ,
|  | void * | anAddress
| ) | `[inline]`

Standard_EXPORT void math_NewtonFunctionSetRoot::Perform | ( | math_FunctionSetWithDerivatives & | F,
|  | const math_Vector & | StartingPoint,
|  | const math_Vector & | InfBound,
|  | const math_Vector & | SupBound
| ) |

void math_NewtonFunctionSetRoot::Root | ( | math_Vector & | Root | ) | const`[inline]`

const math_Vector & math_NewtonFunctionSetRoot::Root | ( |  | ) | const`[inline]`

Standard_EXPORT void math_NewtonFunctionSetRoot::SetTolerance | ( | const math_Vector & | XTol | ) |

Standard_Integer math_NewtonFunctionSetRoot::StateNumber | ( |  | ) | const

## Field Documentation

math_Vector math_NewtonFunctionSetRoot::DeltaX `[protected]`

Standard_Boolean math_NewtonFunctionSetRoot::Done `[private]`

math_Vector math_NewtonFunctionSetRoot::FValues `[protected]`

math_IntegerVector math_NewtonFunctionSetRoot::Indx `[protected]`

Standard_Integer math_NewtonFunctionSetRoot::Iter `[private]`

Standard_Integer math_NewtonFunctionSetRoot::Itermax `[private]`

math_Matrix math_NewtonFunctionSetRoot::Jacobian `[protected]`

math_Vector math_NewtonFunctionSetRoot::Scratch `[protected]`

math_Vector math_NewtonFunctionSetRoot::Sol `[protected]`

Standard_Integer math_NewtonFunctionSetRoot::State `[private]`

Standard_Real math_NewtonFunctionSetRoot::TolF `[protected]`

math_Vector math_NewtonFunctionSetRoot::TolX `[protected]`

The documentation for this class was generated from the following files:

- math_NewtonFunctionSetRoot.hxx
- math_NewtonFunctionSetRoot.lxx