# FoundationClasses
TKMath
math

# math_NewtonMinimum Class Reference

`#include <math_NewtonMinimum.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_NewtonMinimum (math_MultipleVarFunctionWithHessian &F, const math_Vector &StartingPoint, const Standard_Real Tolerance=1.0e-7, const Standard_Integer NbIterations=40, const Standard_Real Convexity=1.0e-6, const Standard_Boolean WithSingularity=Standard_True)
| -- Given the starting point StartingPoint, The tolerance required on the solution is given by Tolerance. Iteration are stopped if (!WithSingularity) and H(F(Xi)) is not definite positive (if the smaller eigenvalue of H < Convexity) or IsConverged() returns True for 2 successives Iterations. Warning: Obsolete Constructor (because IsConverged can not be redefined with this. )
Standard_EXPORT | math_NewtonMinimum (math_MultipleVarFunctionWithHessian &F, const Standard_Real Tolerance=1.0e-7, const Standard_Integer NbIterations=40, const Standard_Real Convexity=1.0e-6, const Standard_Boolean WithSingularity=Standard_True)
| The tolerance required on the solution is given by Tolerance. Iteration are stopped if (!WithSingularity) and H(F(Xi)) is not definite positive (if the smaller eigenvalue of H < Convexity) or IsConverged() returns True for 2 successives Iterations. Warning: This constructor do not computation .
virtual Standard_EXPORT void | Delete ()
virtual Standard_EXPORT | ~math_NewtonMinimum ()
Standard_EXPORT void | Perform (math_MultipleVarFunctionWithHessian &F, const math_Vector &StartingPoint)
| Search the solution. .
virtual Standard_EXPORT Standard_Boolean | IsConverged () const
| This method is called at the end of each iteration to check the convergence : || Xi+1 - Xi || < Tolerance or || F(Xi+1) - F(Xi)|| < Tolerance * || F(Xi) || It can be redefined in a sub-class to implement a specific test. .
Standard_Boolean | IsDone () const
| Tests if an error has occured. .
Standard_Boolean | IsConvex () const
| Tests if the Function is convexe during optimization. .
const math_Vector & | Location () const
| returns the location vector of the minimum. Exception NotDone is raised if an error has occured.
void | Location (math_Vector &Loc) const
| outputs the location vector of the minimum in Loc. Exception NotDone is raised if an error has occured. Exception DimensionError is raised if the range of Loc is not equal to the range of the StartingPoint.
Standard_Real | Minimum () const
| returns the value of the minimum. Exception NotDone is raised if the minimum was not found.
const math_Vector & | Gradient () const
| returns the gradient vector at the minimum. Exception NotDone is raised if an error has occured.the minimum was not found.
void | Gradient (math_Vector &Grad) const
| outputs the gradient vector at the minimum in Grad. Exception NotDone is raised if the minimum was not found. Exception DimensionError is raised if the range of Grad is not equal to the range of the StartingPoint.
Standard_Integer | NbIterations () const
| returns the number of iterations really done in the calculation of the minimum. The exception NotDone is raised if an error has occured.
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_Status | TheStatus
math_Vector | TheLocation
math_Vector | TheGradient
math_Vector | TheStep
math_Matrix | TheHessian
Standard_Real | PreviousMinimum
Standard_Real | TheMinimum
Standard_Real | MinEigenValue
Standard_Real | XTol
Standard_Real | CTol
Standard_Integer | nbiter
Standard_Boolean | NoConvexTreatement
Standard_Boolean | Convex

## Private Attributes

Standard_Boolean | Done
Standard_Integer | Itermax

## Constructor & Destructor Documentation

Standard_EXPORT math_NewtonMinimum::math_NewtonMinimum | ( | math_MultipleVarFunctionWithHessian & | F,
|  | const math_Vector & | StartingPoint,
|  | const Standard_Real | Tolerance = `1.0e-7`,
|  | const Standard_Integer | NbIterations = `40`,
|  | const Standard_Real | Convexity = `1.0e-6`,
|  | const Standard_Boolean | WithSingularity = `Standard_True`
| ) |

Standard_EXPORT math_NewtonMinimum::math_NewtonMinimum | ( | math_MultipleVarFunctionWithHessian & | F,
|  | const Standard_Real | Tolerance = `1.0e-7`,
|  | const Standard_Integer | NbIterations = `40`,
|  | const Standard_Real | Convexity = `1.0e-6`,
|  | const Standard_Boolean | WithSingularity = `Standard_True`
| ) |

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

## Member Function Documentation

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

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

void math_NewtonMinimum::Gradient | ( | math_Vector & | Grad | ) | const`[inline]`

const math_Vector & math_NewtonMinimum::Gradient | ( |  | ) | const`[inline]`

virtual Standard_EXPORT Standard_Boolean math_NewtonMinimum::IsConverged | ( |  | ) | const`[virtual]`

Standard_Boolean math_NewtonMinimum::IsConvex | ( |  | ) | const

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

void math_NewtonMinimum::Location | ( | math_Vector & | Loc | ) | const`[inline]`

const math_Vector & math_NewtonMinimum::Location | ( |  | ) | const`[inline]`

Standard_Real math_NewtonMinimum::Minimum | ( |  | ) | const`[inline]`

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

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

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

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

Standard_EXPORT void math_NewtonMinimum::Perform | ( | math_MultipleVarFunctionWithHessian & | F,
|  | const math_Vector & | StartingPoint
| ) |

## Field Documentation

Standard_Boolean math_NewtonMinimum::Convex `[protected]`

Standard_Real math_NewtonMinimum::CTol `[protected]`

Standard_Boolean math_NewtonMinimum::Done `[private]`

Standard_Integer math_NewtonMinimum::Itermax `[private]`

Standard_Real math_NewtonMinimum::MinEigenValue `[protected]`

Standard_Integer math_NewtonMinimum::nbiter `[protected]`

Standard_Boolean math_NewtonMinimum::NoConvexTreatement `[protected]`

Standard_Real math_NewtonMinimum::PreviousMinimum `[protected]`

math_Vector math_NewtonMinimum::TheGradient `[protected]`

math_Matrix math_NewtonMinimum::TheHessian `[protected]`

math_Vector math_NewtonMinimum::TheLocation `[protected]`

Standard_Real math_NewtonMinimum::TheMinimum `[protected]`

math_Status math_NewtonMinimum::TheStatus `[protected]`

math_Vector math_NewtonMinimum::TheStep `[protected]`

Standard_Real math_NewtonMinimum::XTol `[protected]`

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

- math_NewtonMinimum.hxx
- math_NewtonMinimum.lxx