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// File: math_NewtonMinimum.cxx
// Created: Fri May 3 09:33:31 1996
// Author: Philippe MANGIN
// <pmn@sgi38>
//#ifndef DEB
#define No_Standard_RangeError
#define No_Standard_OutOfRange
#define No_Standard_DimensionError
//#endif
#include <math_NewtonMinimum.ixx>
#include <math_Gauss.hxx>
#include <math_Jacobi.hxx>
//============================================================================
math_NewtonMinimum::math_NewtonMinimum(math_MultipleVarFunctionWithHessian& F,
const math_Vector& StartingPoint,
const Standard_Real Tolerance,
const Standard_Integer NbIterations,
const Standard_Real Convexity,
const Standard_Boolean WithSingularity)
//============================================================================
: TheLocation(1, F.NbVariables()),
TheGradient(1, F.NbVariables()),
TheStep(1, F.NbVariables(), 10*Tolerance),
TheHessian(1, F.NbVariables(), 1, F.NbVariables() )
{
XTol = Tolerance;
CTol = Convexity;
Itermax = NbIterations;
NoConvexTreatement = WithSingularity;
Convex = Standard_True;
// Done = Standard_True;
// TheStatus = math_OK;
Perform ( F, StartingPoint);
}
//============================================================================
math_NewtonMinimum::math_NewtonMinimum(math_MultipleVarFunctionWithHessian& F,
const Standard_Real Tolerance,
const Standard_Integer NbIterations,
const Standard_Real Convexity,
const Standard_Boolean WithSingularity)
//============================================================================
: TheLocation(1, F.NbVariables()),
TheGradient(1, F.NbVariables()),
TheStep(1, F.NbVariables(), 10*Tolerance),
TheHessian(1, F.NbVariables(), 1, F.NbVariables() )
{
XTol = Tolerance;
CTol = Convexity;
Itermax = NbIterations;
NoConvexTreatement = WithSingularity;
Convex = Standard_True;
Done = Standard_False;
TheStatus = math_NotBracketed;
}
//============================================================================
void math_NewtonMinimum::Delete()
{}
//============================================================================
void math_NewtonMinimum::Perform(math_MultipleVarFunctionWithHessian& F,
const math_Vector& StartingPoint)
//============================================================================
{
math_Vector Point1 (1, F.NbVariables());
Point1 = StartingPoint;
math_Vector Point2(1, F.NbVariables());
math_Vector* precedent = &Point1;
math_Vector* suivant = &Point2;
math_Vector* auxiliaire = precedent;
Standard_Boolean Ok = Standard_True;
Standard_Integer NbConv = 0, ii, Nreduction;
Standard_Real VPrecedent, VItere;
Done = Standard_True;
TheStatus = math_OK;
nbiter = 0;
while ( Ok && (NbConv < 2) ) {
nbiter++;
// Positionnement
Ok = F.Values(*precedent, VPrecedent, TheGradient, TheHessian);
if (!Ok) {
Done = Standard_False;
TheStatus = math_FunctionError;
return;
}
if (nbiter==1) {
PreviousMinimum = VPrecedent;
TheMinimum = VPrecedent;
}
// Traitement de la non convexite
math_Jacobi CalculVP(TheHessian);
if ( !CalculVP.IsDone() ) {
Done = Standard_False;
TheStatus = math_FunctionError;
return;
}
MinEigenValue = CalculVP.Values() ( CalculVP.Values().Min());
if ( MinEigenValue < CTol) {
Convex = Standard_False;
if (NoConvexTreatement) {
Standard_Real Delta = CTol+0.1*Abs(MinEigenValue) -MinEigenValue ;
for (ii=1; ii<=TheGradient.Length(); ii++) {
TheHessian(ii, ii) += Delta;
}
}
else {
TheStatus = math_FunctionError;
return;
}
}
// Schemas de Newton
math_Gauss LU(TheHessian, CTol/100);
if ( !LU.IsDone()) {
Done = Standard_False;
TheStatus = math_DirectionSearchError;
return;
}
LU.Solve(TheGradient, TheStep);
*suivant = *precedent - TheStep;
// Gestion de la convergence
F.Value(*suivant, TheMinimum);
if (IsConverged()) { NbConv++; }
else { NbConv=0; }
// Controle et corrections.
VItere = TheMinimum;
TheMinimum = PreviousMinimum;
Nreduction =0;
while (VItere > VPrecedent && Nreduction < 10) {
TheStep *= 0.4;
*suivant = *precedent - TheStep;
F.Value(*suivant, VItere);
Nreduction++;
}
if (VItere <= VPrecedent) {
auxiliaire = precedent;
precedent = suivant;
suivant = auxiliaire;
PreviousMinimum = VPrecedent;
TheMinimum = VItere;
Ok = (nbiter < Itermax);
if (!Ok && NbConv < 2) TheStatus = math_TooManyIterations;
}
else {
Ok = Standard_False;
TheStatus = math_DirectionSearchError;
}
}
TheLocation = *precedent;
}
//============================================================================
Standard_Boolean math_NewtonMinimum::IsConverged() const
//============================================================================
{
return ( (TheStep.Norm() <= XTol ) ||
( Abs(TheMinimum-PreviousMinimum) <= XTol*Abs(PreviousMinimum) ));
}
//============================================================================
void math_NewtonMinimum::Dump(Standard_OStream& o) const
//============================================================================
{
o<< "math_Newton Optimisation: ";
o << " Done =" << Done << endl;
o << " Status = " << (Standard_Integer)TheStatus << endl;
o <<" Location Vector = " << Location() << endl;
o <<" Minimum value = "<< Minimum()<< endl;
o <<" Previous value = "<< PreviousMinimum << endl;
o <<" Number of iterations = " <<NbIterations() << endl;
o <<" Convexity = " << Convex << endl;
o <<" Eigen Value = " << MinEigenValue << endl;
}
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