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//static const char* sccsid = "@(#)math_BFGS.cxx 3.2 95/01/10"; // Do not delete this line. Used by sccs.
//#ifndef DEB
#define No_Standard_RangeError
#define No_Standard_OutOfRange
#define No_Standard_DimensionError
//#endif
#include <math_BFGS.ixx>
#include <math_BracketMinimum.hxx>
#include <math_BrentMinimum.hxx>
#include <math_FunctionWithDerivative.hxx>
#include <math_MultipleVarFunctionWithGradient.hxx>
#include <math_Matrix.hxx>
#define R 0.61803399
#define C (1.0-R)
#define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);
#define SIGN(a, b) ((b) > 0.0 ? fabs(a) : -fabs(a))
#define MOV3(a,b,c, d, e, f) (a)=(d); (b)= (e); (c)=(f);
// l'utilisation de math_BrentMinumim pur trouver un minimum dans une direction
// donnee n'est pas du tout optimale. voir peut etre interpolation cubique
// classique et aussi essayer "recherche unidimensionnelle economique"
// PROGRAMMATION MATHEMATIQUE (theorie et algorithmes) tome1 page 82.
class DirFunction : public math_FunctionWithDerivative {
math_Vector *P0;
math_Vector *Dir;
math_Vector *P;
math_Vector *G;
math_MultipleVarFunctionWithGradient *F;
public :
DirFunction(math_Vector& V1,
math_Vector& V2,
math_Vector& V3,
math_Vector& V4,
math_MultipleVarFunctionWithGradient& f) ;
void Initialize(const math_Vector& p0, const math_Vector& dir) const;
void TheGradient(math_Vector& Grad);
virtual Standard_Boolean Value(const Standard_Real x, Standard_Real& fval) ;
virtual Standard_Boolean Values(const Standard_Real x, Standard_Real& fval, Standard_Real& D) ;
virtual Standard_Boolean Derivative(const Standard_Real x, Standard_Real& D) ;
};
DirFunction::DirFunction(math_Vector& V1,
math_Vector& V2,
math_Vector& V3,
math_Vector& V4,
math_MultipleVarFunctionWithGradient& f) {
P0 = &V1;
Dir = &V2;
P = &V3;
F = &f;
G = &V4;
}
void DirFunction::Initialize(const math_Vector& p0,
const math_Vector& dir) const{
*P0 = p0;
*Dir = dir;
}
void DirFunction::TheGradient(math_Vector& Grad) {
Grad = *G;
}
Standard_Boolean DirFunction::Value(const Standard_Real x,
Standard_Real& fval)
{
*P = *Dir;
P->Multiply(x);
P->Add(*P0);
F->Value(*P, fval);
return Standard_True;
}
Standard_Boolean DirFunction::Values(const Standard_Real x,
Standard_Real& fval,
Standard_Real& D)
{
*P = *Dir;
P->Multiply(x);
P->Add(*P0);
F->Values(*P, fval, *G);
D = (*G).Multiplied(*Dir);
return Standard_True;
}
Standard_Boolean DirFunction::Derivative(const Standard_Real x,
Standard_Real& D)
{
*P = *Dir;
P->Multiply(x);
P->Add(*P0);
Standard_Real fval;
F->Values(*P, fval, *G);
D = (*G).Multiplied(*Dir);
return Standard_True;
}
static Standard_Boolean MinimizeDirection(math_Vector& P,
Standard_Real F0,
math_Vector& Gr,
math_Vector& Dir,
Standard_Real& Result,
DirFunction& F) {
Standard_Real ax, xx, bx, Fax, Fxx, Fbx, F1;
F.Initialize(P, Dir);
Standard_Real dy1, Hnr1, lambda, alfa=0;
dy1 = Gr*Dir;
if (dy1 != 0) {
Hnr1 = Dir.Norm2();
alfa = 0.7*(-F0)/dy1;
lambda = 0.015/Sqrt(Hnr1);
}
else lambda = 1.0;
if (lambda > alfa) lambda = alfa;
F.Value(lambda, F1);
math_BracketMinimum Bracket(F, 0.0, lambda, F0, F1);
if(Bracket.IsDone()) {
Bracket.Values(ax, xx, bx);
Bracket.FunctionValues(Fax, Fxx, Fbx);
Standard_Integer niter = 100;
Standard_Real tol = 1.e-03;
math_BrentMinimum Sol(tol, Fxx, niter, 1.e-08);
Sol.Perform(F, ax, xx, bx);
if(Sol.IsDone()) {
Standard_Real Scale = Sol.Location();
Result = Sol.Minimum();
Dir.Multiply(Scale);
P.Add(Dir);
return Standard_True;
}
}
return Standard_False;
}
void math_BFGS::Perform(math_MultipleVarFunctionWithGradient& F,
const math_Vector& StartingPoint) {
Standard_Boolean Good;
Standard_Integer n = TheLocation.Length();
Standard_Integer j, i;
Standard_Real fae, fad, fac;
math_Vector xi(1, n), dg(1, n), hdg(1, n);
math_Matrix hessin(1, n, 1, n);
hessin.Init(0.0);
math_Vector Temp1(1, n);
math_Vector Temp2(1, n);
math_Vector Temp3(1, n);
math_Vector Temp4(1, n);
DirFunction F_Dir(Temp1, Temp2, Temp3, Temp4, F);
TheLocation = StartingPoint;
Good = F.Values(TheLocation, PreviousMinimum, TheGradient);
if(!Good) {
Done = Standard_False;
TheStatus = math_FunctionError;
return;
}
for(i = 1; i <= n; i++) {
hessin(i, i) = 1.0;
xi(i) = -TheGradient(i);
}
for(nbiter = 1; nbiter <= Itermax; nbiter++) {
TheMinimum = PreviousMinimum;
Standard_Boolean IsGood = MinimizeDirection(TheLocation, TheMinimum,
TheGradient,
xi, TheMinimum, F_Dir);
if(!IsGood) {
Done = Standard_False;
TheStatus = math_DirectionSearchError;
return;
}
if(IsSolutionReached(F)) {
Done = Standard_True;
TheStatus = math_OK;
return;
}
if (nbiter == Itermax) {
Done = Standard_False;
TheStatus = math_TooManyIterations;
return;
}
PreviousMinimum = TheMinimum;
dg = TheGradient;
Good = F.Values(TheLocation, TheMinimum, TheGradient);
if(!Good) {
Done = Standard_False;
TheStatus = math_FunctionError;
return;
}
for(i = 1; i <= n; i++) {
dg(i) = TheGradient(i) - dg(i);
}
for(i = 1; i <= n; i++) {
hdg(i) = 0.0;
for (j = 1; j <= n; j++)
hdg(i) += hessin(i, j) * dg(j);
}
fac = fae = 0.0;
for(i = 1; i <= n; i++) {
fac += dg(i) * xi(i);
fae += dg(i) * hdg(i);
}
fac = 1.0 / fac;
fad = 1.0 / fae;
for(i = 1; i <= n; i++)
dg(i) = fac * xi(i) - fad * hdg(i);
for(i = 1; i <= n; i++)
for(j = 1; j <= n; j++)
hessin(i, j) += fac * xi(i) * xi(j)
- fad * hdg(i) * hdg(j) + fae * dg(i) * dg(j);
for(i = 1; i <= n; i++) {
xi(i) = 0.0;
for (j = 1; j <= n; j++) xi(i) -= hessin(i, j) * TheGradient(j);
}
}
Done = Standard_False;
TheStatus = math_TooManyIterations;
return;
}
Standard_Boolean math_BFGS::IsSolutionReached(
math_MultipleVarFunctionWithGradient&) const {
return 2.0 * fabs(TheMinimum - PreviousMinimum) <=
XTol * (fabs(TheMinimum) + fabs(PreviousMinimum) + EPSZ);
}
math_BFGS::math_BFGS(math_MultipleVarFunctionWithGradient& F,
const math_Vector& StartingPoint,
const Standard_Real Tolerance,
const Standard_Integer NbIterations,
const Standard_Real ZEPS)
: TheLocation(1, StartingPoint.Length()),
TheGradient(1, StartingPoint.Length()) {
XTol = Tolerance;
EPSZ = ZEPS;
Itermax = NbIterations;
Perform(F, StartingPoint);
}
math_BFGS::math_BFGS(math_MultipleVarFunctionWithGradient& F,
const Standard_Real Tolerance,
const Standard_Integer NbIterations,
const Standard_Real ZEPS)
: TheLocation(1, F.NbVariables()),
TheGradient(1, F.NbVariables()) {
XTol = Tolerance;
EPSZ = ZEPS;
Itermax = NbIterations;
}
void math_BFGS::Delete()
{}
void math_BFGS::Dump(Standard_OStream& o) const {
o<< "math_BFGS resolution: ";
if(Done) {
o << " Status = Done \n";
o <<" Location Vector = " << Location() << "\n";
o <<" Minimum value = "<< Minimum()<<"\n";
o <<" Number of iterations = "<<NbIterations() <<"\n";;
}
else {
o<< " Status = not Done because " << (Standard_Integer)TheStatus << "\n";
}
}
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