// Copyright (c) 1997-1999 Matra Datavision
// Copyright (c) 1999-2014 OPEN CASCADE SAS
//
// This file is part of Open CASCADE Technology software library.
//
// This library is free software; you can redistribute it and/or modify it under
// the terms of the GNU Lesser General Public License version 2.1 as published
// by the Free Software Foundation, with special exception defined in the file
// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
// distribution for complete text of the license and disclaimer of any warranty.
//
// Alternatively, this file may be used under the terms of Open CASCADE
// commercial license or contractual agreement.
//#ifndef OCCT_DEBUG
#define No_Standard_RangeError
#define No_Standard_OutOfRange
#define No_Standard_DimensionError
//#endif
#include <math_DirectPolynomialRoots.hxx>
#include <math_FunctionRoots.hxx>
#include <math_FunctionWithDerivative.hxx>
#include <math_BracketedRoot.hxx>
#include <Standard_RangeError.hxx>
#include <StdFail_NotDone.hxx>
#include <TColStd_Array1OfReal.hxx>
#include <stdio.h>
#define ITMAX 100
#define EPS 1e-14
#define EPSEPS 2e-14
#define MAXBIS 100
#ifdef OCCT_DEBUG
static Standard_Boolean myDebug = 0;
static Standard_Integer nbsolve = 0;
#endif
class DerivFunction: public math_Function
{
math_FunctionWithDerivative *myF;
public:
DerivFunction(math_FunctionWithDerivative& theF)
: myF (&theF)
{}
virtual Standard_Boolean Value(const Standard_Real theX, Standard_Real& theFval)
{
return myF->Derivative(theX, theFval);
}
};
static void AppendRoot(TColStd_SequenceOfReal& Sol,
TColStd_SequenceOfInteger& NbStateSol,
const Standard_Real X,
math_FunctionWithDerivative& F,
// const Standard_Real K,
const Standard_Real ,
const Standard_Real dX) {
Standard_Integer n=Sol.Length();
Standard_Real t;
#ifdef OCCT_DEBUG
if (myDebug) {
std::cout << " Ajout de la solution numero : " << n+1 << std::endl;
std::cout << " Valeur de la racine :" << X << std::endl;
}
#endif
if(n==0) {
Sol.Append(X);
F.Value(X,t);
NbStateSol.Append(F.GetStateNumber());
}
else {
Standard_Integer i=1;
Standard_Integer pl=n+1;
while(i<=n) {
t=Sol.Value(i);
if(t >= X) {
pl=i;
i=n;
}
if(Abs(X-t) <= dX) {
pl=0;
i=n;
}
i++;
} //-- while
if(pl>n) {
Sol.Append(X);
F.Value(X,t);
NbStateSol.Append(F.GetStateNumber());
}
else if(pl>0) {
Sol.InsertBefore(pl,X);
F.Value(X,t);
NbStateSol.InsertBefore(pl,F.GetStateNumber());
}
}
}
static void Solve(math_FunctionWithDerivative& F,
const Standard_Real K,
const Standard_Real x1,
const Standard_Real y1,
const Standard_Real x2,
const Standard_Real y2,
const Standard_Real tol,
const Standard_Real dX,
TColStd_SequenceOfReal& Sol,
TColStd_SequenceOfInteger& NbStateSol) {
#ifdef OCCT_DEBUG
if (myDebug) {
std::cout <<"--> Resolution :" << ++nbsolve << std::endl;
std::cout <<" x1 =" << x1 << " y1 =" << y1 << std::endl;
std::cout <<" x2 =" << x2 << " y2 =" << y2 << std::endl;
}
#endif
Standard_Integer iter=0;
Standard_Real tols2 = 0.5*tol;
Standard_Real a,b,c,d=0,e=0,fa,fb,fc,p,q,r,s,tol1,xm,min1,min2;
a=x1;b=c=x2;fa=y1; fb=fc=y2;
for(iter=1;iter<=ITMAX;iter++) {
if((fb>0.0 && fc>0.0) || (fb<0.0 && fc<0.0)) {
c=a; fc=fa; e=d=b-a;
}
if(Abs(fc)<Abs(fb)) {
a=b; b=c; c=a; fa=fb; fb=fc; fc=fa;
}
tol1 = EPSEPS*Abs(b)+tols2;
xm=0.5*(c-b);
if(Abs(xm)<tol1 || fb==0) {
//-- On tente une iteration de newton
Standard_Real Xp,Yp,Dp;
Standard_Integer itern=5;
Standard_Boolean Ok;
Xp=b;
do {
Ok = F.Values(Xp,Yp,Dp);
if(Ok) {
Ok=Standard_False;
if(Dp>1e-10 || Dp<-1e-10) {
Xp = Xp-(Yp-K)/Dp;
}
if(Xp<=x2 && Xp>=x1) {
F.Value(Xp,Yp); Yp-=K;
if(Abs(Yp)<Abs(fb)) {
b=Xp;
fb=Yp;
Ok=Standard_True;
}
}
}
}
while(Ok && --itern>=0);
AppendRoot(Sol,NbStateSol,b,F,K,dX);
return;
}
if(Abs(e)>=tol1 && Abs(fa)>Abs(fb)) {
s=fb/fa;
if(a==c) {
p=xm*s; p+=p;
q=1.0-s;
}
else {
q=fa/fc;
r=fb/fc;
p=s*((xm+xm)*q*(q-r)-(b-a)*(r-1.0));
q=(q-1.0)*(r-1.0)*(s-1.0);
}
if(p>0.0) {
q=-q;
}
p=Abs(p);
min1=3.0*xm*q-Abs(tol1*q);
min2=Abs(e*q);
if((p+p)<( (min1<min2) ? min1 : min2)) {
e=d;
d=p/q;
}
else {
d=xm;
e=d;
}
}
else {
d=xm;
e=d;
}
a=b;
fa=fb;
if(Abs(d)>tol1) {
b+=d;
}
else {
if(xm>=0) b+=Abs(tol1);
else b+=-Abs(tol1);
}
F.Value(b,fb);
fb-=K;
}
#ifdef OCCT_DEBUG
std::cout<<" Non Convergence dans math_FunctionRoots.cxx "<<std::endl;
#endif
}
#define NEWSEQ 1
#define MATH_FUNCTIONROOTS_NEWCODE // Nv Traitement
//#define MATH_FUNCTIONROOTS_OLDCODE // Ancien
//#define MATH_FUNCTIONROOTS_CHECK // Check
math_FunctionRoots::math_FunctionRoots(math_FunctionWithDerivative& F,
const Standard_Real A,
const Standard_Real B,
const Standard_Integer NbSample,
const Standard_Real _EpsX,
const Standard_Real EpsF,
const Standard_Real EpsNull,
const Standard_Real K )
{
#ifdef OCCT_DEBUG
if (myDebug) {
std::cout << "---- Debut de math_FunctionRoots ----" << std::endl;
nbsolve = 0;
}
#endif
#if NEWSEQ
TColStd_SequenceOfReal StaticSol;
#endif
Sol.Clear();
NbStateSol.Clear();
#ifdef MATH_FUNCTIONROOTS_NEWCODE
{
Done = Standard_True;
Standard_Real X0=A;
Standard_Real XN=B;
Standard_Integer N=NbSample;
//-- ------------------------------------------------------------
//-- Verifications de bas niveau
if(B<A) {
X0=B;
XN=A;
}
N*=2;
if(N < 20) {
N=20;
}
//-- On teste si EpsX est trop petit (ie : U+Nn*EpsX == U )
Standard_Real EpsX = _EpsX;
Standard_Real DeltaU = Abs(X0)+Abs(XN);
Standard_Real NEpsX = 0.0000000001 * DeltaU;
if(EpsX < NEpsX) {
EpsX = NEpsX;
}
//-- recherche d un intervalle ou F(xi) et F(xj) sont de signes differents
//-- A .............................................................. B
//-- X0 X1 X2 ........................................ Xn-1 Xn
Standard_Integer i;
Standard_Real X=X0;
Standard_Boolean Ok;
double dx = (XN-X0)/N;
TColStd_Array1OfReal ptrval(0, N);
Standard_Integer Nvalid = -1;
Standard_Real aux = 0;
for(i=0; i<=N ; i++,X+=dx) {
if( X > XN) X=XN;
Ok=F.Value(X,aux);
if(Ok) ptrval(++Nvalid) = aux - K;
// ptrval(i)-=K;
}
//-- Toute la fonction est nulle ?
if( Nvalid < N ) {
Done = Standard_False;
return;
}
AllNull=Standard_True;
// for(i=0;AllNull && i<=N;i++) {
for(i=0;AllNull && i<=N;i++) {
if(ptrval(i)>EpsNull || ptrval(i)<-EpsNull) {
AllNull=Standard_False;
}
}
if(AllNull) {
//-- tous les points echantillons sont dans la tolerance
}
else {
//-- Il y a des points hors tolerance
//-- on detecte les changements de signes STRICTS
Standard_Integer ip1;
// Standard_Boolean chgtsign=Standard_False;
Standard_Real tol = EpsX;
Standard_Real X2;
for(i=0,ip1=1,X=X0;i<N; i++,ip1++,X+=dx) {
X2=X+dx;
if(X2 > XN) X2 = XN;
if(ptrval(i)<0.0) {
if(ptrval(ip1)>0.0) {
//-- --------------------------------------------------
//-- changement de signe dans Xi Xi+1
Solve(F,K,X,ptrval(i),X2,ptrval(ip1),tol,NEpsX,Sol,NbStateSol);
}
}
else {
if(ptrval(ip1)<0.0) {
//-- --------------------------------------------------
//-- changement de signe dans Xi Xi+1
Solve(F,K,X,ptrval(i),X2,ptrval(ip1),tol,NEpsX,Sol,NbStateSol);
}
}
}
//-- On detecte les cas ou la fct s annule sur des Xi et est
//-- non nulle au voisinage de Xi
//--
//-- On prend 2 points u0,u1 au voisinage de Xi
//-- Si (F(u0)-K)*(F(u1)-K) <0 on lance une recherche
//-- Sinon si (F(u0)-K)*(F(u1)-K) !=0 on insere le point X
for(i=0; i<=N; i++) {
if(ptrval(i)==0) {
// Standard_Real Val,Deriv;
X=X0+i*dx;
if (X>XN) X=XN;
Standard_Real u0,u1;
u0=dx*0.5; u1=X+u0; u0+=X;
if(u0<X0) u0=X0;
if(u0>XN) u0=XN;
if(u1<X0) u1=X0;
if(u1>XN) u1=XN;
Standard_Real y0,y1;
F.Value(u0,y0); y0-=K;
F.Value(u1,y1); y1-=K;
if(y0*y1 < 0.0) {
Solve(F,K,u0,y0,u1,y1,tol,NEpsX,Sol,NbStateSol);
}
else {
if(y0!=0.0 || y1!=0.0) {
AppendRoot(Sol,NbStateSol,X,F,K,NEpsX);
}
}
}
}
//-- --------------------------------------------------------------------------------
//-- Il faut traiter differement le cas des points en bout :
if(ptrval(0)<=EpsF && ptrval(0)>=-EpsF) {
AppendRoot(Sol,NbStateSol,X0,F,K,NEpsX);
}
if(ptrval(N)<=EpsF && ptrval(N)>=-EpsF) {
AppendRoot(Sol,NbStateSol,XN,F,K,NEpsX);
}
//-- --------------------------------------------------------------------------------
//-- --------------------------------------------------------------------------------
//-- On detecte les zones ou on a sur les points echantillons un minimum avec f(x)>0
//-- un maximum avec f(x)<0
//-- On reprend une discretisation plus fine au voisinage de ces extremums
//--
//-- Recherche d un minima positif
Standard_Real xm,ym,dym,xm1,xp1;
Standard_Real majdx = 5.0*dx;
Standard_Boolean Rediscr;
// Standard_Real ptrvalbis[MAXBIS];
Standard_Integer im1=0;
ip1=2;
for(i=1,xm=X0+dx; i<N; xm+=dx,i++,im1++,ip1++) {
Rediscr = Standard_False;
if (xm > XN) xm=XN;
if(ptrval(i)>0.0) {
if((ptrval(im1)>ptrval(i)) && (ptrval(ip1)>ptrval(i))) {
//-- Peut on traverser l axe Ox
//-- -------------- Estimation a partir de Xim1
xm1=xm-dx;
if(xm1 < X0) xm1=X0;
F.Values(xm1,ym,dym); ym-=K;
if(dym<-1e-10 || dym>1e-10) { // normalement dym < 0
Standard_Real t = ym / dym; //-- t=xm-x* = (ym-0)/dym
if(t<majdx && t > -majdx) {
Rediscr = Standard_True;
}
}
//-- -------------- Estimation a partir de Xip1
if(Rediscr==Standard_False) {
xp1=xm+dx;
if(xp1 > XN ) xp1=XN;
F.Values(xp1,ym,dym); ym-=K;
if(dym<-1e-10 || dym>1e-10) { // normalement dym > 0
Standard_Real t = ym / dym; //-- t=xm-x* = (ym-0)/dym
if(t<majdx && t > -majdx) {
Rediscr = Standard_True;
}
}
}
}
}
else if(ptrval(i)<0.0) {
if((ptrval(im1)<ptrval(i)) && (ptrval(ip1)<ptrval(i))) {
//-- Peut on traverser l axe Ox
//-- -------------- Estimation a partir de Xim1
xm1=xm-dx;
if(xm1 < X0) xm1=X0;
F.Values(xm1,ym,dym); ym-=K;
if(dym>1e-10 || dym<-1e-10) { // normalement dym > 0
Standard_Real t = ym / dym; //-- t=xm-x* = (ym-0)/dym
if(t<majdx && t > -majdx) {
Rediscr = Standard_True;
}
}
//-- -------------- Estimation a partir de Xim1
if(Rediscr==Standard_False) {
xm1=xm-dx;
if(xm1 < X0) xm1=X0;
F.Values(xm1,ym,dym); ym-=K;
if(dym>1e-10 || dym<-1e-10) { // normalement dym < 0
Standard_Real t = ym / dym; //-- t=xm-x* = (ym-0)/dym
if(t<majdx && t > -majdx) {
Rediscr = Standard_True;
}
}
}
}
}
if(Rediscr) {
Standard_Real x0 = xm - dx;
Standard_Real x3 = xm + dx;
if (x0 < X0) x0 = X0;
if (x3 > XN) x3 = XN;
Standard_Real aSolX1 = 0., aSolX2 = 0.;
Standard_Real aVal1 = 0., aVal2 = 0.;
Standard_Real aDer1 = 0., aDer2 = 0.;
Standard_Boolean isSol1 = Standard_False;
Standard_Boolean isSol2 = Standard_False;
//-- ----------------------------------------------------
//-- Find minimum of the function |F| between x0 and x3
//-- by searching for the zero of the function derivative
DerivFunction aDerF(F);
math_BracketedRoot aBR(aDerF, x0, x3, _EpsX);
if (aBR.IsDone())
{
aSolX1 = aBR.Root();
F.Value(aSolX1, aVal1);
aVal1 = Abs(aVal1);
if (aVal1 < EpsF)
{
isSol1 = Standard_True;
aDer1 = aBR.Value();
}
}
//-- --------------------------------------------------
//-- On recherche un extrema entre x0 et x3
//-- x1 et x2 sont tels que x0<x1<x2<x3
//-- et |f(x0)| > |f(x1)| et |f(x3)| > |f(x2)|
//--
//-- En entree : a=xm-dx b=xm c=xm+dx
Standard_Real x1, x2, f0, f3;
Standard_Real R = 0.61803399;
Standard_Real C = 1.0 - R;
Standard_Real tolCR = NEpsX*10.0;
f0 = ptrval(im1);
f3 = ptrval(ip1);
Standard_Boolean recherche_minimum = (f0 > 0.0);
if (Abs(x3 - xm) > Abs(x0 - xm)) { x1 = xm; x2 = xm + C*(x3 - xm); }
else { x2 = xm; x1 = xm - C*(xm - x0); }
Standard_Real f1, f2;
F.Value(x1, f1); f1 -= K;
F.Value(x2, f2); f2 -= K;
//-- printf("\n *************** RECHERCHE MINIMUM **********\n");
Standard_Real tolX = 0.001 * NEpsX;
while (Abs(x3 - x0) > tolCR*(Abs(x1) + Abs(x2)) && (Abs(x1 - x2) > tolX)) {
//-- printf("\n (%10.5g,%10.5g) (%10.5g,%10.5g) (%10.5g,%10.5g) (%10.5g,%10.5g) ",
//-- x0,f0,x1,f1,x2,f2,x3,f3);
if (recherche_minimum) {
if (f2 < f1) {
x0 = x1; x1 = x2; x2 = R*x1 + C*x3;
f0 = f1; f1 = f2; F.Value(x2, f2); f2 -= K;
}
else {
x3 = x2; x2 = x1; x1 = R*x2 + C*x0;
f3 = f2; f2 = f1; F.Value(x1, f1); f1 -= K;
}
}
else {
if (f2 > f1) {
x0 = x1; x1 = x2; x2 = R*x1 + C*x3;
f0 = f1; f1 = f2; F.Value(x2, f2); f2 -= K;
}
else {
x3 = x2; x2 = x1; x1 = R*x2 + C*x0;
f3 = f2; f2 = f1; F.Value(x1, f1); f1 -= K;
}
}
//-- On ne fait pas que chercher des extremas. Il faut verifier
//-- si on ne tombe pas sur une racine
if (f1*f0 < 0.0) {
//-- printf("\n Recherche entre (%10.5g,%10.5g) (%10.5g,%10.5g) ",x0,f0,x1,f1);
Solve(F, K, x0, f0, x1, f1, tol, NEpsX, Sol, NbStateSol);
}
if (f2*f3 < 0.0) {
//-- printf("\n Recherche entre (%10.5g,%10.5g) (%10.5g,%10.5g) ",x2,f2,x3,f3);
Solve(F, K, x2, f2, x3, f3, tol, NEpsX, Sol, NbStateSol);
}
}
if ((recherche_minimum && f1<f2) || (!recherche_minimum && f1>f2)) {
//-- x1,f(x1) minimum
if (Abs(f1) < EpsF) {
isSol2 = Standard_True;
aSolX2 = x1;
aVal2 = Abs(f1);
}
}
else {
//-- x2.f(x2) minimum
if (Abs(f2) < EpsF) {
isSol2 = Standard_True;
aSolX2 = x2;
aVal2 = Abs(f2);
}
}
// Choose the best solution between aSolX1, aSolX2
if (isSol1 && isSol2)
{
if (aVal2 - aVal1 > EpsF)
AppendRoot(Sol, NbStateSol, aSolX1, F, K, NEpsX);
else if (aVal1 - aVal2 > EpsF)
AppendRoot(Sol, NbStateSol, aSolX2, F, K, NEpsX);
else
{
aDer1 = Abs(aDer1);
F.Derivative(aSolX2, aDer2);
aDer2 = Abs(aDer2);
if (aDer1 < aDer2)
AppendRoot(Sol, NbStateSol, aSolX1, F, K, NEpsX);
else
AppendRoot(Sol, NbStateSol, aSolX2, F, K, NEpsX);
}
}
else if (isSol1)
AppendRoot(Sol, NbStateSol, aSolX1, F, K, NEpsX);
else if(isSol2)
AppendRoot(Sol, NbStateSol, aSolX2, F, K, NEpsX);
} //-- Recherche d un extrema
} //-- for
}
#if NEWSEQ
#ifdef MATH_FUNCTIONROOTS_CHECK
{
StaticSol.Clear();
Standard_Integer n=Sol.Length();
for(Standard_Integer ii=1;ii<=n;ii++) {
StaticSol.Append(Sol.Value(ii));
}
Sol.Clear();
NbStateSol.Clear();
}
#endif
#endif
#endif
}
#ifdef MATH_FUNCTIONROOTS_OLDCODE
{
//-- ********************************************************************************
//-- ANCIEN TRAITEMENT
//-- ********************************************************************************
// calculate all the real roots of a function within the range
// A..B. without condition on A and B
// a solution X is found when
// abs(Xi - Xi-1) <= EpsX and abs(F(Xi)-K) <= Epsf.
// The function is considered as null between A and B if
// abs(F-K) <= EpsNull within this range.
Standard_Real EpsX = _EpsX; //-- Cas ou le parametre va de 100000000 a 1000000001
//-- Il ne faut pas EpsX = 0.000...001 car dans ce cas
//-- U + Nn*EpsX == U
Standard_Real Lowr,Upp;
Standard_Real Increment;
Standard_Real Null2;
Standard_Real FLowr,FUpp,DFLowr,DFUpp;
Standard_Real U,Xu;
Standard_Real Fxu,DFxu,FFxu,DFFxu;
Standard_Real Fyu,DFyu,FFyu,DFFyu;
Standard_Boolean Finish;
Standard_Real FFi;
Standard_Integer Nbiter = 30;
Standard_Integer Iter;
Standard_Real Ambda,T;
Standard_Real AA,BB,CC;
Standard_Integer Nn;
Standard_Real Alfa1=0,Alfa2;
Standard_Real OldDF = RealLast();
Standard_Real Standard_Underflow = 1e-32 ; //-- RealSmall();
Standard_Boolean Ok;
Done = Standard_False;
StdFail_NotDone_Raise_if(NbSample <= 0, " ");
// initialisation
if (A > B) {
Lowr=B;
Upp=A;
}
else {
Lowr=A;
Upp=B;
}
Increment = (Upp-Lowr)/NbSample;
StdFail_NotDone_Raise_if(Increment < EpsX, " ");
Done = Standard_True;
//-- On teste si EpsX est trop petit (ie : U+Nn*EpsX == U )
Standard_Real DeltaU = Abs(Upp)+Abs(Lowr);
Standard_Real NEpsX = 0.0000000001 * DeltaU;
if(EpsX < NEpsX) {
EpsX = NEpsX;
//-- std::cout<<" \n EpsX Init = "<<_EpsX<<" devient : (deltaU : "<<DeltaU<<" ) EpsX = "<<EpsX<<std::endl;
}
//--
Null2 = EpsNull*EpsNull;
Ok = F.Values(Lowr,FLowr,DFLowr);
if(!Ok) {
Done = Standard_False;
return;
}
FLowr = FLowr - K;
Ok = F.Values(Upp,FUpp,DFUpp);
if(!Ok) {
Done = Standard_False;
return;
}
FUpp = FUpp - K;
// Calcul sur U
U = Lowr-EpsX;
Fyu = FLowr-EpsX*DFLowr; // extrapolation lineaire
DFyu = DFLowr;
FFyu = Fyu*Fyu;
DFFyu = Fyu*DFyu; DFFyu+=DFFyu;
AllNull = ( FFyu <= Null2 );
while ( U < Upp) {
Xu = U;
Fxu = Fyu;
DFxu = DFyu;
FFxu = FFyu;
DFFxu = DFFyu;
U = Xu + Increment;
if (U <= Lowr) {
Fyu = FLowr + (U-Lowr)*DFLowr;
DFyu = DFLowr;
}
else if (U >= Upp) {
Fyu = FUpp + (U-Upp)*DFUpp;
DFyu = DFUpp;
}
else {
Ok = F.Values(U,Fyu,DFyu);
if(!Ok) {
Done = Standard_False;
return;
}
Fyu = Fyu - K;
}
FFyu = Fyu*Fyu;
DFFyu = Fyu*DFyu; DFFyu+=DFFyu; //-- DFFyu = 2.*Fyu*DFyu;
if ( !AllNull || ( FFyu > Null2 && U <= Upp) ){
if (AllNull) { //rechercher les vraix zeros depuis le debut
AllNull = Standard_False;
Xu = Lowr-EpsX;
Fxu = FLowr-EpsX*DFLowr;
DFxu = DFLowr;
FFxu = Fxu*Fxu;
DFFxu = Fxu*DFxu; DFFxu+=DFFxu; //-- DFFxu = 2.*Fxu*DFxu;
U = Xu + Increment;
Ok = F.Values(U,Fyu,DFyu);
if(!Ok) {
Done = Standard_False;
return;
}
Fyu = Fyu - K;
FFyu = Fyu*Fyu;
DFFyu = Fyu*DFyu; DFFyu+=DFFyu;//-- DFFyu = 2.*Fyu*DFyu;
}
Standard_Real FxuFyu=Fxu*Fyu;
if ( (DFFyu > 0. && DFFxu <= 0.)
|| (DFFyu < 0. && FFyu >= FFxu && DFFxu <= 0.)
|| (DFFyu > 0. && FFyu <= FFxu && DFFxu >= 0.)
|| (FxuFyu <= 0.) ) {
// recherche d 1 minimun possible
Finish = Standard_False;
Ambda = Increment;
T = 0.;
Iter=0;
FFi=0.;
if (FxuFyu >0.) {
// chercher si f peut s annuler pour eviter
// des iterations inutiles
if ( Fxu*(Fxu + 2.*DFxu*Increment) > 0. &&
Fyu*(Fyu - 2.*DFyu*Increment) > 0. ) {
Finish = Standard_True;
FFi = Min ( FFxu , FFyu); //pour ne pas recalculer yu
}
else if ((DFFxu <= Standard_Underflow && -DFFxu <= Standard_Underflow) ||
(FFxu <= Standard_Underflow && -FFxu <= Standard_Underflow)) {
Finish = Standard_True;
FFxu = 0.0;
FFi = FFyu; // pour recalculer yu
}
else if ((DFFyu <= Standard_Underflow && -DFFyu <= Standard_Underflow) ||
(FFyu <= Standard_Underflow && -FFyu <= Standard_Underflow)) {
Finish = Standard_True;
FFyu =0.0;
FFi = FFxu; // pour recalculer U
}
}
else if (FFxu <= Standard_Underflow && -FFxu <= Standard_Underflow) {
Finish = Standard_True;
FFxu = 0.0;
FFi = FFyu;
}
else if (FFyu <= Standard_Underflow && -FFyu <= Standard_Underflow) {
Finish = Standard_True;
FFyu =0.0;
FFi = FFxu;
}
while (!Finish) {
// calcul des 2 solutions annulant la derivee de l interpolation cubique
// Ambda*t=(U-Xu) F(t)=aa*t*t*t/3+bb*t*t+cc*t+d
// df=aa*t*t+2*bb*t+cc
AA = 3.*(Ambda*(DFFxu+DFFyu)+2.*(FFxu-FFyu));
BB = -2*(Ambda*(DFFyu+2.*DFFxu)+3.*(FFxu-FFyu));
CC = Ambda*DFFxu;
if(Abs(AA)<1e-14 && Abs(BB)<1e-14 && Abs(CC)<1e-14) {
AA=BB=CC=0;
}
math_DirectPolynomialRoots Solv(AA,BB,CC);
if ( !Solv.InfiniteRoots() ) {
Nn=Solv.NbSolutions();
if (Nn <= 0) {
if (Fxu*Fyu < 0.) { Alfa1 = 0.5;}
else Finish = Standard_True;
}
else {
Alfa1 = Solv.Value(1);
if (Nn == 2) {
Alfa2 = Solv.Value(2);
if (Alfa1 > Alfa2){
AA = Alfa1;
Alfa1 = Alfa2;
Alfa2 = AA;
}
if (Alfa1 > 1. || Alfa2 < 0.){
// resolution par dichotomie
if (Fxu*Fyu < 0.) Alfa1 = 0.5;
else Finish = Standard_True;
}
else if ( Alfa1 < 0. ||
( DFFxu > 0. && DFFyu >= 0.) ) {
// si 2 derivees >0
//(cas changement de signe de la distance signee sans
// changement de signe de la derivee:
//cas de 'presque'tangence avec 2
// solutions proches) ,on prend la plus grane racine
if (Alfa2 > 1.) {
if (Fxu*Fyu < 0.) Alfa1 = 0.5;
else Finish = Standard_True;
}
else Alfa1 = Alfa2;
}
}
}
}
else if (Fxu*Fyu < -1e-14) Alfa1 = 0.5;
//-- else if (Fxu*Fyu < 0.) Alfa1 = 0.5;
else Finish = Standard_True;
if (!Finish) {
// petits tests pour diminuer le nombre d iterations
if (Alfa1 <= EpsX ) {
Alfa1+=Alfa1;
}
else if (Alfa1 >= (1.-EpsX) ) {
Alfa1 = Alfa1+Alfa1-1.;
}
Alfa1 = Ambda*(1. - Alfa1);
U = U + T - Alfa1;
if ( U <= Lowr ) {
AA = FLowr + (U - Lowr)*DFLowr;
BB = DFLowr;
}
else if ( U >= Upp ) {
AA = FUpp + (U - Upp)*DFUpp;
BB = DFUpp;
}
else {
Ok = F.Values(U,AA,BB);
if(!Ok) {
Done = Standard_False;
return;
}
AA = AA - K;
}
FFi = AA*AA;
CC = AA*BB; CC+=CC;
if ( ( ( CC < 0. && FFi < FFxu ) || DFFxu > 0.)
&& AA*Fxu > 0. ) {
FFxu = FFi;
DFFxu = CC;
Fxu = AA;
DFxu = BB;
T = Alfa1;
if (Alfa1 > Ambda*0.5) {
// remarque (1)
// determination d 1 autre borne pour diviser
//le nouvel intervalle par 2 au -
Xu = U + Alfa1*0.5;
if ( Xu <= Lowr ) {
AA = FLowr + (Xu - Lowr)*DFLowr;
BB = DFLowr;
}
else if ( Xu >= Upp ) {
AA = FUpp + (Xu - Upp)*DFUpp;
BB = DFUpp;
}
else {
Ok = F.Values(Xu,AA,BB);
if(!Ok) {
Done = Standard_False;
return;
}
AA = AA -K;
}
FFi = AA*AA;
CC = AA*BB; CC+=CC;
if ( (( CC >= 0. || FFi >= FFxu ) && DFFxu <0.)
|| Fxu * AA < 0. ) {
Fyu = AA;
DFyu = BB;
FFyu = FFi;
DFFyu = CC;
T = Alfa1*0.5;
Ambda = Alfa1*0.5;
}
else if ( AA*Fyu < 0. && AA*Fxu >0.) {
// changement de signe sur l intervalle u,U
Fxu = AA;
DFxu = BB;
FFxu = FFi;
DFFxu = CC;
FFi = Min(FFxu,FFyu);
T = Alfa1*0.5;
Ambda = Alfa1*0.5;
U = Xu;
}
else { Ambda = Alfa1;}
}
else { Ambda = Alfa1;}
}
else {
Fyu = AA;
DFyu = BB;
FFyu = FFi;
DFFyu = CC;
if ( (Ambda-Alfa1) > Ambda*0.5 ) {
// meme remarque (1)
Xu = U - (Ambda-Alfa1)*0.5;
if ( Xu <= Lowr ) {
AA = FLowr + (Xu - Lowr)*DFLowr;
BB = DFLowr;
}
else if ( Xu >= Upp ) {
AA = FUpp + (Xu - Upp)*DFUpp;
BB = DFUpp;
}
else {
Ok = F.Values(Xu,AA,BB);
if(!Ok) {
Done = Standard_False;
return;
}
AA = AA - K;
}
FFi = AA*AA;
CC = AA*BB; CC+=CC;
if ( AA*Fyu <=0. && AA*Fxu > 0.) {
FFxu = FFi;
DFFxu = CC;
Fxu = AA;
DFxu = BB;
Ambda = ( Ambda - Alfa1 )*0.5;
T = 0.;
}
else if ( AA*Fxu < 0. && AA*Fyu > 0.) {
FFyu = FFi;
DFFyu = CC;
Fyu = AA;
DFyu = BB;
Ambda = ( Ambda - Alfa1 )*0.5;
T = 0.;
FFi = Min(FFxu , FFyu);
U = Xu;
}
else {
T =0.;
Ambda = Ambda - Alfa1;
}
}
else {
T =0.;
Ambda = Ambda - Alfa1;
}
}
// tests d arrets
if (Abs(FFxu) <= Standard_Underflow ||
(Abs(DFFxu) <= Standard_Underflow && Fxu*Fyu > 0.)
){
Finish = Standard_True;
if (Abs(FFxu) <= Standard_Underflow ) {FFxu =0.0;}
FFi = FFyu;
}
else if (Abs(FFyu) <= Standard_Underflow ||
(Abs(DFFyu) <= Standard_Underflow && Fxu*Fyu > 0.)
){
Finish = Standard_True;
if (Abs(FFyu) <= Standard_Underflow ) {FFyu =0.0;}
FFi = FFxu;
}
else {
Iter = Iter + 1;
Finish = Iter >= Nbiter || (Ambda <= EpsX &&
( Fxu*Fyu >= 0. || FFi <= EpsF*EpsF));
}
}
} // fin interpolation cubique
// restitution du meilleur resultat
if ( FFxu < FFi ) { U = U + T -Ambda;}
else if ( FFyu < FFi ) { U = U + T;}
if ( U >= (Lowr -EpsX) && U <= (Upp + EpsX) ) {
U = Max( Lowr , Min( U , Upp));
Ok = F.Value(U,FFi);
FFi = FFi - K;
if ( Abs(FFi) < EpsF ) {
//coherence
if (Abs(Fxu) <= Standard_Underflow) { AA = DFxu;}
else if (Abs(Fyu) <= Standard_Underflow) { AA = DFyu;}
else if (Fxu*Fyu > 0.) { AA = 0.;}
else { AA = Fyu-Fxu;}
if (!Sol.IsEmpty()) {
if (Abs(Sol.Last() - U) > 5.*EpsX
|| (OldDF != RealLast() && OldDF*AA < 0.) ) {
Sol.Append(U);
NbStateSol.Append(F.GetStateNumber());
}
}
else {
Sol.Append(U);
NbStateSol.Append(F.GetStateNumber());
}
OldDF = AA ;
}
}
DFFyu = 0.;
Fyu = 0.;
Nn = 1;
while ( Nn < 1000000 && DFFyu <= 0.) {
// on repart d 1 pouyem plus loin
U = U + Nn*EpsX;
if ( U <= Lowr ) {
AA = FLowr + (U - Lowr)*DFLowr;
BB = DFLowr;
}
else if ( U >= Upp ) {
AA = FUpp + (U - Upp)*DFUpp;
BB = DFUpp;
}
else {
Ok = F.Values(U,AA,BB);
AA = AA - K;
}
if ( AA*Fyu < 0.) {
U = U - Nn*EpsX;
Nn = 1000001;
}
else {
Fyu = AA;
DFyu = BB;
FFyu = AA*AA;
DFFyu = 2.*DFyu*Fyu;
Nn = 2*Nn;
}
}
}
}
}
#if NEWSEQ
#ifdef MATH_FUNCTIONROOTS_CHECK
{
Standard_Integer n1=StaticSol.Length();
Standard_Integer n2=Sol.Length();
if(n1!=n2) {
printf("\n mathFunctionRoots : n1=%d n2=%d EpsF=%g EpsX=%g\n",n1,n2,EpsF,NEpsX);
for(Standard_Integer x1=1; x1<=n1;x1++) {
Standard_Real v; F.Value(StaticSol(x1),v); v-=K;
printf(" (%+13.8g:%+13.8g) ",StaticSol(x1),v);
}
printf("\n");
for(Standard_Integer x2=1; x2<=n2; x2++) {
Standard_Real v; F.Value(Sol(x2),v); v-=K;
printf(" (%+13.8g:%+13.8g) ",Sol(x2),v);
}
printf("\n");
}
Standard_Integer n=n1;
if(n1>n2) n=n2;
for(Standard_Integer i=1;i<=n;i++) {
Standard_Real t = Sol(i)-StaticSol(i);
if(Abs(t)>NEpsX) {
printf("\n mathFunctionRoots : i:%d/%d delta: %g",i,n,t);
}
}
}
#endif
#endif
}
#endif
}
void math_FunctionRoots::Dump(Standard_OStream& o) const
{
o << "math_FunctionRoots ";
if(Done) {
o << " Status = Done \n";
o << " Number of solutions = " << Sol.Length() << std::endl;
for (Standard_Integer i = 1; i <= Sol.Length(); i++) {
o << " Solution Number " << i << "= " << Sol.Value(i) << std::endl;
}
}
else {
o<< " Status = not Done \n";
}
}