void Do() {
int Fst = 1;
double uinter = 0, dinter = 0, pinter = 0, linter = L, rinter = Ro;
Result::Ufr = 0;
Result::Uto = U2;
Result::Discr = 100;
clc.Init(Fst ? Mat1 : Mat2, Fst ? U2 : 0, 0, uinter, dinter, pinter, rinter, Fst);
Result::Clc(&Mat1Result, dinter, pinter, uinter, rinter, PressureMat);
Fst = !Fst;
clc.Init(Fst ? Mat1 : Mat2, Fst ? U2 : 0, 0, uinter, dinter, pinter, rinter, Fst);
Result::Clc(&Mat2Result, dinter, pinter, uinter, rinter, PressureMat);
Fst = !Fst;
for(int k = 0; k < Times.SetDim(); k++) {
dinter = linter / Times[k];
cout << " Found U " << uinter << " P " << pinter << " Ro " << rinter << " L "
<< linter << " D " << dinter << "\n";
clc.Init(
Fst ? Mat1 : Mat2, Fst ? U2 : 0, 0, uinter, dinter, pinter, rinter, Fst);
Result::Clc(&(U_P[k]), dinter, pinter, uinter, rinter, PressureInter);
uinter = U2 / 2;
if(!Fzero(MisP, 0, U2, uinter, 1e-6, 1e-6, 1000))
cout << "Fzero error\n";
clc.GetPar(uinter, pinter, rinter);
Result::Fin(&(U_P[k]), pinter, uinter, rinter);
linter = L * Ro / rinter;
Fst = !Fst;
}
cout << " Found U " << uinter << " P " << pinter << " Ro " << rinter << " L "
<< linter << " D " << 0 << "\n";
OutputRes();
}
map<Stroka, double> MatterStable::TwoPhaseBoundary::MakeBndPnt() {
VecCl V, D, P;
int SpinIndMin, SpinIndMax;
map<Stroka, double> ret;
ret["T"] = T;
ret["DSr_T"] = 0;
ret["DSl_T"] = 0;
ret["Dr_T"] = 0;
ret["Dl_T"] = 0;
ret["P_T"] = 0;
ret["E_T"] = 0;
ret["dPdT_T"] = 0;
if(!SetDP(V, D, P, SpinIndMin, SpinIndMax))
return ret;
ret["T"] = T;
TwoPhaseBoundary *OldPtr = TwoPhaseBoundaryStaticPtr;
PrepareStatic(P, V);
double PT_From, PT_To;
FindMinMax(V, SpinIndMax, ZeroFunc_Spl_Vmin, PT_From, 1);
ret["DSr_T"] = 1 / ZeroFunc_Spl_Vmin;
FindMinMax(V, SpinIndMin, ZeroFunc_Spl_Vmax, PT_To, 0);
ret["DSl_T"] = 1 / ZeroFunc_Spl_Vmax;
IntegralFunc_Negative = 0;
double PT_est =
IntegralFunc_PV_Int_Static((ZeroFunc_Spl_Vmin + ZeroFunc_Spl_Vmax) * 0.5);
Fzero(
ZeroFunc_PV_Int_Static,
max<double>(PT_From, sqrt(MathZer)),
max<double>(PT_To, sqrt(MathZer)),
PT_est,
Mis * 0.1,
Mis * 0.1,
100);
//Fzero(ZeroFunc_PV_Int_Static, PT_From, PT_To, PT_est, Mis*0.1, Mis*0.1, 100);
ZeroFunc_PV_Int_Static(PT_est);
//ret["P_T"] = PT_est;
ret["Dl_T"] = 1 / ZeroFunc_SplRes_Bmax;
ret["Dr_T"] = 1 / ZeroFunc_SplRes_Bmin;
ret["P_T"] = 0.5 * (Mat->Pressure(ret["Dr_T"], T) + Mat->Pressure(ret["Dl_T"], T));
ret["E_T"] = Mat->Energy(ret["Dr_T"], T);
double E0 = ret["E_T"]; //,P0=Mat->Pressure(ret["Dr_T"],T);
double E1 = Mat->Energy(ret["Dl_T"], T);
ret["dPdT_T"] = -(E0 - E1) / (1 / ret["Dr_T"] - 1 / ret["Dl_T"]);
ret["Pr_T"] = Mat->Pressure(ret["Dr_T"], T);
ret["Pl_T"] = Mat->Pressure(ret["Dl_T"], T);
ret["PSr_T"] = Mat->Pressure(ret["DSr_T"], T);
ret["PSl_T"] = Mat->Pressure(ret["DSl_T"], T);
//if (fabs(ret["Pr_T"]-ret["Pl_T"])>Mis) cout<<" BinodalBndPres l "<<ret["PSl_T"]<<" r "<<ret["PSr_T"]<<"\n";
TwoPhaseBoundaryStaticPtr = OldPtr;
return ret;
}
main()
{ int i; float x, Fzero(),Fone();
for( i=0; i< 100; i++)
{
x = i;
printf("%f %f %f\n",x,Fzero(x*x),Fone(x*x));
}
}
void Hug2(Int_Par &P1, Int_Par &P2, Int_Par &Pr1,
double &Dr1, Int_Par &Pr2, double &Dr2,
MatterIO *Mat1, MatterIO *Mat2) {
double Pest; //,Delta;
MatterAdiabat = Mat1;
P1.Pres = PressurePorous(P1.Dens, P1.Ener);
MatterAdiabat = Mat2;
if(!GetInitialPressure)
P2.Pres = PressurePorous(P2.Dens, P2.Ener);
else
P2.Pres = 0.0001;
if(Norm(P1 - P2) < StndErr) {
Pr1 = P1;
Pr2 = P2;
Dr1 = Mat1->Sound(P1.Dens, P1.Ener) + P1.Velo;
Dr2 = Dr1;
return;
}
double A1 = max<double>(0.1, P1.Dens * Mat1->Sound(P1.Dens, P1.Ener));
double A2 = max<double>(0.1, P2.Dens * Mat2->Sound(P2.Dens, P2.Ener));
Pest = (P2.Pres * A1 + P1.Pres * A2 + A1 * A2 * (P1.Velo - P2.Velo)) / (A1 + A2);
S_Par1 = P1;
S_Par2 = P2;
S_Mat1 = Mat1;
S_Mat2 = Mat2;
#ifdef FZERO_HUGONIO_SEARCH
//int Fzero(X_func f,double From,double To,double &Guess,double ErrorAbs,double ErrorRel,
// int MaxIter);
Fzero(MisU, 1e6, M_Eps2, Pest, StndErr, StndErr, 200);
// if (3<Fzero(MisU,-1e6,1e6,Pest,StndErr,StndErr,200));
//{ cout <<" Error, could not find Hug2 ZeroFzeroIt\n";}
//int ZeroNewtonIt(X_func Func,double &CurPnt,double Tol,int MaxIter,
// double Up,double Down,double MaxStp,double BegStp)
#else
#ifdef NEWTON_HUGONIO_SEARCH
if(!ZeroNewtonIt(MisU, Pest, StndErr, 100, 1e6, -1e6, 5 * fabs(Pest))) {
double Ctrl = MisU(Pest);
cout << " Error, could not find Hug2";
}
#else
if(!FindZeroPos(MisU, Pest, Delta, StndErr, 0.5 * Pest))
cout << " Error, could not find Hug2";
#endif
#endif
Pr1 = S_Res1;
Pr2 = S_Res2;
Dr1 = -S_ResD1 + S_Par1.Velo;
Dr2 = -S_ResD2 + S_Par2.Velo;
Pr2.Velo = -Pr2.Velo + 2 * P2.Velo;
Pr1.Pres = Pest;
Pr2.Pres = Pest;
};
double MatterStable::TwoPhaseBoundary::ZeroFunc_PV_Int(double pres) {
double Vmin, Vmax, Smin = ZeroFunc_Spl_Vmin, Smax = ZeroFunc_Spl_Vmax,
Ds = Smax - Smin; //,PresInt,ResErr
Vmin = Smin - Ds / 2;
Vmax = Smax + Ds / 2;
IntegralFunc_Negative = 0;
IntegralFunc_Add = -pres;
//cout<<" pres "<<pres<<" Vmin "<<1/Dmax<<" pmin "<<Mat->Pressure(Dmax,T)<<" spl "<<IntegralSpline_P_V.Evaluate(1/Dmax)<<" vmax "<<Smin<<" pmax "<<Mat->Pressure(1/Smin,T)<<"\n";
Fzero(
IntegralFunc_PV_Int_Static,
1 / Dmax,
Smin,
Vmin,
ZeroFunc_Misf * 0.1,
ZeroFunc_Misf * 0.1,
100);
Fzero(
IntegralFunc_PV_Int_Static,
Smax,
1 / Dmin,
Vmax,
ZeroFunc_Misf * 0.1,
ZeroFunc_Misf * 0.1,
100);
//Fzero(IntegralFunc_PV_Int_Static,Smin-Ds,Smin,Vmin,ZeroFunc_Misf*0.1,ZeroFunc_Misf*0.1,100);
//Fzero(IntegralFunc_PV_Int_Static,Smax,Smax+10000*Ds,Vmax,ZeroFunc_Misf*0.1,ZeroFunc_Misf*0.1,100);
ZeroFunc_SplRes_Bmin = Vmin;
ZeroFunc_SplRes_Bmax = Vmax;
//double MisPmin=fabs(Mat->Pressure(1/Vmin,T)-pres),
// MisPmax=fabs(Mat->Pressure(1/Vmax,T)-pres);
//if (MisPmin+MisPmax>ZeroFunc_Misf)
//cout<<" P "<<pres<<"\nmax V "<<Vmax<<" P "<<Mat->Pressure(1/Vmax,T)<<" spl "<<IntegralSpline_P_V.Evaluate(Vmax)<<
//"\nmin V " <<Vmin<<" Pmin "<<Mat->Pressure(1/Vmin,T)<<" spl "<<IntegralSpline_P_V.Evaluate(Vmin)<<"\n";
return Mat->FreeE(1 / Vmin, T) - Mat->FreeE(1 / Vmax, T) + pres * (Vmin - Vmax);
}
double MatterFreeE::TemperatureFind(double En,double Den,double Low,double Up,
double Start,double Err,int NumIt)
{
Current=this;
E=En;D=Den;
double T0=Start;
int err;
#ifdef FZERO_TEMPERATURE_ITERATION
if (4<(err=Fzero(DeltaFree,Low,Up,T0,Err,Err,100)) )
{cout<<" Bad ZeroFzeroFreeE in MatterFreeE::TemperatureFind Not Zero\nfound T "
<<T0<<" Mis "<<DeltaFree(T0)<<" err "<<err<<"\n";T0=Zero_Temp;}
#else
#ifdef FZERO_LOGTEMPERATURE_ITERATION
// ln(50)=3.91 ln(1e6)=13.8 ln(100)=4.6
T0=log(Start);Low=log(Low);Up=log(Up);Err=0.1*Err;
if (4<(err=Fzero(DeltaFreeLog,Low,Up,T0,Err,Err,100)) ) {
cout<<" Bad ZeroFzeroFreeE in MatterFreeE::Temperature Not Zero\nfound T "
<<exp(T0)<<" Mis "<<DeltaFreeLog(T0)<<" err "<<err<<"\n";
T0 = MinimTmin;
} else
T0=exp(T0);
#else
MinFind1DClass *min1d=new MinFind1DClass(1,NULL);
double MinError=Err,FoundEMis;
int Cont=1,MaxIt=7,NumT=MaxIt,it;
VecCl TmpPar(1),TmpStp(1);TmpPar[1]=L_T;TmpStp[1]=500;
T0=Start;
#ifdef MULTIDIM_TEMPERATURE_ITERATION
Derive2DStd *D2=new Derive2DStd(new DeriveStaticFunc(DeltaFree));
MinFindNDimClass MinNd(D2,min1d,1e-10,1e-8,MinError);
for (it=1;((it<=NumT)&&(Cont));it++) Cont=MinNd.Execute(TmpPar,TmpStp,1,FoundEMis);
if (it>MaxIt)
if (4<(err=Fzero(DeltaFree,Low,Up,T0,Err,Err,100)) )
{cout<<" Bad ZeroFzeroFreeE in MatterFreeE::TemperatureFind Not Zero\nfound T "
<<T0<<" Mis "<<DeltaFree(T0)<<" err "<<err<<"\n";T0=Zero_Temp;}
else T0=TmpPar[1];
#else
T0=log(Start);Low=log(Low);Up=log(Up);Err=0.1*Err;
TmpPar[1]=log(TmpPar[1]);TmpStp[1]=log(TmpStp[1]);
Derive2DStd *D2=new Derive2DStd(new DeriveStaticFunc(DeltaFreeLog));
MinFindNDimClass MinNd(D2,min1d,1e-10,1e-8,MinError);
for (it=1;((it<=NumT)&&(Cont));it++) Cont=MinNd.Execute(TmpPar,TmpStp,1,FoundEMis);
if (it>MaxIt)
if (4<(err=Fzero(DeltaFreeLog,Low,Up,T0,Err,Err,100)) )
{cout<<" Bad ZeroFzeroFreeE in MatterFreeE::Temperature Not Zero\nfound T "
<<exp(T0)<<" Mis "<<DeltaFreeLog(T0)<<" err "<<err<<"\n";T0=Zero_Temp;}
else T0=exp(T0);
else T0=exp(TmpPar[1]);
#endif
#endif
#endif
//#ifdef FZERO_TEMPERATURE_ITERATION
//// if (!ZeroNewtonIt(DeltaFree,T0,StndErr*0.1,100,1e6,Zero_Temp,0.8*T0,0.01))
////int Fzero(X_func f,double From,double To,double &Guess,double ErrorAbs,double ErrorRel,
//// int MaxIter)
// if (4<(err=Fzero(DeltaFree,50,1e6,T0,StndErr*0.1,StndErr*0.1,100)) )
// {cout<<" Bad ZeroFzeroFreeE in MatterFreeE::Temperature Not Zero\nfound T "
// <<T0<<" Mis "<<DeltaFree(T0)<<" err "<<err<<"\n";T0=Zero_Temp;}
////if (err!=0) cout<<" Mis E "<<DeltaFree(T0)<<" T "<<T0<<" err "<<err<<"\n";
return T0;
}
int coarsepitch(
Float *xw,
Float *xwdm,
Float *dfm, /* (i/o) ellipse low pass filter memory */
int cpplast)
{
Float xwd[LXD];
Float cor[MAXPPD1], cor2[MAXPPD1], energy[MAXPPD1];
Float cor2i[HMAXPPD], energyi[HMAXPPD], mplth;
Float tmp[DFO+FRSZ], threshold;
Float *fp0, *fp1, *fp2, *fp3, s, t, a, b, c, deltae;
Float cor2max, energymax, cor2m, energym, ci, eni;
int i, j, k, n, npeaks, imax, im, idx[HMAXPPD], plag[HMAXPPD];
int cpp, maxdev, flag, mpflag;
/* reset local buffers */
Fzero(cor, MAXPPD1);
Fzero(energy, MAXPPD1);
/* LOWPASS FILTER xw() TO 800 Hz; SHIFT & OUTPUT INTO xwd() */
/* copy xwd[] from memory to buffer */
Fcopy(xwd, xwdm, XDOFF);
/* copy memory to temp buffer */
Fcopy(tmp, dfm, DFO);
/* AP and AZ filtering and decimation */
fp0 = xwd + XDOFF;
fp1 = tmp + DFO;
fp3 = xw;
for (i=0;i<FRSZD;i++) {
for (k=0;k<DECF;k++) {
t = *fp3++; fp2 = fp1-1;
for (j=0;j<DFO;j++) t -= adf[j+1]*(*fp2--);
*fp1++ = t;
}
fp2 = fp1-1;
t = bdf[0] * (*fp2--);
for (j=0;j<DFO;j++) t += bdf[j+1] * (*fp2--);
*fp0++ = t;
}
/* copy temp buffer to memory */
fp1 -= DFO;
for (i=0;i<DFO;i++) dfm[i] = *fp1++;
/* update xwd() memory */
Fcopy(xwdm, xwd+FRSZD, XDOFF);
/* COMPUTE CORRELATION & ENERGY OF PREDICTION BASIS VECTOR */
fp0 = xwd+MAXPPD1;
fp1 = xwd+MAXPPD1-M1;
s = t = 0.;
for (i=0;i<(LXD-MAXPPD1);i++) {
s += (*fp1) * (*fp1);
t += (*fp0++)*(*fp1++);
}
energy[M1-1] = s;
cor[M1-1] = t;
if (t > 0.0F)
cor2[M1-1] = t*t;
else
cor2[M1-1] = -t*t;
fp2 = xwd+LXD-M1-1;
fp3 = xwd+MAXPPD1-M1-1;
for (i=M1;i<M2;i++) {
fp0 = xwd+MAXPPD1;
fp1 = xwd+MAXPPD1-i-1;
t = 0.;
for (j=0;j<(LXD-MAXPPD1);j++) t += (*fp0++) * (*fp1++);
cor[i] = t;
if (t > 0.0F)
cor2[i] = t*t;
else
cor2[i] = -t*t;
s = s - (*fp2)*(*fp2) + (*fp3)*(*fp3);
fp2--; fp3--;
energy[i] = s;
}
/* FIND POSITIVE COR*COR/ENERGY PEAKS */
npeaks = 0;
n = MINPPD-1;
while ((n<MAXPPD) && (npeaks<MAX_NPEAKS)) {
if ((cor2[n]*energy[n-1]>cor2[n-1]*energy[n]) &&
(cor2[n]*energy[n+1]>cor2[n+1]*energy[n]) && (cor2[n]>0)) {
idx[npeaks] = n;
npeaks++;
}
n++;
}
/* RETURN EARLY IF THERE IS NO PEAK OR ONLY ONE PEAK */
if (npeaks == 0) /* if there are no positive peak, */
return MINPPD*cpp_scale; /* minimum pitch period in decimated domain */
if (npeaks == 1) /* if there is exactly one peak, */
return (idx[0]+1)*cpp_scale; /* the time lag for this single peak */
/* IF PROGRAM PROCEEDS TO HERE, THERE ARE 2 OR MORE PEAKS */
cor2max=-1e30;
energymax=1.0F;
imax=0;
for (i=0; i < npeaks; i++) {
/* USE QUADRATIC INTERPOLATION TO FIND THE INTERPOLATED cor[] AND
energy[] CORRESPONDING TO INTERPOLATED PEAK OF cor2[]/energy[] */
/* first calculate coefficients of y(x)=ax^2+bx+c; */
n=idx[i];
a=0.5F*(cor[n+1] + cor[n-1]) - cor[n];
b=0.5F*(cor[n+1] - cor[n-1]);
c=cor[n];
/* INITIALIZE VARIABLES BEFORE SEARCHING FOR INTERPOLATED PEAK */
im=0;
cor2m=cor2[n];
energym=energy[n];
eni=energy[n];
/* DERTERMINE WHICH SIDE THE INTERPOLATED PEAK FALLS IN, THEN
DO THE SEARCH IN THE APPROPRIATE RANGE */
if (cor2[n+1]*energy[n-1] > cor2[n-1]*energy[n+1]) { /* if right side */
deltae=(energy[n+1] - eni) * INVDECF; /*increment for linear interp.*/
for (k = 0; k < HDECF; k++) {
ci = a*x2[k] + b*x[k] + c; /* quadratically interpolated cor[] */
eni += deltae; /* linearly interpolated energy[] */
if (ci*ci*energym > cor2m*eni) {
im = k+1;
cor2m=ci*ci;
energym=eni;
}
}
} else { /* if interpolated peak is on the left side */
deltae=(energy[n-1] - eni) * INVDECF; /*increment for linear interp.*/
for (k = 0; k < HDECF; k++) {
ci = a*x2[k] - b*x[k] + c;
eni += deltae;
if (ci*ci*energym > cor2m*eni) {
im = -k-1;
cor2m=ci*ci;
energym=eni;
}
}
}
/* SEARCH DONE; ASSIGN cor2[] AND energy[] CORRESPONDING TO
INTERPOLATED PEAK */
plag[i]=(idx[i]+1)*cpp_scale + im; /* lag of interp. peak */
cor2i[i]=cor2m; /* interpolated cor2[] of i-th interpolated peak */
energyi[i]=energym; /* interpolated energy[] of i-th interpolated peak */
/* SEARCH FOR GLOBAL MAXIMUM OF INTERPOLATED cor2[]/energy[] peak */
if (cor2m*energymax > cor2max*energym) {
imax=i;
cor2max=cor2m;
energymax=energym;
}
}
cpp=plag[imax]; /* first candidate for coarse pitch period */
mplth=plag[npeaks-1]*1./DECF; /* plag[] is Q2 */
/* FIND THE LARGEST PEAK (IF THERE IS ANY) AROUND THE LAST PITCH */
maxdev=(int) (DEVTH*cpplast); /* maximum deviation from last pitch */
im = -1;
cor2m = -1e30;
energym = 1.0F;
for (i=0;i<npeaks;i++) { /* loop thru the peaks before the largest peak */
if (abs(plag[i]-cpplast) <= maxdev) {
if (cor2i[i]*energym > cor2m*energyi[i]) {
im=i;
cor2m=cor2i[i];
energym=energyi[i];
}
}
} /* if there is no peaks around last pitch, then im is still -1 */
/* NOW SEE IF WE SHOULD PICK ANY ALTERNATICE PEAK */
/* FIRST, SEARCH FIRST HALF OF PITCH RANGE, SEE IF ANY QUALIFIED PEAK
HAS LARGE ENOUGH PEAKS AT EVERY MULTIPLE OF ITS LAG */
i=0;
while (plag[i] < 0.5*mplth*DECF) {
/* DETERMINE THE APPROPRIATE THRESHOLD FOR THIS PEAK */
if (i != im) { /* if not around last pitch, */
threshold = TH1; /* use a higher threshold */
} else { /* if around last pitch */
threshold = TH2; /* use a lower threshold */
}
/* IF THRESHOLD EXCEEDED, TEST PEAKS AT MULTIPLES OF THIS LAG */
if (cor2i[i]*energymax > threshold*cor2max*energyi[i]) {
flag=1;
j=i+1;
k=0;
s=2.0F*plag[i]; /* initialize t to twice the current lag */
while (s<=mplth*DECF) { /* loop thru all multiple lag <= mplth */
mpflag=0; /* initialize multiple pitch flag to 0 */
a=MPR1*s; /* multiple pitch range lower bound */
b=MPR2*s; /* multiple pitch range upper bound */
while (j < npeaks) { /* loop thru peaks with larger lags */
if (plag[j] > b) { /* if range exceeded, */
break; /* break the innermost while loop */
} /* if didn't break, then plag[j] <= b */
if (plag[j] > a) { /* if current peak lag within range, */
/* then check if peak value large enough */
if (k < 4) {
c = MPTH[k];
} else {
c = MPTH4;
}
if (cor2i[j]*energymax > c*cor2max*energyi[j]) {
mpflag=1; /* if peak large enough, set mpflag, */
break; /* and break the innermost while loop */
}
}
j++;
}
/* if no qualified peak found at this multiple lag */
if (mpflag == 0) {
flag=0; /* disqualify the lag plag[i] */
break; /* and break the while (s<=mplth) loop */
}
k++;
s += plag[i]; /* update s to the next multiple pitch lag */
}
/* if there is a qualified peak at every multiple of plag[i], */
if (flag == 1) {
return plag[i]; /* and return to calling function */
}
}
i++;
if (i == npeaks)
break; /* to avoid out of array bound error */
}
/* IF PROGRAM PROCEEDS TO HERE, NONE OF THE PEAKS WITH LAGS < 0.5*mplth
QUALIFIES AS THE FINAL PITCH. IN THIS CASE, CHECK IF
THERE IS ANY PEAK LARGE ENOUGH AROUND LAST PITCH. IF SO, USE ITS
LAG AS THE FINAL PITCH. */
if (im != -1) { /* if there is at least one peak around last pitch */
if (im == imax) { /* if this peak is also the global maximum, */
return cpp; /* return first pitch candidate at global max */
}
if (im < imax) { /* if lag of this peak < lag of global max, */
if (cor2m*energymax > LPTH2*cor2max*energym) {
if (plag[im] > HMAXPPD*cpp_scale) {
return plag[im];
}
for (k=2; k<=5;k++) { /* check if current candidate pitch */
s=plag[imax]/(float)(k); /* is a sub-multiple of */
a=SMDTH1*s; /* the time lag of */
b=SMDTH2*s; /* the global maximum peak */
if (plag[im]>a && plag[im]<b) { /* if so, */
return plag[im]; /* and return as pitch */
}
}
}
} else { /* if lag of this peak > lag of global max, */
if (cor2m*energymax > LPTH1*cor2max*energym) {
return plag[im]; /* accept its lag */
}
}
}
/* IF PROGRAM PROCEEDS TO HERE, WE HAVE NO CHOICE BUT TO ACCEPT THE
LAG OF THE GLOBAL MAXIMUM */
return cpp;
}
