int main()
{
read_pars("input");
read_ensemble_pars(base_path,T,ibeta,nmass,mass,iml_un,nlights,data_list_file);
TH=L=T/2;
init_latpars();
int ncombo=nmass*nmass;
//load all the corrs
double *buf=new double[4*ncombo*T*(njack+1)];
FILE *fin=open_file(combine("%s/%s",base_path,corr_name).c_str(),"r");
int stat=fread(buf,sizeof(double),4*ncombo*(njack+1)*T,fin);
if(stat!=4*ncombo*(njack+1)*T)
{
cerr<<"Error loading data!"<<endl;
exit(1);
}
jvec M(ncombo,njack);
jvec Z2(ncombo,njack);
//define minuit staff
TMinuit minu(2);
minu.SetPrintLevel(-1);
minu.SetFCN(chi2);
corr_fit=new double[TH+1];
corr_err=new double[TH+1];
//fit each combo
int ic=0;
for(int ims=0;ims<nmass;ims++)
for(int imc=ims;imc<nmass;imc++)
{
//take into account corr
jvec corr1(T,njack),corr2(T,njack),corr;
int ic1=0+2*(ims+nmass*(0+2*imc));
int ic2=1+2*(ims+nmass*(1+2*imc));
cout<<ims<<" "<<imc<<" "<<ic1<<" "<<ic2<<endl;
corr1.put(buf+ic1*T*(njack+1));
corr2.put(buf+ic2*T*(njack+1));
corr=(corr1+corr2)/2;
cout<<corr1[0]<<" "<<corr2[0]<<endl;
//choose the index of the fitting interval
if(ims>=nlights) ifit_int=2;
else
if(imc>=nlights) ifit_int=1;
else ifit_int=0;
//simmetrize
corr=corr.simmetrized(parity);
int ttmin=tmin[ifit_int];
int ttmax=tmax[ifit_int];
jvec Mcor=effective_mass(corr),Z2cor(TH+1,njack);
jack Meff=constant_fit(Mcor,ttmin,ttmax);
for(int t=0;t<=TH;t++)
for(int ijack=0;ijack<=njack;ijack++)
Z2cor[t].data[ijack]=corr[t].data[ijack]/fun_fit(1,Meff[ijack],t);
jack Z2eff=constant_fit(Z2cor,ttmin,ttmax);
if(!isnan(Z2eff[0])) minu.DefineParameter(0,"Z2",Z2eff[0],Z2eff.err(),0,2*Z2eff[0]);
if(!isnan(Meff[0])) minu.DefineParameter(1,"M",Meff[0],Meff.err(),0,2*Meff[0]);
for(int t=tmin[ifit_int];t<=tmax[ifit_int];t++) corr_err[t]=corr.data[t].err();
//jacknife analysis
for(int ijack=0;ijack<njack+1;ijack++)
{
//copy data so that glob function may access it
for(int t=tmin[ifit_int];t<=tmax[ifit_int];t++) corr_fit[t]=corr.data[t].data[ijack];
//fit
double dum;
minu.Migrad();
minu.GetParameter(0,Z2.data[ic].data[ijack],dum);
minu.GetParameter(1,M.data[ic].data[ijack],dum);
}
//if((ims==iml_un||ims==nlights-1||ims==nlights||ims==nmass-1)&&
//(imc==iml_un||imc==nlights-1||imc==nlights||imc==nmass-1))
{
//plot eff mass
{
ofstream out(combine("eff_mass_plot_%02d_%02d.xmg",ims,imc).c_str());
out<<"@type xydy"<<endl;
out<<"@s0 line type 0"<<endl;
out<<Mcor<<endl;
out<<"&"<<endl;
out<<"@type xy"<<endl;
double av_mass=M[ic].med();
double er_mass=M[ic].err();
out<<tmin[ifit_int]<<" "<<av_mass-er_mass<<endl;
out<<tmax[ifit_int]<<" "<<av_mass-er_mass<<endl;
out<<tmax[ifit_int]<<" "<<av_mass+er_mass<<endl;
out<<tmin[ifit_int]<<" "<<av_mass+er_mass<<endl;
out<<tmin[ifit_int]<<" "<<av_mass-er_mass<<endl;
}
//plot fun
{
ofstream out(combine("fun_plot_%02d_%02d.xmg",ims,imc).c_str());
out<<"@type xydy"<<endl;
out<<"@s0 line type 0"<<endl;
out<<corr<<endl;
out<<"&"<<endl;
out<<"@type xy"<<endl;
for(int t=tmin[ifit_int];t<tmax[ifit_int];t++)
out<<t<<" "<<fun_fit(Z2[ic][njack],M[ic][njack],t)<<endl;
}
}
cout<<mass[ims]<<" "<<mass[imc]<<" "<<M[ic]<<" "<<Z2[ic]<<" f:"<<sqrt(Z2[ic])/(sinh(M[ic])*M[ic])*(mass[ims]+mass[imc])<<" fV:"<<Za_med[ibeta]*sqrt(Z2[ic])/M[ic]/lat[ibeta].med()<<endl;
ic++;
}
ofstream out("fitted_mass.xmg");
out<<"@type xydy"<<endl;
for(int ims=0;ims<nmass;ims++)
{
//out<<"s0 line type 0"<<endl;
for(int imc=0;imc<nmass;imc++) out<<mass[imc]<<" "<<M[icombo(ims,imc,nmass,nlights,0)]<<endl;
out<<"&"<<endl;
}
M.write_to_binfile(out_file);
Z2.append_to_binfile(out_file);
return 0;
}
INLINE P YgooSmathYPfsinh(P x) {
INTFLO iz, ix; ix.i = (PINT)x;
iz.f = (float)sinh((double)ix.f);
return (P)iz.i;
}
float
sinhf (float x)
{
return (float) sinh ((double) x);
}
inline double _sinh(double arg) { return sinh(arg); }
void c_qd_sinh(const double *a, double *b) {
qd_real bb;
bb = sinh(qd_real(a));
TO_DOUBLE_PTR(bb, b);
}
double Formulaeditor::factor(qint32& nPosition, QString& strCharacter)
{
qreal f = 0.0;
qint32 wI = 0, wL = 0, wBeginn = 0, wError = 0;
if (strCharacter == str_char(0)) return 0.0;
// read digit and save as float in f
if (((strCharacter >= "0") && (strCharacter <= "9")) || (strCharacter == "."))
{
wBeginn = nPosition;
do
{
char_n(nPosition, strCharacter);
}
while ((((strCharacter >= "0") && (strCharacter <= "9")) || (strCharacter == ".")));
if (strCharacter == ".")
{
do
{
char_n(nPosition, strCharacter);
}
while (!(((qint8)strCharacter.at(0).digitValue() >= 0) && ((qint8)strCharacter.at(0).digitValue() <= 9)) || (strCharacter.at(0) == '.'));
}
QString g_strF = m_strFunction.mid(wBeginn - 1, nPosition - wBeginn);
f = g_strF.toFloat();
}
else
{
QString strCharacterUpper = strCharacter.toUpper();
if (strCharacter == "(")
{
char_n(nPosition, strCharacter);
f = expression(nPosition, strCharacter);
if (strCharacter == ")")
char_n(nPosition, strCharacter);
}
else if (strCharacterUpper == "X")
{
char_n(nPosition, strCharacter);
f = m_dFktValue;
}
else
{
bool gefunden = false;
qint32 AnzStdFunctions = m_strStandardFunction.length() - 1;
for (wI = 1; wI <= AnzStdFunctions; wI++)
{
wL = m_strStandardFunction.at(wI).length();
QString strFunktionUpper = m_strFunction.mid(nPosition - 1, wL);
strFunktionUpper = strFunktionUpper.toUpper();
QString strDummy(m_strStandardFunction.at(wI));
strDummy = strDummy.toUpper();
if (strFunktionUpper == strDummy)
{
gefunden = true;
nPosition = nPosition + wL - 1;
char_n(nPosition, strCharacter);
// ! recursion !!!!!!!!!!!!!!!!!!!!!!
f = factor(nPosition, strCharacter);
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
if (strFunktionUpper == "ABS")
f = fabs(f);
else if (strFunktionUpper == "SQRT")
if (f >= 0)
f = sqrt(f);
else
wError = -1;
else if (strFunktionUpper == "SINH")
f = sinh(f);
else if (strFunktionUpper == "COSH")
f = cosh(f);
else if (strFunktionUpper == "TANH")
f = tanh(f);
else if (strFunktionUpper == "ARCTAN")
f = atan(f);
else if (strFunktionUpper == "LN")
{
if (f >= 0)
f = log(f);
else
wError = -1;
}
else if (strFunktionUpper == "LOG")
{
if (f >= 0)
f = log10(f);
else
wError = -1;
}
else if (strFunktionUpper == "EXP")
{
//if (f <= 41)
f = exp(f);
//else
//wError = -1;
}
else if (strFunktionUpper == "SIN")
f = sin(f);
else if (strFunktionUpper == "COS")
f = cos(f);
else if (strFunktionUpper == "COT")
f = cot(f);
else if (strFunktionUpper == "TAN")
{
if (cos(f) != 0)
f = tan(f);
else
wError = -1;
}
else if (strFunktionUpper == "ARCSIN")
{
if (fabs(f) < 1)
f = asin(f);
else
wError = -1;
}
else if (strFunktionUpper == "ARCCOS")
{
if (fabs(f) <= 1)
f = acos(f);
else
wError = -1;
}
else if (strFunktionUpper == "SIGN")
f = signl(f);
else if (strFunktionUpper == "RAD")
f = RAD(f);
else if (strFunktionUpper == "DEG")
f = DEG(f);
else if (strFunktionUpper == "ARSINH")
f = ArSinh(f);
else if (strFunktionUpper == "ARCOSH")
{
if (fabs(f) >= 1)
f = ArCosh(f);
else
wError = -1;
}
else if (strFunktionUpper == "ARTANH")
{
if (fabs(f) <= 1)
f = ArTanh(f);
else
wError = -1;
}
break;
}
}
if (!gefunden)
{
char_n(nPosition, strCharacter);
if (strCharacterUpper == "A")
f = m_dFunctionConstant[0];
else if (strCharacterUpper == "B")
f = m_dFunctionConstant[1];
else if (strCharacterUpper == "C")
f = m_dFunctionConstant[2];
else if (strCharacterUpper == "D")
f = m_dFunctionConstant[3];
else if (strCharacterUpper == "E")
f = m_dFunctionConstant[4];
else if (strCharacterUpper == "F")
f = m_dFunctionConstant[5];
else if (strCharacterUpper == "G")
f = m_dFunctionConstant[6];
else if (strCharacterUpper == "H")
f = m_dFunctionConstant[7];
}
}
}
if (wError == -1) errorText = QString("General Parser Error blocked!");
return f;
}
static int math_sinh (lua_State *L) {
lua_pushnumber(L, sinh(luaL_checknumber(L, 1)));
return 1;
}
static VALUE
math_sinh(VALUE obj, VALUE x)
{
Need_Float(x);
return DBL2NUM(sinh(RFLOAT_VALUE(x)));
}
//function to fit
double fun_fit(double Z2,double M,int t)
{
if(parity==1) return Z2*exp(-M*TH)*cosh(M*(TH-t))/sinh(M);
else return Z2*exp(-M*TH)*sin(M*(TH-t))/sinh(M);
}
int StringFragmentation::decayStringIntoParticles( TLorentzVector *vArr, double fictionRhoPt )
{
if ( !fRand )
{
printf("StringFragmentation: fRand is not set!!!\n" );
return 0;
}
// double yStringSize = fabs( fRand->Gaus(1,0.2) ) + fabs( fRand->Gaus(0,fYmax-fYmin) );
// double yStringShift = fRand->Gaus(0,fStringShiftSigma);
// double yStringSize = fabs( fRand->Gaus(4,0.4) ) + 2*fabs( fRand->Gaus(0,2) );
// double yStringSize = fabs( fRand->Gaus(4,0.2) ) + 2*fabs( fRand->Gaus(0,4) );
//WAS USED FOR PROCEEDING... double yStringSize = 10;//fRand->Uniform(2,10);
double yStringSize = fYmax-fYmin;//fRand->Uniform(2,10);
// double yStringSize = fabs( fRand->Gaus(fYmax-fYmin,0.2) ) + 2*fabs( fRand->Gaus(0,0.5) );
// double yStringSize = fYmax-fYmin;//fabs( fRand->Gaus(3.6,0.2) ) + 2*fabs( fRand->Gaus(0,5) );
// double yStringShift = fRand->Uniform(-fStringShiftSigma,fStringShiftSigma) + fRand->Gaus(0,fStringShiftSigma);
double yStringShift = (fYmax+fYmin)/2;//fRand->Gaus(0,fStringShiftSigma);
// double yStringShift = fRand->Gaus(0,2);
// double yStringSize = fabs( fRand->Gaus(3.6,0.2) ) + 2*fabs( fRand->Gaus(0,5) );
// double yStringSize = fabs( fRand->Gaus(3.6,0.2) ) + 2*fabs( fRand->Gaus(0,5) );
// double yStringSize = fabs( fRand->Gaus(3.6,0.2) ) + 2*fabs( fRand->Gaus(0,5) );
// double yStringSize = fRand->Uniform(0., fYmax-fYmin);
// double yStringSize = fabs( fRand->Gaus(2.,0.001) ) + 2*fabs( fRand->Gaus(0,0.2) );
// funcStringDecay->SetParameter( 0, yStringSize );
// funcStringDecay->SetParameter( 1, 1 );
// cout << nParticlesInString << endl;
if(0)if ( fRand->Uniform() > 0.25) //ministrings
{
// yStringSize = TMath::Max(4., fabs(fRand->Gaus(0,2)) );
yStringSize = fabs( fRand->Gaus(2,0.2) ) + 2*fabs( fRand->Gaus(0,1) );
// yStringSize = TMath::Max(0.5, fabs(fRand->Gaus(0,1)) );
//TMath::Max( 0.5, fabs( fRand->Gaus(1.5,0.3) ) + 2*fabs( fRand->Gaus(0,0.2) ) );
}
// int nParticlesInString = 0.72 /*coeffToTuneMult*/ * TMath::Max(1,TMath::Nint( fRand->Gaus(yStringSize,yStringSize/10) )); // /2270*1550;
// nParticlesInString *= 1.14; //for energy-dependence! (30.01.2015, tuning basing on STAR)
int nParticlesInString = TMath::Max(1,TMath::Nint( fRand->Gaus(yStringSize,yStringSize/10) )); // /2270*1550;
// nParticlesInString *= 1.25; //arbitrary factor to increase multiplicity
nParticlesInString *= 1.25*0.7; //arbitrary factor to tune multiplicity IN CASE OF ALL PARTICLES - RHOS
//nParticlesInString; // to take into account two pions from single rho!!!!!!!
// int nParticlesInString = TMath::Max(1,TMath::Nint( fRand->Gaus(yStringSize,yStringSize/5) ));
//WAS USED FOR PROCEEDING... int nParticlesInString = TMath::Max(2,TMath::Nint( fRand->Gaus(1.2,0.5) ));
int nCutPoints = nParticlesInString + 1;
for ( int iBreak = 0; iBreak < nCutPoints; iBreak++ )
{
// double y = fRand->Uniform( fRand->Gaus(fYmin,0.2)+yStringShift, fRand->Gaus(fYmax,0.2)+yStringShift );
// double y = fRand->Uniform( fYmin+yStringShift, fYmax+yStringShift );
// double y = funcStringDecay->GetRandom();
double y = fRand->Uniform( -yStringSize/2 + yStringShift, yStringSize/2+yStringShift );
// double y = fRand->Gaus( 0, fRand->Gaus(fYmin,0.2) ) + yStringShift;
//y += yStringShift; //fRand->Gaus(0,2);
yBreakPoints[iBreak] = y;
}
//sort cut points
TMath::Sort<double, int>( nCutPoints, yBreakPoints, indecesCutsSorted, kFALSE );
//fill array with sorted y of the string cuts
for ( int iBreak = 0; iBreak < nCutPoints; iBreak++ )
yBreakPointsSorted[iBreak] = yBreakPoints[ indecesCutsSorted[iBreak] ];
// double particleMass = mRho;
// double particleMass = mPion;
// possible LOGICAL ERROR HERE!!! (if use the mass in cut point calculations)
//double factorToPtExp = ( particleMass == mPion ? 2.5 : 1.57 );
//make pTs at string cuts
for ( int iBreak = 0; iBreak < nCutPoints; iBreak++ )
{
/*
https://arxiv.org/pdf/1101.2599v1.pdf :
page 86:
The transverse dimensions of the tube are of typical hadronic sizes, roughly 1 fm.
From hadron mass spectroscopy the string constant k, i.e. the amount of energy per unit length, is known to
be k ≈ 1 GeV/fm ≈ 0.2 GeV2.
page 87:
...The expression “massless” relativistic string is somewhat of a misnomer:
k effectively corresponds to a “mass density” along the string.
Typically, a break occurs when the q and the qbar
ends of a colour singlet system are 1–5 fm apart in the qqbar rest frame,
but note that the higher-momentum particles at the outskirts of the system are
appreciably Lorentz contracted.
At the end of the process, the string has broken by the creation of a set
of new qiqbari pairs, with i running from 1 to n − 1 for a system that fragments
into n primary hadrons (i.e. hadrons before secondary decays). Each hadron
is formed by the quark from one break (or an endpoint) and the antiquark
from an adjacent break: qqbar1, q1qbar2, q2qbar3, . . . , qn−1qbar.
page 90:
The factorization of the transverse-momentum and the mass terms leads
to a flavour-independent Gaussian spectrum for the q'qbar' pairs.
Since the
string is assumed to have no transverse excitations, this p⊥ is locally compensated
between the quark and the antiquark of the pair, and <pT_q^2> = sigma^2 = κ/π ≈ (250 MeV)2.
Experimentally a number closer to σ2 ≈ (350 MeV)2 is required,
which could be explained as the additional effect of soft-gluon
radiation below the shower cutoff scale. That radiation would have a nonGaussian
shape but, when combined with the ordinary fragmentation p⊥, the
overall shape is close to Gaussian, and is parameterized correspondingly in
the program. Hadrons receive p⊥ contributions from two q'qbar' pairs and have
<pT_hadron^2> = sigma^2 2σ^2.
The formula also implies a suppression of heavy quark production,
u : d : s : c ≈ 1 : 1 : 0.3 : 10−11.
The simplest scheme for baryon production is that, in addition to quark–
antiquark pairs, also antidiquark–diquark pairs are occasionally produced in
the field, in a triplet–antitriplet representation.
*/
// !!! use some numerical factor to MATCH MEAN PT when later merge two quarks of string fragments
// if ( particleMass == mPion )
// breakPointPt[iBreak] = fRand->Exp( 0.25 ); //0.3); //funcPt->GetRandom();//fRand->Exp(pTtau);
// else //rho
// breakPointPt[iBreak] = fRand->Exp( 0.25 ); //0.75 );//fictionRhoPt ); //0.3); //funcPt->GetRandom();//fRand->Exp(pTtau);
// breakPointPt[iBreak] = fRand->Exp( 0.25 ); //0.75 );//fictionRhoPt ); //0.3); //funcPt->GetRandom();//fRand->Exp(pTtau);
// GOOD: breakPointPt[iBreak] = fabs(fRand->Gaus( 0, 0.35 )); //0.75 );//fictionRhoPt ); //0.3); //funcPt->GetRandom();//fRand->Exp(pTtau);
// breakPointPt[iBreak] = funcPt->GetRandom( /*fictionRhoPt*/ ); //0.3); //funcPt->GetRandom();//fRand->Exp(pTtau);
// const double kPtFor_u_d_quarks = 0.35;
// ##### July 2016: NEW STRING DECAY INTO QUARKS:
bool flagFineQuarkConfig = false;
while ( !flagFineQuarkConfig )
{
double probQuarkType = fRand->Uniform( 0, 2.3); // u:d:s = 1:1:0.3 from Generators overview paper
if ( probQuarkType < 0.01 ) // Sept 2017: ASSUME SOME PROBABILITY TO DECAY INTO C-QUARK!
{
breakPointType[iBreak] = 3; // c - quark
breakPointPt[iBreak] = fabs(fRand->Exp( 0.35 ));
}
else if ( probQuarkType < 0.2 )
{
breakPointType[iBreak] = 1; // s - quark
// breakPointPt[iBreak] = fabs(fRand->Gaus( 0, 0.47 )); //0.45 ));
// breakPointPt[iBreak] = fabs(fRand->Gaus( 0.1, 0.35 )); //0.45 ));
breakPointPt[iBreak] = fabs(fRand->Exp( 0.35 )); //0.45 ));
}
else //if ( probQuarkType < 0.05 )
{
double probQuarkDiquark = fRand->Uniform( 0, 1 );
if ( probQuarkDiquark < 0.04 )
{
breakPointType[iBreak] = 2; // diquark
// breakPointPt[iBreak] = fabs(fRand->Gaus( 0, 0.56 )); //0.55 ));
// breakPointPt[iBreak] = fabs(fRand->Gaus( 0.3, 0.35 )); //0.55 ));
breakPointPt[iBreak] = fabs(fRand->Exp( 0.48 ));
}
else
{
breakPointType[iBreak] = 0; // u and d quarks
// breakPointPt[iBreak] = fabs(fRand->Gaus( 0, 0.28 ) ); //0.28 ));// 0.35 ));
breakPointPt[iBreak] = fabs(fRand->Exp( 0.2 )); //0.45 ));
}
}
if ( iBreak == 0 ) // first break: always allowed
flagFineQuarkConfig = true;
else
{
if ( breakPointType[iBreak-1] == 2 && breakPointType[iBreak] == 2 ) // NOT ALLOWED CONFIG! ("pentaquark? :) )
continue;
else
flagFineQuarkConfig = true;
}
}
// ...
// if ( fictionRhoPt == 0 )
// breakPointPt[iBreak] = 0;
// else
// breakPointPt[iBreak] = fRand->Gaus(fictionRhoPt,0.01); //funcPt->GetRandom();//fRand->Exp(pTtau);
// breakPointPt[iBreak] = fRand->Uniform( 0.1, 0.5 );
breakPointPhi[iBreak] = fRand->Uniform( 0, 2*TMath::Pi() );
}
//calc kinematic params of "particles"=string fragments
for ( int iBreak = 0; iBreak < nParticlesInString; iBreak++ )
{
double pT1 = breakPointPt[iBreak];
double pT2 = breakPointPt[iBreak+1];
double phi1 = breakPointPhi[iBreak];
double phi2 = breakPointPhi[iBreak+1];
phi2 += TMath::Pi();
FixAngleInTwoPi(phi2);
double ptX = pT1*cos( phi1 ) + pT2*cos( phi2 );
double ptY = pT1*sin( phi1 ) + pT2*sin( phi2 );
double ptParticle = sqrt( ptX*ptX+ptY*ptY );
// double ptParticle = fRand->Exp(0.9);
if ( ptParticle < 0.01 )
ptParticle = 0.01;
// FOR TESTS!!!
if(0)
{
if ( fictionRhoPt == 0 )
ptParticle = 0.01;
else
ptParticle = fRand->Exp(fictionRhoPt);
// ptParticle = fRand->Gaus(fictionRhoPt,0.01); //funcPt->GetRandom();//fRand->Exp(pTtau);
}
// FOR TESTS!!!
if(0)
ptParticle = fRand->Exp(0.75);
// !!! RANDOMIZE PT for generated particles:
// fParticles[iBreak].pt = funcPt->GetRandom();
// cout << fParticles[iP].pt << endl;
double phiVectorSum = asin( ptY/ptParticle );
if ( ptX < 0 )
phiVectorSum = TMath::Pi()-phiVectorSum;
FixAngleInTwoPi(phiVectorSum);
FixAngleInTwoPi(phiVectorSum);
// histPhi->Fill(phiVectorSum);
// histPtRho->Fill(ptParticle );
// histPtRhoWithWeight->Fill(ptParticle, 1./2/TMath::Pi()/ptParticle );
double phiParticle = phiVectorSum;
if(0)
phiParticle = fRand->Uniform( 0, 2*TMath::Pi() );//phiVectorSum;
double yParticle = (yBreakPointsSorted[iBreak] + yBreakPointsSorted[iBreak+1])/2;
if(0)
yParticle = fRand->Uniform( -yStringSize/2, yStringSize/2 );
// yParticle = fRand->Uniform( fYmin+yStringShift, fYmax+yStringShift ); //use it to "shuffle" particles in y!
// yParticle += fRand->Gaus(0,1);
// yParticle = fRand->Uniform( -yStringSize/2, yStringSize/2 );
yParticle = fRand->Uniform( -yStringSize/2+yStringShift, yStringSize/2+yStringShift );
// to get pions = 0.8 when half of them goes from rho decays:
// probabilities for rho, pions, kaons+protons should be 0.25, 0.5, 0.25
// k=1 //ratio of pions from rho-s to pions from string
// a=0.8 //ratio of final state pions to all charged
// x=(a*k)/(2*k+2-a*k)
// y=(a*k)/(2*k+2-a*k)*2/k
// z=1-x-y
// check: (2*x+y)/(2*x+y+z)
// TMP: just assign mass for particle. Todo?: separate mechanisms for mesons and proton (?)
double particleMass = mPion;
// ##### tune particle ratios!
if (0) // only rho mesons!!!
{
while ( fabs(particleMass-mRho) > mRhoWidth/2 )
particleMass = fRand->Gaus(mRho,mRhoWidth/2);//( fRand->Uniform(0,1) > 0.5 ? fRand->Gaus(mRho,mRhoWidth/2) : mPion );
}
// else //if (0)
// {
// double probPID = fRand->Uniform(0,1);
// if ( probPID < 0.0 )
// particleMass = fRand->Gaus(mRho,mRhoWidth/2);//( fRand->Uniform(0,1) > 0.5 ? fRand->Gaus(mRho,mRhoWidth/2) : mPion );
// else if ( probPID < 0.75 )
// particleMass = mPion;
// else //kaon or proton (13% and 4%)
// {
// if ( fRand->Uniform(0,1) < 13./(13+4) )
// particleMass = mKaon;
// else
// particleMass = mProton;
// }
// }
else
{
short q1 = breakPointType[iBreak];
short q2 = breakPointType[iBreak+1];
if ( q1 == 0 && q2 == 0 ) // u/d quarks => pions
particleMass = mPion;
else if ( (q1 == 0 && q2 == 1)
|| (q1 == 1 && q2 == 0) ) // u/d and s quarks => kaons
particleMass = mKaon;
else if ( q1 == 1 && q2 == 1 ) // two s quarks => phi
particleMass = mPhi;
else if ( (q1 == 0 && q2 == 2)
|| (q1 == 2 && q2 == 0) ) // u/d quarks and diquark => protons/neutrons (!!! also neutrons!)
particleMass = mProton;
else if ( (q1 == 1 && q2 == 2)
|| (q1 == 2 && q2 == 1) ) // s quark and diquark => Lambda
particleMass = mLambda;
else if ( q1 == 3 || q2 == 3 ) // KOSTYL': if at least one of the two string ends is a c-quark
//(q1 == 0 && q2 == 3)
// || (q1 == 3 && q2 == 0) ) // u/d quarks and c quark => D-meson
particleMass = mD0;
else
{
cout << "breakPointTypes: impossible configuration! "
<< q1 << " and " << q2 << endl;
particleMass = mLambda;
}
}
// cout << particleMass << endl;
// ptParticle = fRand->Exp(0.45);
// prepare lorentz vector
if (1) //use direct sampling of pt "boltzman" distr
{
if ( fabs( particleMass-mPion) < 0.001 )
ptParticle = funcPtBoltzmanLikePion->GetRandom();
else if ( fabs( particleMass-mKaon) < 0.001 )
ptParticle = funcPtBoltzmanLikeKaon->GetRandom();
else if ( fabs( particleMass-mProton) < 0.001 )
ptParticle = funcPtBoltzmanLikeProton->GetRandom();
else if ( fabs( particleMass-mD0) < 0.001 )
ptParticle = funcPtBoltzmanLikeDmeson->GetRandom();
}
if (0)
phiParticle = fRand->Uniform( 0, TMath::TwoPi() );
double mT = sqrt( ptParticle*ptParticle + particleMass*particleMass );
double pX = ptParticle * cos(phiParticle);
double pY = ptParticle * sin(phiParticle);
double pZ = mT*sinh(yParticle);
vArr[iBreak].SetXYZM( pX, pY, pZ, particleMass );
}
return nParticlesInString;
}
double HHVM_FUNCTION(sinh, double arg) { return sinh(arg); }
Constante& Rationnel::sinush()const
{
Reel* res = new Reel(sinh((float)num/den));
return *res;
}
#include <stdio.h>
#include <math.h>
printf("%f\n", sin(0.12));
printf("%f\n", cos(0.12));
printf("%f\n", tan(0.12));
printf("%f\n", asin(0.12));
printf("%f\n", acos(0.12));
printf("%f\n", atan(0.12));
printf("%f\n", sinh(0.12));
printf("%f\n", cosh(0.12));
printf("%f\n", tanh(0.12));
printf("%f\n", exp(0.12));
printf("%f\n", fabs(-0.12));
printf("%f\n", log(0.12));
printf("%f\n", log10(0.12));
printf("%f\n", pow(0.12, 0.12));
printf("%f\n", sqrt(0.12));
printf("%f\n", round(12.34));
printf("%f\n", ceil(12.34));
printf("%f\n", floor(12.34));
void main() {}
double r_sinh(real *x)
#endif
{
return( sinh(*x) );
}
//! RHS: x->z (x'=z).
inline void operator()(double t,double x[],double z[]) const
{
// references to clarify (?) the code:
const double& nConIntraK =x[0];
const double& nConIntraNa =x[1];
const double& nConIntraCa =x[2];
const double& nConIntraCl =x[3];
const double& nConIntraglu =x[4];
const double& aConIntraK =x[5];
const double& aConIntraNa =x[6];
const double& aConIntraCa =x[7];
const double& aConIntraCl =x[8];
const double& aConIntraglu =x[9];
const double& ConExtraK =x[10];
const double& ConExtraNa =x[11];
const double& ConExtraCa =x[12];
const double& ConExtraCl =x[13];
const double& ConExtraglu =x[14];
const double& nVm =x[15];
const double& aVm =x[16];
const double& nPropVol =x[17];
const double& aPropVol =x[18];
//------------Compute------------------
double depol=fdepol(t,x[20]);
// calcul des potentiels d'équilibre par la loi de Nernst
double nEK = (RTF)*log(ConExtraK/nConIntraK);
//double nECa = ((RT)/(2*F))*log(ConExtraCa/nConIntraCa);
double nENa = (RTF)*log(ConExtraNa/nConIntraNa);
double nEglu = (-RTF)*log(ConExtraglu/nConIntraglu);
double nECl = (-RTF)*log(ConExtraCl/nConIntraCl);
double aEK = (RTF)*log(ConExtraK/aConIntraK);
//double aECa = ((RT)/(2*F))*log(ConExtraCa/aConIntraCa);
double aENa = (RTF)*log(ConExtraNa/aConIntraNa);
double aEglu = (-RTF)*log(ConExtraglu/aConIntraglu);
double aECl = (-RTF)*log(ConExtraCl/aConIntraCl);
//courant du canal potassique KDR
double nmeqKDR = (0.0047*(nVm - 8)/(1 - exp(-(nVm - 8)/12))) /
(0.0047*( nVm - 8)/(1 - exp(-(nVm - 8)/12.0)) + exp(-(nVm + 127)/30.0));
double nheqKDR = 1/(1 + exp((nVm + 25)/4.0));
double nIKDR = 1.e-3 * ngKDR * nmeqKDR*nmeqKDR * nheqKDR *(nVm - nEK);
double ameqKDR = (0.0047*(aVm - 8)/(1 - exp(-(aVm - 8)/12))) /
(0.0047*( aVm - 8)/(1 - exp(-(aVm - 8)/12)) + exp(-(aVm + 127)/30));
double aheqKDR = 1/(1 + exp((aVm + 25)/4));
double aIKDR = 1.e-3 * agKDR * ameqKDR* ameqKDR * aheqKDR *(aVm - aEK);
//courant du canal potassique BK
double nmeqBK = 250*nConIntraCa*exp(nVm/24)/(250*nConIntraCa*exp(nVm/24) +
0.1*exp(-nVm/24));
double nIBK = 1.e-3 * ngBK * nmeqBK *(nVm - nEK);
double ameqBK = 250*aConIntraCa*exp(aVm/24)/(250*aConIntraCa*exp(aVm/24) +
0.1*exp(-aVm/24));
double aIBK = 1.e-3 * agBK * ameqBK * (aVm - aEK);
//courant du canal potassiques Kir
double ameqKir = 1/(2+exp(1.62*(FRT)*(aVm-aEK)));
double aIKir = 1.e-3 * agKir * ameqKir * (ConExtraK/(ConExtraK+13))*
(aVm - aEK);
//courant du canal calcique CaHVA
double nCurlyPhi= FRT*nVm;
double nA1 = (nConIntraCa*exp(2*nCurlyPhi)-ConExtraCa) /
(exp(2*nCurlyPhi) - 1);
double namCaHVA = 8.5/(1 + exp(-(nVm - 8)/12.5));
double nbmCaHVA = 35/(1 + exp((nVm + 74)/14.5));
double nmeqCaHVA = namCaHVA/(namCaHVA + nbmCaHVA) ;
double nahCaHVA = 0.0015/(1 + exp((nVm + 29)/8));
double nbhCaHVA = 0.0055/(1 + exp(-(nVm + 23)/8));
double nheqCaHVA = nahCaHVA/(nahCaHVA + nbhCaHVA) ;
double nICaHVA = 10 * F * npHVA * ngCaHVA * 4 * nCurlyPhi *
nmeqCaHVA * nheqCaHVA * nA1 ;
//nICaHVA*=bCaHVA;
double aCurlyPhi= FRT*aVm;
double aA1 = (aConIntraCa*exp(2*aCurlyPhi)-ConExtraCa) /
(exp(2*aCurlyPhi) - 1);
double aamCaHVA = 8.5/(1 + exp(-(aVm - 8)/12.5));
double abmCaHVA = 35/(1 + exp((aVm + 74)/14.5));
double ameqCaHVA = aamCaHVA/(aamCaHVA + abmCaHVA) ;
double aahCaHVA = 0.0015/(1 + exp((aVm + 29)/8));
double abhCaHVA = 0.0055/(1 + exp(-(aVm + 23)/8));
double aheqCaHVA = aahCaHVA/(aahCaHVA + abhCaHVA) ;
double aICaHVA = 10 * F * apHVA * agCaHVA * 4 * aCurlyPhi *
ameqCaHVA * aheqCaHVA * aA1 ;
//aICaHVA*=bCaHVA;
//courant du canal sodique NaP
double namNaP =200/(1 + exp(-(nVm - 18)/16));
double nbmNaP = 25/(1 + exp((nVm + 58)/8));
double nmeqNaP = namNaP/(namNaP + nbmNaP) ;
double nINaP = (1.e-3 * ngNaP * nmeqNaP * (nVm - nENa));// *bNap;
double aamNaP =200/(1 + exp(-(aVm - 18)/16));
double abmNaP = 25/(1 + exp((aVm + 58)/8));
double ameqNaP = aamNaP/(aamNaP + abmNaP) ;
double aINaP = (1.e-3 * agNaP * ameqNaP * (aVm - aENa));//*bNap;
//courants dus au récepteur NMDA et AMPA
double nConGLU=ConExtraglu;
double nA2 = 72*nConGLU/(72*nConGLU + 6.6) ;
double nB2 = 1/(1 + 0.028*exp(-0.062*nVm)) ;
double nCK = ((nConIntraK/ConExtraK)*exp(nCurlyPhi)- 1)/
(exp(nCurlyPhi)- 1);
double ngKNMDA = ((nPK*F*F)/(RT))*ConExtraK ;
double nIKNMDA = 1.e-3 * ngKNMDA * nA2 * nB2 * nCK * nVm;
double nCNa = ((nConIntraNa/ConExtraNa)*exp(nCurlyPhi)- 1)/
(exp(nCurlyPhi)- 1);
double ngNaNMDA = ((nPK*F*F)/(RT))*ConExtraNa;
double nINaNMDA = 1.e-3 * ngNaNMDA * nA2 * nB2 * nCNa * nVm;
double nCCa = ((nConIntraCa/ConExtraCa)*exp(2*nCurlyPhi)- 1)/
(exp(2*nCurlyPhi)- 1);
double ngCaNMDA = ((4*6*nPK*F*F)/(RT))*ConExtraCa;
double nICaNMDA = 1.e-3 * ngCaNMDA * nA2 * nB2 * nCCa * nVm;
//nIKNMDA*=bNMDA;
//nINaNMDA*=bNMDA;
//nICaNMDA*=bNMDA;
double aConGLU=ConExtraglu;
double aA2 = 1100*aConGLU/(1100*aConGLU + 190) ;
double aCK = ((aConIntraK/ConExtraK)*exp(aCurlyPhi)- 1)/
(exp(aCurlyPhi)- 1);
double agKAMPA = ((aPK*F*F)/(RT))*ConExtraK ;
double aIKAMPA = 1.e-3 * agKAMPA * aA2 * aCK * aVm;
double aCNa = ((aConIntraNa/ConExtraNa)*exp(aCurlyPhi)- 1)/
(exp(aCurlyPhi)- 1);
double agNaAMPA = ((aPK*F*F)/(RT))*ConExtraNa;
double aINaAMPA = 1.e-3 * agNaAMPA * aA2 * aCNa * aVm;
//aIKAMPA*=bAMPA;
//aINaAMPA*= bAMPA;
//courants de la pompe Na+/K+
double nCapitalPhi = FRT*(nVm + 176.5);
double nA3 = pow(ConExtraK/(ConExtraK + 3.7),2) ;
double nB3 = pow(nConIntraNa/(nConIntraNa + 0.6),3) ;
double nC3 = (0.052*sinh(nCapitalPhi))/(0.026*exp(nCapitalPhi) +
22.5*exp(-nCapitalPhi));
double nIKpompeKNa = -0.01 * nrNaK * depol * nA3 * nB3 * nC3 ;
//double nINapompeKNa = (3/2)*(-10)^(-2) * nrNaK * depol * nA3 * nB3 * nC3;
double nINapompeKNa = (1.5)*0.01 * nrNaK * depol * nA3 * nB3 * nC3;
double aCapitalPhi = FRT*(aVm + 176.5);
double aA3 = pow(ConExtraK/(ConExtraK + 3.7),2) ;
double aB3 = pow(aConIntraNa/(aConIntraNa + 0.6),3) ;
double aC3 = (0.052*sinh(aCapitalPhi))/(0.026*exp(aCapitalPhi) +
22.5*exp(-aCapitalPhi));
double aIKpompeKNa = -0.01 * arNaK * depol * aA3 * aB3 * aC3 ;
double aINapompeKNa = (1.5)*0.01 * arNaK * depol * aA3 * aB3 * aC3;
//courant de la pompe Ca2+
double nICapompe = depol*ngCapompe*0.01*nConIntraCa/(nConIntraCa+0.0002);
double aICapompe = depol*agCapompe*0.01*aConIntraCa/(aConIntraCa+0.0002);
//courant de la pompe Cl-
double nIClpompe=-0.01 * depol *ngClpompe * nConIntraCl/(nConIntraCl+25);
double aIClpompe=-0.01 * depol *agClpompe * aConIntraCl/(aConIntraCl+25);
//courants de l'antiport Na+/Ca2+
double aa=F/(2*RT);
double nA4 = pow(nConIntraNa,3)*ConExtraCa*exp(aa*nVm)
- pow(ConExtraNa,3)*nConIntraCa*exp(-aa*nVm);
double nB4 = 1 + 0.0001*(pow(ConExtraNa,3)*nConIntraCa
+ pow(nConIntraNa,3)*ConExtraCa);
double nICaantiport = -0.01*(nrNaCa/20736.0) * nA4/nB4;
double nINaantiport = (1.5)* 0.01*(nrNaCa/20736.0) * nA4/nB4;
double aA4 = pow(aConIntraNa,3)*ConExtraCa*exp(aa*aVm)
- pow(ConExtraNa,3)*aConIntraCa*exp(-aa*aVm);
double aB4 = 1 + 0.0001*(pow(ConExtraNa,3)*aConIntraCa
+ pow(aConIntraNa,3)*ConExtraCa);
double aICaantiport = -0.01* (arNaCa/20736.0) * aA4/aB4;
double aINaantiport = (1.5)* 0.01*(arNaCa/20736.0) * aA4/aB4;
//nICaantiport*=bNaCa; nINaantiport*=bNaCa;
//aICaantiport*=bNaCa; aINaantiport*=bNaCa;
//courants du transporteur du glutamate
double nEtransp = (RT/F)*log(
pow(ConExtraNa/nConIntraNa,3)*
(nConIntraK/ConExtraK)*
(ConExtraglu/nConIntraglu)
);
//double nIglu = -0.001 * ngtransp * (nVm - nEtransp);
double nINatransporteur = 3*0.001 * ngtransp * (nVm - nEtransp);
double nIKtransporteur = -0.001 * ngtransp * (nVm - nEtransp);
double nIglutransporteur = -0.001 * ngtransp * (nVm - nEtransp);
double aEtransp = (RT/F)*log(
pow(ConExtraNa/aConIntraNa,3)*
(aConIntraK/ConExtraK)*
(ConExtraglu/aConIntraglu)
);
//double aIglu = -0.001 * agtransp * (aVm - aEtransp);
double aINatransporteur = 3*0.001 * agtransp * (aVm - aEtransp);
double aIKtransporteur = -0.001 * agtransp * (aVm - aEtransp);
double aIglutransporteur = -0.001 * agtransp * (aVm - aEtransp);
// nINatransporteur*=bGLU; nIKtransporteur*=bGLU;
// nIglutransporteur*=bGLU;aINatransporteur*=bGLU;
// aIKtransporteur*=bGLU; aIglutransporteur*=bGLU;
// courants du transporteur Na/K/Cl
double aEinvNaKCl = -2*aECl + aEK + aENa;
double aINacotransp = -0.001*arNaKCl * aEinvNaKCl;
double aIKcotransp = -0.001*arNaKCl * aEinvNaKCl;
double aIClcotransp = 2*0.001*arNaKCl * aEinvNaKCl;
// aINacotransp*=bNaKCl;
// aIKcotransp*=bNaKCl;
// aIClcotransp*=bNaKCl;
//courants de glutamate
double nIgludiff = 0.001 * ngglu * (nVm - nEglu);
double aIgludiff = 0.001 * agglu * (aVm - aEglu);
//courant du canal Cl-
double nEinvKCl = nECl - nEK;
double nIClglob = -0.001 * ngClglob * nEinvKCl;
double nIKglob = 0.001 * ngClglob * nEinvKCl;
double aEinvKCl = aECl - aEK;
double aIClglob = -0.001 * agClglob * aEinvKCl;
double aIKglob = 0.001 * agClglob * aEinvKCl;
//courants stretch pour le Cl
double nIstre = - ngstre *
(nPropVol0 + 50 * (nPropVol - nPropVol0))/nPropVol0;
double aIstre = - agstre *
(aPropVol0 + 50 * (aPropVol - aPropVol0))/aPropVol0;
// courants Cl
double nICl = 0.001 * ngCl*(nVm-nECl);
double aICl = 0.001 * agCl*(aVm-aECl);
//somme des courants
double nSommeCourantsK = nIKDR + nIBK + nIKNMDA + nIKpompeKNa +
nIKtransporteur + nIKglob;
double nSommeCourantsCa = nICaHVA + nICaNMDA + nICaantiport + nICapompe;
double nSommeCourantsNa = nINaP + nINaNMDA + nINapompeKNa +
nINaantiport + nINatransporteur ;
double nSommeCourantsglu = nIglutransporteur + nIgludiff ;
double nSommeCourantsCl = nICl + nIClglob + nIClpompe + nIstre;
// double nSommeCourantsCat = nSommeCourantsNa + nSommeCourantsK +
// nSommeCourantsCa ;
// double ncourants = nSommeCourantsCat + nSommeCourantsCl +
// nSommeCourantsglu ;
double aSommeCourantsK = aIKDR + aIKir + aIBK + aIKAMPA + aIKpompeKNa +
aIKtransporteur + aIKcotransp + aIKglob;
double aSommeCourantsCa = aICaHVA + aICaantiport +
aICapompe;
double aSommeCourantsNa = aINaP + aINaAMPA + aINapompeKNa +
aINaantiport + aINatransporteur + aINacotransp ;
double aSommeCourantsglu = aIglutransporteur + aIgludiff ;
double aSommeCourantsCl = aICl + aIClglob + aIClpompe + aIClcotransp +
aIstre;
// double aSommeCourantsCat = aSommeCourantsNa + aSommeCourantsK +
// aSommeCourantsCa ;
// double acourants = aSommeCourantsCat + aSommeCourantsCl +
// aSommeCourantsglu ;
//------ F:------------------------------------------
double snfv=1000*n1*nsurf/(F*v);
z[0]=-snfv*nSommeCourantsK;
z[1]=-snfv*nSommeCourantsNa;
z[2]=-snfv*nSommeCourantsCa/2.0;
z[3]= snfv*nSommeCourantsCl;
z[4]= snfv*nSommeCourantsglu;
const double safv=1000*n2*asurf/(F*v);
z[5]=-safv*aSommeCourantsK;
z[6]=-safv*aSommeCourantsNa;
z[7]=-safv*aSommeCourantsCa/2.0;
z[8]= safv*aSommeCourantsCl;
z[9]=safv*aSommeCourantsglu;
z[10]=snfv*nSommeCourantsK+safv*aSommeCourantsK;
z[11]=snfv*nSommeCourantsNa+safv*aSommeCourantsNa;
z[12]=snfv*nSommeCourantsCa/2.0+safv*aSommeCourantsCa/2.0;
z[13]=-snfv*nSommeCourantsCl-safv*aSommeCourantsCl;
z[14]=-snfv*nSommeCourantsglu-safv*aSommeCourantsglu;
//---Vmn et Vma:
z[15]=-1000.0*(nsurf/ncap)*(nSommeCourantsNa+nSommeCourantsK+
nSommeCourantsCa+
nSommeCourantsCl+nSommeCourantsglu);
z[16]= -1000.0*(asurf/acap)*(aSommeCourantsNa+
aSommeCourantsK+aSommeCourantsCa+
aSommeCourantsCl+aSommeCourantsglu);
//
double Cn=nConIntraK+nConIntraNa+nConIntraCa+nConIntraCl+nConIntraglu;
double Ca=aConIntraK+aConIntraNa+aConIntraCa+aConIntraCl+aConIntraglu;
double Ce=ConExtraK+ConExtraNa+ConExtraCa+ConExtraCl+ConExtraglu;
//---fn:
z[17]=alpha_n*(Cn+nnP0/(v*nPropVol)-Ce);
//---fa:
z[18]=alpha_a*(Ca+anP0/(v*aPropVol)-Ce);
//---transformation pour utiliser les variables "primales":
for(int i=0;i<5;i++)
z[i]=(z[i]-x[i]*z[17])/nPropVol;
for(int i=5;i<10;i++)
z[i]=(z[i]-x[i]*z[18])/aPropVol;
for(int i=10;i<15;i++)
z[i]=(z[i]+x[i]*(z[17]+z[18]))/(1.0-aPropVol-nPropVol);
//---recuperation:
recup(x,z[19],z[20]);
}
void ctss_calculate_biquad_coeff(CTSS_DSPNode *node,
CTSS_BiquadType type,
float freq,
float dbGain,
float bandwidth) {
CTSS_BiquadState *state = node->state;
float a0, a1, a2, b0, b1, b2;
float A = powf(10.0f, dbGain / 40.0f);
float omega = HZ_TO_RAD(freq);
float sn = sinf(omega);
float cs = cosf(omega);
float alpha = sn * sinh(CT_LN2 / 2.0f * bandwidth * omega / sn);
float beta = sqrtf(A + A);
switch (type) {
case LPF:
default:
b0 = (1.0f - cs) / 2.0f;
b1 = 1.0f - cs;
b2 = (1.0f - cs) / 2.0f;
a0 = 1.0f + alpha;
a1 = -2.0f * cs;
a2 = 1.0f - alpha;
break;
case HPF:
b0 = (1.0f + cs) / 2.0f;
b1 = -(1.0f + cs);
b2 = (1.0f + cs) / 2.0f;
a0 = 1.0f + alpha;
a1 = -2.0f * cs;
a2 = 1.0f - alpha;
break;
case BPF:
b0 = alpha;
b1 = 0;
b2 = -alpha;
a0 = 1.0f + alpha;
a1 = -2.0f * cs;
a2 = 1.0f - alpha;
break;
case NOTCH:
b0 = 1.0f;
b1 = -2.0f * cs;
b2 = 1.0f;
a0 = 1.0f + alpha;
a1 = -2.0f * cs;
a2 = 1.0f - alpha;
break;
case PEQ:
b0 = 1.0f + (alpha * A);
b1 = -2.0f * cs;
b2 = 1.0f - (alpha * A);
a0 = 1.0f + (alpha / A);
a1 = -2.0f * cs;
a2 = 1.0f - (alpha / A);
break;
case LSH:
b0 = A * ((A + 1.0f) - (A - 1.0f) * cs + beta * sn);
b1 = 2.0f * A * ((A - 1.0f) - (A + 1.0f) * cs);
b2 = A * ((A + 1.0f) - (A - 1.0f) * cs - beta * sn);
a0 = (A + 1.0f) + (A - 1.0f) * cs + beta * sn;
a1 = -2.0f * ((A - 1.0f) + (A + 1.0f) * cs);
a2 = (A + 1.0f) + (A - 1.0f) * cs - beta * sn;
break;
case HSH:
b0 = A * ((A + 1.0f) + (A - 1.0f) * cs + beta * sn);
b1 = -2.0f * A * ((A - 1.0f) + (A + 1.0f) * cs);
b2 = A * ((A + 1.0f) + (A - 1.0f) * cs - beta * sn);
a0 = (A + 1.0f) - (A - 1.0f) * cs + beta * sn;
a1 = 2.0f * ((A - 1.0f) - (A + 1.0f) * cs);
a2 = (A + 1.0f) - (A - 1.0f) * cs - beta * sn;
break;
}
a0 = 1.0f / a0;
state->f[0] = b0 * a0;
state->f[1] = b1 * a0;
state->f[2] = b2 * a0;
state->f[3] = a1 * a0;
state->f[4] = a2 * a0;
state->f[5] = state->f[6] = state->f[7] = state->f[8] = 0.0f;
}
void MathSinh(struct ParseState *Parser, struct Value *ReturnValue, struct Value **Param, int NumArgs)
{
ReturnValue->Val->FP = sinh(Param[0]->Val->FP);
}
void bessjy(double x, double xnu, double *rj, double *ry)
{
void beschb(double x, double *gam1, double *gam2, double *gampl, double
*gammi);
int i,isign,l,nl;
double a,b,br,bi,c,cr,ci,d,del,del1,den,di,dlr,dli,dr,e,f,fact,fact2,
fact3,ff,gam,gam1,gam2,gammi,gampl,h,p,pimu,pimu2,q,r,rjl,
rjl1,rjmu,rjp1,rjpl,rjtemp,ry1,rymu,rymup,rytemp,sum,sum1,
temp,w,x2,xi,xi2,xmu,xmu2;
if (x <= 0.0 || xnu<0.0) nrerror("bad argumnets in bessjy");
nl=(x < XMIN ? (int)(xnu+0.5) : IMAX(0,(int)(xnu+1.5)));
xmu=xnu-nl;
xmu2=xmu*xmu;
xi=1.0/x;
xi2=2.0*xi;
w=xi2/M_PI;
isign=1;
h=xnu*xi;
if(h<FPMIN) h=FPMIN;
b=xi2*xnu;
d=0.0;
c=h;
for (i=1;i<=MAXIT;i++)
{
b+=xi2;
d=b-d;
if(fabs(d)< FPMIN) d=FPMIN;
c=b-1.0/c;
if(fabs(c)<FPMIN) c=FPMIN;
d=1.0/d;
del=c*d;
h=del*h;
if(d<0.0) isign=-isign;
if(fabs(del-1.0)<EPS) break;
}
if(i>MAXIT) nrerror("x too large in bessjy; try asymptotic expansion");
rjl=isign*FPMIN;
rjpl=h*rjl;
rjl1=rjl;
rjp1=rjpl;
fact=xnu*xi;
for (l=nl;l>=1;l--){
rjtemp=fact*rjl+rjpl;
fact-=xi;
rjpl=fact*rjtemp-rjl;
rjl=rjtemp;
}
if(rjl ==0.0) rjl=EPS;
f=rjpl/rjl;
if (x<XMIN) {
x2=0.5*x;
pimu=M_PI*xmu;
fact=(fabs(pimu)<EPS ? 1.0 : pimu/sin(pimu));
d=-log(x2);
e=xmu*d;
fact2=(fabs(e)< EPS ? 1.0 : sinh(e)/e);
beschb(xmu,&gam1,&gam2,&gampl,&gammi);
ff=2.0/M_PI*fact*(gam1*cosh(e)+gam2*fact2*d);
e=exp(e);
p=e/(gampl*M_PI);
q=1.0/(e*M_PI*gammi);
pimu2=0.5*pimu;
fact3=(fabs(pimu2) <EPS ? 1.0 : sin(pimu2)/pimu2);
r=M_PI*pimu2*fact3*fact3;
c=1.0;
d=-x2*x2;
sum=ff+r*q;
sum1=p;
for (i=1;i<=MAXIT;i++)
{ff=(i*ff+p+q)/(i*i-xmu2);
c *=(d/i);
p/= (i-xmu);
q/=(i+xmu);
del=c*(ff+r*q);
sum+=del;
del1=c*p-i*del;
sum1 +=del1;
if(fabs(del) < (1.0+fabs(sum))*EPS) break;
}
if(i > MAXIT) nrerror("bessy series failed to converge");
rymu=-sum;
ry1=-sum1*xi2;
rymup=xmu*xi*rymu-ry1;
rjmu=w/(rymup-f*rymu);
} else {
a=0.25-xmu2;
p=-0.5*xi;
q=1.0;
br=2.0*x;
bi=2.0;
fact=a*xi/(p*p+q*q);
cr=br+q*fact;
ci=bi+p*fact;
den=br*br+bi*bi;
dr=br/den;
di=-bi/den;
dlr=cr*dr-ci*di;
dli=cr*di+ci*dr;
temp=p*dlr-q*dli;
q=p*dli+q*dlr;
p=temp;
for(i=2;i<=MAXIT;i++)
{a+=2*(i-1);
bi +=2.0;
dr=a*dr+br;
di=a*di+bi;
if (fabs(dr)+fabs(di) < FPMIN) dr=FPMIN;
fact=a/(cr*cr+ci*ci);
cr=br+cr*fact;
ci=bi-ci*fact;
if(fabs(cr)+fabs(ci)<FPMIN) cr=FPMIN;
den=dr*dr+di*di;
dr/=den;
di /=-den;
dlr=cr*dr-ci*di;
dli=cr*di+ci*dr;
temp=p*dlr-q*dli;
q=p*dli+q*dlr;
p=temp;
if (fabs(dlr-1.0)+fabs(dli) < EPS) break;
}
if(i>MAXIT) nrerror("cf2 failed in bessjy");
gam=(p-f)/q;
rjmu=sqrt(w/((p-f)*gam+q));
rjmu=SIGN(rjmu,rjl);
rymu=rjmu*gam;
rymup=rymu*(p+q/gam);
ry1=xmu*xi*rymu-rymup;
}
fact=rjmu/rjl;
*rj=rjl1*fact;
for(i=1;i<=nl;i++)
{rytemp=(xmu+i)*xi2*ry1-rymu;
rymu=ry1;
ry1=rytemp;
}
*ry=rymu;
}
double
tanh(double x)
{
return sinh(x) / cosh(x);
}
int decode_function(char *ptr,int argnum,double *argptr,
double *value,void *data) {
int i;
for (i=0;fnlist[i] !=0;i++) if (strcmp(ptr,fnlist[i])==0) break;
switch(i) {
case 0:
*value=fabs(argptr[0]);
break;
case 1:
*value=acos(argptr[0]);
break;
case 2:
*value=acosh(argptr[0]);
break;
case 3:
*value=asin(argptr[0]);
break;
case 4:
*value=asinh(argptr[0]);
break;
case 5:
*value=atan(argptr[0]);
break;
case 6:
*value=atan2(argptr[0],argptr[1]);
break;
case 7:
*value=atanh(argptr[0]);
break;
case 8:
*value=ceil(argptr[0]);
break;
case 9:
*value=cos(argptr[0]);
break;
case 10:
*value=cosh(argptr[0]);
break;
case 11:
*value=exp(argptr[0]);
break;
case 12:
*value=floor(argptr[0]);
break;
case 13:
*value=(int) argptr[0];
break;
case 14:
*value=log(argptr[0]);
break;
case 15:
*value=log10(argptr[0]);
break;
case 16:
*value=sin(argptr[0]);
break;
case 17:
*value=sinh(argptr[0]);
break;
case 18:
*value=sqrt(argptr[0]);
break;
case 19:
*value=tan(argptr[0]);
break;
case 20:
*value=tanh(argptr[0]);
break;
}
return 0;
}
void test_extra(T)
{
T t = 1;
t = abs(t);
t = abs(t*t);
t = fabs(t);
t = fabs(t*t);
t = sqrt(t);
t = sqrt(t*t);
t = floor(t);
t = floor(t*t);
t = ceil(t);
t = ceil(t*t);
t = trunc(t);
t = trunc(t*t);
t = round(t);
t = round(t*t);
t = exp(t);
t = exp(t*t);
t = log(t);
t = log(t*t);
t = log10(t);
t = log10(t*t);
t = cos(t);
t = cos(t*t);
t = sin(t);
t = sin(t*t);
t = tan(t);
t = tan(t*t);
t = asin(t);
t = asin(t*t);
t = atan(t);
t = atan(t*t);
t = acos(t);
t = acos(t*t);
t = cosh(t);
t = cosh(t*t);
t = sinh(t);
t = sinh(t*t);
t = tanh(t);
t = tanh(t*t);
double dval = 2;
t = pow(t, t);
t = pow(t, t*t);
t = pow(t, dval);
t = pow(t*t, t);
t = pow(t*t, t*t);
t = pow(t*t, dval);
t = pow(dval, t);
t = pow(dval, t*t);
t = atan2(t, t);
t = atan2(t, t*t);
t = atan2(t, dval);
t = atan2(t*t, t);
t = atan2(t*t, t*t);
t = atan2(t*t, dval);
t = atan2(dval, t);
t = atan2(dval, t*t);
t = fmod(t, t);
t = fmod(t, t*t);
t = fmod(t, dval);
t = fmod(t*t, t);
t = fmod(t*t, t*t);
t = fmod(t*t, dval);
t = fmod(dval, t);
t = fmod(dval, t*t);
typedef typename T::backend_type backend_type;
typedef typename backend_type::exponent_type exp_type;
exp_type e = 0;
int i = 0;
t = ldexp(t, i);
t = ldexp(t*t, i);
t = ldexp(t, e);
t = ldexp(t*t, e);
t = frexp(t, &i);
t = frexp(t*t, &i);
t = frexp(t, &e);
t = frexp(t*t, &e);
}
npy_double npy_sinh(npy_double x)
{
return sinh(x);
}
void eval_sinh(Expr *expr)
{
expr->l->fn(expr->l);
expr->v.x = sinh(expr->l->v.x);
}
void Parser::optimise_call(ExprNode *node)
{
DBL result = 0.0;
bool have_result = true;;
if(node->op != OP_CALL)
return;
if(node->child == NULL)
return;
if(node->child->op != OP_CONSTANT)
return;
switch(node->call.token)
{
case SIN_TOKEN:
result = sin(node->child->number);
break;
case COS_TOKEN:
result = cos(node->child->number);
break;
case TAN_TOKEN:
result = tan(node->child->number);
break;
case ASIN_TOKEN:
result = asin(node->child->number);
break;
case ACOS_TOKEN:
result = acos(node->child->number);
break;
case ATAN_TOKEN:
result = atan(node->child->number);
break;
case SINH_TOKEN:
result = sinh(node->child->number);
break;
case COSH_TOKEN:
result = cosh(node->child->number);
break;
case TANH_TOKEN:
result = tanh(node->child->number);
break;
case ASINH_TOKEN:
result = asinh(node->child->number);
break;
case ACOSH_TOKEN:
result = acosh(node->child->number);
break;
case ATANH_TOKEN:
result = atanh(node->child->number);
break;
case ABS_TOKEN:
result = fabs(node->child->number);
break;
case RADIANS_TOKEN:
result = node->child->number * M_PI / 180.0;
break;
case DEGREES_TOKEN:
result = node->child->number * 180.0 / M_PI;
break;
case FLOOR_TOKEN:
result = floor(node->child->number);
break;
case INT_TOKEN:
result = (int)(node->child->number);
break;
case CEIL_TOKEN:
result = ceil(node->child->number);
break;
case SQRT_TOKEN:
result = sqrt(node->child->number);
break;
case EXP_TOKEN:
result = exp(node->child->number);
break;
case LN_TOKEN:
if(node->child->number > 0.0)
result = log(node->child->number);
else
Error("Domain error in 'ln'.");
break;
case LOG_TOKEN:
if(node->child->number > 0.0)
result = log10(node->child->number);
else
Error("Domain error in 'log'.");
break;
case MIN_TOKEN:
have_result = false;
break;
case MAX_TOKEN:
have_result = false;
break;
case ATAN2_TOKEN:
have_result = false;
break;
case POW_TOKEN:
have_result = false;
break;
case MOD_TOKEN:
have_result = false;
break;
case SELECT_TOKEN:
have_result = false;
break;
case FUNCT_ID_TOKEN:
have_result = false;
break;
case VECTFUNCT_ID_TOKEN:
have_result = false;
break;
default:
have_result = false;
break;
}
if(have_result == true)
{
POV_FREE(node->call.name);
node->number = result;
node->op = OP_CONSTANT;
POV_FREE(node->child);
node->child = NULL;
}
}
inline double _d0_cosh(double arg) { return (sinh(arg)); }
double complex
ccosh(double complex z)
{
double x, y, h;
int32_t hx, hy, ix, iy, lx, ly;
x = creal(z);
y = cimag(z);
EXTRACT_WORDS(hx, lx, x);
EXTRACT_WORDS(hy, ly, y);
ix = 0x7fffffff & hx;
iy = 0x7fffffff & hy;
/* Handle the nearly-non-exceptional cases where x and y are finite. */
if (ix < 0x7ff00000 && iy < 0x7ff00000) {
if ((iy | ly) == 0)
return (cpack(cosh(x), x * y));
if (ix < 0x40360000) /* small x: normal case */
return (cpack(cosh(x) * cos(y), sinh(x) * sin(y)));
/* |x| >= 22, so cosh(x) ~= exp(|x|) */
if (ix < 0x40862e42) {
/* x < 710: exp(|x|) won't overflow */
h = exp(fabs(x)) * 0.5;
return (cpack(h * cos(y), copysign(h, x) * sin(y)));
} else if (ix < 0x4096bbaa) {
/* x < 1455: scale to avoid overflow */
z = __ldexp_cexp(cpack(fabs(x), y), -1);
return (cpack(creal(z), cimag(z) * copysign(1, x)));
} else {
/* x >= 1455: the result always overflows */
h = huge * x;
return (cpack(h * h * cos(y), h * sin(y)));
}
}
/*
* cosh(+-0 +- I Inf) = dNaN + I sign(d(+-0, dNaN))0.
* The sign of 0 in the result is unspecified. Choice = normally
* the same as dNaN. Raise the invalid floating-point exception.
*
* cosh(+-0 +- I NaN) = d(NaN) + I sign(d(+-0, NaN))0.
* The sign of 0 in the result is unspecified. Choice = normally
* the same as d(NaN).
*/
if ((ix | lx) == 0 && iy >= 0x7ff00000)
return (cpack(y - y, copysign(0, x * (y - y))));
/*
* cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0.
*
* cosh(NaN +- I 0) = d(NaN) + I sign(d(NaN, +-0))0.
* The sign of 0 in the result is unspecified.
*/
if ((iy | ly) == 0 && ix >= 0x7ff00000) {
if (((hx & 0xfffff) | lx) == 0)
return (cpack(x * x, copysign(0, x) * y));
return (cpack(x * x, copysign(0, (x + x) * y)));
}
/*
* cosh(x +- I Inf) = dNaN + I dNaN.
* Raise the invalid floating-point exception for finite nonzero x.
*
* cosh(x + I NaN) = d(NaN) + I d(NaN).
* Optionally raises the invalid floating-point exception for finite
* nonzero x. Choice = don't raise (except for signaling NaNs).
*/
if (ix < 0x7ff00000 && iy >= 0x7ff00000)
return (cpack(y - y, x * (y - y)));
/*
* cosh(+-Inf + I NaN) = +Inf + I d(NaN).
*
* cosh(+-Inf +- I Inf) = +Inf + I dNaN.
* The sign of Inf in the result is unspecified. Choice = always +.
* Raise the invalid floating-point exception.
*
* cosh(+-Inf + I y) = +Inf cos(y) +- I Inf sin(y)
*/
if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
if (iy >= 0x7ff00000)
return (cpack(x * x, x * (y - y)));
return (cpack((x * x) * cos(y), x * sin(y)));
}
/*
* cosh(NaN + I NaN) = d(NaN) + I d(NaN).
*
* cosh(NaN +- I Inf) = d(NaN) + I d(NaN).
* Optionally raises the invalid floating-point exception.
* Choice = raise.
*
* cosh(NaN + I y) = d(NaN) + I d(NaN).
* Optionally raises the invalid floating-point exception for finite
* nonzero y. Choice = don't raise (except for signaling NaNs).
*/
return (cpack((x * x) * (y - y), (x + x) * (y - y)));
}
double
d_sinh(double *x)
{
return( sinh(*x) );
}
//------------------------Sampling the transition probability (v(0)=X_t, v(1)=int_0^t X_s ds)
//-------------------------dX_t = kappa(theta-X_t)dt + sigma sqrt(X_t)dW_t
//-------------------------------------In the case of the troncation serie
static void Sample_C( PnlVect* v,double t, double kappa, double sigma, double theta ,int generator)
{
//----------Declaration of variable
double gamma, lambda;
double tmp;
double tmp2;
int j,pss;
int order_tr; // Default value is equal to 20
//----------Initialization of parammter
tmp=0.;
j=0;
gamma = 4.*kappa/(sigma*sigma*(1.-exp(-kappa*t)));
lambda = pnl_vect_get(v,0)*gamma*exp(-kappa*t);
order_tr = 20;
//----------Begin operations
//----generate vt --> tmp
pss = pnl_rand_poisson(lambda*0.5,generator);
for(j=1;j<= pss;j++)
tmp = tmp + pnl_rand_gamma(1.,2., generator);
tmp = tmp +pnl_rand_gamma(2.*kappa*theta/(sigma*sigma),2.,generator);
tmp = tmp/gamma;
//----generate the variable Z
tmp2 =0.;
j=0;
pss = pnl_rand_bessel(2.*theta*kappa/(sigma*sigma)-1.,2.*kappa*sqrt(pnl_vect_get(v,0)*tmp)/(sigma*sigma*sinh(kappa*t*0.5)),generator);
for(j=1;j<=pss;j++)
{
tmp2=tmp2+X_3_sample( order_tr, t, kappa, sigma, generator);
}
//----generate int_0^t vs = X1 +X2 +X3 --> lambda
lambda=tmp2+X_2_sample( order_tr, t, kappa, sigma, theta , generator)+X_1_sample( order_tr, t, kappa, sigma, pnl_vect_get(v,0), tmp, generator);
//----set the new value
pnl_vect_set(v,0,tmp);
pnl_vect_set(v,1,lambda);
}
static double kepler( const double ecc, double mean_anom)
{
double curr, err, thresh, offset = 0.;
double delta_curr = 1.;
bool is_negative = false;
unsigned n_iter = 0;
if( !mean_anom)
return( 0.);
if( ecc < 1.)
{
if( mean_anom < -PI || mean_anom > PI)
{
double tmod = fmod( mean_anom, PI * 2.);
if( tmod > PI) /* bring mean anom within -pi to +pi */
tmod -= 2. * PI;
else if( tmod < -PI)
tmod += 2. * PI;
offset = mean_anom - tmod;
mean_anom = tmod;
}
if( ecc < .9) /* low-eccentricity formula from Meeus, p. 195 */
{
curr = atan2( sin( mean_anom), cos( mean_anom) - ecc);
do
{
err = (curr - ecc * sin( curr) - mean_anom) / (1. - ecc * cos( curr));
curr -= err;
}
while( fabs( err) > THRESH);
return( curr + offset);
}
}
if( mean_anom < 0.)
{
mean_anom = -mean_anom;
is_negative = true;
}
curr = mean_anom;
thresh = THRESH * fabs( 1. - ecc);
/* Due to roundoff error, there's no way we can hope to */
/* get below a certain minimum threshhold anyway: */
if( thresh < MIN_THRESH)
thresh = MIN_THRESH;
if( (ecc > .8 && mean_anom < PI / 3.) || ecc > 1.) /* up to 60 degrees */
{
double trial = mean_anom / fabs( 1. - ecc);
if( trial * trial > 6. * fabs(1. - ecc)) /* cubic term is dominant */
{
if( mean_anom < PI)
trial = CUBE_ROOT( 6. * mean_anom);
else /* hyperbolic w/ 5th & higher-order terms predominant */
trial = asinh( mean_anom / ecc);
}
curr = trial;
if( thresh > THRESH) /* happens if e > 2. */
thresh = THRESH;
}
if( ecc < 1.)
while( fabs( delta_curr) > thresh)
{
if( n_iter++ > MAX_ITERATIONS)
err = near_parabolic( curr, ecc) - mean_anom;
else
err = curr - ecc * sin( curr) - mean_anom;
delta_curr = -err / (1. - ecc * cos( curr));
curr += delta_curr;
}
else
while( fabs( delta_curr) > thresh)
{
if( n_iter++ > MAX_ITERATIONS)
err = -near_parabolic( curr, ecc) - mean_anom;
else
err = ecc * sinh( curr) - curr - mean_anom;
delta_curr = -err / (ecc * cosh( curr) - 1.);
curr += delta_curr;
}
return( is_negative ? offset - curr : offset + curr);
}
void
iterate (control_point *cp,
int n,
int fuse,
point *points)
{
int i, j, count_large = 0, count_nan = 0;
int xform_distrib[CHOOSE_XFORM_GRAIN];
double p[3], t, r, dr;
p[0] = points[0][0];
p[1] = points[0][1];
p[2] = points[0][2];
/*
* first, set up xform, which is an array that converts a uniform random
* variable into one with the distribution dictated by the density
* fields
*/
dr = 0.0;
for (i = 0; i < NXFORMS; i++)
dr += cp->xform[i].density;
dr = dr / CHOOSE_XFORM_GRAIN;
j = 0;
t = cp->xform[0].density;
r = 0.0;
for (i = 0; i < CHOOSE_XFORM_GRAIN; i++)
{
while (r >= t)
{
j++;
t += cp->xform[j].density;
}
xform_distrib[i] = j;
r += dr;
}
for (i = -fuse; i < n; i++)
{
/* FIXME: the following is supported only by gcc and c99 */
int fn = xform_distrib[g_random_int_range (0, CHOOSE_XFORM_GRAIN)];
double tx, ty, v;
if (p[0] > 100.0 || p[0] < -100.0 ||
p[1] > 100.0 || p[1] < -100.0)
count_large++;
if (p[0] != p[0])
count_nan++;
#define coef cp->xform[fn].c
#define vari cp->xform[fn].var
/* first compute the color coord */
p[2] = (p[2] + cp->xform[fn].color) / 2.0;
/* then apply the affine part of the function */
tx = coef[0][0] * p[0] + coef[1][0] * p[1] + coef[2][0];
ty = coef[0][1] * p[0] + coef[1][1] * p[1] + coef[2][1];
p[0] = p[1] = 0.0;
/* then add in proportional amounts of each of the variations */
v = vari[0];
if (v > 0.0)
{
/* linear */
double nx, ny;
nx = tx;
ny = ty;
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[1];
if (v > 0.0)
{
/* sinusoidal */
double nx, ny;
nx = sin (tx);
ny = sin (ty);
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[2];
if (v > 0.0)
{
/* spherical */
double nx, ny;
double r2 = tx * tx + ty * ty + 1e-6;
nx = tx / r2;
ny = ty / r2;
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[3];
if (v > 0.0)
{
/* swirl */
double r2 = tx * tx + ty * ty; /* /k here is fun */
double c1 = sin (r2);
double c2 = cos (r2);
double nx = c1 * tx - c2 * ty;
double ny = c2 * tx + c1 * ty;
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[4];
if (v > 0.0)
{
/* horseshoe */
double a, c1, c2, nx, ny;
if (tx < -EPS || tx > EPS ||
ty < -EPS || ty > EPS)
a = atan2(tx, ty); /* times k here is fun */
else
a = 0.0;
c1 = sin (a);
c2 = cos (a);
nx = c1 * tx - c2 * ty;
ny = c2 * tx + c1 * ty;
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[5];
if (v > 0.0)
{
/* polar */
double nx, ny;
if (tx < -EPS || tx > EPS ||
ty < -EPS || ty > EPS)
nx = atan2 (tx, ty) / G_PI;
else
nx = 0.0;
ny = sqrt (tx * tx + ty * ty) - 1.0;
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[6];
if (v > 0.0)
{
/* bent */
double nx, ny;
nx = tx;
ny = ty;
if (nx < 0.0) nx = nx * 2.0;
if (ny < 0.0) ny = ny / 2.0;
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[7];
if (v > 0.0)
{
/* folded handkerchief */
double theta, r2, nx, ny;
if (tx < -EPS || tx > EPS ||
ty < -EPS || ty > EPS)
theta = atan2( tx, ty );
else
theta = 0.0;
r2 = sqrt (tx * tx + ty * ty);
nx = sin (theta + r2) * r2;
ny = cos (theta - r2) * r2;
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[8];
if (v > 0.0)
{
/* heart */
double theta, r2, nx, ny;
if (tx < -EPS || tx > EPS ||
ty < -EPS || ty > EPS)
theta = atan2( tx, ty );
else
theta = 0.0;
r2 = sqrt (tx * tx + ty * ty);
theta *= r2;
nx = sin (theta) * r2;
ny = cos (theta) * -r2;
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[9];
if (v > 0.0)
{
/* disc */
double theta, r2, nx, ny;
if ( tx < -EPS || tx > EPS ||
ty < - EPS || ty > EPS)
theta = atan2 (tx, ty);
else
theta = 0.0;
nx = tx * G_PI;
ny = ty * G_PI;
r2 = sqrt (nx * nx * ny * ny);
p[0] += v * sin(r2) * theta / G_PI;
p[1] += v * cos(r2) * theta / G_PI;
}
v = vari[10];
if (v > 0.0)
{
/* spiral */
double theta, r2;
if (tx < -EPS || tx > EPS ||
ty < -EPS || ty > EPS)
theta = atan2( tx, ty );
else
theta = 0.0;
r2 = sqrt (tx * tx + ty * ty) + 1e-6;
p[0] += v * (cos (theta) + sin (r2)) / r2;
p[1] += v * (cos (theta) + cos (r2)) / r2;
}
v = vari[11];
if (v > 0.0)
{
/* hyperbolic */
double theta, r2;
if (tx < -EPS || tx > EPS ||
ty < -EPS || ty > EPS)
theta = atan2 (tx, ty);
else
theta = 0.0;
r2 = sqrt (tx * tx + ty * ty) + 1e-6;
p[0] += v * sin (theta) / r2;
p[1] += v * cos (theta) * r2;
}
v = vari[12];
if (v > 0.0 )
{
double theta, r2;
/* diamond */
if ( tx < -EPS || tx > EPS ||
ty < -EPS || ty > EPS)
theta = atan2 (tx, ty);
else
theta = 0.0;
r2 = sqrt( tx * tx + ty * ty );
p[0] += v * sin (theta) * cos (r2);
p[1] += v * cos (theta) * sin (r2);
}
v = vari[13];
if (v > 0.0)
{
/* ex */
double theta, r2, n0, n1, m0, m1;
if ( tx < -EPS || tx > EPS ||
ty < -EPS || ty > EPS)
theta = atan2 (tx, ty);
else
theta = 0.0;
r2 = sqrt( tx * tx + ty * ty );
n0 = sin(theta + r2);
n1 = cos(theta - r2);
m0 = n0 * n0 * n0 * r2;
m1 = n1 * n1 * n1 * r2;
p[0] += v * (m0 + m1);
p[1] += v * (m0 - m1);
}
v = vari[14];
if ( v > 0.0)
{
double theta, r2, nx, ny;
/* julia */
if (tx < -EPS || tx > EPS ||
ty < -EPS || ty > EPS)
theta = atan2 (tx, ty);
else
theta = 0.0;
if (flam3_random_bit ())
theta += G_PI;
r2 = pow (tx * tx + ty * ty, 0.25);
nx = r2 * cos (theta);
ny = r2 * sin (theta);
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[15];
if (v > 0.0)
{
/* waves */
double dx, dy, nx, ny;
dx = coef[2][0];
dy = coef[2][1];
nx = tx + coef[1][0] * sin (ty / ((dx * dx) + EPS));
ny = ty + coef[1][1] * sin (tx / ((dy * dy) + EPS));
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[16];
if (v > 0.0)
{
/* fisheye */
double theta, r2, nx, ny;
if (tx < -EPS || tx > EPS ||
ty < -EPS || ty > EPS)
theta = atan2 (tx, ty);
else
theta = 0.0;
r2 = sqrt (tx * tx + ty * ty);
r2 = 2 * r2 / (r2 + 1);
nx = r2 * cos (theta);
ny = r2 * sin (theta);
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[17];
if (v > 0.0)
{
/* popcorn */
double dx, dy, nx, ny;
dx = tan (3 * ty);
dy = tan (3 * tx);
nx = tx + coef[2][0] * sin (dx);
ny = ty + coef[2][1] * sin (dy);
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[18];
if (v > 0.0)
{
/* exponential */
double dx, dy, nx, ny;
dx = exp (tx - 1.0);
dy = G_PI * ty;
nx = cos (dy) * dx;
ny = sin (dy) * dx;
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[19];
if (v > 0.0)
{
/* power */
double theta, r2, tsin, tcos, nx, ny;
if (tx < -EPS || tx > EPS ||
ty < -EPS || ty > EPS)
theta = atan2 (tx, ty);
else
theta = 0.0;
tsin = sin (theta);
tcos = cos (theta);
r2 = sqrt (tx * tx + ty * ty);
r2 = pow (r2, tsin);
nx = r2 * tcos;;
ny = r2 * tsin;
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[20];
if (v > 0.0)
{
/* cosine */
double nx, ny;
nx = cos (tx * G_PI) * cosh (ty);
ny = -sin (tx * G_PI) * sinh (ty);
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[21];
if (v > 0.0)
{
/* rings */
double theta, r2, dx, nx, ny;
if (tx < -EPS || tx > EPS ||
ty < -EPS || ty > EPS)
theta = atan2 (tx, ty);
else
theta = 0;
dx = coef[2][0];
dx = dx * dx + EPS;
r2 = sqrt (tx * tx + ty * ty);
r2 = fmod (r2 + dx, 2 * dx) - dx + r2 * (1 - dx);
nx = cos (theta) * r2;
ny = sin (theta) * r2;
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[22];
if (v > 0.0)
{
/* fan */
double theta, r2, dx, dy, dx2, nx, ny;
if (tx < -EPS || tx > EPS ||
ty < -EPS || ty > EPS)
theta = atan2 (tx, ty);
else
theta = 0.0;
dx = coef[2][0];
dy = coef[2][1];
dx = G_PI * (dx * dx + EPS);
dx2 = dx / 2;
r2 = sqrt (tx * tx + ty * ty );
theta += (fmod (theta + dy, dx) > dx2) ? -dx2: dx2;
nx = cos (theta) * r2;
ny = sin (theta) * r2;
p[0] += v * nx;
p[1] += v * ny;
}
v = vari[23];
if (v > 0.0)
{
/* eyefish */
double r2;
r2 = 2.0 * v / (sqrt(tx * tx + ty * ty) + 1.0);
p[0] += r2 * tx;
p[1] += r2 * ty;
}
v = vari[24];
if (v > 0.0)
{
/* bubble */
double r2;
r2 = v / ((tx * tx + ty * ty) / 4 + 1);
p[0] += r2 * tx;
p[1] += r2 * ty;
}
v = vari[25];
if (v > 0.0)
{
/* cylinder */
double nx;
nx = sin (tx);
p[0] += v * nx;
p[1] += v * ty;
}
v = vari[26];
if (v > 0.0)
{
/* noise */
double rx, sinr, cosr, nois;
rx = flam3_random01 () * 2 * G_PI;
sinr = sin (rx);
cosr = cos (rx);
nois = flam3_random01 ();
p[0] += v * nois * tx * cosr;
p[1] += v * nois * ty * sinr;
}
v = vari[27];
if (v > 0.0)
{
/* blur */
double rx, sinr, cosr, nois;
rx = flam3_random01 () * 2 * G_PI;
sinr = sin (rx);
cosr = cos (rx);
nois = flam3_random01 ();
p[0] += v * nois * cosr;
p[1] += v * nois * sinr;
}
v = vari[28];
if (v > 0.0)
{
/* gaussian */
double ang, sina, cosa, r2;
ang = flam3_random01 () * 2 * G_PI;
sina = sin (ang);
cosa = cos (ang);
r2 = v * (flam3_random01 () + flam3_random01 () + flam3_random01 () +
flam3_random01 () - 2.0);
p[0] += r2 * cosa;
p[1] += r2 * sina;
}
/* if fuse over, store it */
if (i >= 0)
{
points[i][0] = p[0];
points[i][1] = p[1];
points[i][2] = p[2];
}
}
}