/*! Draw connected line segments in page coordinates (pts), with options to close
* /and/or fill the curve, or to set the curve as a clip area.
*/
void PSpage::polyline(VecDoub &x, VecDoub &y, Int close, Int fill, Int clip)
{
Int i,n = min(x.size(),y.size());
fprintf(PSpage::PLT,"np %g %g mt\n",x[0],y[0]);
for (i=1;i<n;i++) fprintf(PSpage::PLT,"%g %g lt\n",x[i],y[i]);
if (close || fill || clip) fprintf(PSpage::PLT,"cp ");
if (fill) fprintf(PSpage::PLT,"fi\n");
else if (clip) fprintf(PSpage::PLT,"clip\n");
else fprintf(PSpage::PLT,"st\n");
}
VecDoub SphericalPolarToCartesian(const VecDoub& Spherical){
VecDoub SPolar = {Spherical[0]*sin(Spherical[2])*cos(Spherical[1]),
Spherical[0]*sin(Spherical[2])*sin(Spherical[1]),
Spherical[0]*cos(Spherical[2])};
if(Spherical.size()==3) return SPolar;
return SPolar;
}
std::vector<VecDoub> EquatorialToGalacticwithErrors(const VecDoub &Equatorial,
const VecDoub &Errors){
//alpha, dec, s => l,b,s
double alpha = Equatorial[0], delta = Equatorial[1];
double cd = cos(delta), sd = sin(delta);
double dalpha = alpha-RA_GP;
double b=asin(sdGP*sd+cdGP*cd*cos(dalpha));
double l=lCP-atan2(cd*sin(alpha-RA_GP),cdGP*sd-sdGP*cd*cos(dalpha));
if(l<0.)l+=2.*PI;
if(Equatorial.size()==3){ std::vector<VecDoub> Galactic {{l,b,Equatorial[2]},Errors};
return Galactic;}
else{
//vlos, ma_cos(d), md => vlos, ml_cos(b), mb
double cb = cos(b), sb = sin(b);
double A11=(sdGP*cd-cdGP*sd*cos(dalpha))/cb;
double A12=-cdGP*sin(dalpha)/cb;
double A21,A22;
double dl = lCP-l;
if(fabs(cos(dl))>fabs(sin(dl))){
A21=(sd*sin(dalpha)-sb*sin(dl)*A11)/cos(dl);
A22=-(cos(dalpha)+sb*sin(dl)*A12)/cos(dl);
}else{
A21=(cdGP*cd+sdGP*sd*cos(dalpha)+sb*cos(dl)*A11)/sin(dl);
A22=(sdGP*sin(dalpha)+sb*cos(dl)*A12)/sin(dl);
}
std::vector<VecDoub> Galactic {
{l,b,Equatorial[2],Equatorial[3],
A21*Equatorial[5]+A22*Equatorial[4],A11*Equatorial[5]+A12*Equatorial[4]}
,{Errors[0],Errors[1],Errors[2],Errors[3],
sqrt(A21*A21*Errors[5]*Errors[5]+A22*A22*Errors[4]*Errors[4]),
sqrt(A11*A11*Errors[5]*Errors[5]+A12*A12*Errors[4]*Errors[4])}};
return Galactic;
}
}
VecDoub EquatorialToGalactic(const VecDoub &Equatorial){
//alpha, dec, s => l,b,s
double alpha = Equatorial[0], delta = Equatorial[1];
double cd = cos(delta), sd = sin(delta);
double dalpha = alpha-RA_GP;
double b=asin(sdGP*sd+cdGP*cd*cos(dalpha));
double l=lCP-atan2(cd*sin(alpha-RA_GP),cdGP*sd-sdGP*cd*cos(dalpha));
if(l<0.)l+=2.*PI;
VecDoub Galactic {l,b,Equatorial[2]};
if(Equatorial.size()==3)return Galactic;
else{
//vlos, ma_cos(d), md => vlos, ml_cos(b), mb
double cb = cos(b), sb = sin(b);
double dl = lCP-l;
double A11=(sdGP*cd-cdGP*sd*cos(dalpha))/cb;
double A12=-cdGP*sin(dalpha)/cb;
double A21,A22;
if(fabs(cos(dl))>fabs(sin(dl))){
A21= (sd*sin(dalpha)-sb*sin(dl)*A11)/cos(dl);
A22=-( cos(dalpha)+sb*sin(dl)*A12)/cos(dl);
}else{
A21=(cdGP*cd+sdGP*sd*cos(dalpha)+sb*cos(dl)*A11)/sin(dl);
A22=(sdGP*sin(dalpha)+sb*cos(dl)*A12)/sin(dl);
}
VecDoub GalVel {Equatorial[3],A21*Equatorial[5]+A22*Equatorial[4],
A11*Equatorial[5]+A12*Equatorial[4]};
for ( VecDoub::iterator it = GalVel.begin();
it != GalVel.end(); ++it) Galactic.push_back(*it);
return Galactic;
}
}
VecDoub GalacticToEquatorial(const VecDoub &Galactic){
//l,b,s => alpha, dec, s
double l = Galactic[0], b = Galactic[1];
double cb = cos(b),sb = sin(b);
double dl = lCP-l;
double delta=asin(cdGP*cb*cos(-dl)+sb*sdGP);
double alpha=RA_GP+atan2(cb*sin(dl),sb*cdGP-cb*sdGP*cos(-dl));
if(alpha>2.*PI)alpha-=2.*PI;
VecDoub Equatorial {alpha,delta,Galactic[2]};
if(Galactic.size()==3)return Equatorial;
else{
double dalpha = alpha-RA_GP;
//vlos, ml_cos(b), mb => vlos, ma_cos(d), md
double cd = cos(delta), sd = sin(delta);
double A11=(sdGP*cd-cdGP*sd*cos(dalpha))/cb;
double A12=-cdGP*sin(dalpha)/cb;
double A21,A22;
if(fabs(cos(dl))>fabs(sin(dl))){
A21=(sd*sin(dalpha)-sb*sin(dl)*A11)/cos(dl);
A22=-(cos(dalpha)+sb*sin(dl)*A12)/cos(dl);
}else{
A21=(cdGP*cd+sdGP*sd*cos(dalpha)+sb*cos(dl)*A11)/sin(dl);
A22=(sdGP*sin(dalpha)+sb*cos(dl)*A12)/sin(dl);
}
double Prod = A11*A22-A12*A21;
VecDoub EqVel {Galactic[3],(A11*Galactic[4]-A21*Galactic[5])/Prod,
(A22*Galactic[5]-A12*Galactic[4])/Prod};
for ( VecDoub::iterator it = EqVel.begin();
it != EqVel.end(); ++it) Equatorial.push_back(*it);
return Equatorial;
}
}
VecDoub CartesianToGalactic(const VecDoub &Cartesian,
const VecDoub& SolarPosition){
// X,Y,Z->l,b,s
double tmp1 = SolarPosition[0]-Cartesian[0];
double tmp2 = -Cartesian[1];
double tmp3 = Cartesian[2]-SolarPosition[1];
// Need to rotate to account for the height of the Sun above the plane
double h = sqrt(SolarPosition[0]*SolarPosition[0]
+SolarPosition[1]*SolarPosition[1]);
double ct = SolarPosition[0]/h, st = SolarPosition[1]/h;
double x = tmp1*ct-tmp3*st, z = tmp1*st+tmp3*ct;
double Distance = norm<double>({x,tmp2,z});
VecDoub Galactic { atan2(tmp2,x),
asin(z/Distance),
Distance};
if(Cartesian.size()==3)return Galactic;
// vx,vy,vz -> vlos,mu_lcos(b),mu_b
// in units km/s -> km/s mas/yr
else{ double vx=-Cartesian[3]*ct-Cartesian[5]*st-SolarPosition[2];
double vy = -Cartesian[4]-SolarPosition[3];
double vz = Cartesian[5]*ct+Cartesian[3]*st-SolarPosition[4];
double cl = cos(Galactic[0]), sl = sin(Galactic[0]),
cb = cos(Galactic[1]), sb = sin(Galactic[1]);
VecDoub GalVel {vx*cl*cb+vy*sl*cb+vz*sb,(-vx*sl+vy*cl)/(PM_Const*Distance),
(-vx*cl*sb-vy*sl*sb+vz*cb)/(PM_Const*Distance)};
for ( VecDoub::iterator it = GalVel.begin();
it != GalVel.end(); ++it) Galactic.push_back(*it);
return Galactic;
}
}
// ======================================================================================
// Galactic <==> Cartesian
VecDoub GalacticToCartesian(const VecDoub &Galactic,
const VecDoub& SolarPosition){
// l,b,s->X,Y,Z
double cl = cos(Galactic[0]), sl = sin(Galactic[0]),
cb = cos(Galactic[1]), sb = sin(Galactic[1]);
double x = Galactic[2]*cb*cl;
double z = Galactic[2]*sb;
// Need to rotate to account for the height of the Sun above the plane
double h = sqrt(SolarPosition[0]*SolarPosition[0]
+SolarPosition[1]*SolarPosition[1]);
double ct = SolarPosition[0]/h, st = SolarPosition[1]/h;
VecDoub Cartesian { SolarPosition[0]-ct*x-st*z,
-Galactic[2]*cb*sl,
-st*x+ct*z+SolarPosition[1]};
if(Galactic.size()==3)return Cartesian;
// vlos,mu_lcos(b),mu_b -> vx,vy,vz
// in units km/s, mas/yr -> km/s
else{
double vl = PM_Const*Galactic[2]*Galactic[4];
double vb = PM_Const*Galactic[2]*Galactic[5];
double tmp = cb*Galactic[3]-sb*vb;
double vx = cl*tmp-sl*vl+SolarPosition[2];
double vy = sl*tmp+cl*vl+SolarPosition[3];
double vz = sb*Galactic[3]+cb*vb+SolarPosition[4];
VecDoub CartVel{-(vx*ct+vz*st),-vy,-vx*st+vz*ct};
for ( VecDoub::iterator it = CartVel.begin();
it != CartVel.end(); ++it) Cartesian.push_back(*it);
return Cartesian;
}
}
VecDoub CartesianToSphericalPolar(const VecDoub& Cartesian){
double r = sqrt(Cartesian[0]*Cartesian[0]+Cartesian[1]*Cartesian[1]+Cartesian[2]*Cartesian[2]);
VecDoub SPolar = {r,atan2(Cartesian[1],Cartesian[0]),acos(Cartesian[2]/r)};
if(Cartesian.size()==3) return SPolar;
SPolar.push_back((Cartesian[3]*cos(SPolar[1])+Cartesian[4]*sin(SPolar[1]))*sin(SPolar[2])+cos(SPolar[2])*Cartesian[5]);
SPolar.push_back(-Cartesian[3]*sin(SPolar[1])+Cartesian[4]*cos(SPolar[1]));
SPolar.push_back((Cartesian[3]*cos(SPolar[1])+Cartesian[4]*sin(SPolar[1]))*cos(SPolar[2])-sin(SPolar[2])*Cartesian[5]);
return SPolar;
}
/*
Utility method used by the Spectral method to find
which node, when moved gives the maximum change in the
Modularity value.
*/
void maxModularity(double &qmax) {
int N = si.size();
VecDoub qstored(N);
for(int i=0; i<N; i++)
qstored[i] = 0;
double Q = 0.0;
for(int k=0; k<N; k++) {
if( visited[k] < 1 ) {
Q = 0.0;
deltaModularityMax( k, Q );
qstored[k] = Q;
}
}
qmax = 0;//qstored(0);
int ind_max = -1;//0;
for(int i=0; i<N; i++) {
if( qstored[i] > qmax ) {
qmax = qstored[i];
ind_max = i;
}
}
for(int i=0; i<N; i++) {
if( i != ind_max )
;
else {
visited[i] = 1;
if( si[i] == 1 ) {
si[i] = -1;
SI[i][0] = 0;
SI[i][1] = 1;
} else {
si[i] = 1;
SI[i][0] = 1;
SI[i][1] = 0;
}
}
}
}
// ============================================================================
// Dehnen Potential
// ============================================================================
double Dehnen::Phi(const VecDoub &x){
/* potential at Cartesian x */
assert(x.size()==3);
double r = norm<double>(x);
double chi = pow(r/rs,1./alpha);
chi=chi/(1+chi);
return -conv::FPG*rhoS*rs*rs*alpha*
(rs/r*incomplete_beta(alpha*(3-gamma),alpha*(beta-3),chi)
+incomplete_beta(alpha*(beta-2),alpha*(2-gamma),1-chi));
}
VecDoub Dehnen::Forces(const VecDoub &x){
/* Forces at Cartesian x */
assert(x.size()==3);
double r = norm<double>(x);
double chi = pow(r/rs,1./alpha);
double dchi = chi/r/alpha/(1+chi)*(1.-chi/(1+chi));
chi = chi/(1+chi);
r = -conv::FPG*rhoS*rs*rs*alpha*
(-rs/r/r*incomplete_beta(alpha*(3-gamma),alpha*(beta-3),chi)
+rs/r*pow(chi,alpha*(3-gamma)-1)*pow(1-chi,alpha*(beta-3)-1)*dchi
-pow(1-chi,alpha*(beta-2)-1)*pow(chi,alpha*(2-gamma)-1)*dchi);
VecDoub F = x*-r;
return F;
}
VecDoub PolarToCartesian(const VecDoub& Polar){
// R,phi,z -> X,Y,Z
double cp = cos(Polar[1]), sp = sin(Polar[1]);
VecDoub Cartesian { Polar[0]*cp,
Polar[0]*sp,
Polar[2]};
if(Polar.size()==3) return Cartesian;
// vR,vphi,vz -> vx,vy,vz
else{
VecDoub CartVel {Polar[3]*cp-Polar[4]*sp,Polar[4]*cp+Polar[3]*sp,Polar[5]};
for ( VecDoub::iterator it = CartVel.begin();
it != CartVel.end(); ++it) Cartesian.push_back(*it);
return Cartesian;
}
}
// ======================================================================================
// Cartesian <==> Polar
VecDoub CartesianToPolar(const VecDoub& Cartesian){
// X,Y,Z -> R,phi,z
VecDoub Polar { sqrt(Cartesian[0]*Cartesian[0]+Cartesian[1]*Cartesian[1]),
atan2(Cartesian[1],Cartesian[0]),
Cartesian[2]};
if(Cartesian.size()==3) return Polar;
// vx,vy,vz -> vR,vphi,vz
else{
double cp = cos(Polar[1]), sp = sin(Polar[1]);
VecDoub PolarVel { Cartesian[3]*cp+Cartesian[4]*sp,Cartesian[4]*cp-Cartesian[3]*sp,
Cartesian[5]};
for ( VecDoub::iterator it = PolarVel.begin();
it != PolarVel.end(); ++it) Polar.push_back(*it);
return Polar;
}
}
/*
Utility method used by the Spectral method fine-tune an initial
given community split.
*/
void modifySplit( double tol, int countmax ) {
double qmax = 0;
double qold = 0;
int count = 0;
int Ng = si.size();
visited.resize(Ng);
VecDoub Gsi(Ng);
MatDoub GSI(Ng,2);
for(int i=0; i<Ng; i++) {
Gsi[i] = si[i];
GSI[i][0] = SI[i][0];
GSI[i][1] = SI[i][1];
}
maxModularity( qmax );
while( count < countmax ) {
if( qmax > qold ) {
for(int i=0; i<Ng; i++) {
Gsi[i] = si[i];
GSI[i][0] = SI[i][0];
GSI[i][1] = SI[i][1];
}
}
qold = qmax;
qmax = 0.0;
maxModularity(qmax);
count++;
}
for(int i=0; i<Ng; i++) {
si[i] = Gsi[i];
SI[i][0] = GSI[i][0];
SI[i][1] = GSI[i][1];
}
}
/*
The change in Modularity used during the fine-tuning
method; where node si_i is moved from one community to
the other: if si^old_i = +-1 => si^new_i = -+1
deltaQ = deltaQ^new - deltaQ^old
= Sum_ij { Big_ij * si^new_i * si^new_j }
- Sum_ij { Big_ij * si^old_i * si^old_j }
= Sum_(i!=k,j!=k) { Bgi_ij * si^new_i * si^new_j
+ Sum_(j!=k) Big_kj * si^new_k * si^new_j
+ Sum_(i!=k) Big_ik * si^new_i * si^new_k
+ Big_kk }
- Sum_(i!=k,j!=k) { Big_ij si^old_i * si^old_j
- Sum_(j!=k) Big_kj * si^old_k * si^old_j
- Sum_(i!=k) Big_ik * si^old_i * si^old_k
- Big_kk }
= Sum_(j!=k) { Big_kj * ( si^new_k - si^old_k ) * si^old_j }
+ Sum_(i!=k) { Big_ik * si^old_i * ( si^new_k - si^old_k ) }
= 2 * ( si^new_k - si^old_k ) * Sum_(i!=k) { Big_ik * si^old_i }
= -4 * si^old_k * Sum_(i!=k) { Big_ik * si^old_i }
*/
void deltaModularityMax( int k, double &mod ) {
mod = 0;
int N = si.size();
double sumi = 0.0;
for(int i=0; i<N; i++) {
if( i!=k )
sumi += Bgi[i][k] * si[i];
}
mod = -4.0 * si[k] * sumi;
}
/*
The change in Modularity used for the Spectral method.
deltaQ = Sum_k { Sum_ij { si_ki * Bgi_ij * si_jk } }
*/
void deltaModularity( double &mod ) {
mod = 0;
int N = si.size();
double ele = 0.0;
double sum = 0.0;
MatDoub deltaQ(2,2);
MatDoub SIt(N,2);
for(int i=0; i<N; i++) {
SIt[i][0] = 0;
SIt[i][1] = 0;
for(int j=0; j<N; j++) {
SIt[i][0] += Bgi[i][j] * SI[j][0];
SIt[i][1] += Bgi[i][j] * SI[j][1];
}
}
for(int i=0; i<2; i++) {
double sum1 = 0;
double sum2 = 0;
for(int j=0; j<N; j++) {
sum1 += SI[j][0] * SIt[j][0];
sum2 += SI[j][1] * SIt[j][1];
}
deltaQ[i][0] = sum1;
deltaQ[i][1] = sum2;
}
for(int k=0; k<2; k++)
sum += deltaQ[k][k];
mod = _norm * sum;
}
double Dehnen::Density(const VecDoub& x){
assert(x.size()==3);
double r = norm<double>(x)/rs;
return rhoS*pow(r,-gamma)*pow(1.+pow(r,1./alpha),(gamma-beta)*alpha);
}
double Potential_JS::R_E(const VecDoub &x){
assert(x.size()==6);
return R_E(H(x),norm<double>({x[0],x[1],x[2]}));
}
int main(int argc, char*argv[]){
#ifdef TORUS
GalPot Pot("pot/Piffl14.Tpot");
WrapperTorusPotential TPot(&Pot);
// GalPot Pot("../Torus/pot/PJM11.Tpot");
std::cout<<TPot.KapNuOm(8.29)*conv::kpcMyr2kms<<std::endl;
#else
Logarithmic Pot(220.,1.,0.9);
#endif
VecDoub X(6,1e-4);
if(argc>2)
X[0]=atof(argv[2]);
else
X[0]=conv::StandardSolarPAUL[0];
X[2]=0.001;
X[4]=sqrt(X[0]*-Pot.Forces(X)[0]);
printVector(X);
Orbit O(&Pot,1e-8);
// Fudge
Actions_AxisymmetricStackel_Fudge AA(&Pot,-30.);
// Iterative Torus
#ifdef TORUS
IterativeTorusMachine Tor(&AA,&Pot,1e-8,5,1e-3);
#endif
// Generating Function
Actions_Genfunc AG(&Pot,"axisymmetric");
// Average generating Function
Actions_Genfunc_Average AGav(&Pot,"axisymmetric");
// uvorb
uv_orb UV(&Pot,4.,30.,50,50,"example.delta_uv");
// Cylindrical Adiabatic
Actions_CylindricalAdiabaticApproximation PAA(&Pot,"example.paa",true,false,4.,30.,15.,100);
// Spheroidal Adiabatic
Actions_SpheroidalAdiabaticApproximation SAA(&Pot,"example.saa",true,false,100.,4.,30.,15.,100);
// Spheroidal Adiabatic
Actions_StackelFit SF(&Pot,1e-8);
std::ofstream outfile;
outfile.open(argv[1]);
outfile<<"# JR Lz Jz JRJzLz ";
#ifdef TORUS
outfile<<"Rperi Rapo Zmax ";
#endif
outfile<<"OmR Omp Omz Fudgev1 ItTC O2GF AvGF Fudgev2 CAA SAA Fit\n";
double VMax = sqrt((Pot.Phi({50.,0.,50.})-Pot.Phi(X))-.5*X[4]*X[4]);
int number = 500;
if(argc>3)
number=atoi(argv[3]);
VecDoub range = create_log_range(0.03*VMax,0.8*VMax,number);
int count=0;
high_resolution_clock::time_point t1 = high_resolution_clock::now();
for(auto j: range){
count+=1;
X[3]=j;
X[5]=j*.8;
printVector(X);
double Torb = Pot.torb(X), tstep=0.204*Torb, tmax=10.*Torb;
O.integrate(X,tmax,tstep);
int guess_alpha=1;
MatDoub FResults,ITResults,GResults,GAvResults,UVResults,PAAResults,SAAResults,FITResults;
VecDoub Fudge, ITorus, Genfunc, GenfuncAv, uvAct, paaAct, saaAct, fitAct,Energy;
MatDoub dvdJ_e;
t1 = high_resolution_clock::now();
std::vector<nanoseconds> times(8,duration_cast<nanoseconds>(t1-t1));
for(auto i:O.results()){
t1 = high_resolution_clock::now();
Genfunc = AG.actions(i);
times[2]+=duration_cast<nanoseconds>(high_resolution_clock::now()-t1);GenfuncAv.resize(3);
VecDoub aa = AG.angles(i);
GResults.push_back({Genfunc[0],Genfunc[2],aa[0],aa[1],aa[2],aa[3],aa[4],aa[5]});
Energy.push_back(Pot.H(i));
}
VecDoub acts = {columnMean(GResults)[0],Pot.Lz(X),columnMean(GResults)[1],columnMean(GResults)[5],columnMean(GResults)[6],columnMean(GResults)[7]};
VecDoub GF_SD = columncarefulSD(GResults);
outfile<<acts[0]<<" "<<acts[1]<<" "<<acts[2]<<" "<<(acts[0]+acts[2])/fabs(acts[1])<<" ";
#ifdef TORUS
Actions J;J[0]=acts[0]/conv::kpcMyr2kms;
J[2]=acts[1]/conv::kpcMyr2kms;J[1]=acts[2]/conv::kpcMyr2kms;
Torus T; T.AutoFit(J,&TPot,1e-5);
outfile<<T.minR()<<" "<<T.maxR()<<" "<<" "<<T.maxz()<<" ";
MatDoub Hess = dOmdJ(J,.1*J,&TPot);
#endif
outfile<<acts[3]<<" "<<acts[4]<<" "<<acts[5]<<" "<<carefulSD(Energy)/Mean(Energy)<<" ";
int N=0;
for(auto i:O.results()){
VecDoub ang = AG.angles(i);
t1 = high_resolution_clock::now();
Fudge = AA.actions(i,&guess_alpha);
times[0]+=duration_cast<nanoseconds>(high_resolution_clock::now()-t1);
VecDoub ang2 = AA.angles(i,&guess_alpha);
FResults.push_back({Fudge[0]-acts[0],Fudge[2]-acts[2],ang2[0]-ang[0],ang2[1]-ang[1],ang2[2]-ang[2],ang2[3]-ang[3],ang2[4]-ang[4],ang2[5]-ang[5]});
for(unsigned k=2;k<5;++k){
if(FResults[N][k]>PI) FResults[N][k] = 2.*PI-FResults[N][k];
if(FResults[N][k]<-PI) FResults[N][k] = 2.*PI+FResults[N][k];
}
t1 = high_resolution_clock::now();
#ifdef TORUS
ITorus = Tor.actions(i);
times[1]+=duration_cast<nanoseconds>(high_resolution_clock::now()-t1);
ITResults.push_back({ITorus[0]-acts[0],ITorus[2]-acts[2],ITorus[6]-ang[0],ITorus[7]-ang[1],ITorus[8]-ang[2],ITorus[3]-ang[3],ITorus[4]-ang[4],ITorus[5]-ang[5]});
for(unsigned k=2;k<5;++k){
if(ITResults[N][k]>PI) ITResults[N][k]=2.*PI-ITResults[N][k];
if(ITResults[N][k]<-PI) ITResults[N][k]=2.*PI+ITResults[N][k];
}
#endif
t1 = high_resolution_clock::now();
GenfuncAv = AGav.actions(i);
times[3]+=duration_cast<nanoseconds>(high_resolution_clock::now()-t1);
GAvResults.push_back({GenfuncAv[0]-acts[0],GenfuncAv[2]-acts[2],0.,0.,0.,0.,0.,0.});
t1 = high_resolution_clock::now();
uvAct = UV.actions(i);
times[4]+=duration_cast<nanoseconds>(high_resolution_clock::now()-t1);
ang2 = UV.angles(i);
UVResults.push_back({uvAct[0]-acts[0],uvAct[2]-acts[2],ang2[0]-ang[0],ang2[1]-ang[1],ang2[2]-ang[2],ang2[3]-ang[3],ang2[4]-ang[4],ang2[5]-ang[5]});
for(unsigned k=2;k<5;++k){
if(UVResults[N][k]>PI) UVResults[N][k]=2.*PI-UVResults[N][k];
if(UVResults[N][k]<-PI) UVResults[N][k]=2.*PI+UVResults[N][k];
}
t1 = high_resolution_clock::now();
paaAct = PAA.actions(i);
times[5]+=duration_cast<nanoseconds>(high_resolution_clock::now()-t1);
ang2 = PAA.angles(i);
PAAResults.push_back({paaAct[0]-acts[0],paaAct[2]-acts[2],ang2[0]-ang[0],ang2[1]-ang[1],ang2[2]-ang[2],ang2[3]-ang[3],ang2[4]-ang[4],ang2[5]-ang[5]});
for(unsigned k=2;k<5;++k){
if(PAAResults[N][k]>PI)PAAResults[N][k]=2.*PI-PAAResults[N][k];
if(PAAResults[N][k]<-PI)PAAResults[N][k]=2.*PI+PAAResults[N][k];
}
t1 = high_resolution_clock::now();
saaAct = SAA.actions(i,&guess_alpha);
times[6]+=duration_cast<nanoseconds>(high_resolution_clock::now()-t1);
ang2 = SAA.angles(i,&guess_alpha);
SAAResults.push_back({saaAct[0]-acts[0],saaAct[2]-acts[2],ang2[0]-ang[0],ang2[1]-ang[1],ang2[2]-ang[2],ang2[3]-ang[3],ang2[4]-ang[4],ang2[5]-ang[5]});
for(unsigned k=2;k<5;++k){
if(SAAResults[N][k]>PI)SAAResults[N][k]=2.*PI-SAAResults[N][k];
if(SAAResults[N][k]<-PI)SAAResults[N][k]=2.*PI+SAAResults[N][k];
}
t1 = high_resolution_clock::now();
fitAct = SF.actions(i);
times[7]+=duration_cast<nanoseconds>(high_resolution_clock::now()-t1);
ang2 = SF.angles(i);
FITResults.push_back({fitAct[0]-acts[0],fitAct[2]-acts[2],ang2[0]-ang[0],ang2[1]-ang[1],ang2[2]-ang[2],ang2[3]-ang[3],ang2[4]-ang[4],ang2[5]-ang[5]});
for(unsigned k=2;k<5;++k){
if(FITResults[N][k]>PI)FITResults[N][k]=2.*PI-FITResults[N][k];
if(FITResults[N][k]<-PI)FITResults[N][k]=2.*PI+FITResults[N][k];
}
++N;
}
double timeT=tstep;VecDoub freqs;
for(int i=1;i<N;++i){
freqs=columnMean(GResults)*timeT;
GResults[i][2]-=GResults[0][2]+freqs[5];
GResults[i][3]-=GResults[0][3]+freqs[6];
GResults[i][4]-=GResults[0][4]+freqs[7];
timeT+=tstep;
for(unsigned k=2;k<5;++k)
while(GResults[i][k]<-PI)GResults[i][k]+=2.*PI;
}
for(int k=2;k<5;++k) GResults[0][k]=0.;
for(auto k:columnRMS(FResults)) outfile<<k<<" ";
#ifdef TORUS
for(auto k:columnRMS(ITResults)) outfile<<k<<" ";
#endif
for(auto k:columncarefulSD(GResults)) outfile<<k<<" ";
for(auto k:columnRMS(GAvResults)) outfile<<k<<" ";
for(auto k:columnRMS(UVResults)) outfile<<k<<" ";
for(auto k:columnRMS(PAAResults)) outfile<<k<<" ";
for(auto k:columnRMS(SAAResults)) outfile<<k<<" ";
for(auto k:columnRMS(FITResults)) outfile<<k<<" ";
for(unsigned N=0;N<8;++N) outfile<<times[N].count()/range.size()<<" ";
#ifdef TORUS
for(unsigned kk=0;kk<3;++kk)
for(unsigned pp=0;pp<3;++pp)
outfile<<Hess[kk][pp]<<" ";
#endif
outfile<<std::endl;
}
outfile.close();
}
//-------------------------------------------------------------------
// Method to calculate the Spectral Modularity
//-------------------------------------------------------------------
void calculateSpectralModularity() {
int N = si.size();
MatDoub Bg(N,N);
Bg.resize(N,N);
Bg = Bgi;
//--- Calculate eigenvectors, and values, from Bgi...
calculateEigenVectors();
int ind = -1;
findLeadingEigenVectors(ind);
cout << "> max EigenValue is " << betai[ind] << " with ind " << ind << endl;
//--- set up the index vectors, si and SI, for the initial split
maximiseIndexVectors(ind);
double tol = 0.00001;//the tolerance value, 10^-5; eigenvalues below this threshold are not used
int dummy = -1000;
double deltaQ_old = 0.0;
double deltaQ_new = 0.0;
//--- Calculate the Spectral Modularity
deltaModularity(deltaQ_old);
cout << "> Spectral Q: " << deltaQ_old << endl;
double diff = deltaQ_old;
//--- Fine tuning stage to maximum deltaModularity for the initial split
while( diff > tol ) {
modifySplit( tol, N );
deltaModularity( deltaQ_new );
cout << "> Modified Q: " << deltaQ_new << endl;
diff = fabs( deltaQ_new - deltaQ_old );
deltaQ_old = deltaQ_new;
}
//--- Keep recorded of maximum fine-tuned Modularity value.
specQ += deltaQ_old;
cout << "> node list " << endl;
for(int i=1; i<n.size(); i++) {
keys_p[i-1] = 0;
keys_n[i-1] = 0;
if(si[i-1] > 0) {
keys_p[i-1] = n[i].k;
keys_n[i-1] = dummy;
n[i].c = 1;
} else {
keys_p[i-1] = dummy;
keys_n[i-1] = n[i].k;
n[i].c = 2;
}
n[i].print();
}
//--- Recursively split the group of positive eigenvector nodes
splitP(Bg, keys_p, dummy, tol);
//--- Recursively split the group of negative eigenvector nodes
splitN(Bg, keys_n, dummy, tol);
}