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bkg.cpp
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bkg.cpp
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// bkg.cpp
// Defines functions for calculating the background phi, phiprime, H
#include "bkg.h"
int bkg::psiprime(double lna, const double psi[], double psip[], void* params){
//psi is a vector whose elements are phi, phiprime, H
(void)(lna);
psip[0] = psi[1];
psip[1] = ( (((psi[1]*psi[1]/(2.*Mpl*Mpl)) - 3.)*psi[1]) - (pot::Vp(psi[0], *(step_params*)params)/(psi[2]*psi[2])) );
psip[2] = -1.*psi[2]*psi[1]*psi[1]/(2.*Mpl*Mpl);
return GSL_SUCCESS;
}
void bkg::bkg_calc(){
printf("Calling bkg_calc\n");
//step_params p;
std::cout << "in BKG_CALC " << p.c << std::endl;
gsl_odeiv2_system sys = {psiprime, nullptr, 3, &p};
gsl_odeiv2_driver * d = gsl_odeiv2_driver_alloc_y_new(&sys, gsl_odeiv2_step_rkf45, 0.001, 0., 1.e-13);
double lna_step = (lna1 - lna0)/nsteps;
double psi[3] = {phi_init, phip_init, H_init};
double lna_i;
int status;
bool fillin1 = true;
bool fillin2 = false;
double factor;
if(p.d>0.005){
factor = 3.;
} else if (p.d > 0.0005){
factor = 4.;
} else {
factor = 8.;
} // this is a bad solution but OK for now
//Add initial conditions to bkg arrays
lna.push_back(lna0);
a.push_back(exp(lna0));
lna_matched.push_back(lna0);
a_matched.push_back(exp(lna0));
phi.push_back(phi_init);
phip.push_back(phip_init);
H.push_back(H_init);
epsH.push_back(phip_init*phip_init/2.);
/*
etaH.push_back( -1.*( ( (((phip_init*phip_init/2.) - 3.)*phip_init) - (pot::Vp(phi_init, p)/(H_init*H_init))) - (phip_init*phip_init*phip_init/2.) )/phip_init);
delta2.push_back(( (pow(phip_init, 5.)/4.)
+ (( (pot::Vp(phi_init, p)/(H_init*H_init)) - (phip_init*((phip_init*phip_init/4.) - 3.)) )*phip_init*phip_init)
- ((3.*phip_init*phip_init/2.) * ( (((phip_init*phip_init/2.)-3.)*phip_init) - (pot::Vp(phi_init, p)/(H_init*H_init)) ))
+ ((3.*((phip_init*phip_init/2.)-1.)*( (((phip_init*phip_init/2.)-3.)*phip_init) - (pot::Vp(phi_init, p)/(H_init*H_init)) )) - (phip_init*phip_init*pot::Vp(phi_init, p)/(H_init*H_init)) - (phip_init*pot::Vpp(phi_init, p)/(H_init*H_init))) )
/phip_init);
*/
//printf("%.9e %.9e %.9e %.9e %.9e %.9e %.9e %.9e\n", lna[0], exp(lna[0]), phi[0], phip[0], H_init, phip[0]*phip[0]/2., etaH.back(), delta2.back());
//Evolve initial conditions and fill bkg arrays until inflation ends
for(int i=1; i<=nsteps; i++){
//std::cout <<(14.668 + (3.*p.d)) << " " << (14.668 - (3.*p.d)) << " " << phi.back() << std::endl;
if ( phi.back() > (14.668 + (factor*p.d)) || phi.back() < (14.668 - (5.*p.d)) ){
if(fillin2){
indexetalo = i;
fillin2 = false;
}
lna_i = lna0+lna_step;
} else {
if(fillin1){
indexetahi = i;
fillin1 = false;
fillin2 = true;
}
lna_i = lna0 + (lna_step/30.); //make this factor a function of c and d (likely c/d^2) but OK for now
}
status = gsl_odeiv2_driver_apply(d, &lna0, lna_i, psi);
if(status!=GSL_SUCCESS){
printf("Error, bkg integrator return value=%d\n", status);
break;
}
lna.push_back(lna0);
a.push_back(exp(lna0));
lna_matched.push_back(lna0);
a_matched.push_back(exp(lna0));
phi.push_back(psi[0]);
phip.push_back(psi[1]);
H.push_back(psi[2]);
epsH.push_back(psi[1]*psi[1]/(2.*Mpl*Mpl));
/*
etaH.push_back( -1.*( ( (((psi[1]*psi[1]/2.) - 3.)*psi[1]) - (pot::Vp(psi[0], p)/(psi[2]*psi[2])))
- (psi[1]*psi[1]*psi[1]/2.) )
/psi[1]);
delta2.push_back(( (pow(psi[1], 5.)/4.)
+ (( (pot::Vp(psi[0], p)/(psi[2]*psi[2])) - (psi[1]*((psi[1]*psi[1]/4.) - 3.)) )*psi[1]*psi[1])
- ((3.*psi[1]*psi[1]/2.) * ( (((psi[1]*psi[1]/2.)-3.)*psi[1]) - (pot::Vp(psi[0], p)/(psi[2]*psi[2])) ))
+ ((3.*((psi[1]*psi[1]/2.)-1.)*( (((psi[1]*psi[1]/2.)-3.)*psi[1]) - (pot::Vp(psi[0], p)/(psi[2]*psi[2])) )) - (psi[1]*psi[1]*pot::Vp(psi[0], p)/(psi[2]*psi[2])) - (psi[1]*pot::Vpp(psi[0], p)/(psi[2]*psi[2]))) )
/psi[1]);
*/
//printf("%.9e %.9e %.9e %.9e %.9e %.9e %.9e %.9e\n", lna0, exp(lna0), psi[0], psi[1], psi[2], epsH.back(), etaH.back(), delta2.back());
if((phip.back()*phip.back()/(2.*Mpl*Mpl)) >= 1.){
double Nefolds = lna.back() - lna[0]; //improve this by some interpolation but OK for now
int index50ef;
if(Nefolds < 50.){
printf("Error, not enough efolds\n");
} else {
for(int i=0; i<lna.size(); i++){
if((lna.back()-lna[i]) <= 50.){
index50ef = i;
break;
}
}
}
matching = log(0.05) - log(H[index50ef]) + 50. - lna.back();// + log(mpcconv);
printf("aH 50 ef = %.9e\n", exp(lna[index50ef]) * H[index50ef]);
printf("Nefolds before end = %.9e\n", (lna.back() - lna[index50ef]));
printf("logH50ef, lnaend = %.9e %.9e\n", log(H[index50ef]), lna.back());
printf("matching value = %.9e %.9e\n", exp(matching), matching);
printf("H_pivot = %.5e\n", H[index50ef]);
printf("alpha_e = %.5e %.5e\n", lna.back(), lna.rbegin()[1]);
printf("conversion factor = %.5e\n", mpcconv);
printf("lna0 and last = %.5e %.5e\n", lna[0], lna.back());
//Consider saving the matching condition to prevent dealing with large numbers
std::transform(lna_matched.begin(), lna_matched.end(), lna_matched.begin(), std::bind2nd(std::plus<double>(), matching));
std::transform(a_matched.begin(), a_matched.end(), a_matched.begin(), std::bind2nd(std::multiplies<double>(), exp(matching)));
std::transform(lna.begin(), lna.end(), lna.begin(), std::bind2nd(std::plus<double>(), matching));
std::transform(a.begin(), a.end(), a.begin(), std::bind2nd(std::multiplies<double>(), exp(matching)));
printf("aH 50 ef = %.9e\n", exp(lna[index50ef]) * H[index50ef]);
printf("Nefolds before end = %.9e\n", (lna.back() - lna[index50ef]));
printf("logH50ef, lnaend = %.9e %.9e\n", log(H[index50ef]), lna.back());
printf("lna0 and last = %.5e %.5e\n", lna[0], lna.back());
printf("Inflation ended with %.5e efolds\n", Nefolds);
break;
} // end of inflation and matching
//printf("%.5e %.5e %.5e %.5e\n", lna0, psi[0], psi[1], psi[2]);
} // end of integration loop
//Calculating eta
Nag_Comm Icomm;
double etatemp;
double etaerr;
eta_params etap(&a, &H);
double ruser[1] = {-1.0};
Icomm.user = ruser;
Icomm.p = (Pointer) &etap;
//eta.push_back(0.); lneta.push_back(-1.*std::numeric_limits<double>::infinity());
// will figure something out with these but OK for now
eta.push_back(0.);
lneta.push_back(-1.*std::numeric_limits<double>::infinity());
for(int i=1; i<a.size();i++){
//nag_1d_quad_vals((Integer) i, &lna[a.size()-i], &etaintegrand[a.size()-i], &etatemp, &etaerr, &etafail);
nag_quad_1d_fin_smooth(etaintegrand, lna[lna.size() - 1 - i], lna[lna.size()-1] , 1.e-13, 1.e-13, &etatemp, &etaerr, &Icomm);
eta.push_back(etatemp);
lneta.push_back(log(etatemp));
//printf("%.9e %.9e %.9e %.9e %.9e %.9e %.9e %.9e %.9e\n", lna[i], exp(lna[i]), lneta.back(), phi[i], phip[i], H[i], epsH[i], etaH[i], delta2[i]);
//printf("%.15e %.15e %.15e %.15e\n",lna[i], eta.back(), lneta.back(), etaerr);
}
std::reverse(eta.begin(), eta.end());
std::reverse(lneta.begin(), lneta.end());
//maybe recalculate refined bkg here
} // end of bkg_calc
void bkg::approx_init(){
//Calculate eta, f, fp, fpp, G, and Gp for GSR and NL
//Calculate eta, fix this to know what to do based on the size of lna but OK for now
std::cout << "SIZES. a = " << a.size() << " H = " << H.size() << std::endl;
std::vector<double>::reverse_iterator ait = a.rbegin();
std::vector<double>::reverse_iterator Hit = H.rbegin();
double h = lna[1] - lna[0];
eta.push_back(0.);
lneta.push_back(-1.*std::numeric_limits<double>::infinity());
//std::cout << lneta.rbegin()[0] << std::endl;
eta.push_back(h*((1./(ait[0]*Hit[0])) + (1./(ait[1]*Hit[1])))/2.);
lneta.push_back(log(eta.rbegin()[0]));
//std::cout << lneta.rbegin()[0] << std::endl;
//eta.push_back(h*((1./(ait[0]*Hit[0])) + 4.*(1./(ait[1]*Hit[1])) + (1./(ait[2]*Hit[2])))/3.); //Simpson's rule
ait += 1;
Hit += 1;
for(ait; ait!=a.rend(); ait+=2, Hit+=2){
//std::cout << ait[0] << " " << ait[1] << " " << ait[2] << std::endl;
//std::cout << Hit[0] << " " << Hit[1] << " " << Hit[2] << std:: endl;
eta.push_back(eta.back() + (h*((1./(ait[0]*Hit[0])) + (1./(ait[1]*Hit[1])))/2.));
//std::cout <<"COMPLETED ONCE" << std::endl;
lneta.push_back(log(eta.rbegin()[0]));
//std::cout << lneta.back() << std::endl;
eta.push_back(eta.rbegin()[1] + (h*((1./(ait[0]*Hit[0])) + 4.*(1./(ait[1]*Hit[1])) + (1./(ait[2]*Hit[2])))/3.));
lneta.push_back(log(eta.rbegin()[0]));
//std::cout << lneta.rbegin()[0] << std::endl;
}
std::reverse(eta.begin(), eta.end());
std::reverse(lneta.begin(), lneta.end());
//std::cout << "THIS IS ETA " << eta[1000] << " " << eta[eta.size() - 25] << " " << eta.size() << " " << std::endl;
//Calculate f, dfdlneta
for(int i=0; i!=eta.size(); i++){
double Hp = -1.*H[i]*phip[i]*phip[i]/(2.*Mpl*Mpl);
double phipp = ( (((phip[i]*phip[i]/(2.*Mpl*Mpl)) - 3.)*phip[i]) - (pot::Vp(phi[i], p)/(H[i]*H[i])) );
double phippp = (3.*phipp*((phip[i]*phip[i]/2.) - 1.)) - (phip[i]*phip[i]*pot::Vp(phi[i], p)/(H[i]*H[i])) - (phip[i]*pot::Vpp(phi[i],p)/(H[i]*H[i]));
f.push_back(2.*M_PI*phip[i]*a[i]*eta[i]);
dfdlneta.push_back(a[i]*H[i]*eta[i]*((2.*M_PI*phip[i]/H[i]) - (f[i]) - (2.*M_PI*phipp*a[i]*eta[i])));
ddfdlneta.push_back(2.*M_PI*a[i]*a[i]*eta[i]*eta[i]*H[i]*
((phip[i]/(a[i]*H[i]*eta[i])) +
((phippp + (3.*phipp) + (2.*phip[i]))*a[i]*H[i]*eta[i]) +
((phipp + phip[i])*((a[i]*Hp*eta[i]) - 3.))));
G.push_back(log(1./(f[i]*f[i])) + (2.*dfdlneta[i]/(3.*f[i])));
Gp.push_back( 2.*((f[i]*ddfdlneta[i]) - (3.*f[i]*dfdlneta[i]) - (dfdlneta[i]*dfdlneta[i]))/(3.*f[i]*f[i]) );
//Numerical fp, fpp, Gp
//df_num.push_back(-1.*a[i]*H[i]*eta[i]*);
//ddf_num.push_back();
printf("%.15e %.15e %.15e %.15e %.15e %.15e %.15e %.15e %.15e %.15e %.15e\n", log(a[i]), a[i], phi[i], phip[i], H[i], eta[i], f[i], dfdlneta[i], ddfdlneta[i], G[i], Gp[i]);
fflush(stdout);
// df should be O(100) and ddf should be O(1)
} // end of f, fp, fpp, G, Gp loop
//lna a phi phip H eta f dfdlneta ddfdlneta G Gp
/*
lnetar = NAG_ALLOC(lneta.size() - 4, double);
Gpr = NAG_ALLOC(lneta.size() - 4, double);
for(int i=0; i<(lneta.size() - 4); i++){
Gpr[i] = Gp.rbegin()[2+i];
lnetar[i] = lneta.rbegin()[2+i];
} //end of for loop to fill Gpr and lnetar
nag_1d_spline_interpolant((Integer)lneta.size() - 4, lnetar, Gpr, &Gpr_sp, &Gpr_fail);
//Add some form of error checking but OK for now
std::cout << "TESTIN INTERP " << interp_Gp((lneta[1000] + lneta[1001])/2.) << std::endl;
*/
} // end of approx_init
void bkg::nag_approx_init(){
std::cout << "SIZES. a = " << a.size() << " H = " << H.size() << std::endl;
/*
Nag_Comm Icomm;
double etatemp;
double etaerr;
eta_params etap(&a, &H);
static double ruser[1] = {-1.0};
Icomm.user = ruser;
Icomm.p = (Pointer) &etap;
//eta.push_back(0.); lneta.push_back(-1.*std::numeric_limits<double>::infinity());
// will figure something out with these but OK for now
for(int i=0; i<a.size();i++){
//nag_1d_quad_vals((Integer) i, &lna[a.size()-i], &etaintegrand[a.size()-i], &etatemp, &etaerr, &etafail);
nag_quad_1d_fin_smooth(etaintegrand, lna[lna.size() - 1 - i], lna[lna.size()-1] , 1.e-13, 1.e-13, &etatemp, &etaerr, &Icomm);
eta.push_back(etatemp);
lneta.push_back(log(etatemp));
//printf("%.15e %.15e %.15e %.15e\n",lna[i], eta.back(), lneta.back(), etaerr);
}
std::reverse(eta.begin(), eta.end());
std::reverse(lneta.begin(), lneta.end());
*/
double Hp, phipp, phippp;
double iphi, iphip, ia, ieta, iH;
double ft, dft, ddft;
//for reconstruction test
/*
std::fstream Gpfile("pows/Gp_c0.001505_d0.02705_rate10.dat", std::ios_base::in);
std::string Gptemp;
std::string::size_type sz;
while (Gpfile >> Gptemp){
if (Gptemp == "-inf") {
Gp.push_back(-1.*std::numeric_limits<double>::infinity());
} else if (Gptemp == "nan"){
Gp.push_back(std::nan(""));
} else {
Gp.push_back(std::stod(Gptemp, &sz));
}
}
Gpfile.close();
std::cout << "size of Gprime " << Gp.size() << std::endl;
*/
for(int i=0; i!=eta.size(); i++){
iphi = phi[i];
iphip = phip[i];
ia = a[i];
ieta = eta[i];
iH = H[i];
Hp = -1.*iH*iphip*iphip/(2.*Mpl*Mpl);
phipp = ( (((iphip*iphip/(2.*Mpl*Mpl)) - 3.)*iphip) - (pot::Vp(iphi, p)/(iH*iH)) );
phippp = (3.*phipp*((iphip*iphip/2.) - 1.)) - (iphip*iphip*pot::Vp(iphi, p)/(iH*iH)) - (iphip*pot::Vpp(iphi,p)/(iH*iH));
ft = 2.*M_PI*iphip*ia*ieta;
dft = ia*iH*ieta*((2.*M_PI*iphip/iH) - (ft) - (2.*M_PI*phipp*ia*ieta));
ddft = 2.*M_PI*ia*ia*ieta*ieta*iH*
((iphip/(ia*iH*ieta)) +
((phippp + (3.*phipp) + (2.*iphip))*ia*iH*ieta) +
((phipp + iphip)*((ia*Hp*ieta) - 3.)));
f.push_back(ft);
dfdlneta.push_back(dft);
ddfdlneta.push_back(ddft);
G.push_back(log(1./(ft*ft)) + (2.*dft/(3.*ft)));
Gp.push_back( 2.*((ft*ddft) - (3.*ft*dft) - (dft*dft))/(3.*ft*ft) );
//For reconstruction test comment the above line
//Numerical fp, fpp, Gp
//df_num.push_back(-1.*a[i]*H[i]*eta[i]*);
//ddf_num.push_back();
//printf("%.15e %.15e %.15e %.15e %.15e %.15e %.15e %.15e %.15e %.15e %.15e\n", log(a[i]), a[i], phi[i], phip[i], H[i], eta[i], f[i], dfdlneta[i], ddfdlneta[i], G[i], Gp[i]);
//fflush(stdout);
// df should be O(100) and ddf should be O(1)
} // end of f, fp, fpp, G, Gp loop
std::cout << "size of eta " << eta.size() << std::endl;
} //end of nag_approx_init()