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monofonIC/include/cosmology_calculator.hh
Oliver Hahn 68ae67f3db WIP: higher order baryons
2020-05-23 15:12:51 +02:00

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#pragma once
#include <array>
#include <vec.hh>
#include <cosmology_parameters.hh>
#include <physical_constants.hh>
#include <transfer_function_plugin.hh>
#include <math/ode_integrate.hh>
#include <logger.hh>
#include <math/interpolate.hh>
#include <gsl/gsl_integration.h>
#include <gsl/gsl_errno.h>
namespace cosmology
{
/*!
* @class cosmology::calculator
* @brief provides functions to compute cosmological quantities
*
* This class provides member functions to compute cosmological quantities
* related to the Friedmann equations and linear perturbation theory
*/
class calculator
{
public:
//! data structure to store cosmological parameters
cosmology::parameters cosmo_param_;
//! pointer to an instance of a transfer function plugin
std::unique_ptr<TransferFunction_plugin> transfer_function_;
private:
static constexpr double REL_PRECISION = 1e-10;
interpolated_function_1d<true,true,false> D_of_a_, f_of_a_, a_of_D_;
double Dnow_, Dplus_start_, Dplus_target_, astart_, atarget_;
real_t integrate(double (*func)(double x, void *params), double a, double b, void *params) const
{
gsl_function F;
F.function = func;
F.params = params;
double result;
double error;
gsl_set_error_handler_off();
gsl_integration_workspace *w = gsl_integration_workspace_alloc(100000);
gsl_integration_qag(&F, a, b, 0, REL_PRECISION, 100000, 6, w, &result, &error);
gsl_integration_workspace_free(w);
gsl_set_error_handler(NULL);
if (error / result > REL_PRECISION)
music::wlog << "no convergence in function 'integrate', rel. error=" << error / result << std::endl;
return (real_t)result;
}
void compute_growth( std::vector<double>& tab_a, std::vector<double>& tab_D, std::vector<double>& tab_f )
{
using v_t = vec_t<3, double>;
// set ICs
const double a0 = 1e-10;
const double D0 = a0;
const double Dprime0 = 2.0 * D0 * H_of_a(a0) / std::pow(phys_const::c_SI, 2);
const double t0 = 1.0 / (a0 * H_of_a(a0));
v_t y0({a0, D0, Dprime0});
// set up integration
double dt = 1e-9;
double dtdid, dtnext;
const double amax = 2.0;
v_t yy(y0);
double t = t0;
const double eps = 1e-10;
while (yy[0] < amax)
{
// RHS of ODEs
auto rhs = [&](double t, v_t y) -> v_t {
auto a = y[0];
auto D = y[1];
auto Dprime = y[2];
v_t dy;
// da/dtau = a^2 H(a)
dy[0] = a * a * H_of_a(a);
// d D/dtau
dy[1] = Dprime;
// d^2 D / dtau^2
dy[2] = -a * H_of_a(a) * Dprime + 3.0 / 2.0 * cosmo_param_.Omega_m * std::pow(cosmo_param_.H0, 2) * D / a;
return dy;
};
// scale by predicted value to get approx. constant fractional errors
v_t yyscale = yy.abs() + dt * rhs(t, yy).abs();
// call integrator
ode_integrate::rk_step_qs(dt, t, yy, yyscale, rhs, eps, dtdid, dtnext);
tab_a.push_back(yy[0]);
tab_D.push_back(yy[1]);
tab_f.push_back(yy[2]);
dt = dtnext;
}
// compute f, before we stored here D'
for (size_t i = 0; i < tab_a.size(); ++i)
{
tab_f[i] = tab_f[i] / (tab_a[i] * H_of_a(tab_a[i]) * tab_D[i]);
tab_D[i] = tab_D[i];
tab_a[i] = tab_a[i];
}
}
public:
calculator() = delete;
calculator(const calculator& c) = delete;
//! constructor for a cosmology calculator object
/*!
* @param acosmo a cosmological parameters structure
* @param pTransferFunction pointer to an instance of a transfer function object
*/
explicit calculator(config_file &cf)
: cosmo_param_(cf), astart_( 1.0/(1.0+cf.get_value<double>("setup","zstart")) ),
atarget_( 1.0/(1.0+cf.get_value_safe<double>("cosmology","ztarget",1./astart_-1.)))
{
// pre-compute growth factors and store for interpolation
std::vector<double> tab_a, tab_D, tab_f;
this->compute_growth(tab_a, tab_D, tab_f);
D_of_a_.set_data(tab_a,tab_D);
f_of_a_.set_data(tab_a,tab_f);
a_of_D_.set_data(tab_D,tab_a);
Dnow_ = D_of_a_(1.0);
Dplus_start_ = D_of_a_( astart_ ) / Dnow_;
Dplus_target_ = D_of_a_( atarget_ ) / Dnow_;
music::ilog << "D+ = " << Dplus_target_ << ", " << Dplus_start_ << std::endl;
// set up transfer functions and compute normalisation
transfer_function_ = std::move(select_TransferFunction_plugin(cf));
transfer_function_->intialise();
if( !transfer_function_->tf_isnormalised_ )
cosmo_param_.pnorm = this->compute_pnorm_from_sigma8();
else{
cosmo_param_.pnorm = 1.0/Dplus_target_/Dplus_target_;
auto sigma8 = this->compute_sigma8();
music::ilog << "Measured sigma_8 for given PS normalisation is " << sigma8 << std::endl;
}
cosmo_param_.sqrtpnorm = std::sqrt(cosmo_param_.pnorm);
music::ilog << std::setw(32) << std::left << "TF supports distinct CDM+baryons"
<< " : " << (transfer_function_->tf_is_distinct() ? "yes" : "no") << std::endl;
music::ilog << std::setw(32) << std::left << "TF maximum wave number"
<< " : " << transfer_function_->get_kmax() << " h/Mpc" << std::endl;
}
~calculator()
{
}
//! Write out a correctly scaled power spectrum at time a
void write_powerspectrum(real_t a, std::string fname) const
{
// const real_t Dplus0 = this->get_growth_factor(a);
if (CONFIG::MPI_task_rank == 0)
{
double kmin = std::max(1e-4, transfer_function_->get_kmin());
// write power spectrum to a file
std::ofstream ofs(fname.c_str());
std::stringstream ss;
ss << " ,ap=" << a << "";
ofs << "# " << std::setw(18) << "k [h/Mpc]"
<< std::setw(20) << ("P_dtot(k,a=ap)")
<< std::setw(20) << ("P_dcdm(k,a=ap)")
<< std::setw(20) << ("P_dbar(k,a=ap)")
<< std::setw(20) << ("P_tcdm(k,a=ap)")
<< std::setw(20) << ("P_tbar(k,a=ap)")
<< std::setw(20) << ("P_dtot(k,a=1)")
<< std::setw(20) << ("P_dcdm(k,a=1)")
<< std::setw(20) << ("P_dbar(k,a=1)")
<< std::setw(20) << ("P_tcdm(k,a=1)")
<< std::setw(20) << ("P_tbar(k,a=1)")
<< std::setw(20) << ("P_dtot(K,a=1)")
<< std::endl;
for (double k = kmin; k < transfer_function_->get_kmax(); k *= 1.05)
{
ofs << std::setw(20) << std::setprecision(10) << k
<< std::setw(20) << std::setprecision(10) << std::pow(this->get_amplitude(k, total)*Dplus_start_, 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->get_amplitude(k, cdm)*Dplus_start_, 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->get_amplitude(k, baryon)*Dplus_start_, 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->get_amplitude(k, vcdm)*Dplus_start_, 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->get_amplitude(k, vbaryon)*Dplus_start_, 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->get_amplitude(k, total0), 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->get_amplitude(k, cdm0), 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->get_amplitude(k, baryon0), 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->get_amplitude(k, vcdm0), 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->get_amplitude(k, vbaryon0), 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->get_amplitude(k, vtotal), 2.0)
<< std::endl;
}
}
music::ilog << "Wrote power spectrum at a=" << a << " to file \'" << fname << "\'" << std::endl;
}
const cosmology::parameters &get_parameters(void) const noexcept
{
return cosmo_param_;
}
//! return the value of the Hubble function H(a) = dloga/dt
inline double H_of_a(double a) const noexcept
{
double HH2 = 0.0;
HH2 += cosmo_param_.Omega_r / (a * a * a * a);
HH2 += cosmo_param_.Omega_m / (a * a * a);
HH2 += cosmo_param_.Omega_k / (a * a);
HH2 += cosmo_param_.Omega_DE * std::pow(a, -3. * (1. + cosmo_param_.w_0 + cosmo_param_.w_a)) * exp(-3. * (1.0 - a) * cosmo_param_.w_a);
return cosmo_param_.H0 * std::sqrt(HH2);
}
//! Computes the linear theory growth factor D+, normalised to D+(a=1)=1
real_t get_growth_factor(real_t a) const noexcept
{
return D_of_a_(a) / Dnow_;
}
//! Computes the inverse of get_growth_factor
real_t get_a( real_t Dplus ) const noexcept
{
return a_of_D_( Dplus * Dnow_ );
}
//! Computes the linear theory growth rate f
/*! Function computes (by interpolating on precalculated table)
* f = dlog D+ / dlog a
*/
real_t get_f(real_t a) const noexcept
{
return f_of_a_(a);
}
//! Compute the factor relating particle displacement and velocity
/*! Function computes
* vfac = a * (H(a)/h) * dlogD+ / dlog a
*/
real_t get_vfact(real_t a) const noexcept
{
return f_of_a_(a) * a * H_of_a(a) / cosmo_param_.h;
}
//! Integrand for the sigma_8 normalization of the power spectrum
/*! Returns the value of the primordial power spectrum multiplied with
the transfer function and the window function of 8 Mpc/h at wave number k */
static double dSigma8(double k, void *pParams)
{
if (k <= 0.0)
return 0.0f;
cosmology::calculator *pcc = reinterpret_cast<cosmology::calculator *>(pParams);
double x = k * 8.0;
double w = 3.0 * (sin(x) - x * cos(x)) / (x * x * x);
static double nspect = (double)pcc->cosmo_param_.nspect;
double tf = pcc->transfer_function_->compute(k, total);
//... no growth factor since we compute at z=0 and normalize so that D+(z=0)=1
return k * k * w * w * pow((double)k, (double)nspect) * tf * tf;
}
//! Integrand for the sigma_8 normalization of the power spectrum
/*! Returns the value of the primordial power spectrum multiplied with
the transfer function and the window function of 8 Mpc/h at wave number k */
static double dSigma8_0(double k, void *pParams)
{
if (k <= 0.0)
return 0.0f;
cosmology::calculator *pcc = reinterpret_cast<cosmology::calculator *>(pParams);
double x = k * 8.0;
double w = 3.0 * (std::sin(x) - x * std::cos(x)) / (x * x * x);
static double nspect = static_cast<double>(pcc->cosmo_param_.nspect);
double tf = pcc->transfer_function_->compute(k, total0);
//... no growth factor since we compute at z=0 and normalize so that D+(z=0)=1
return k * k * w * w * std::pow(k, nspect) * tf * tf;
}
//! Computes the amplitude of a mode from the power spectrum
/*! Function evaluates the supplied transfer function ptransfer_fun_
* and returns the amplitude of fluctuations at wave number k at z=0
* @param k wave number at which to evaluate
*/
inline real_t get_amplitude( const real_t k, const tf_type type) const
{
return std::pow(k, 0.5 * cosmo_param_.nspect) * transfer_function_->compute(k, type) * cosmo_param_.sqrtpnorm;// * ((type!=deltabc)? 1.0 : 1.0/Dplus_target_);
}
inline real_t get_amplitude_phibc( const real_t k ) const
{
// need to multiply with Dplus_target since sqrtpnorm rescales like that
return -std::pow(k, 0.5 * cosmo_param_.nspect-2.0) * transfer_function_->compute(k, deltabc) * cosmo_param_.sqrtpnorm * Dplus_target_;// / Dplus_start_;// * ((type!=deltabc)? 1.0 : 1.0/Dplus_target_);
}
//! Computes the normalization for the power spectrum
/*!
* integrates the power spectrum to fix the normalization to that given
* by the sigma_8 parameter
*/
real_t compute_sigma8(void)
{
real_t sigma0, kmin, kmax;
kmax = transfer_function_->get_kmax();
kmin = transfer_function_->get_kmin();
if (!transfer_function_->tf_has_total0())
sigma0 = 4.0 * M_PI * integrate(&dSigma8, static_cast<double>(kmin), static_cast<double>(kmax), this);
else{
sigma0 = 4.0 * M_PI * integrate(&dSigma8_0, static_cast<double>(kmin), static_cast<double>(kmax), this);
}
return std::sqrt(sigma0);
}
//! Computes the normalization for the power spectrum
/*!
* integrates the power spectrum to fix the normalization to that given
* by the sigma_8 parameter
*/
real_t compute_pnorm_from_sigma8(void)
{
auto measured_sigma8 = this->compute_sigma8();
return cosmo_param_.sigma8 * cosmo_param_.sigma8 / (measured_sigma8 * measured_sigma8);
}
};
//! compute the jeans sound speed
/*! given a density in g/cm^-3 and a mass in g it gives back the sound
* speed in cm/s for which the input mass is equal to the jeans mass
* @param rho density
* @param mass mass scale
* @returns jeans sound speed
*/
inline double jeans_sound_speed(double rho, double mass)
{
const double G = 6.67e-8;
return pow(6.0 * mass / M_PI * std::sqrt(rho) * std::pow(G, 1.5), 1.0 / 3.0);
}
} // namespace cosmology
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