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monofonIC/include/cosmology_calculator.hh

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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 <ode_integrate.hh>
#include <logger.hh>
#include <gsl/gsl_integration.h>
#include <gsl/gsl_spline.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
//TransferFunction_plugin *ptransfer_fun_;
std::unique_ptr<TransferFunction_plugin> transfer_function_;
private:
static constexpr double REL_PRECISION = 1e-5;
std::vector<double> tab_a_, tab_D_, tab_f_;
gsl_interp_accel *gsl_ia_a_, *gsl_ia_D_, *gsl_ia_f_;
gsl_spline *gsl_sp_a_, *gsl_sp_D_, *gsl_sp_f_;
double Dnow_;
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)
csoca::wlog << "no convergence in function 'integrate', rel. error=" << error / result << std::endl;
return (real_t)result;
}
void compute_growth(void)
{
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] = std::log(tab_f_[i] / (tab_a_[i] * H_of_a(tab_a_[i]) * tab_D_[i]));
tab_D_[i] = std::log(tab_D_[i]);
tab_a_[i] = std::log(tab_a_[i]);
}
gsl_ia_D_ = gsl_interp_accel_alloc();
gsl_ia_f_ = gsl_interp_accel_alloc();
gsl_sp_D_ = gsl_spline_alloc(gsl_interp_cspline, tab_a_.size());
gsl_sp_f_ = gsl_spline_alloc(gsl_interp_cspline, tab_a_.size());
gsl_spline_init(gsl_sp_D_, &tab_a_[0], &tab_D_[0], tab_a_.size());
gsl_spline_init(gsl_sp_f_, &tab_a_[0], &tab_f_[0], tab_a_.size());
Dnow_ = std::exp(gsl_spline_eval(gsl_sp_D_, 0.0, gsl_ia_D_));
}
public:
//! 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(ConfigFile &cf)
: cosmo_param_(cf)
{
transfer_function_ = std::move(select_TransferFunction_plugin(cf));
transfer_function_->intialise();
cosmo_param_.pnorm = this->ComputePNorm();
cosmo_param_.sqrtpnorm = std::sqrt(cosmo_param_.pnorm);
csoca::ilog << std::setw(32) << std::left << "TF supports distinct CDM+baryons"
<< " : " << (transfer_function_->tf_is_distinct() ? "yes" : "no") << std::endl;
csoca::ilog << std::setw(32) << std::left << "TF maximum wave number"
<< " : " << transfer_function_->get_kmax() << " h/Mpc" << std::endl;
// pre-compute growth factors and store for interpolation
this->compute_growth();
}
~calculator()
{
gsl_spline_free(gsl_sp_D_);
gsl_spline_free(gsl_sp_f_);
gsl_interp_accel_free(gsl_ia_D_);
gsl_interp_accel_free(gsl_ia_f_);
}
//! 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 << " ,a=" << a << "";
ofs << "# " << std::setw(18) << "k [h/Mpc]"
<< std::setw(20) << ("P_dtot(k" + ss.str() + "|BS)")
<< std::setw(20) << ("P_dcdm(k" + ss.str() + "|BS)")
<< std::setw(20) << ("P_dbar(k" + ss.str() + "|BS)")
<< std::setw(20) << ("P_tcdm(k" + ss.str() + "|BS)")
<< std::setw(20) << ("P_tbar(k" + ss.str() + "|BS)")
<< std::setw(20) << ("P_dtot(k" + ss.str() + ")")
<< std::setw(20) << ("P_dcdm(k" + ss.str() + ")")
<< std::setw(20) << ("P_dbar(k" + ss.str() + ")")
<< std::setw(20) << ("P_tcdm(k" + ss.str() + ")")
<< std::setw(20) << ("P_tbar(k" + ss.str() + ")")
<< 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->GetAmplitude(k, total) * Dplus0, 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->GetAmplitude(k, cdm) * Dplus0, 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->GetAmplitude(k, baryon) * Dplus0, 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->GetAmplitude(k, vcdm) * Dplus0, 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->GetAmplitude(k, vbaryon) * Dplus0, 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->GetAmplitude(k, total0), 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->GetAmplitude(k, cdm0), 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->GetAmplitude(k, baryon0), 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->GetAmplitude(k, vcdm0), 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->GetAmplitude(k, vbaryon0), 2.0)
<< std::setw(20) << std::setprecision(10) << std::pow(this->GetAmplitude(k, total), 2.0)
<< std::endl;
}
}
csoca::ilog << "Wrote power spectrum at a=" << a << " to file \'" << fname << "\'" << std::endl;
}
const cosmology::parameters &GetParams(void) const
{
return cosmo_param_;
}
//! returns the amplitude of amplitude of the power spectrum
/*!
* @param k the wave number in h/Mpc
* @param a the expansion factor of the universe
* @returns power spectrum amplitude for wave number k at time a
*/
inline real_t Power(real_t k, real_t a)
{
real_t Dplus = this->get_growth_factor(a);
real_t pNorm = ComputePNorm();
return pNorm * Dplus * Dplus * TransferSq(k) * pow((double)k, (double)cosmo_param_.nspect);
}
//! return the value of the Hubble function H(a) = dloga/dt
inline double H_of_a(double a) const
{
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
{
return std::exp(gsl_spline_eval(gsl_sp_D_, std::log(a), gsl_ia_D_)) / 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
{
return std::exp(gsl_spline_eval(gsl_sp_f_, std::log(a), gsl_ia_f_));
}
//! 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
{
return a * H_of_a(a) / cosmo_param_.h * this->get_f(a);
}
//! 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 * (sin(x) - x * cos(x)) / (x * x * x);
static double nspect = (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 * pow((double)k, (double)nspect) * tf * tf;
}
//! Computes the square of the transfer function
/*! Function evaluates the supplied transfer function ptransfer_fun_
* and returns the square of its value at wave number k
* @param k wave number at which to evaluate the transfer function
*/
inline real_t TransferSq(real_t k) const
{
//.. parameter supplied transfer function
real_t tf1 = transfer_function_->compute(k, total);
return tf1 * tf1;
}
//! 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 GetAmplitude(real_t k, tf_type type) const
{
return std::pow(k, 0.5 * cosmo_param_.nspect) * transfer_function_->compute(k, type) * cosmo_param_.sqrtpnorm;
}
//! 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 ComputePNorm(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, (double)kmin, (double)kmax, this);
else
sigma0 = 4.0 * M_PI * integrate(&dSigma8_0, (double)kmin, (double)kmax, this);
return cosmo_param_.sigma8 * cosmo_param_.sigma8 / sigma0;
}
};
//! 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 * sqrt(rho) * pow(G, 1.5), 1.0 / 3.0);
}
} // namespace cosmology
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