Forecast.cpp

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/********************************************************************
 *  Copyright (C) 2010 by Federico Marulli and Alfonso Veropalumbo  *
 *  federico.marulli3@unibo.it                                      *
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 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the   *
 *  GNU General Public License for more details.                    *
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#include "Data1D.h"
#include "GlobalFunc.h"
 
using namespace std;
 
using namespace cbl;
 
 
// ============================================================================
 
 
std::vector<double> cbl::fit_covariance_matrix_2PCF_monopole (const std::vector<double> mean, const std::vector<std::vector<double>> mock_xi0, const bool doJK, const cbl::cosmology::Cosmology cosmology, const double nObjects, const double Volume, const double bias, const double redshift, const double rMin, const double rMax, const int nbins, const cbl::BinType bin_type, const std::string method_Pk, const double sigma_NL, const bool NL)
{
  coutCBL << "Fitting the Covariance Matrix" << endl;
  const int nmock = mock_xi0.size();
 
  double term = (doJK) ? nmock-1 : 1.;
  vector<double> mock_mean(nbins, 0);
 
  if (mean.size()==0) {
    vector<vector<double>> vv = transpose(mock_xi0);
    for (int i=0; i<nbins; i++)
      mock_mean[i] = Average(vv[i]);
  }
  else
    for (int i=0; i<nbins; i++)
      mock_mean[i] = mean[i];
 
  vector<vector<double>> diff(nmock, vector<double>(nbins, 0));
  for (int i=0; i<nmock; i++)
    for (int j=0; j<nbins; j++)
      diff[i][j] = mock_xi0[i][j]-mock_mean[j];
 
  cosmology::Cosmology cosmo = cosmology;
  vector<double> kk = logarithmic_bin_vector(200, 1.e-4, 1.e2);
  vector<double> Pk0(kk.size()), Pk2(kk.size()), Pk4(kk.size());
  double linear_growth_rate = cosmo.linear_growth_rate(redshift, 1);
  double beta = linear_growth_rate/bias;
  
  double pk0_fact = bias*bias*(1+2.*beta/3+beta*beta/5);
  double pk2_fact = 4./3*beta+4./7*beta*beta;
  double pk4_fact = 8./35*beta+beta;
 
  if (sigma_NL==0 or NL==true) {
    vector<double> pkDM = cosmo.Pk_matter(kk, method_Pk, NL, redshift);
    for (size_t i=0; i<kk.size(); i++) {
      Pk0[i] = pkDM[i]*pk0_fact;
      Pk2[i] = pkDM[i]*pk2_fact;
      Pk4[i] = pkDM[i]*pk4_fact;
    }
  }
  else {
    vector<double> PkDM = cosmo.Pk_matter_DeWiggled(method_Pk, "EisensteinHu", kk, redshift, sigma_NL);
    for (size_t i=0; i<kk.size(); i++) {
      Pk0[i] = PkDM[i]*pk0_fact;
      Pk2[i] = PkDM[i]*pk2_fact;
      Pk4[i] = PkDM[i]*pk4_fact;
    }
  }
 
  vector<double> nObj = linear_bin_vector(20, 0.2*nObjects, nObjects);
  vector<double> Vol = linear_bin_vector(20, 0.2*Volume, Volume);
 
  auto func = [&] (vector<double> &parameters)
  {
    const double _nObjects = parameters[0];
    const double _Volume = parameters[1];
    if (_nObjects<0.2*nObjects || _nObjects>nObjects ) return 1.e30;
    if (_Volume<0.2*Volume || _Volume>Volume ) return 1.e30;
 
    vector<double> rr;
    vector<vector<double>> covariance, icovariance;
    Covariance_XiMultipoles (rr, covariance, nbins, rMin, rMax, _nObjects, _Volume, kk, {Pk0, Pk2, Pk4}, {0}, bin_type);
    for (int i=0; i<nbins; i++)
      for (int j=0; j<nbins; j++)
    covariance[i][j] /=term;
 
    invert_matrix(covariance, icovariance);
    double chi2 = 0.;
    for (int i=0; i<nmock; i++)
      chi2+=v_M_vt(diff[i], icovariance);
    double LL = nmock*nbins*nbins*log(2*par::pi)+nmock*log(determinant_matrix(covariance))+chi2;
    return LL;
  };
  
  double min_nObj = 0., min_Vol = 0.;
  double max_nObj = 50*nObjects, max_Vol = 50*Volume;
  double min_LL = 1.e30;
  for (size_t i=0; i<nObj.size(); i++)
    for (size_t j=0; j<Vol.size(); j++) {
      vector<double> pars = {nObj[i], Vol[j]};
      double LL = func(pars);
      if (LL<min_LL) {
    min_LL = LL;
    min_nObj = nObj[i];
    min_Vol = Vol[j];
      }
    }
 
  vector<double> start = {nObjects, Volume};
  vector<vector<double>> limits = { {min_nObj, max_nObj}, {min_Vol, max_Vol}};
  return wrapper::gsl::GSL_minimize_nD(func, start, limits);
}
 
 
// ============================================================================
 
 
std::shared_ptr<cbl::data::Data> cbl::generate_mock_2PCF_monopole (const cbl::cosmology::Cosmology cosmology, const double bias, const double nObjects, const double Volume, const double redshift, const double rMin, const double rMax, const int nbins, const cbl::BinType bin_type, const std::string method_Pk, const double sigma_NL, const bool NL)
{
  auto data = generate_mock_2PCF_multipoles(cosmology, bias, nObjects, Volume, redshift, rMin, rMax, nbins, bin_type, method_Pk, sigma_NL, NL);
 
  int ndata = data->ndata()/3;
 
  vector<double> rad(ndata, 0), xi0(ndata, 0);
  vector<vector<double>> covariance(ndata, vector<double>(ndata, 0));
 
  for (int i=0; i<ndata; i++) {
    rad[i] = data->xx(i);
    xi0[i] = data->data(i);
    for (int j=0; j<ndata; j++)
      covariance[i][j] = data->covariance(i, j);
  }
 
  return make_shared<data::Data1D> (data::Data1D(rad, xi0, covariance));
}
 
// ============================================================================
 
 
std::shared_ptr<cbl::data::Data> cbl::generate_mock_2PCF_multipoles (const cbl::cosmology::Cosmology cosmology, const double bias, const double nObjects, const double Volume, const double redshift, const double rMin, const double rMax, const int nbins, const cbl::BinType bin_type, const std::string method_Pk, const double sigma_NL, const bool NL)
{
  cosmology::Cosmology cosmo = cosmology;
  vector<double> kk = logarithmic_bin_vector(200, 1.e-4, 1.e2);
  vector<double> Pk0(kk.size()), Pk2(kk.size()), Pk4(kk.size());
  double linear_growth_rate = cosmo.linear_growth_rate(redshift, 1);
  double beta = linear_growth_rate/bias;
  
  double pk0_fact = bias*bias*(1+2.*beta/3+beta*beta/5);
  double pk2_fact = 4./3*beta+4./7*beta*beta;
  double pk4_fact = 8./35*beta+beta;
 
  if (sigma_NL==0 or NL==true) {
    vector<double> pkDM = cosmo.Pk_matter(kk, method_Pk, NL, redshift);
    for (size_t i=0; i<kk.size(); i++) {
      Pk0[i] = pkDM[i]*pk0_fact;
      Pk2[i] = pkDM[i]*pk2_fact;
      Pk4[i] = pkDM[i]*pk4_fact;
    }
  }
  else {
    vector<double> PkDM = cosmo.Pk_matter_DeWiggled(method_Pk, "EisensteinHu", kk, redshift, sigma_NL);
    for (size_t i=0; i<kk.size(); i++) {
      Pk0[i] = PkDM[i]*pk0_fact;
      Pk2[i] = PkDM[i]*pk2_fact;
      Pk4[i] = PkDM[i]*pk4_fact;
    }
  }
 
 
   vector<double> rr;
   vector<vector<double>> xil(3), covariance;
 
   Covariance_XiMultipoles (rr, covariance, nbins, rMin, rMax, nObjects, Volume, kk, {Pk0, Pk2, Pk4}, {0, 2, 4}, bin_type);
 
  xil[0] = wrapper::fftlog::transform_FFTlog(rr, 1, kk, Pk0, 0);
  xil[1] = wrapper::fftlog::transform_FFTlog(rr, 1, kk, Pk2, 2);
  xil[2] = wrapper::fftlog::transform_FFTlog(rr, 1, kk, Pk4, 4);
 
  vector<double> rad, xi;
  for (int i=0; i<3; i++) {
    for (int j=0; j<nbins; j++) {
      rad.push_back(rr[j]);
      xi.push_back(xil[i][j]);
    }
  }
 
  return make_shared<data::Data1D>(data::Data1D(rad, xi, covariance));
}