704 lines
17 KiB
C++
704 lines
17 KiB
C++
/*+
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This is CosmoTool (./src/powerSpectrum.cpp) -- Copyright (C) Guilhem Lavaux (2007-2013)
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guilhem.lavaux@gmail.com
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This software is a computer program whose purpose is to provide a toolbox for cosmological
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data analysis (e.g. filters, generalized Fourier transforms, power spectra, ...)
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This software is governed by the CeCILL license under French law and
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abiding by the rules of distribution of free software. You can use,
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modify and/ or redistribute the software under the terms of the CeCILL
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license as circulated by CEA, CNRS and INRIA at the following URL
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"http://www.cecill.info".
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As a counterpart to the access to the source code and rights to copy,
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modify and redistribute granted by the license, users are provided only
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with a limited warranty and the software's author, the holder of the
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economic rights, and the successive licensors have only limited
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liability.
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In this respect, the user's attention is drawn to the risks associated
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with loading, using, modifying and/or developing or reproducing the
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software by the user in light of its specific status of free software,
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that may mean that it is complicated to manipulate, and that also
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therefore means that it is reserved for developers and experienced
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professionals having in-depth computer knowledge. Users are therefore
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encouraged to load and test the software's suitability as regards their
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requirements in conditions enabling the security of their systems and/or
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data to be ensured and, more generally, to use and operate it in the
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same conditions as regards security.
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The fact that you are presently reading this means that you have had
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knowledge of the CeCILL license and that you accept its terms.
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+*/
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#include <cassert>
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#include <vector>
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#include <algorithm>
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#include <iostream>
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#include <cmath>
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#include <fstream>
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#include <gsl/gsl_integration.h>
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#include "powerSpectrum.hpp"
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using namespace std;
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#define USE_GSL
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#define TOLERANCE 1e-6
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#define NUM_ITERATION 8000
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#define POWER_EFSTATHIOU 1
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#define HU_WIGGLES 2
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#define HU_BARYON 3
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#define OLD_POWERSPECTRUM 4
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#define POWER_BARDEEN 5
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#define POWER_SUGIYAMA 6
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#define POWER_BDM 7
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#define POWER_TEST 8
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#define POWER_SPECTRUM POWER_EFSTATHIOU
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namespace Cosmology {
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double n = 1.0;
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double K0 = 1;
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double V0 = 627;
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double CMB_VECTOR[3] = {
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56.759,
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-540.02,
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313.50
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};
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// WMAP5
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double h = 0.719;
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double SIGMA8 = 0.77;
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double OMEGA_B = 0.043969;
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double OMEGA_C = 0.21259;
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// WMAP5-modification
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//double h = 0.719;
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//double SIGMA8 = 0.77;
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//double OMEGA_B = 0;
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//double OMEGA_C = 0.21259+0.043969;
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// LCDM STRAUSS ?
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//double h = 0.67;
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//double SIGMA8 = 0.67;
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//double OMEGA_B = 0;
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//double OMEGA_C = 0.30;
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// SCDM STRAUSS
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//double h = 0.5;
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//double SIGMA8= 1.05;
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//double OMEGA_B = 0;
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//double OMEGA_C = 1;
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// Sugiyama test
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//double h = 0.5;
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//double SIGMA8= 0.5;//1.05;
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//double OMEGA_B = 0.0125*4;
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//double OMEGA_C = 0.1-OMEGA_B;
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// HU TEST
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//double h = 0.5;
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//double SIGMA8 = 0.5;
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//double OMEGA_B = 0.09;
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//double OMEGA_C = 0.21;
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// HDM STRAUSS
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//double h = 0.5;
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//double SIGMA8 = 0.86;
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//double OMEGA_B = 0;
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//double OMEGA_C = 1;
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// FOR "BEST FIT"
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//double h = 0.82;
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//double SIGMA8 = 0.76;
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//double OMEGA_B = 0.043969;
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//double OMEGA_C = 0.15259;
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// FOR JUSZKIEWICZ CHECKING (CDM) ! WARNING ! He smoothes
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// with a gaussian filter the density field, i.e. one has
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// to multiply P(k) by exp(-k^2 R^2) with R the radius
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// of the filter. Dammit !
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//double h = 0.5;
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//double SIGMA8=1/2.5;
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//double OMEGA_B=0.;
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//double OMEGA_C=1;
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//#define JUSZKIEWICZ_PATCH
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//#define RJUSZ 6.0
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// (BDM)
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//double h = 0.5;
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//double SIGMA8=1;
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//double OMEGA_B=0.0;
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//double OMEGA_C=0.4;
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// FOR HU CHECKING
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//double h = 0.5;
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//double SIGMA8= 1;
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//double OMEGA_B=0.09;
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//double OMEGA_C=0.21;
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double OMEGA_0 = OMEGA_B+OMEGA_C;
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double Omega = OMEGA_0;
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double Theta_27 = 2.728 / 2.7;
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double beta = pow(OMEGA_0, 5./9);
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double OmegaEff = OMEGA_0 * h * h;
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double Gamma0 = OMEGA_0 * h * h;
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/*
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* This is \hat{tophat}
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*/
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double tophatFilter(double u)
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{
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if (u != 0)
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return 3 / (u*u*u) * (sin(u) - u * cos(u));
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else
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return 1;
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}
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/*
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* This is \tilde{w}
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*/
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double externalFilter(double u)
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{
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if (u != 0)
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return 1 - sin(u)/u;
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return 0.;
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}
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double powC(double q, double alpha_c)
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{
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return 14.2 / alpha_c + 386 / (1 + 69.9 * pow(q, 1.08));
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}
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double T_tilde_0(double q, double alpha_c, double beta_c)
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{
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double a = log(M_E + 1.8 * beta_c * q);
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return a / ( a + powC(q, alpha_c) * q * q);
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}
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double j_0(double x)
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{
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if (x == 0)
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return 1.0;
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return sin(x)/x;
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}
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double powG(double y)
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{
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double a = sqrt(1 + y);
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return y * (-6 * a + (2 + 3 * y) *log((a + 1)/(a - 1)));
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}
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/*
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* This function returns the power spectrum evaluated at k (in Mpc, not in Mpc/h).
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*/
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double powerSpectrum(double k, double normPower)
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{
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#if POWER_SPECTRUM == POWER_EFSTATHIOU
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double a = 6.4/Gamma0;
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double b = 3/Gamma0;
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double c = 1.7/Gamma0;
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double nu = 1.13;
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double f = (a*k) + pow(b*k,1.5) + pow(c*k,2);
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// EFSTATHIOU ET AL. (1992)
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return normPower * pow(k,n) * pow(1+pow(f,nu),(-2/nu));
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#endif
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// EISENSTEIN ET HU (1998)
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// FULL POWER SPECTRUM WITH BARYONS AND WIGGLES
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#if POWER_SPECTRUM == HU_WIGGLES
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// EISENSTEIN ET HU (1998)
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// FULL POWER SPECTRUM WITH BARYONS AND WIGGLES
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double k_silk = 1.6 * pow(OMEGA_B * h * h, 0.52) * pow(OmegaEff, 0.73) * (1 + pow(10.4 * OmegaEff, -0.95));
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double z_eq = 2.50e4 * OmegaEff * pow(Theta_27, -4);
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double s = 44.5 * log(9.83 / OmegaEff) / (sqrt(1 + 10 * pow(OMEGA_B * h * h, 0.75)));
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double f = 1 / (1 + pow(k * s / 5.4, 4));
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double k_eq = 7.46e-2 * OmegaEff * pow(Theta_27, -2);
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double a1 = pow(46.9 * OmegaEff, 0.670) * (1 + pow(32.1 * OmegaEff, -0.532));
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double a2 = pow(12.0 * OmegaEff, 0.424) * (1 + pow(45.0 * OmegaEff, -0.582));
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double alpha_c = pow(a1, -OMEGA_B/ OMEGA_0) * pow(a2, -pow(OMEGA_B / OMEGA_0, 3));
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double q = k / (13.41 * k_eq);
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double b1_betac = 0.944 * 1/(1 + pow(458 * OmegaEff, -0.708));
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double b2_betac = pow(0.395 * OmegaEff, -0.0266);
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double beta_c = 1/ ( 1 + b1_betac * (pow(OMEGA_C / OMEGA_0, b2_betac) - 1) );
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double T_c = f * T_tilde_0(q, 1, beta_c) + (1 - f) * T_tilde_0(q, alpha_c, beta_c);
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double b1_zd = 0.313 * pow(OmegaEff, -0.419) * (1 + 0.607 * pow(OmegaEff, 0.674));
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double b2_zd = 0.238 * pow(OmegaEff, 0.223);
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double z_d = 1291 * pow(OmegaEff, 0.251) / (1 + 0.659 * pow(OmegaEff, 0.828)) * (1 + b1_zd * pow(OmegaEff, b2_zd));
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double R_d = 31.5 * OMEGA_B * h * h * pow(Theta_27, -4) * 1e3 / z_d;
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double alpha_b = 2.07 * k_eq * s * pow(1 + R_d, -0.75) * powG((1 + z_eq)/(1 + z_d));
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double beta_b = 0.5 + OMEGA_B / OMEGA_0 + (3 - 2 * OMEGA_B / OMEGA_0) * sqrt(pow(17.2 * OmegaEff, 2) + 1);
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double beta_node = 8.41 * pow(OmegaEff, 0.435);
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double s_tilde = s * pow(1 + pow(beta_node / (k * s), 3), -1./3);
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double T_b = (T_tilde_0(q, 1, 1) / (1 + pow(k * s / 5.2, 2)) + alpha_b / (1 + pow(beta_b / (k * s), 3)) * exp(-pow(k/k_silk, 1.4))) * j_0(k * s_tilde);
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double T_k = OMEGA_B/OMEGA_0 * T_b + OMEGA_C/OMEGA_0 * T_c;
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return normPower * pow(k,n) * T_k * T_k;
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#endif
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// EISENSTEIN ET AL. (2008), SHAPED POWER SPECTRUM WITH BARYON, WITHOUT WIGGLES
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#if POWER_SPECTRUM == HU_BARYON
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double s = 44.5 * log(9.83 / OmegaEff) / (sqrt(1 + 10 * pow(OMEGA_B * h * h, 0.75)));
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double alpha_Gamma = 1 - 0.328 * log(431 * OmegaEff) * OMEGA_B / OMEGA_0 + 0.38 * log(22.3 * OmegaEff) * pow(OMEGA_B / OMEGA_0, 2);
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double GammaEff = OMEGA_0 * h * (alpha_Gamma + (1 - alpha_Gamma)/(1 + pow(0.43 * k * s, 4)));
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double q = k/(h*GammaEff) * pow(Theta_27, 2);
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double L_0 = log(2 * M_E + 1.8 * q);
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double C_0 = 14.2 + 731 / (1 + 62.5 * q);
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double T0 = L_0 / (L_0 + C_0 * q * q);
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return normPower * pow(k,n) * T0 * T0;
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#endif
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#if POWER_SPECTRUM == OLD_POWERSPECTRUM
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// OLD FUNCTION:
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static const double l = 1/(Omega * h*h);
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static const double alpha = 1.7 * l, beta = 9.0 * pow(l, 1.5), gamma = l*l;
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return normPower * pow(k,n) * pow(1 + alpha * k + beta * pow(k,1.5) + gamma *k*k,-2);
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#endif
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#if POWER_SPECTRUM == POWER_SUGIYAMA
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double q = k * Theta_27*Theta_27 / (OmegaEff * exp(-OMEGA_B - sqrt(h/0.5)*OMEGA_B/OMEGA_0));
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double L0 = log(2*M_E + 1.8 * q);
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double C0 = 14.2 + 731 / (1 + 62.5 * q);
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double T_k = L0 / (L0 + C0 * q*q);
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// double poly = 1 + 3.89 * q + pow(16.1*q,2) + pow(5.46*q,3) + pow(6.71*q,4);
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// double T_k = log(1+2.34*q)/(2.34*q) * pow(poly,-0.25);
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return normPower * pow(k,n) * T_k * T_k;
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#endif
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#if POWER_SPECTRUM == POWER_BARDEEN
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double q = k / (OmegaEff);
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double poly = 1 + 3.89 * q + pow(16.1*q,2) + pow(5.46*q,3) + pow(6.71*q,4);
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double T_k = log(1+2.34*q)/(2.34*q) * pow(poly,-0.25);
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return normPower * pow(k,n) * T_k * T_k;
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#endif
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#if POWER_SPECTRUM == POWER_BDM
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k /= h*h;
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double alpha1 = 190;
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double Gmu = 4.6;
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double alpha2 = 11.5;
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double alpha3 = 11;
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double alpha4 = 12.55;
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double alpha5 = 0.0004;
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return normPower*k*alpha1*alpha1*Gmu*Gmu/(1+(alpha2*k)+pow(alpha3*k,2)+pow(alpha4*k,3))*pow(1+pow(alpha5/k,2), -2);
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#endif
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#if POWER_SPECTRUM == POWER_TEST
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return 1/(1+k*k);
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#endif
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}
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/*
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* This function computes the normalization of the power spectrum. It requests
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* a sigma8 (density fluctuations within 8 Mpc/h)
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*/
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double gslPowSpecNorm(double k, void *params)
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{
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double f = tophatFilter(k*8.0/h);
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return powerSpectrum(k, 1.0)*k*k*f*f;
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}
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double computePowSpecNorm(double sigma8)
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{
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int Nsteps = 30000;
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double normVal = 0;
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#ifndef USE_GSL
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for (int i = 1; i <= Nsteps; i++)
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{
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double t = i * 1.0/(Nsteps+1);
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// Change of variable !
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double k = (1-t)/t * K0;
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// The filter
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double filter_val = tophatFilter(k*8.0/h);
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// The powerspectrum
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double powVal = powerSpectrum(k, 1.0);
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// Multiply by the tophat filter
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powVal *= filter_val*filter_val;
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powVal *= k*k;
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// Account for change of variable
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powVal /= (t*t);
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// Integrate !
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normVal += powVal;
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}
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normVal /= 2*M_PI*M_PI;
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// The dt element
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normVal *= 1.0/(Nsteps+1) * K0;
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#else
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double abserr;
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gsl_integration_workspace *w = gsl_integration_workspace_alloc(NUM_ITERATION);
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gsl_function f;
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f.function = gslPowSpecNorm;
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f.params = 0;
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gsl_integration_qagiu(&f, 0, 0, TOLERANCE, NUM_ITERATION, w, &normVal, &abserr);
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gsl_integration_workspace_free(w);
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normVal /= (2*M_PI*M_PI);
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#endif
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return sigma8*sigma8/normVal;
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}
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/*
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* This function computes the variance of the Local Group velocity components
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* for a survey which depth is topHatRad1 (in Mpc/h). This variance should
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* be multiplied by (H \beta)^2 to be equal to a velocity^2.
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*/
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double gslVariance(double k, void *params)
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{
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double R1 = *(double *)params;
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double f = externalFilter(k * R1 / h);
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double a = f*f;
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#ifdef JUSZKIEWICZ_PATCH
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a *= exp(-k*k*(RJUSZ*RJUSZ/(h*h)));
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#endif
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a *= powerSpectrum(k, 1.0);
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return a;
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}
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double computeVariance(double powNorm, double topHatRad1)
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{
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int Nsteps = 100000;
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double varVal = 0;
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#ifndef USE_GSL
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for (int i = 1; i <= Nsteps; i++)
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{
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double t = i * 1.0/(Nsteps+1);
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// Change of variable !
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double k = (1-t)/t * K0;
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double powVal = powerSpectrum(k, powNorm);
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double filter1Val = externalFilter(k*topHatRad1/h);
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#ifdef JUSZKIEWICZ_PATCH
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powVal *= exp(-k*k*(RJUSZ*RJUSZ/(h*h)));
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#endif
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powVal *= filter1Val*filter1Val;
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powVal /= (t*t);
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varVal += powVal;
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}
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varVal *= 1.0/(Nsteps) * K0;
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varVal *= 1.0/(6*M_PI*M_PI);
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#else
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double abserr;
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gsl_integration_workspace *w = gsl_integration_workspace_alloc(NUM_ITERATION);
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gsl_function f;
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f.function = gslVariance;
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f.params = &topHatRad1;
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gsl_integration_qagiu(&f, 0, 0, TOLERANCE, NUM_ITERATION, w, &varVal, &abserr);
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gsl_integration_workspace_free(w);
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varVal *= powNorm/(6*M_PI*M_PI);
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#endif
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return varVal;
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}
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/*
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* This function computes the same quantity as computeVariance but
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* for a survey infinitely deep.
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*/
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double gslVarianceZero(double k, void *params)
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{
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double a = 1.0;
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#ifdef JUSZKIEWICZ_PATCH
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a *= exp(-k*k*(RJUSZ*RJUSZ/(h*h)));
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#endif
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a *= powerSpectrum(k, 1.0);
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return a;
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}
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double computeVarianceZero(double powNorm)
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{
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int Nsteps = 100000;
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double varVal = 0;
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#ifndef USE_GSL
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for (int i = 1; i <= Nsteps; i++)
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{
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double t = i * 1.0/(Nsteps+1);
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// Change of variable !
|
|
double k = (1-t)/t * K0;
|
|
double powVal = powerSpectrum(k, powNorm);
|
|
|
|
#ifdef JUSZKIEWICZ_PATCH
|
|
powVal *= exp(-k*k*(RJUSZ*RJUSZ/h*h));
|
|
#endif
|
|
|
|
powVal /= (t*t);
|
|
|
|
varVal += powVal;
|
|
}
|
|
|
|
varVal *= 1.0/(Nsteps+1) * K0;
|
|
varVal *= 1.0/(6*M_PI*M_PI);
|
|
|
|
#else
|
|
|
|
double abserr;
|
|
gsl_integration_workspace *w = gsl_integration_workspace_alloc(NUM_ITERATION);
|
|
gsl_function f;
|
|
|
|
f.function = gslVarianceZero;
|
|
f.params = 0;
|
|
|
|
gsl_integration_qagiu(&f, 0, 0, TOLERANCE, NUM_ITERATION, w, &varVal, &abserr);
|
|
|
|
gsl_integration_workspace_free(w);
|
|
|
|
varVal *= powNorm/(6*M_PI*M_PI);
|
|
#endif
|
|
|
|
return varVal;
|
|
}
|
|
|
|
/*
|
|
* This function computes the correlation between the infinitely deep
|
|
* velocity of the Local Group and the one estimated from a survey
|
|
* which depth is topHatRad1.
|
|
* This corresponds to \gamma.
|
|
* This quantity must be multiplied by H \beta to be equal to a velocity^2.
|
|
*/
|
|
double gslCorrel(double k, void *params)
|
|
{
|
|
double R1 = ((double *)params)[0];
|
|
double a = externalFilter(k * R1 / h);// * externalFilter(k * R2 / h);
|
|
|
|
#ifdef JUSZKIEWICZ_PATCH
|
|
a *= exp(-k*k*(RJUSZ*RJUSZ/(h*h)));
|
|
#endif
|
|
a *= powerSpectrum(k, 1.0);
|
|
|
|
return a;
|
|
}
|
|
|
|
double gslCorrelBis(double t, void *params)
|
|
{
|
|
double k = (1-t)/t;
|
|
double v = gslCorrel(k, params);
|
|
|
|
return v/(t*t);
|
|
}
|
|
|
|
double gslCorrel2(double k, void *params)
|
|
{
|
|
double R1 = ((double *)params)[0];
|
|
double R2 = ((double *)params)[1];
|
|
double a = externalFilter(k * R1 / h) * externalFilter(k * R2 / h);
|
|
|
|
#ifdef JUSZKIEWICZ_PATCH
|
|
a *= exp(-k*k*(RJUSZ*RJUSZ/(h*h)));
|
|
#endif
|
|
a *= powerSpectrum(k, 1.0) ;
|
|
|
|
return a;
|
|
}
|
|
|
|
double gslCorrel2bis(double t, void *params)
|
|
{
|
|
double k = (1-t)/t;
|
|
double v = gslCorrel2(k, params);
|
|
|
|
return v/(t*t);
|
|
}
|
|
|
|
|
|
double computeCorrel(double powNorm, double topHatRad1)
|
|
{
|
|
int Nsteps = 100000;
|
|
double varVal = 0;
|
|
|
|
#ifndef USE_GSL
|
|
|
|
for (int i = 1; i <= Nsteps; i++)
|
|
{
|
|
double t = i * 1.0/(Nsteps+1);
|
|
// Change of variable !
|
|
double k = (1-t)/t * K0;
|
|
double powVal = powerSpectrum(k, powNorm);
|
|
|
|
double filter1Val = externalFilter(k*topHatRad1/h);
|
|
|
|
#ifdef JUSZKIEWICZ_PATCH
|
|
powVal*=exp(-k*k*(RJUSZ*RJUSZ/h*h));
|
|
#endif
|
|
|
|
powVal *= filter1Val;
|
|
|
|
powVal /= (t*t);
|
|
|
|
varVal += powVal;
|
|
}
|
|
|
|
varVal *= 1.0/(Nsteps) * K0;
|
|
varVal *= 1.0/(6*M_PI*M_PI);
|
|
#else
|
|
|
|
double abserr;
|
|
gsl_integration_workspace *w = gsl_integration_workspace_alloc(NUM_ITERATION);
|
|
gsl_function f;
|
|
|
|
f.params = &topHatRad1;
|
|
|
|
#if 1
|
|
f.function = gslCorrelBis;
|
|
gsl_integration_qag (&f, 0, 1, 0, TOLERANCE, NUM_ITERATION, GSL_INTEG_GAUSS61, w, &varVal, &abserr);
|
|
#else
|
|
f.function = gslCorrel;
|
|
gsl_integration_qagiu(&f, 0, 0, TOLERANCE, NUM_ITERATION, w, &varVal, &abserr);
|
|
#endif
|
|
|
|
gsl_integration_workspace_free(w);
|
|
|
|
varVal *= powNorm/(6*M_PI*M_PI);
|
|
|
|
#endif
|
|
return varVal;
|
|
}
|
|
|
|
/*
|
|
* This function computes the correlation between the infinitely deep
|
|
* velocity of the Local Group and the one estimated from a survey
|
|
* which depth is topHatRad1.
|
|
* This corresponds to \gamma.
|
|
* This quantity must be multiplied by H \beta to be equal to a velocity^2.
|
|
*/
|
|
double computeCorrel2(double powNorm, double topHatRad1, double topHatRad2)
|
|
{
|
|
int Nsteps = 100000;
|
|
double varVal = 0;
|
|
#ifndef USE_GSL
|
|
|
|
for (int i = 1; i <= Nsteps; i++)
|
|
{
|
|
double t = i * 1.0/(Nsteps+1);
|
|
// Change of variable !
|
|
double k = (1-t)/t * K0;
|
|
double powVal = powerSpectrum(k, powNorm);
|
|
|
|
double filter1Val = externalFilter(k*topHatRad1/h);
|
|
double filter2Val = externalFilter(k*topHatRad2/h);
|
|
|
|
powVal *= filter1Val * filter2Val;
|
|
|
|
powVal /= (t*t);
|
|
|
|
varVal += powVal;
|
|
}
|
|
|
|
varVal *= 1.0/(Nsteps) * K0;
|
|
varVal *= 1.0/(6*M_PI*M_PI);
|
|
|
|
#else
|
|
|
|
double abserr;
|
|
gsl_integration_workspace *w = gsl_integration_workspace_alloc(NUM_ITERATION);
|
|
gsl_function f;
|
|
double rads[] = {topHatRad1, topHatRad2 };
|
|
|
|
f.params = rads;
|
|
|
|
#if 1
|
|
f.function = gslCorrel2bis;
|
|
gsl_integration_qag (&f, 0, 1, 0, TOLERANCE, NUM_ITERATION, GSL_INTEG_GAUSS61, w, &varVal, &abserr);
|
|
#else
|
|
f.function = gslCorrel2;
|
|
gsl_integration_qagiu(&f, 0, 0, TOLERANCE, NUM_ITERATION, w, &varVal, &abserr);
|
|
#endif
|
|
|
|
gsl_integration_workspace_free(w);
|
|
|
|
varVal *= powNorm/(6*M_PI*M_PI);
|
|
|
|
#endif
|
|
|
|
return varVal;
|
|
}
|
|
|
|
|
|
void updateCosmology()
|
|
{
|
|
OMEGA_0 = OMEGA_B+OMEGA_C;
|
|
Omega = OMEGA_0;
|
|
Theta_27 = 2.728 / 2.7;
|
|
beta = pow(OMEGA_0, 5./9);
|
|
OmegaEff = OMEGA_0 * h * h;
|
|
Gamma0 = OMEGA_0 * h * h;
|
|
|
|
#if 0
|
|
cout << "Cosmology is :" << endl
|
|
<< " O0=" << OMEGA_0 << " Theta=" << Theta_27 << " beta=" << beta << " h=" << h << " G0=" << Gamma0 << endl
|
|
<< " OmegaB=" << OMEGA_B << " Omega_C=" << OMEGA_C << endl;
|
|
#endif
|
|
}
|
|
|
|
double vvCorrection(double P_deltadelta, double k)
|
|
{
|
|
static const double alpha0 = -12480.5, alpha1 = 1.824, alpha2 = 2165.87, alpha3=1.796;
|
|
if (k > 0.3)
|
|
return 0;
|
|
double r =(alpha0*sqrt(P_deltadelta) + alpha1*P_deltadelta*P_deltadelta)/(alpha2 + alpha3*P_deltadelta);
|
|
assert(P_deltadelta > 0);
|
|
|
|
if (r < 0)
|
|
return 0;
|
|
return r;
|
|
}
|
|
|
|
};
|