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music-panphasia/transfer_function.hh
glatterf42 1e32e12349 First commit of original files.
2022-04-29 14:37:23 +02:00

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/*
transfer_function.hh - This file is part of MUSIC -
a code to generate multi-scale initial conditions
for cosmological simulations
Copyright (C) 2010 Oliver Hahn
*/
#ifndef __TRANSFERFUNCTION_HH
#define __TRANSFERFUNCTION_HH
#include <vector>
#include <sstream>
#include <fstream>
#include <iostream>
#include <cmath>
#include <stdexcept>
#include <complex>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_spline.h>
#include <gsl/gsl_sf_gamma.h>
#include "Numerics.hh"
#include "config_file.hh"
enum tf_type{
total, cdm, baryon, vtotal, vcdm, vbaryon, total0
};
#define GSL_INTEGRATION_ERR 1e-5
//! Abstract base class for transfer functions
/*!
This class implements a purely virtual interface that can be
used to derive instances implementing various transfer functions.
*/
class transfer_function_plugin{
public:
Cosmology cosmo_; //!< cosmological parameter, read from config_file
config_file *pcf_; //!< pointer to config_file from which to read parameters
bool tf_distinct_; //!< bool if density transfer function is distinct for baryons and DM
bool tf_withvel_; //!< bool if also have velocity transfer functions
bool tf_withtotal0_; //!< have the z=0 spectrum for normalisation purposes
bool tf_velunits_; //!< velocities are in velocity units (km/s)
public:
//! constructor
transfer_function_plugin( config_file& cf )
: pcf_( &cf ), tf_distinct_(false), tf_withvel_(false), tf_withtotal0_(false), tf_velunits_(false)
{
real_t zstart;
zstart = pcf_->getValue<real_t>( "setup", "zstart" );
cosmo_.astart = 1.0/(1.0+zstart);
cosmo_.Omega_b = pcf_->getValue<real_t>( "cosmology", "Omega_b" );
cosmo_.Omega_m = pcf_->getValue<real_t>( "cosmology", "Omega_m" );
cosmo_.Omega_DE = pcf_->getValue<real_t>( "cosmology", "Omega_L" );
cosmo_.H0 = pcf_->getValue<real_t>( "cosmology", "H0" );
cosmo_.sigma8 = pcf_->getValue<real_t>( "cosmology", "sigma_8" );
cosmo_.nspect = pcf_->getValue<real_t>( "cosmology", "nspec" );
}
//! destructor
virtual ~transfer_function_plugin(){ };
//! compute value of transfer function at waven umber
virtual double compute( double k, tf_type type) = 0;
//! return maximum wave number allowed
virtual double get_kmax( void ) = 0;
//! return minimum wave number allowed
virtual double get_kmin( void ) = 0;
//! return if density transfer function is distinct for baryons and DM
bool tf_is_distinct( void )
{ return tf_distinct_; }
//! return if we also have velocity transfer functions
bool tf_has_velocities( void )
{ return tf_withvel_; }
//! return if we also have a z=0 transfer function for normalisation
bool tf_has_total0( void )
{ return tf_withtotal0_; }
//! return if velocity returned is in velocity or in displacement units
bool tf_velocity_units( void )
{ return tf_velunits_; }
};
//! Implements abstract factory design pattern for transfer function plug-ins
struct transfer_function_plugin_creator
{
//! create an instance of a transfer function plug-in
virtual transfer_function_plugin * create( config_file& cf ) const = 0;
//! destroy an instance of a plug-in
virtual ~transfer_function_plugin_creator() { }
};
//! Write names of registered transfer function plug-ins to stdout
std::map< std::string, transfer_function_plugin_creator *>& get_transfer_function_plugin_map();
void print_transfer_function_plugins( void );
//! Concrete factory pattern for transfer function plug-ins
template< class Derived >
struct transfer_function_plugin_creator_concrete : public transfer_function_plugin_creator
{
//! register the plug-in by its name
transfer_function_plugin_creator_concrete( const std::string& plugin_name )
{
get_transfer_function_plugin_map()[ plugin_name ] = this;
}
//! create an instance of the plug-in
transfer_function_plugin * create( config_file& cf ) const
{
return new Derived( cf );
}
};
typedef transfer_function_plugin transfer_function;
transfer_function_plugin *select_transfer_function_plugin( config_file& cf );
/**********************************************************************/
/**********************************************************************/
/**********************************************************************/
//! k-space transfer function
class TransferFunction_k
{
public:
static transfer_function *ptf_;
static real_t nspec_;
double pnorm_, sqrtpnorm_;
static tf_type type_;
TransferFunction_k( tf_type type, transfer_function *tf, real_t nspec, real_t pnorm )
: pnorm_(pnorm)
{
ptf_ = tf;
nspec_ = nspec;
sqrtpnorm_ = sqrt( pnorm_ );
type_ = type;
std::string fname("input_powerspec.txt");
if( type == cdm || type == total )
{
std::ofstream ofs(fname.c_str());
double kmin=log10(tf->get_kmin()), kmax= log10(tf->get_kmax());
double dk=(kmax-kmin)/300.;
if( tf->tf_is_distinct() )
{
ofs << "#"
<< std::setw(15) << "k [h/Mpc]"
<< std::setw(16) << "P_cdm"
<< std::setw(16) << "P_vcdm"
<< std::setw(16) << "P_bar"
<< std::setw(16) << "P_vbar"
<< std::setw(16) << "P_total"
<< std::setw(16) << "P_vtotal"
<< std::endl;
for( int i=0; i<300; ++i )
{
double k = pow(10.0,kmin+i*dk);
ofs << std::setw(16) << k
<< std::setw(16) << pow(sqrtpnorm_*pow(k,0.5*nspec_)*ptf_->compute(k,cdm),2)
<< std::setw(16) << pow(sqrtpnorm_*pow(k,0.5*nspec_)*ptf_->compute(k,vcdm),2)
<< std::setw(16) << pow(sqrtpnorm_*pow(k,0.5*nspec_)*ptf_->compute(k,baryon),2)
<< std::setw(16) << pow(sqrtpnorm_*pow(k,0.5*nspec_)*ptf_->compute(k,vbaryon),2)
<< std::setw(16) << pow(sqrtpnorm_*pow(k,0.5*nspec_)*ptf_->compute(k,total),2)
<< std::setw(16) << pow(sqrtpnorm_*pow(k,0.5*nspec_)*ptf_->compute(k,vtotal),2)
<< std::endl;
}
}
else
{
ofs << "#"
<< std::setw(16) << "k [h/Mpc]"
<< std::setw(16) << "P_cdm"
<< std::setw(16) << "P_vcdm"
<< std::setw(16) << "P_total"
<< std::endl;
for( int i=0; i<300; ++i )
{
double k = pow(10.0,kmin+i*dk);
ofs << std::setw(16) << k
<< std::setw(16) << pow(sqrtpnorm_*pow(k,0.5*nspec_)*ptf_->compute(k,cdm),2)
<< std::setw(16) << pow(sqrtpnorm_*pow(k,0.5*nspec_)*ptf_->compute(k,vcdm),2)
<< std::setw(16) << pow(sqrtpnorm_*pow(k,0.5*nspec_)*ptf_->compute(k,total),2)
<< std::endl;
}
}
}
}
inline real_t compute( real_t k ) const
{
return sqrtpnorm_*pow(k,0.5*nspec_)*ptf_->compute(k,type_);
}
};
/**********************************************************************/
/**********************************************************************/
/**********************************************************************/
#define NZERO_Q
typedef std::complex<double> complex;
class TransferFunction_real
{
public:
double Tr0_;
real_t Tmin_, Tmax_, Tscale_;
real_t rneg_, rneg2_, kny_;
static transfer_function *ptf_;
static real_t nspec_;
protected:
real_t krgood( real_t mu, real_t q, real_t dlnr, real_t kr )
{
double krnew = kr;
complex cdgamma, zm, zp;
double arg, iarg, xneg, xpos, y;
gsl_sf_result g_a, g_p;
xpos = 0.5*(mu+1.0+q);
xneg = 0.5*(mu+1.0-q);
y = M_PI/(2.0*dlnr);
zp=complex(xpos,y);
zm=complex(xneg,y);
gsl_sf_lngamma_complex_e (zp.real(), zp.imag(), &g_a, &g_p);
zp=std::polar(exp(g_a.val),g_p.val);
real_t zpa = g_p.val;
gsl_sf_lngamma_complex_e (zm.real(), zm.imag(), &g_a, &g_p);
zm=std::polar(exp(g_a.val),g_p.val);
real_t zma = g_p.val;
arg=log(2.0/kr)/dlnr+(zpa+zma)/M_PI;
iarg=(real_t)((int)(arg + 0.5));
if( arg!=iarg )
krnew=kr*exp((arg-iarg)*dlnr);
return krnew;
}
void transform( real_t pnorm, unsigned N, real_t q, std::vector<double>& rr, std::vector<double>& TT )
{
const double mu = 0.5;
double qmin = 1.0e-7, qmax = 1.0e+7;
q = 0.0;
//N = 16384;
N = 1<<12;
#ifdef NZERO_Q
q=0.4;
//q=-0.1;
#endif
double kmin = qmin, kmax=qmax;
double rmin = qmin, rmax = qmax;
double k0 = exp(0.5*(log(kmax)+log(kmin)));
double r0 = exp(0.5*(log(rmax)+log(rmin)));
double L = log(rmax)-log(rmin);
double k0r0 = k0*r0;
double dlnk = L/N, dlnr = L/N;
double sqrtpnorm = sqrt(pnorm);
double dir = 1.0;
double fftnorm = 1.0/N;
fftw_complex *in, *out;
in = new fftw_complex[N];
out = new fftw_complex[N];
//... perform anti-ringing correction from Hamilton (2000)
k0r0 = krgood( mu, q, dlnr, k0r0 );
std::string ofname;
switch( type_ )
{
case cdm:
ofname = "input_powerspec_cdm.txt"; break;
case baryon:
ofname = "input_powerspec_baryon.txt"; break;
case total:
ofname = "input_powerspec_total.txt"; break;
case vcdm:
ofname = "input_powerspec_vcdm.txt"; break;
case vbaryon:
ofname = "input_powerspec_vbaryon.txt"; break;
default:
throw std::runtime_error("Unknown transfer function type in TransferFunction_real::transform");
}
std::ofstream ofsk(ofname.c_str());
double sum_in = 0.0;
for( unsigned i=0; i<N; ++i )
{
double k = k0*exp(((int)i - (int)N/2+1) * dlnk);
double T = ptf_->compute( k, type_ );
double del = sqrtpnorm*T*pow(k,0.5*nspec_);
RE(in[i]) = del*pow(k,1.5-q);
IM(in[i]) = 0.0;
sum_in += RE(in[i]);
ofsk << std::setw(16) << k <<std::setw(16) << del*del << std::setw(16) << T << std::endl;
}
ofsk.close();
#ifdef FFTW3
#ifdef SINGLE_PRECISION
fftwf_plan p,ip;
p = fftwf_plan_dft_1d(N, in, out, FFTW_FORWARD, FFTW_ESTIMATE);
ip = fftwf_plan_dft_1d(N, out, in, FFTW_BACKWARD, FFTW_ESTIMATE);
fftwf_execute(p);
#else
fftw_plan p,ip;
p = fftw_plan_dft_1d(N, in, out, FFTW_FORWARD, FFTW_ESTIMATE);
ip = fftw_plan_dft_1d(N, out, in, FFTW_BACKWARD, FFTW_ESTIMATE);
fftw_execute(p);
#endif
#else
fftw_plan p,ip;
p = fftw_create_plan(N, FFTW_FORWARD, FFTW_ESTIMATE);
ip = fftw_create_plan(N, FFTW_BACKWARD, FFTW_ESTIMATE);
fftw_one(p, in, out);
#endif
//... compute the Hankel transform by convolution with the Bessel function
for( unsigned i=0; i<N; ++i )
{
int ii=i;
if( ii > (int)N/2 )
ii -= N;
#ifndef NZERO_Q
double y=ii*M_PI/L;
complex zp((mu+1.0)*0.5,y);
gsl_sf_result g_a, g_p;
gsl_sf_lngamma_complex_e(zp.real(), zp.imag(), &g_a, &g_p);
double arg = 2.0*(log(2.0/k0r0)*y+g_p.val);
//complex cu = complex(out[i].re,out[i].im)*std::polar(1.0,arg);
//out[i].re = cu.real()*fftnorm;
//out[i].im = cu.imag()*fftnorm;
complex cu = complex( RE(out[i]), IM(out[i]) ) * std::polar(1.0,arg);
RE(out[i]) = cu.real()*fftnorm;
IM(out[i]) = cu.imag()*fftnorm;
#else
complex x(dir*q, (double)ii*2.0*M_PI/L);
gsl_sf_result g_a, g_p;
complex g1, g2, garg, U, phase;
complex twotox = pow(complex(2.0,0.0),x);
/////////////////////////////////////////////////////////
//.. evaluate complex Gamma functions
garg = 0.5*(mu+1.0+x);
gsl_sf_lngamma_complex_e (garg.real(), garg.imag(), &g_a, &g_p);
g1 = std::polar(exp(g_a.val),g_p.val);
garg = 0.5*(mu+1.0-x);
gsl_sf_lngamma_complex_e (garg.real(), garg.imag(), &g_a, &g_p);
g2 = std::polar(exp(g_a.val),g_p.val);
/////////////////////////////////////////////////////////
//.. compute U
if( (fabs(g2.real()) < 1e-19 && fabs(g2.imag()) < 1e-19) )
{
//std::cerr << "Warning : encountered possible singularity in TransferFunction_real::transform!\n";
g1 = 1.0; g2 = 1.0;
}
U = twotox * g1 / g2;
phase = pow(complex(k0r0,0.0),complex(0.0,2.0*M_PI*(double)ii/L));
complex cu = complex(RE(out[i]),IM(out[i]))*U*phase*fftnorm;
RE(out[i]) = cu.real();
IM(out[i]) = cu.imag();
/*if( (RE(out[i]) != RE(out[i]))||(IM(out[i]) != IM(out[i])) )
{ std::cerr << "NaN @ i=" << i << ", U= " << U << ", phase = " << phase << ", g1 = " << g1 << ", g2 = " << g2 << std::endl;
std::cerr << "mu+1+q = " << mu+1.0+q << std::endl;
//break;
}*/
#endif
}
#ifdef FFTW3
#ifdef SINGLE_PRECISION
fftwf_execute(ip);
#else
fftw_execute(ip);
#endif
#else
fftw_one(ip, out, in);
#endif
rr.assign(N,0.0);
TT.assign(N,0.0);
r0 = k0r0/k0;
for( unsigned i=0; i<N; ++i )
{
int ii = i;
ii -= N/2-1;
double r = r0*exp(-ii*dlnr);
rr[N-i-1] = r;
TT[N-i-1] = 4.0*M_PI* sqrt(M_PI/2.0) * RE(in[i]) * pow(r,-(1.5+q));
}
{
std::string fname;
if(type_==total) fname = "transfer_real_total.txt";
if(type_==cdm) fname = "transfer_real_cdm.txt";
if(type_==baryon) fname = "transfer_real_baryon.txt";
if(type_==vcdm) fname = "transfer_real_vcdm.txt";
if(type_==vbaryon) fname = "transfer_real_vbaryon.txt";
std::ofstream ofs(fname.c_str());
for( unsigned i=0; i<N; ++i )
{
int ii = i;
ii -= N/2-1;
double r = r0*exp(-ii*dlnr);//r0*exp(ii*dlnr);
double T = 4.0*M_PI* sqrt(M_PI/2.0) * RE(in[i]) * pow(r,-(1.5+q));
ofs << r << "\t\t" << T << "\t\t" << IM(in[i]) << std::endl;
}
}
delete[] in;
delete[] out;
#if defined(FFTW3) && defined(SINGLE_PRECISION)
fftwf_destroy_plan(p);
fftwf_destroy_plan(ip);
#else
fftw_destroy_plan(p);
fftw_destroy_plan(ip);
#endif
}
std::vector<real_t> m_xtable,m_ytable,m_dytable;
double m_xmin, m_xmax, m_dx, m_rdx;
static tf_type type_;
public:
TransferFunction_real( double boxlength, int nfull, tf_type type, transfer_function *tf,
real_t nspec, real_t pnorm, real_t rmin, real_t rmax, real_t knymax, unsigned nr )
{
real_t q = 0.8;
ptf_ = tf;
nspec_ = nspec;
type_ = type;
kny_ = knymax;
/*****************************************************************/
//... compute the FFTlog transform of the k^n T(k) kernel
std::vector<double> r,T;
transform( pnorm, nr, q, r, T );
gsl_set_error_handler_off ();
/*****************************************************************/
//... compute T(r=0) by 3D k-space integration
{
const double REL_PRECISION=1.e-5;
gsl_integration_workspace * ws = gsl_integration_workspace_alloc (1000);
gsl_function ff;
double kmin = 2.0*M_PI/boxlength;
double kmax = nfull*M_PI/boxlength;
//... integrate 0..kmax
double a[6];
a[3] = 0.1*kmin;
a[4] = kmax;
ff.function = &call_x;
ff.params = reinterpret_cast<void*> (a);
double res, err, res2, err2;
gsl_integration_qags( &ff, a[3], a[4], 0.0, GSL_INTEGRATION_ERR, 1000, ws, &res, &err );
if( err/res > REL_PRECISION )
std::cerr << " - Warning: no convergence in \'TransferFunction_real\', rel. error=" << err/res << std::endl;
//... integrate 0..kmin
a[3] = 0.1*kmin;
a[4] = kmin;
gsl_integration_qags( &ff, a[3], a[4], 0.0, GSL_INTEGRATION_ERR, 1000, ws, &res2, &err2 );
if( err2/res2 > 10*REL_PRECISION )
std::cerr << " - Warning: no convergence in \'TransferFunction_real\', rel. error=" << err2/res2 << std::endl;
gsl_integration_workspace_free ( ws );
//.. get kmin..kmax
res -= res2;
//.. *8 because we only integrated one octant
res *= 8.0*sqrt(pnorm);
Tr0_ = res;
}
/*****************************************************************/
//... store as table for spline interpolation
gsl_interp_accel *accp;
gsl_spline *splinep;
std::vector<double> xsp, ysp;
for( unsigned i=0; i<r.size(); ++i )
{
if( r[i] > rmin/512. && r[i] < rmax )
{
xsp.push_back( log10(r[i]) );
ysp.push_back( T[i]*r[i]*r[i] );
}
}
accp = gsl_interp_accel_alloc ();
//... spline interpolation is only marginally slower here
splinep = gsl_spline_alloc (gsl_interp_akima, xsp.size() );
//... set up everything for spline interpolation
gsl_spline_init (splinep, &xsp[0], &ysp[0], xsp.size() );
//.. build lookup table using spline interpolation
m_xmin = log10(rmin);
m_xmax = log10(rmax);
m_dx = (m_xmax-m_xmin)/nr;
m_rdx = 1.0/m_dx;
for(unsigned i=0; i<nr; ++i )
{
m_xtable.push_back( m_xmin+i*m_dx );
m_ytable.push_back( gsl_spline_eval(splinep, (m_xtable.back()), accp) );
}
for(unsigned i=0; i<nr-1; ++i )
{
real_t dy,dr;
dy = m_ytable[i+1]/pow(m_xtable[i+1],2)-m_ytable[i]/pow(m_xtable[i],2);
dr = pow(10.0,m_xtable[i+1])-pow(10.0,m_xtable[i]);
m_dytable.push_back(dy/dr);
}
gsl_spline_free (splinep);
gsl_interp_accel_free (accp);
}
static double call_wrapper( double k, void *arg )
{
double *a = (double*)arg;
double T = ptf_->compute( k, type_ );
return 4.0*M_PI*a[0]*T*pow(k,0.5*nspec_)*k*k;
}
static double call_x( double kx, void *arg )
{
gsl_integration_workspace * wx = gsl_integration_workspace_alloc (1000);
double *a = (double*)arg;
double kmin = a[3], kmax = a[4];
a[0] = kx;
gsl_function FX;
FX.function = &call_y;
FX.params = reinterpret_cast<void*> (a);
double resx, errx;
gsl_integration_qags( &FX, kmin, kmax, 0.0, GSL_INTEGRATION_ERR, 1000, wx, &resx, &errx );
gsl_integration_workspace_free (wx);
return resx;
}
static double call_y( double ky, void *arg )
{
gsl_integration_workspace * wy = gsl_integration_workspace_alloc (1000);
double *a = (double*)arg;
double kmin = a[3], kmax = a[4];
a[1] = ky;
gsl_function FY;
FY.function = &call_z;
FY.params = reinterpret_cast<void*> (a);
double resy, erry;
gsl_integration_qags( &FY, kmin, kmax, 0.0, GSL_INTEGRATION_ERR, 1000, wy, &resy, &erry );
gsl_integration_workspace_free (wy);
return resy;
}
static double call_z( double kz, void *arg )
{
double *a = (double*)arg;
double kx = a[0], ky = a[1];
double kk = sqrt(kx*kx+ky*ky+kz*kz);
double T = ptf_->compute( kk, type_ );
return pow(kk,0.5*nspec_)*T;
}
~TransferFunction_real()
{ }
inline real_t get_grad( real_t r2 ) const
{
double r = 0.5*fast_log10(r2);
double ii = (r-m_xmin)*m_rdx;
int i = (int)ii;
i=std::max(0,i);
i=std::min(i, (int)m_xtable.size()-2);
return (real_t)m_dytable[i];
}
//... fast version
inline real_t compute_real( real_t r2 ) const
{
const double EPS = 1e-8;
const double Reps2 = EPS*EPS;
if( r2 <Reps2 )
return Tr0_;
//double r = 0.5*log10(r2);
double r = 0.5*fast_log10(r2);
double ii = (r-m_xmin)*m_rdx;
int i = (int)ii;
i=std::max(0,i);
i=std::min(i, (int)m_xtable.size()-2);
double y1,y2;
y1 = m_ytable[i];
y2 = m_ytable[i+1];
//divide by r**2 because r^2 T is tabulated
//return (real_t)((y1 + (y2-y1)*(ii-(double)i))/r2);
real_t retval = (real_t)((y1 + (y2-y1)*(ii-(double)i))/r2);
if( retval != retval ){
std::cerr << "FAILURE FAILURE FAILURE" << std::endl;
fprintf(stderr,"r2 = %f, r = %f, i = %d, y1 = %f, y2 = %f, xtable[i]=%f",r2,r,i,y1,y2, m_xtable[i]);
abort();
}
return retval;
}
};
#endif
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