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fitting_functions.py
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fitting_functions.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Thu Sep 28 12:58:56 2023
@author: ana
"""
import numpy as np
def Dmid_mchirp(m1_det, m2_det, cte):
"""
Dmid values (distance where Pdet = 0.5) as a function of the masses
in the detector frame (our first guess)
Parameters
----------
m1_det : detector frame mass1, float or 1D array
m2_det: detector frame mass2, float or 1D array
cte : parameter that we will be optimizing, float
Returns
-------
Dmid(m1,m2) in the detector's frame
"""
M = m1_det + m2_det
Mc = (m1_det * m2_det)**(3/5) / M**(1/5)
return cte * Mc**(5/6)
def Dmid_mchirp_expansion(m1_det, m2_det, params):
"""
Dmid values (distance where Pdet = 0.5) as a function of the masses
in the detector frame
Parameters
----------
m1_det : detector frame mass1, float or 1D array
m2_det: detector frame mass2, float or 1D array
params : parameters that we will be optimizing, 1D array
Returns
-------
Dmid(m1,m2) in the detector's frame
"""
cte , a_20, a_01, a_21, a_30, a_10 = params
M = m1_det + m2_det
eta = m1_det * m2_det / M**2
Mc = (m1_det * m2_det)**(3/5) / M**(1/5)
pol = cte *(1+ a_20 * M**2 + a_01 * (1 - 4*eta) + a_21 * M**2 * (1 - 4*eta) + a_30 * M**3 + a_10 * M )
return pol * Mc**(5/6)
def Dmid_mchirp_expansion_asqrt(m1_det, m2_det, params):
"""
Dmid values (distance where Pdet = 0.5) as a function of the masses
in the detector frame
Parameters
----------
m1_det : detector frame mass1, float or 1D array
m2_det: detector frame mass2, float or 1D array
params : parameters that we will be optimizing, 1D array
Returns
-------
Dmid(m1,m2) in the detector's frame
"""
cte , a_20, a_01, a_21, a_30, a_sqrt = params
M = m1_det + m2_det
eta = m1_det * m2_det / M**2
Mc = (m1_det * m2_det)**(3/5) / M**(1/5)
pol = cte *(1+ a_20 * M**2 + a_01 * (1 - 4*eta) + a_21 * M**2 * (1 - 4*eta) + a_30 * M**3 + a_sqrt * M**(1/2) )
return pol * Mc**(5/6)
def Dmid_mchirp_expansion_a11(m1_det, m2_det, params):
"""
Dmid values (distance where Pdet = 0.5) as a function of the masses
in the detector frame
Parameters
----------
m1_det : detector frame mass1, float or 1D array
m2_det: detector frame mass2, float or 1D array
params : parameters that we will be optimizing, 1D array
Returns
-------
Dmid(m1,m2) in the detector's frame
"""
cte , a_20, a_01, a_21, a_30, a_10, a_11 = params
M = m1_det + m2_det
eta = m1_det * m2_det / M**2
Mc = (m1_det * m2_det)**(3/5) / M**(1/5)
pol = cte *(1+ a_20 * M**2 + a_01 * (1 - 4*eta) + a_21 * M**2 * (1 - 4*eta) + a_30 * M**3 + a_10 * M + a_11 * M * (1 - 4*eta))
return pol * Mc**(5/6)
def Dmid_mchirp_power(m1_det, m2_det, params):
"""
Dmid values (distance where Pdet = 0.5) as a function of the masses
in the detector frame
Parameters
----------
m1_det : detector frame mass1, float or 1D array
m2_det: detector frame mass2, float or 1D array
params : parameters that we will be optimizing, 1D array
Returns
-------
Dmid(m1,m2) in the detector's frame
"""
cte , a_20, a_01, a_21, a_30, power_param = params
M = m1_det + m2_det
eta = m1_det * m2_det / M**2
Mc = (m1_det * m2_det)**(3/5) / M**(1/5)
pol = cte *(1+ a_20 * M**2 / 2 + a_01 * (1 - 4*eta) + a_21 * M**2 * (1 - 4*eta) / 2 + a_30 * M**3 )
return pol * Mc**((5+power_param)/6)
def Dmid_mchirp_expansion_exp(m1_det, m2_det, params):
"""
Dmid values (distance where Pdet = 0.5) as a function of the masses
in the detector frame
Parameters
----------
m1_det : detector frame mass1, float or 1D array
m2_det: detector frame mass2, float or 1D array
params : parameters that we will be optimizing, 1D array
Returns
-------
Dmid(m1,m2) in the detector's frame
"""
cte , a_20, a_01, a_21, a_30, a_10, a_11, Mstar = params
M = m1_det + m2_det
eta = m1_det * m2_det / M**2
Mc = (m1_det * m2_det)**(3/5) / M**(1/5)
pol = cte *(1+ a_20 * M**2 + a_01 * (1 - 4*eta) + a_21 * M**2 * (1 - 4*eta) + a_30 * M**3 + a_10 * M + a_11 * M * (1 - 4*eta))
return pol * Mc**(5/6) * np.exp(-M/Mstar)
def Dmid_mchirp_expansion_noa30(m1_det, m2_det, params):
"""
Dmid values (distance where Pdet = 0.5) as a function of the masses
in the detector frame
Parameters
----------
m1_det : detector frame mass1, float or 1D array
m2_det: detector frame mass2, float or 1D array
params : parameters that we will be optimizing, 1D array
Returns
-------
Dmid(m1,m2) in the detector's frame
"""
cte , a_20, a_01, a_21, a_10, a_11 = params
M = m1_det + m2_det
eta = m1_det * m2_det / M**2
Mc = (m1_det * m2_det)**(3/5) / M**(1/5)
pol = cte *(1+ a_20 * M**2 + a_01 * (1 - 4*eta) + a_21 * M**2 * (1 - 4*eta) + a_10 * M + a_11 * M * (1 - 4*eta))
return pol * Mc**(5/6)
def emax_exp(m1_det, m2_det, params):
"""
maximum search sensitivity (emax) as a function of the masses
in the detector frame
Parameters
----------
m1_det : detector frame mass1, float or 1D array
m2_det: detector frame mass2, float or 1D array
params : parameters that we will be optimizing, 1D array
Returns
-------
emax(m1, m2) in the detector frame
"""
Mtot = m1_det + m2_det
b_0, b_1, b_2 = params
return 1 - np.exp(b_0 + b_1 * Mtot + b_2 * Mtot**2)
def emax_sigmoid(m1_det, m2_det, params):
"""
maximum search sensitivity (emax) as a function of the masses
in the detector frame
Parameters
----------
m1_det : detector frame mass1, float or 1D array
m2_det: detector frame mass2, float or 1D array
params : parameters that we will be optimizing, 1D array
Returns
-------
emax(m1, m2) in the detector frame
"""
Mtot = m1_det + m2_det
b_0, k, M_0 = params
L = 1 - np.exp(b_0)
return L / (1 + np.exp(k * (Mtot - M_0)))