__author__ = "sibirrer"
import scipy.optimize
import scipy.interpolate as interpolate
import numpy as np
from astropy.cosmology import FlatLambdaCDM
from lenstronomy.Cosmo.lens_cosmo import LensCosmo
from lenstronomy.Util.package_util import exporter
export, __all__ = exporter()
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@export
def cosmo2angular_diameter_distances(H_0, omega_m, z_lens, z_source):
"""
:param H_0: Hubble constant [km/s/Mpc]
:param omega_m: dimensionless matter density at z=0
:param z_lens: deflector redshift
:param z_source: source redshift
:return: angular diameter distances Dd and Ds/Dds
"""
cosmo = FlatLambdaCDM(H0=H_0, Om0=omega_m, Ob0=0.0)
lensCosmo = LensCosmo(z_lens=z_lens, z_source=z_source, cosmo=cosmo)
Dd = lensCosmo.dd
Ds = lensCosmo.ds
Dds = lensCosmo.dds
return Dd, Ds / Dds
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@export
def ddt2h0(ddt, z_lens, z_source, cosmo):
"""Converts time-delay distance to H0 for a given expansion history.
:param ddt: time-delay distance in Mpc
:param z_lens: deflector redshift
:param z_source: source redshift
:param cosmo: astropy.cosmology class instance
:return: h0 value which matches the cosmology class effectively replacing the h0
value used in the creation of this class
"""
h0_fiducial = cosmo.H0.value
lens_cosmo = LensCosmo(z_lens=z_lens, z_source=z_source, cosmo=cosmo)
ddt_fiducial = lens_cosmo.ddt
h0 = h0_fiducial * ddt_fiducial / ddt
return h0
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@export
class SolverFlatLCDM(object):
"""Class to solve multidimensional non-linear equations to determine the
cosmological parameters H0 and omega_m given the angular diameter distance
relations."""
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def __init__(self, z_d, z_s):
self.z_d = z_d
self.z_s = z_s
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def F(self, x, Dd, Ds_Dds):
"""
:param x: array of parameters (H_0, omega_m)
:return:
"""
[H_0, omega_m] = x
omega_m = abs(omega_m) % 1
Dd_new, Ds_Dds_new = cosmo2angular_diameter_distances(
H_0, omega_m, self.z_d, self.z_s
)
y = np.zeros(2)
y[0] = Dd - Dd_new
y[1] = Ds_Dds - Ds_Dds_new
return y
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def solve(self, init, dd, ds_dds):
x = scipy.optimize.fsolve(
self.F, init, args=(dd, ds_dds), xtol=1.49012e-08, factor=0.1
)
x[1] = abs(x[1]) % 1
y = self.F(x, dd, ds_dds)
if abs(y[0]) >= 0.1 or abs(y[1]) > 0.1:
x = np.array([-1, -1])
return x
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@export
class InvertCosmo(object):
"""Class to do an interpolation and call the inverse of this interpolation to get
H_0 and omega_m."""
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def __init__(self, z_d, z_s, H0_range=None, omega_m_range=None):
self.z_d = z_d
self.z_s = z_s
if H0_range is None:
H0_range = np.linspace(10, 100, 90)
if omega_m_range is None:
omega_m_range = np.linspace(0.05, 1, 95)
self._H0_range = H0_range
self._omega_m_range = omega_m_range
def _make_interpolation(self):
"""Creates an interpolation grid in H_0, omega_m and computes quantities in Dd
and Ds_Dds.
:return:
"""
grid2d = np.dstack(np.meshgrid(self._H0_range, self._omega_m_range)).reshape(
-1, 2
)
H0_grid = grid2d[:, 0]
omega_m_grid = grid2d[:, 1]
Dd_grid = np.zeros_like(H0_grid)
Ds_Dds_grid = np.zeros_like(H0_grid)
for i in range(len(H0_grid)):
Dd, Ds_Dds = cosmo2angular_diameter_distances(
H0_grid[i], omega_m_grid[i], self.z_d, self.z_s
)
Dd_grid[i] = Dd
Ds_Dds_grid[i] = Ds_Dds
self._f_H0 = interpolate.interp2d(
Dd_grid,
Ds_Dds_grid,
H0_grid,
kind="linear",
copy=False,
bounds_error=False,
fill_value=-1,
)
print("H0 interpolation done")
self._f_omega_m = interpolate.interp2d(
Dd_grid,
Ds_Dds_grid,
omega_m_grid,
kind="linear",
copy=False,
bounds_error=False,
fill_value=0,
)
print("omega_m interpolation done")
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def get_cosmo(self, Dd, Ds_Dds):
"""Return the values of H0 and omega_m computed with an interpolation.
:param Dd: flat
:param Ds_Dds: float
:return:
"""
if not hasattr(self, "_f_H0") or not hasattr(self, "_f_omega_m"):
self._make_interpolation()
H0 = self._f_H0(Dd, Ds_Dds)
print(H0, "H0")
omega_m = self._f_omega_m(Dd, Ds_Dds)
Dd_new, Ds_Dds_new = cosmo2angular_diameter_distances(
H0[0], omega_m[0], self.z_d, self.z_s
)
if abs(Dd - Dd_new) / Dd > 0.01 or abs(Ds_Dds - Ds_Dds_new) / Ds_Dds > 0.01:
return -1, -1
else:
return H0[0], omega_m[0]