def scale_einstein_radius(z_lens, z_src, H0=70, Om0=0.3, Ode0=0.7):
cosmo = LambdaCDM(H0=H0, Om0=Om0, Ode0=Ode0)
d_ls = cosmo.angular_diameter_distance_z1z2(z_lens, z_src)
d_s = cosmo.angular_diameter_distance_z1z2(0, z_src)
d = d_ls / d_s
return d.value
def partial_profile(RA0, DEC0, Z, RIN, ROUT, ndots, h):
ndots = int(ndots)
cosmo = LambdaCDM(H0=100 * h, Om0=0.25, Ode0=0.75)
dl = cosmo.angular_diameter_distance(Z).value
KPCSCALE = dl * (((1.0 / 3600.0) * np.pi) / 180.0) * 1000.0
delta = ROUT / (3600 * KPCSCALE)
t0 = time.time()
mask = (S.ra < (RA0 + delta)) & (S.ra > (RA0 - delta)) & (
S.dec > (DEC0 - delta)) & (S.dec < (DEC0 + delta)) & (S.z_v >
(Z + 0.1))
catdata = S[mask]
ds = cosmo.angular_diameter_distance(catdata.z_v).value
dls = cosmo.angular_diameter_distance_z1z2(Z, catdata.z_v).value
BETA_array = dls / ds
Dl = dl * 1.e6 * pc
sigma_c = (((cvel**2.0) / (4.0 * np.pi * G * Dl)) *
(1. / BETA_array)) * (pc**2 / Msun)
rads, theta, test1, test2 = eq2p2(np.deg2rad(catdata.ra),
np.deg2rad(catdata.dec), np.deg2rad(RA0),
np.deg2rad(DEC0))
r = np.rad2deg(rads) * 3600 * KPCSCALE
e1 = catdata.gamma1
e2 = -1. * catdata.gamma2
#get tangential ellipticities
et = (-e1 * np.cos(2 * theta) - e2 * np.sin(2 * theta)) * sigma_c
k = catdata.kappa * sigma_c
r = np.rad2deg(rads) * 3600 * KPCSCALE
bines = np.logspace(np.log10(RIN), np.log10(ROUT), num=ndots + 1)
dig = np.digitize(r, bines)
SIGMA = []
DSIGMA = []
for nbin in range(ndots):
mbin = dig == nbin + 1
SIGMA = np.append(SIGMA, np.average(k[mbin]))
DSIGMA = np.append(DSIGMA, np.average(k[mbin]))
return [SIGMA, DSIGMA]
class AstroPyCosmology(CLMMCosmology):
def __init__(self, **kwargs):
super(AstroPyCosmology, self).__init__(**kwargs)
# this tag will be used to check if the cosmology object is accepted by the modeling
self.backend = 'ct'
assert isinstance(self.be_cosmo, LambdaCDM)
def _init_from_cosmo(self, be_cosmo):
assert isinstance(be_cosmo, LambdaCDM)
self.be_cosmo = be_cosmo
def _init_from_params(self, H0, Omega_b0, Omega_dm0, Omega_k0):
Om0 = Omega_b0 + Omega_dm0
Ob0 = Omega_b0
self.be_cosmo = FlatLambdaCDM(H0=H0,
Om0=Om0,
Ob0=Ob0,
Tcmb0=2.7255,
Neff=3.046,
m_nu=([0.06, 0.0, 0.0] * units.eV))
if Omega_k0 != 0.0:
Ode0 = self.be_cosmo.Ode0 - Omega_k0
self.be_cosmo = LambdaCDM(H0=H0,
Om0=Om0,
Ob0=Ob0,
Ode0=Ode0,
Tcmb0=2.7255,
Neff=3.046,
m_nu=([0.06, 0.0, 0.0] * units.eV))
def _set_param(self, key, value):
raise NotImplementedError("Astropy do not support changing parameters")
def _get_param(self, key):
if key == "Omega_m0":
return self.be_cosmo.Om0
elif key == "Omega_b0":
return self.be_cosmo.Ob0
elif key == "Omega_dm0":
return self.be_cosmo.Odm0
elif key == "Omega_k0":
return self.be_cosmo.Ok0
elif key == 'h':
return self.be_cosmo.H0.to_value() / 100.0
elif key == 'H0':
return self.be_cosmo.H0.to_value()
else:
raise ValueError(f"Unsupported parameter {key}")
def get_Omega_m(self, z):
return self.be_cosmo.Om(z)
def get_E2Omega_m(self, z):
return self.be_cosmo.Om(z) * (self.be_cosmo.H(z) / self.be_cosmo.H0)**2
def eval_da_z1z2(self, z1, z2):
return self.be_cosmo.angular_diameter_distance_z1z2(z1, z2).to_value(
units.Mpc)
def eval_sigma_crit(self, z_len, z_src):
if np.any(np.array(z_src) <= z_len):
warnings.warn(
f'Some source redshifts are lower than the cluster redshift. Returning Sigma_crit = np.inf for those galaxies.'
)
# Constants
clight_pc_s = const.CLIGHT_KMS.value * 1000. / const.PC_TO_METER.value
gnewt_pc3_msun_s2 = const.GNEWT.value * const.SOLAR_MASS.value / const.PC_TO_METER.value**3
d_l = self.eval_da_z1z2(0, z_len)
d_s = self.eval_da_z1z2(0, z_src)
d_ls = self.eval_da_z1z2(z_len, z_src)
beta_s = np.maximum(0., d_ls / d_s)
return clight_pc_s**2 / (4.0 * np.pi *
gnewt_pc3_msun_s2) * 1 / d_l * np.divide(
1., beta_s) * 1.0e6
class TestCosmoInterp(object):
"""
"""
def setup(self):
self.H0_true = 70
self.omega_m_true = 0.3
self._ok_true = 0.1
self.cosmo = FlatLambdaCDM(H0=self.H0_true,
Om0=self.omega_m_true,
Ob0=0.05)
self.cosmo_interp = CosmoInterp(cosmo=self.cosmo,
z_stop=3,
num_interp=100)
self.cosmo_ok = LambdaCDM(H0=self.H0_true,
Om0=self.omega_m_true,
Ode0=1.0 - self.omega_m_true - self._ok_true)
self.cosmo_interp_ok = CosmoInterp(cosmo=self.cosmo_ok,
z_stop=3,
num_interp=100)
self.cosmo_ok_neg = LambdaCDM(H0=self.H0_true,
Om0=self.omega_m_true,
Ode0=1.0 - self.omega_m_true +
self._ok_true)
self.cosmo_interp_ok_neg = CosmoInterp(cosmo=self.cosmo_ok_neg,
z_stop=3,
num_interp=100)
def test_angular_diameter_distance(self):
z = 1.
da = self.cosmo.angular_diameter_distance(z=[z])
da_interp = self.cosmo_interp.angular_diameter_distance(z=[z])
npt.assert_almost_equal(da_interp / da, 1, decimal=3)
assert da.unit == da_interp.unit
da = self.cosmo_ok.angular_diameter_distance(z=z)
da_interp = self.cosmo_interp_ok.angular_diameter_distance(z=z)
npt.assert_almost_equal(da_interp / da, 1, decimal=3)
assert da.unit == da_interp.unit
da = self.cosmo_ok_neg.angular_diameter_distance(z=z)
da_interp = self.cosmo_interp_ok_neg.angular_diameter_distance(z=z)
npt.assert_almost_equal(da_interp / da, 1, decimal=3)
assert da.unit == da_interp.unit
def test_angular_diameter_distance_array(self):
# test for array input
z1 = 1.
z2 = 2.
da_z1 = self.cosmo.angular_diameter_distance(z=[z1])
da_z2 = self.cosmo.angular_diameter_distance(z=[z2])
da_interp = self.cosmo_interp.angular_diameter_distance(z=[z1, z2])
npt.assert_almost_equal(da_interp[0] / da_z1, 1, decimal=3)
npt.assert_almost_equal(da_interp[1] / da_z2, 1, decimal=3)
assert da_z1.unit == da_interp.unit
assert len(da_interp) == 2
da_z12 = self.cosmo.angular_diameter_distance(z=[z1, z2])
npt.assert_almost_equal(da_z12[0] / da_z1, 1, decimal=3)
npt.assert_almost_equal(da_z12[1] / da_z2, 1, decimal=3)
def test_angular_diameter_distance_z1z2(self):
z1 = .3
z2 = 2.
delta_a = self.cosmo.angular_diameter_distance_z1z2(z1=z1, z2=z2)
delta_a_interp = self.cosmo_interp.angular_diameter_distance_z1z2(
z1=z1, z2=z2)
npt.assert_almost_equal(delta_a_interp / delta_a, 1, decimal=3)
assert delta_a.unit == delta_a_interp.unit
delta_a = self.cosmo_ok.angular_diameter_distance_z1z2(z1=z1, z2=z2)
delta_a_interp = self.cosmo_interp_ok.angular_diameter_distance_z1z2(
z1=z1, z2=z2)
npt.assert_almost_equal(delta_a_interp / delta_a, 1, decimal=3)
assert delta_a.unit == delta_a_interp.unit
Zs = np.repeat(zb[mask1], sum_mask)
#DS = cd.angular_diameter_distance(Zs, z0=0, **cosmo)
DS = np.array(cosmo.angular_diameter_distance(Zs))
print '#---------- parameters of group cat'
#gcat = grupos[ind_g]
gcat = grupos[1].data[ind_g]
DL = dl[ind_g]
Zl = zl[ind_g]
del (ind_g)
print '#-------------- computing distances'
DLS = np.array(cosmo.angular_diameter_distance_z1z2(Zl, Zs))
#DLS=np.zeros(sum_mask.sum())
del (sum_mask)
print '-----------------------------------------------------------------'
print ' MAKING THE CATALOGUE FOR GALAXIES '
print '================================================================='
tbhdu = fits.BinTableHDU.from_columns([
fits.Column(name='SE_ID', format='E', array=lcat[:, 0]),
fits.Column(name='IM_NUM', format='D', array=lcat[:, 1]),
fits.Column(name='RAJ2000', format='D', array=lcat[:, 2]),
fits.Column(name='DECJ2000', format='D', array=lcat[:, 3]),
fits.Column(name='X_IMAGE', format='E', array=lcat[:, 4]),
fits.Column(name='Y_IMAGE', format='E', array=lcat[:, 5]),
def partial_map(RA0, DEC0, Z, angles, ROUT, ndots, h):
lsize = int(np.sqrt(ndots))
cosmo = LambdaCDM(H0=100 * h, Om0=0.25, Ode0=0.75)
dl = cosmo.angular_diameter_distance(Z).value
KPCSCALE = dl * (((1.0 / 3600.0) * np.pi) / 180.0) * 1000.0
delta = (ROUT * 1.5) / (3600 * KPCSCALE)
rarray = [[-1. * (ROUT * 1.e-3), (ROUT * 1.e-3)],
[-1. * (ROUT * 1.e-3), (ROUT * 1.e-3)]]
t0 = time.time()
mask = (S.ra < (RA0 + delta)) & (S.ra > (RA0 - delta)) & (
S.dec > (DEC0 - delta)) & (S.dec < (DEC0 + delta)) & (S.z_v >
(Z + 0.1))
catdata = S[mask]
ds = cosmo.angular_diameter_distance(catdata.z_v).value
dls = cosmo.angular_diameter_distance_z1z2(Z, catdata.z_v).value
BETA_array = dls / ds
Dl = dl * 1.e6 * pc
sigma_c = (((cvel**2.0) / (4.0 * np.pi * G * Dl)) *
(1. / BETA_array)) * (pc**2 / Msun)
rads, theta, test1, test2 = eq2p2(np.deg2rad(catdata.ra),
np.deg2rad(catdata.dec), np.deg2rad(RA0),
np.deg2rad(DEC0))
theta2 = (2. * np.pi - theta) + np.pi / 2.
theta_ra = theta2
theta_ra[theta2 > 2. * np.pi] = theta2[theta2 > 2. * np.pi] - 2. * np.pi
e1 = catdata.gamma1
e2 = -1. * catdata.gamma2
#get tangential ellipticities
et = (-e1 * np.cos(2 * theta) - e2 * np.sin(2 * theta)) * sigma_c
#get cross ellipticities
ex = (-e1 * np.sin(2 * theta) + e2 * np.cos(2 * theta)) * sigma_c
# '''
k = catdata.kappa * sigma_c
wcs.wcs.crval = [RA0, DEC0]
dx, dy = wcs.wcs_world2pix(catdata.ra, catdata.dec, 0)
dx = dx * KPCSCALE * 1.e-3
dy = dy * KPCSCALE * 1.e-3
# del(e1)
# del(e2)
r = np.rad2deg(rads) * 3600 * KPCSCALE
del (rads)
Ntot = len(catdata)
# del(catdata)
t = np.tile(theta_ra, (3, 1)).T
an = np.tile(angles, (len(theta_ra), 1))
at = t - an
GTsum = np.zeros((ndots, 3))
GXsum = np.zeros((ndots, 3))
Ksum = np.zeros((ndots, 3))
Ninbin = np.zeros((ndots, 3))
for j in range(3):
x_t = (dx * np.cos(an[:, j]) + dy * np.sin(an[:, j]))
y_t = (-1. * dx * np.sin(an[:, j]) + dy * np.cos(an[:, j]))
m = (abs(x_t) < (ROUT * 1.e-3)) * (abs(y_t) < (ROUT * 1.e-3))
out = stats.binned_statistic_2d(x_t[m],
y_t[m],
et[m],
'count',
bins=lsize,
range=rarray)
Ninbin[:, j] = out.statistic.flatten()
out = stats.binned_statistic_2d(x_t[m],
y_t[m],
et[m],
'sum',
bins=lsize,
range=rarray)
GTsum[:, j] = out.statistic.flatten()
out = stats.binned_statistic_2d(x_t[m],
y_t[m],
ex[m],
'sum',
bins=lsize,
range=rarray)
GXsum[:, j] = out.statistic.flatten()
out = stats.binned_statistic_2d(x_t[m],
y_t[m],
k[m],
'sum',
bins=lsize,
range=rarray)
Ksum[:, j] = out.statistic.flatten()
Ntot = m.sum()
output = {
'GTsum': GTsum,
'GXsum': GXsum,
'Ksum': Ksum,
'Ninbin': Ninbin,
'Ntot': Ntot
}
return output
def partial_profile(RA0,DEC0,Z,angles,
RIN,ROUT,ndots,h,roff,phi_off):
ndots = int(ndots)
cosmo = LambdaCDM(H0=100*h, Om0=0.25, Ode0=0.75)
dl = cosmo.angular_diameter_distance(Z).value
KPCSCALE = dl*(((1.0/3600.0)*np.pi)/180.0)*1000.0
delta = ROUT/(3600*KPCSCALE)
t0 = time.time()
mask = (S.ra < (RA0+delta))&(S.ra > (RA0-delta))&(S.dec > (DEC0-delta))&(S.dec < (DEC0+delta))&(S.z_v > (Z+0.1))
t1 = time.time()
# print(t1-t0)
catdata = S[mask]
ds = cosmo.angular_diameter_distance(catdata.z_v).value
dls = cosmo.angular_diameter_distance_z1z2(Z, catdata.z_v).value
BETA_array = dls/ds
Dl = dl*1.e6*pc
sigma_c = (((cvel**2.0)/(4.0*np.pi*G*Dl))*(1./BETA_array))*(pc**2/Msun)
t2 = time.time()
# print(RA0,DEC0,t2-t1)
rads, theta, test1,test2 = eq2p2(np.deg2rad(catdata.ra),
np.deg2rad(catdata.dec),
np.deg2rad(RA0),
np.deg2rad(DEC0))
theta2 = (2.*np.pi - theta) +np.pi/2.
theta_ra = theta2
theta_ra[theta2 > 2.*np.pi] = theta2[theta2 > 2.*np.pi] - 2.*np.pi
e1 = catdata.gamma1
e2 = -1.*catdata.gamma2
#get tangential ellipticities
et = (-e1*np.cos(2*theta)-e2*np.sin(2*theta))*sigma_c
#get cross ellipticities
ex = (-e1*np.sin(2*theta)+e2*np.cos(2*theta))*sigma_c
# '''
k = catdata.kappa*sigma_c
del(e1)
del(e2)
r = np.rad2deg(rads)*3600*KPCSCALE
r = np.sqrt(roff**2 + r**2 + 2.*roff*r*np.cos(phi_off))
del(rads)
Ntot = len(catdata)
del(catdata)
bines = np.round(np.logspace(np.log10(RIN),np.log10(ROUT),num=ndots+1),0)
dig = np.digitize(r,bines)
t = np.tile(theta_ra,(3,1)).T
an = np.tile(angles,(len(theta_ra),1))
at = t - an
SIGMAwsum = []
DSIGMAwsum_T = []
DSIGMAwsum_X = []
N_inbin = []
GAMMATcos_wsum = np.zeros((ndots,3))
GAMMAXsin_wsum = np.zeros((ndots,3))
COS2_2theta = np.zeros((ndots,3))
SIN2_2theta = np.zeros((ndots,3))
for nbin in range(ndots):
mbin = dig == nbin+1
SIGMAwsum = np.append(SIGMAwsum,k[mbin].sum())
DSIGMAwsum_T = np.append(DSIGMAwsum_T,et[mbin].sum())
DSIGMAwsum_X = np.append(DSIGMAwsum_X,ex[mbin].sum())
GAMMATcos_wsum[nbin,:] = np.sum((np.tile(et[mbin],(3,1))*np.cos(2.*at[mbin]).T),axis=1)
GAMMAXsin_wsum[nbin,:] = np.sum((np.tile(ex[mbin],(3,1))*np.sin(2.*at[mbin]).T),axis=1)
COS2_2theta[nbin,:] = np.sum((np.cos(2.*at[mbin]).T)**2,axis=1)
SIN2_2theta[nbin,:] = np.sum((np.sin(2.*at[mbin]).T)**2,axis=1)
N_inbin = np.append(N_inbin,len(et[mbin]))
index = np.arange(mbin.sum())
output = {'SIGMAwsum':SIGMAwsum,'DSIGMAwsum_T':DSIGMAwsum_T,
'DSIGMAwsum_X':DSIGMAwsum_X,
'GAMMATcos_wsum': GAMMATcos_wsum, 'GAMMAXsin_wsum': GAMMAXsin_wsum,
'COS2_2theta_wsum':COS2_2theta,'SIN2_2theta_wsum':SIN2_2theta,
'N_inbin':N_inbin,'Ntot':Ntot}
return output