def plot_DM(filename):
"""The dimensionless proper motion distance DM/DH.
"""
# Set up an array of redshift values.
dz = 0.1
z = numpy.arange(0., 10. + 1.1 * dz, dz)
# Set up a cosmology dictionary, with an array of matter density values.
cosmo = {}
dom = 0.01
om = numpy.atleast_2d(numpy.linspace(0.1, 1.0,
(1. - 0.1) / dom)).transpose()
cosmo['omega_M_0'] = om
cosmo['omega_lambda_0'] = 1. - cosmo['omega_M_0']
cosmo['h'] = 0.701
cosmo['omega_k_0'] = 0.0
# Calculate the hubble distance.
dh = cd.hubble_distance_z(0, **cosmo)
# Calculate the comoving distance.
dm = cd.comoving_distance_transverse(z, **cosmo)
# Make plots.
plot_dist(z, dz, om, dom, dm, dh, 'proper motion distance', r'D_M',
filename)
plot_dist_ony(z, dz, om, dom, dm, dh, 'proper motion distance', r'D_M',
filename)
def plot_DA(filename):
"""The dimensionless angular diameter distance DA/DH.
"""
# Set up an array of redshift values.
dz = 0.1
z = numpy.arange(0., 10. + dz, dz)
# Set up a cosmology dictionary, with an array of matter density values.
cosmo = {}
dom = 0.01
om = numpy.atleast_2d(numpy.linspace(0.1, 1.0,
(1. - 0.1) / dom)).transpose()
cosmo['omega_M_0'] = om
cosmo['omega_lambda_0'] = 1. - cosmo['omega_M_0']
cosmo['h'] = 0.701
cosmo['omega_k_0'] = 0.0
# Calculate the hubble distance.
dh = cd.hubble_distance_z(0, **cosmo)
# Calculate the angular diameter distance.
da = cd.angular_diameter_distance(z, **cosmo)
# Make plots.
plot_dist(z, dz, om, dom, da, dh, 'angular diameter distance', r'D_A',
filename)
plot_dist_ony(z, dz, om, dom, da, dh, 'angular diameter distance', r'D_A',
filename)
def plot_DM(filename):
"""
The dimensionless proper motion distance DM/DH.
"""
# Set up an array of redshift values.
dz = 0.1
z = numpy.arange(0., 10. + 1.1 * dz, dz)
# Set up a cosmology dictionary, with an array of matter density values.
cosmo = {}
dom = 0.01
om = numpy.atleast_2d(numpy.linspace(0.1, 1.0, (1. - 0.1) / dom)).transpose()
cosmo['omega_M_0'] = om
cosmo['omega_lambda_0'] = 1. - cosmo['omega_M_0']
cosmo['h'] = 0.701
cosmo['omega_k_0'] = 0.0
# Calculate the hubble distance.
dh = cd.hubble_distance_z(0, **cosmo)
# Calculate the comoving distance.
dm, dm_err = cd.comoving_distance_transverse(z, **cosmo)
# Make plots.
plot_dist(z, dz, om, dom, dm, dh, 'proper motion distance', r'D_M',
filename)
plot_dist_ony(z, dz, om, dom, dm, dh, 'proper motion distance', r'D_M',
filename)
def plot_DA(filename):
"""
The dimensionless angular diameter distance DA/DH.
"""
# Set up an array of redshift values.
dz = 0.1
z = numpy.arange(0., 10. + dz, dz)
# Set up a cosmology dictionary, with an array of matter density values.
cosmo = {}
dom = 0.01
om = numpy.atleast_2d(numpy.linspace(0.1, 1.0, (1. - 0.1) / dom)).transpose()
cosmo['omega_M_0'] = om
cosmo['omega_lambda_0'] = 1. - cosmo['omega_M_0']
cosmo['h'] = 0.701
cosmo['omega_k_0'] = 0.0
# Calculate the hubble distance.
dh = cd.hubble_distance_z(0, **cosmo)
# Calculate the angular diameter distance.
da, da_err1, da_err2 = cd.angular_diameter_distance(z, **cosmo)
# Make plots.
plot_dist(z, dz, om, dom, da, dh, 'angular diameter distance', r'D_A',
filename)
plot_dist_ony(z, dz, om, dom, da, dh, 'angular diameter distance', r'D_A',
filename)
def Hz_cosmo(z):
cosmo = {'omega_M_0' : 0.24, 'omega_lambda_0' : 0.76, 'h' : 0.73}
cosmo = cd.set_omega_k_0(cosmo)
'''___________Hz___________________________'''
H_z = cd.hubble_distance_z(z, **cosmo)
#print z, H_z
#print 0, cd.hubble_distance_z(0, **cosmo)
return H_z
def testCosmo():
'''
'''
import cosmolopy.distance as cosmology
### Constants
z = 2.4
### Magneville:
# omegaM = 0.267804
# omegaL = 0.73
# omegaK = 0.002117
# h = 0.71
### Fiduciel BAOFIT
# omegaM = 0.27
# omegaL = 0.73
# omegaK = 0
# h = 0.7
# rd = 149.7
cosmoCMV = {'omega_M_0':0.267804, 'omega_lambda_0':0.73, 'omega_k_0':0.002117, 'h':0.71}
cosmoFID = {'omega_M_0':0.27, 'omega_lambda_0':0.73, 'omega_k_0':0, 'h':0.70}
DAZ_CMV = cosmology.angular_diameter_distance(z,**cosmoCMV)
HZ_CMV = cosmology.hubble_distance_z(z,**cosmoCMV) #cosmology.hubble_z(z,**cosmoCMV)*3.085677581e22/1.e3
DAZ_FID = cosmology.angular_diameter_distance(z,**cosmoFID)
HZ_FID = cosmology.hubble_distance_z(z,**cosmoFID) #cosmology.hubble_z(z,**cosmoFID)*3.085677581e22/1.e3
print DAZ_CMV, DAZ_FID
print HZ_CMV, HZ_FID
print DAZ_FID/DAZ_CMV
print HZ_FID/HZ_CMV
return
def err_Dv(z):
'''___________DA__________________________'''
cosmo = {'omega_M_0' : 0.24, 'omega_lambda_0' : 0.76, 'h' : 0.73}
cosmo = cd.set_omega_k_0(cosmo)
d_a = cd.angular_diameter_distance(z, **cosmo)
'''___________Hz___________________________'''
H_z = cd.hubble_distance_z(z, **cosmo)
'''________________The error on Dv___________________'''
part1 = ( dasigma/ d_a ) **2
part2 = (Hsigma/ H_z)**2
part3 = 0.0 #(cov_DaH/ (d_a* H_z))
sigma_Dv = sqrt(Dv(Z)**2 * (part1 + part2 + part3 ))
return sigma_Dv
def getMeanMag(z, dz=1e-4):
#return 0.1311
cosmo = {'omega_M_0': 0.3086, 'omega_lambda_0': 0.6914, 'h': 0.6777}
cosmo = dist.set_omega_k_0(cosmo)
distanceEB = 0
distanceFB = 0
for i in np.arange(0., z, dz):
dist_hz = dist.hubble_distance_z(i, **cosmo)
distanceEB += dz * dist_hz / (1 + i)**2
distanceFB += dz * dist_hz
distanceFB /= 1. + z
return (distanceEB / distanceFB)**2 - 1.
def test_figure2():
"""Plot Hogg fig. 2: The dimensionless angular diameter distance DA/DH.
The three curves are for the three world models,
- Einstein-de Sitter (omega_M, omega_lambda) = (1, 0) [solid]
: Low-density (0.05, 0) [dotted]
-- High lambda, (0.2, 0.8) [dashed]
Hubble distance DH = c / H0
z from 0--5
DA / DH from 0--0.5
"""
z = numpy.arange(0, 5.05, 0.05)
cosmo = {}
cosmo['omega_M_0'] = numpy.array([[1.0], [0.05], [0.2]])
cosmo['omega_lambda_0'] = numpy.array([[0.0], [0.0], [0.8]])
cosmo['h'] = 0.5
cd.set_omega_k_0(cosmo)
linestyle = ['-', ':', '--']
dh = cd.hubble_distance_z(0, **cosmo)
da = cd.angular_diameter_distance(z, **cosmo)
# Also test the pathway with non-zero z0
da2 = cd.angular_diameter_distance(z, z0=1e-8, **cosmo)
pylab.figure(figsize=(6, 6))
for i in range(len(linestyle)):
pylab.plot(z, (da / dh)[i], ls=linestyle[i])
pylab.plot(z, (da2 / dh)[i], ls=linestyle[i])
pylab.xlim(0, 5)
pylab.ylim(0, 0.5)
pylab.xlabel("redshift z")
pylab.ylabel(r"angular diameter distance $D_A/D_H$")
pylab.title("compare to " + inspect.stack()[0][3].replace('test_', '') +
" (astro-ph/9905116v4)")
def test_figure2():
"""Plot Hogg fig. 2: The dimensionless angular diameter distance DA/DH.
The three curves are for the three world models,
- Einstein-de Sitter (omega_M, omega_lambda) = (1, 0) [solid]
: Low-density (0.05, 0) [dotted]
-- High lambda, (0.2, 0.8) [dashed]
Hubble distance DH = c / H0
z from 0--5
DA / DH from 0--0.5
"""
z = numpy.arange(0, 5.05, 0.05)
cosmo = {}
cosmo['omega_M_0'] = numpy.array([[1.0],[0.05],[0.2]])
cosmo['omega_lambda_0'] = numpy.array([[0.0],[0.0],[0.8]])
cosmo['h'] = 0.5
cd.set_omega_k_0(cosmo)
linestyle = ['-', ':', '--']
dh = cd.hubble_distance_z(0, **cosmo)
da = cd.angular_diameter_distance(z, **cosmo)
# Also test the pathway with non-zero z0
da2 = cd.angular_diameter_distance(z, z0=1e-8, **cosmo)
pylab.figure(figsize=(6,6))
for i in range(len(linestyle)):
pylab.plot(z, (da/dh)[i], ls=linestyle[i])
pylab.plot(z, (da2/dh)[i], ls=linestyle[i])
pylab.xlim(0,5)
pylab.ylim(0,0.5)
pylab.xlabel("redshift z")
pylab.ylabel(r"angular diameter distance $D_A/D_H$")
pylab.title("compare to " + inspect.stack()[0][3].replace('test_', '') +
" (astro-ph/9905116v4)")
def test_figure5():
"""Plot Hogg fig. 5: The dimensionless comoving volume element (1/DH)^3(dVC/dz).
The three curves are for the three world models, (omega_M, omega_lambda) =
(1, 0), solid; (0.05, 0), dotted; and (0.2, 0.8), dashed.
"""
z = numpy.arange(0, 5.05, 0.05)
cosmo = {}
cosmo['omega_M_0'] = numpy.array([[1.0], [0.05], [0.2]])
cosmo['omega_lambda_0'] = numpy.array([[0.0], [0.0], [0.8]])
cosmo['h'] = 0.5
cd.set_omega_k_0(cosmo)
linestyle = ['-', ':', '--']
dh = cd.hubble_distance_z(0, **cosmo)
dVc = cd.diff_comoving_volume(z, **cosmo)
dVc_normed = dVc / (dh**3.)
Vc = cd.comoving_volume(z, **cosmo)
dz = z[1:] - z[:-1]
dVc_numerical = (Vc[:, 1:] - Vc[:, :-1]) / dz / (4. * numpy.pi)
dVc_numerical_normed = dVc_numerical / (dh**3.)
pylab.figure(figsize=(6, 6))
for i in range(len(linestyle)):
pylab.plot(z, dVc_normed[i], ls=linestyle[i], lw=2.)
pylab.plot(z[:-1],
dVc_numerical_normed[i],
ls=linestyle[i],
c='k',
alpha=0.1)
pylab.xlim(0, 5)
pylab.ylim(0, 1.1)
pylab.xlabel("redshift z")
pylab.ylabel(r"comoving volume element $[1/D_H^3]$ $dV_c/dz/d\Omega$")
pylab.title("compare to " + inspect.stack()[0][3].replace('test_', '') +
" (astro-ph/9905116v4)")
def test_figure3():
"""Plot Hogg fig. 3: The dimensionless luminosity distance DL/DH
The three curves are for the three world models,
- Einstein-de Sitter (omega_M, omega_lambda) = (1, 0) [solid]
: Low-density (0.05, 0) [dotted]
-- High lambda, (0.2, 0.8) [dashed]
Hubble distance DH = c / H0
z from 0--5
DL / DH from 0--16
"""
z = numpy.arange(0, 5.05, 0.05)
cosmo = {}
cosmo['omega_M_0'] = numpy.array([[1.0], [0.05], [0.2]])
cosmo['omega_lambda_0'] = numpy.array([[0.0], [0.0], [0.8]])
cosmo['h'] = 0.5
cd.set_omega_k_0(cosmo)
linestyle = ['-', ':', '--']
dh = cd.hubble_distance_z(0, **cosmo)
dl = cd.luminosity_distance(z, **cosmo)
pylab.figure(figsize=(6, 6))
for i in range(len(linestyle)):
pylab.plot(z, (dl / dh)[i], ls=linestyle[i])
pylab.xlim(0, 5)
pylab.ylim(0, 16)
pylab.xlabel("redshift z")
pylab.ylabel(r"luminosity distance $D_L/D_H$")
pylab.title("compare to " + inspect.stack()[0][3].replace('test_', '') +
" (astro-ph/9905116v4)")
def test_figure3():
"""Plot Hogg fig. 3: The dimensionless luminosity distance DL/DH
The three curves are for the three world models,
- Einstein-de Sitter (omega_M, omega_lambda) = (1, 0) [solid]
: Low-density (0.05, 0) [dotted]
-- High lambda, (0.2, 0.8) [dashed]
Hubble distance DH = c / H0
z from 0--5
DL / DH from 0--16
"""
z = numpy.arange(0, 5.05, 0.05)
cosmo = {}
cosmo['omega_M_0'] = numpy.array([[1.0],[0.05],[0.2]])
cosmo['omega_lambda_0'] = numpy.array([[0.0],[0.0],[0.8]])
cosmo['h'] = 0.5
cd.set_omega_k_0(cosmo)
linestyle = ['-', ':', '--']
dh = cd.hubble_distance_z(0, **cosmo)
dl = cd.luminosity_distance(z, **cosmo)
pylab.figure(figsize=(6,6))
for i in range(len(linestyle)):
pylab.plot(z, (dl/dh)[i], ls=linestyle[i])
pylab.xlim(0,5)
pylab.ylim(0,16)
pylab.xlabel("redshift z")
pylab.ylabel(r"luminosity distance $D_L/D_H$")
pylab.title("compare to " + inspect.stack()[0][3].replace('test_', '') +
" (astro-ph/9905116v4)")
def test_figure5():
"""Plot Hogg fig. 5: The dimensionless comoving volume element (1/DH)^3(dVC/dz).
The three curves are for the three world models, (omega_M, omega_lambda) =
(1, 0), solid; (0.05, 0), dotted; and (0.2, 0.8), dashed.
"""
z = numpy.arange(0, 5.05, 0.05)
cosmo = {}
cosmo['omega_M_0'] = numpy.array([[1.0],[0.05],[0.2]])
cosmo['omega_lambda_0'] = numpy.array([[0.0],[0.0],[0.8]])
cosmo['h'] = 0.5
cd.set_omega_k_0(cosmo)
linestyle = ['-', ':', '--']
dh = cd.hubble_distance_z(0, **cosmo)
dVc = cd.diff_comoving_volume(z, **cosmo)
dVc_normed = dVc/(dh**3.)
Vc = cd.comoving_volume(z, **cosmo)
dz = z[1:] - z[:-1]
dVc_numerical = (Vc[:,1:] - Vc[:,:-1])/dz/(4. * numpy.pi)
dVc_numerical_normed = dVc_numerical/(dh**3.)
pylab.figure(figsize=(6,6))
for i in range(len(linestyle)):
pylab.plot(z, dVc_normed[i], ls=linestyle[i], lw=2.)
pylab.plot(z[:-1], dVc_numerical_normed[i], ls=linestyle[i],
c='k', alpha=0.1)
pylab.xlim(0,5)
pylab.ylim(0,1.1)
pylab.xlabel("redshift z")
pylab.ylabel(r"comoving volume element $[1/D_H^3]$ $dV_c/dz/d\Omega$")
pylab.title("compare to " + inspect.stack()[0][3].replace('test_', '') +
" (astro-ph/9905116v4)")
def test_figure1():
"""Plot Hogg fig. 1: The dimensionless proper motion distance DM/DH.
The three curves are for the three world models, Einstein-de
Sitter (omega_M, omega_lambda) = (1, 0), solid; low-density,
(0.05, 0), dotted; and high lambda, (0.2, 0.8), dashed.
Hubble distance DH = c / H0
z from 0--5
DM / DH from 0--3
"""
z = numpy.arange(0, 5.05, 0.05)
cosmo = {}
cosmo['omega_M_0'] = numpy.array([[1.0], [0.05], [0.2]])
cosmo['omega_lambda_0'] = numpy.array([[0.0], [0.0], [0.8]])
cosmo['h'] = 0.5
cd.set_omega_k_0(cosmo)
linestyle = ['-', ':', '--']
dh = cd.hubble_distance_z(0, **cosmo)
dm = cd.comoving_distance_transverse(z, **cosmo)
pylab.figure(figsize=(6, 6))
for i in range(len(linestyle)):
pylab.plot(z, (dm / dh)[i], ls=linestyle[i])
#pylab.plot(z, (dm_err/dh)[i], ls=linestyle[i])
pylab.xlim(0, 5)
pylab.ylim(0, 3)
pylab.xlabel("redshift z")
pylab.ylabel(r"proper motion distance $D_M/D_H$")
pylab.title("compare to " + inspect.stack()[0][3].replace('test_', '') +
" (astro-ph/9905116v4)")
def test_figure1():
"""Plot Hogg fig. 1: The dimensionless proper motion distance DM/DH.
The three curves are for the three world models, Einstein-de
Sitter (omega_M, omega_lambda) = (1, 0), solid; low-density,
(0.05, 0), dotted; and high lambda, (0.2, 0.8), dashed.
Hubble distance DH = c / H0
z from 0--5
DM / DH from 0--3
"""
z = numpy.arange(0, 5.05, 0.05)
cosmo = {}
cosmo['omega_M_0'] = numpy.array([[1.0],[0.05],[0.2]])
cosmo['omega_lambda_0'] = numpy.array([[0.0],[0.0],[0.8]])
cosmo['h'] = 0.5
cd.set_omega_k_0(cosmo)
linestyle = ['-', ':', '--']
dh = cd.hubble_distance_z(0, **cosmo)
dm = cd.comoving_distance_transverse(z, **cosmo)
pylab.figure(figsize=(6,6))
for i in range(len(linestyle)):
pylab.plot(z, (dm/dh)[i], ls=linestyle[i])
#pylab.plot(z, (dm_err/dh)[i], ls=linestyle[i])
pylab.xlim(0,5)
pylab.ylim(0,3)
pylab.xlabel("redshift z")
pylab.ylabel(r"proper motion distance $D_M/D_H$")
pylab.title("compare to " + inspect.stack()[0][3].replace('test_', '') +
" (astro-ph/9905116v4)")
def H(z):
cosmo = {'omega_M_0' : 0.24, 'omega_lambda_0' : 1. - 0.24-0.0418, 'h' : 0.73}
return cd.hubble_distance_z(z, **cosmo)
PlotNumber = 8
N=200
z=numpy.arange(0.001,5,1./N)
val = numpy.zeros(len(z))
for i in xrange(len(z)):
#Hubble Distance
dh = cd.hubble_distance_z(z[i],**Cosmology)*cd.e_z(z[i],**Cosmology)
#In David Hogg's (arXiv:astro-ph/9905116v4) formalism, this is equivalent to D_H / E(z) = c / (H_0 E(z)) [see his eq. 14], which
#appears in the definitions of many other distance measures.
dm = cd.comoving_distance_transverse(z[i],**Cosmology)
#See equation 16 of David Hogg's arXiv:astro-ph/9905116v4
da = cd.angular_diameter_distance(z[i],**Cosmology)
#See equations 18-19 of David Hogg's arXiv:astro-ph/9905116v4
dl = cd.luminosity_distance(z[i],**Cosmology)
#Units are Mpc
dVc = cd.diff_comoving_volume(z[i], **Cosmology)
#The differential comoving volume element dV_c/dz/dSolidAngle.
#Dimensions are volume per unit redshift per unit solid angle.
'omega_lambda_0': 1 - 0.2,
'omega_k_0': 0.0,
'h': 0.71
}
PlotNumber = 8
N = 200
z = numpy.arange(0.001, 5, 1. / N)
val = numpy.zeros(len(z))
for i in xrange(len(z)):
#Hubble Distance
dh = cd.hubble_distance_z(z[i], **Cosmology) * cd.e_z(z[i], **Cosmology)
#In David Hogg's (arXiv:astro-ph/9905116v4) formalism, this is equivalent to D_H / E(z) = c / (H_0 E(z)) [see his eq. 14], which
#appears in the definitions of many other distance measures.
dm = cd.comoving_distance_transverse(z[i], **Cosmology)
#See equation 16 of David Hogg's arXiv:astro-ph/9905116v4
da = cd.angular_diameter_distance(z[i], **Cosmology)
#See equations 18-19 of David Hogg's arXiv:astro-ph/9905116v4
dl = cd.luminosity_distance(z[i], **Cosmology)
#Units are Mpc
dVc = cd.diff_comoving_volume(z[i], **Cosmology)
#The differential comoving volume element dV_c/dz/dSolidAngle.
#Dimensions are volume per unit redshift per unit solid angle.
def H(z): return cd.hubble_distance_z(z, **cosmo)