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_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 test_distances(threshold = 1e-3):
"""Compare distance measures with calculations from http://icosmo.org/"""
cosmo = cosmo_wmap_5()
print "Comparing distances with calculations from http://icosmo.org/"
# load external distance calculations
# z DA(z) DT(z) DL(z)
distance_file = os.path.dirname(os.path.abspath(__file__))
distance_file = os.path.join(distance_file, 'icosmo_testdata',
'distances.txt')
ic_dists = numpy.loadtxt(distance_file)
z = ic_dists[:,0]
cd_da = cd.angular_diameter_distance(z, **cosmo)
cd_dt = cd.light_travel_distance(z, **cosmo)
cd_dl = cd.luminosity_distance(z, **cosmo)
cd_dm = cd.comoving_distance_transverse(z, **cosmo)
cd_dists = numpy.vstack((cd_dm, cd_da, cd_dt, cd_dl))
labels = [ r'$D_M$', r'$D_A$', r'$D_T$', r'$D_L$']
threshold = [1e-7, 1e-7, 1e-3, 1e-7 ]
# print ic_dists[-1].transpose()
# print cd_dists[:,-1]
pylab.figure()
for i in range(len(labels)):
pylab.plot(ic_dists[:,0], ic_dists[:,i+1],
label=labels[i] +' IC', ls=':')
pylab.plot(z, cd_dists[i], label=labels[i] +' distance.py', ls='-')
pylab.legend(loc='best')
pylab.figure()
for i in range(len(labels)):
diff = (cd_dists[i] - ic_dists[:,i+1]) / ic_dists[:,i+1]
maxdiff = numpy.max(numpy.abs(diff[ic_dists[:,i+1] > 0]))
print "Maximum fraction difference in %s is %e." % (labels[i],
maxdiff)
assert(numpy.all(maxdiff < threshold[i]))
pylab.plot(ic_dists[:,0],
diff,
label=labels[i], ls='-')
#pylab.plot(z, err2, label=labels[1] + ' err.', ls=':')
#pylab.plot(z, err3, label=labels[2] + ' err.', ls=':')
#pylab.plot(z, err5, label=labels[3] + ' err.', ls=':')
#pylab.plot(z, err6, label=labels[0] + ' err.', ls=':')
pylab.legend(loc='best')
def test_distances(threshold = 1e-3):
"""Compare distance measures with calculations from http://icosmo.org/"""
cosmo = cosmo_wmap_5()
print("Comparing distances with calculations from http://icosmo.org/")
# load external distance calculations
# z DA(z) DT(z) DL(z)
distance_file = os.path.dirname(os.path.abspath(__file__))
distance_file = os.path.join(distance_file, 'icosmo_testdata',
'distances.txt')
ic_dists = numpy.loadtxt(distance_file)
z = ic_dists[:,0]
cd_da = cd.angular_diameter_distance(z, **cosmo)
cd_dt = cd.light_travel_distance(z, **cosmo)
cd_dl = cd.luminosity_distance(z, **cosmo)
cd_dm = cd.comoving_distance_transverse(z, **cosmo)
cd_dists = numpy.vstack((cd_dm, cd_da, cd_dt, cd_dl))
labels = [ r'$D_M$', r'$D_A$', r'$D_T$', r'$D_L$']
threshold = [1e-7, 1e-7, 1e-3, 1e-7 ]
# print ic_dists[-1].transpose()
# print cd_dists[:,-1]
pylab.figure()
for i in range(len(labels)):
pylab.plot(ic_dists[:,0], ic_dists[:,i+1],
label=labels[i] +' IC', ls=':')
pylab.plot(z, cd_dists[i], label=labels[i] +' distance.py', ls='-')
pylab.legend(loc='best')
pylab.figure()
for i in range(len(labels)):
diff = (cd_dists[i] - ic_dists[:,i+1]) / ic_dists[:,i+1]
maxdiff = numpy.max(numpy.abs(diff[ic_dists[:,i+1] > 0]))
print("Maximum fraction difference in %s is %e." % (labels[i],
maxdiff))
assert(numpy.all(maxdiff < threshold[i]))
pylab.plot(ic_dists[:,0],
diff,
label=labels[i], ls='-')
#pylab.plot(z, err2, label=labels[1] + ' err.', ls=':')
#pylab.plot(z, err3, label=labels[2] + ' err.', ls=':')
#pylab.plot(z, err5, label=labels[3] + ' err.', ls=':')
#pylab.plot(z, err6, label=labels[0] + ' err.', ls=':')
pylab.legend(loc='best')
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 plot_DM():
"""The dimensionless proper motion distance DM/DH.
"""
# Set up an array of redshift values.
dz = 0.01
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()
dzt = 0.01
zt = numpy.atleast_2d(numpy.linspace(0.1, 1.0, (1.-0.1)/dzt)).transpose()
cosmo['omega_M_0'] = om
cosmo['transition_redshift'] = zt
cosmo['omega_lambda_0'] = 1/2 * cosmo['omega_M_0'] * (1 + cosmo['transition_redshift'])**3
cosmo['h'] = 0.701
cosmo['omega_k_0'] = 1 - cosmo['omega_M_0'] - 1/2 * cosmo['omega_M_0'] * ( cosmo['transition_redshift'] + 1 )**3
# Calculate the hubble distance.
dhc = cd.comoving_distance(z,z0=0, **cosmo)
# Calculate the comoving distance.
dm = cd.comoving_distance_transverse(z, **cosmo)
# Make plots
print om.ravel()
fig = plt.figure()
ax = fig.gca(projection='3d')
om, zt = meshgrid(om.ravel(),zt.ravel())
hub = cd.comoving_distance(1,z0=0,**cosmo)
surf = ax.plot_surface(om,zt,hub,rstride=1,cstride=1,cmap=cm.jet,linewidth=0,antialiased=False)
# ax.set_zlim()
plt.show()
def r2z(r):
zrange = np.linspace(0, 6, 1000)
r_to_z = sp.interpolate.interp1d(
cd.comoving_distance_transverse(zrange, **params.cosmo), zrange)
return r_to_z(r).astype('float32')
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.
#Units are Mpc**3 Steradians^-1.
#See David Hogg's arXiv:astro-ph/9905116v4, equation 28
tl = cd.lookback_time(z[i], **Cosmology)
zrec_cst = inhodist.x2z_inho_lightcone(lightcone_cst, h)
theseed=None
lightcone = ln.lightcone_1d(xmax, nnx, seed=theseed, pklib=pklib, omegam=(omegac+omegab)/h2, smoothing=None)
clf()
plot(lightcone.xx, lightcone.alldelta[0,:])
np.mean(lightcone.alldelta[0,:])
zrec = inhodist.x2z_inho_lightcone(lightcone, h)
zvals = np.linspace(0,np.max(zrec_cst),1000)
open = cd.set_omega_k_0({'omega_M_0' : (omegac+omegab)/h2, 'omega_lambda_0' : 0., 'h' : 0.7})
d_open = cd.comoving_distance_transverse(zvals, **open)
lcdm = cd.set_omega_k_0({'omega_M_0' : (omegac+omegab)/h2, 'omega_lambda_0' : 0.7, 'h' : 0.7})
d_lcdm = cd.comoving_distance_transverse(zvals, **lcdm)
empty = cd.set_omega_k_0({'omega_M_0' : 0, 'omega_lambda_0' : 0., 'h' : 0.7})
d_empty = cd.comoving_distance_transverse(zvals, **empty)
clf()
plot(zvals, d_open/d_lcdm, lw=2, label='Standard: Open $\Omega_m=0.3$')
plot(zvals, d_lcdm/d_lcdm, lw=2, label='Standard: $\Lambda$CDM')
plot(zvals, d_empty/d_lcdm, lw=2, label='Standard: Empty $\Omega_m=0.$')
plot(zrec_cst, lightcone_cst.xx/np.interp(zrec_cst, zvals, d_lcdm), '--', lw=2, label='JC: Uniform Open $\Omega_m=0.3$')
plot(zrec, lightcone.xx/np.interp(zrec, zvals, d_lcdm), lw=2, label='JC: Inhomogeneous Open $\Omega_m=0.3$')
legend(loc='upper left', fontsize=10, frameon=False)
import cosmolopy
import cosmolopy.distance as cd
qso_zmin = 2.2
qso_zmax = 2.8
area =5800 #deg2
zvals = np.linspace(0,1e5,1e5)
lcdm = cd.set_omega_k_0({'omega_M_0' : 0.3, 'omega_lambda_0' : 0.7, 'h' : 0.7})
d_lcdm = cd.comoving_distance_transverse(zvals, **lcdm)
clf()
plot(zvals,d_lcdm)
xscale('log')
d_bb = np.max(d_lcdm)
d_min = cd.comoving_distance_transverse(qso_zmin, **lcdm)
d_min = cd.comoving_distance_transverse(qso_zmin, **lcdm)
def D_transverse(z):
return cd.comoving_distance_transverse(z, **cosmo) / h # Mpc/h
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.
#Units are Mpc**3 Steradians^-1.
#See David Hogg's arXiv:astro-ph/9905116v4, equation 28
tl = cd.lookback_time(z[i],**Cosmology)
xscale('log')
#### P(K) library at various redshifts
nz = 100
zmin = 0
zmax = 1100
# BUILD IT ###############################################################################
#pklib = ln.build_pklib(params, zmin, zmax, nz)
# RESTORE IT ##############################################################################
pklib = ln.read_pklib(zmin, zmax, nz)
#### Skewers library with the same seed at different reshifts
# set the x range so that it extends well beyond the distance at maximum redshift
zvals = np.linspace(0,zmax,1000)
lcdm = cd.set_omega_k_0({'omega_M_0' : 0.3, 'omega_lambda_0' : 0.7, 'h' : 0.7})
d_lcdm = cd.comoving_distance_transverse(zvals, **lcdm)
maxd = np.max(d_lcdm)*1.2
theseed = 1
nn = 2**18
lightcone = ln.lightcone_1d(maxd, nn, pklib, seed=theseed)
thezinit = linspace(0,zmax, 10000)
dinit = cd.comoving_distance_transverse(thezinit, **lcdm)
nbvals = 2**19
zz = linspace(0, zmax*0.99, nbvals)
dd = np.interp(zz, thezinit, dinit)
