def tot_num_src(redshift_evolution, cosmology, zmax, density):
integrand = lambda z: redshift_evolution(z) * \
diff_comoving_volume(z, **cosmology)
norm = 4 * np.pi * scipy.integrate.quad(integrand, 0, zmax)[0]
area = 4 * np.pi * scipy.integrate.quad(integrand, 0, 0.01)[0]
vlocal = comoving_volume(0.01, **cosmology)
Ntotal = density * vlocal / (area / norm)
return Ntotal, norm
def dvdz(z):
# Planck best-fit parameters
cosmo = {'omega_M_0': 0.316,
'omega_lambda_0': 0.684,
'omega_b_0': 0.049,
'N_eff': 3.046,
'h': 0.67,
'ns': 0.962,
'sigma_8': 0.834,
'gamma': 0.55,
'w0': -1.,
'wa': 0.,
'sigma_nl': 7.}
cosmo = cd.set_omega_k_0(cosmo)
Vc = cd.diff_comoving_volume(z, **cosmo)
return Vc
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 dvdz(z):
''' this function is to calculate the diff comoving volume
the results are given in units of Mpc^3.
to use this function you need to install cosmolopy.
Also note that the cosmological
parameters are Planck best-fit parameters.
'''
cosmo = {'omega_M_0': 0.316,
'omega_lambda_0': 0.684,
'omega_b_0': 0.049,
'N_eff': 3.046,
'h': 0.67,
'ns': 0.962,
'sigma_8': 0.834,
'gamma': 0.55,
'w0': -1.,
'wa': 0.,
'sigma_nl': 7.}
cosmo = cd.set_omega_k_0(cosmo)
Vc = cd.diff_comoving_volume(z, **cosmo)
return Vc
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 volume(z, area, cosmo=cosmo):
omega = (area / 41253.0) * 4.0 * np.pi # str
volperstr = cd.diff_comoving_volume(z, **cosmo) # cMpc^3 str^-1 dz^-1
return omega * volperstr # cMpc^3 dz^-1
def volwmag(z):
#if __name__ == "__main__":
if (len(sys.argv)>1):
lensmodels = sys.argv[1]
else:
# lensmodels='lensmodels.lis'
lensmodels='vp_lensmodels.lis'
if not (os.path.isfile(lensmodels)):
print 'missing startup file'
sys.exit()
clist=asciitable.read(lensmodels,
names=['alias','clusterdir','deflxfile','deflyfile','segfile','zcluster','zmodel'])
# Observed F160W AB magnitude is 25.7. Its restframe B-band magnitude
# is approximately -22.4, uncorrected for the magnification of ~15.5.
# So the corrected absolute magnitude is -22.4+2.5*log(15.5) = -19.4.
# a reasonable grid of magnifications
#mu=np.linspace(0.2,120,100)
mu=np.linspace(1,100,100)
# representative magnifications
###magref=[5.4, 8.0, 13.5, 14.5, 18.7, 57.7]
magref=[1, 2, 3, 4, 5, 5.4, 6, 6.6, 7, 7.5, 8.0, 9, 10, 11, 12, 13, 13.5, 14, 14.5, 15, 16, 17, 18, 18.7, 20, 25, 30, 35, 40, 45, 50, 57.7, 60]
# set the anchor point of Mref <-> muref
### Mref, muref = -19.5, 14.5
Mref, muref = -19.5, 9.0
Mlim = Mref+2.5*np.log10(mu/muref)
def getmu(Mag):
return muref*10**(0.4*(Mag-Mref))
TotalVolarrayWithSeg = np.zeros(mu.shape)
TotalVolarray = np.zeros(mu.shape)
# target source redshift for rescaling model deflection maps
# ***
#ztarget = 9.5
#ztarget = 9.6
#ztarget = 5.5
ztarget = z
# Plot stuff
fig=plt.figure()
MFig=fig.add_subplot(111)
MFig.set_xlabel('Magnification [$\mu$]')
MFig.set_ylabel('Effective Volume (>$\mu$) [Mpc$^3$]')
MFig.set_xlim(0.2,100)
MFig.set_ylim(1.0,2e5)
MFig.set_xscale('log')
MFig.set_yscale('log')
# some annotations
# ***
MFig.text(30,2e4,'z=[9,10]',size=13)
#MFig.text(30,2e4,'z=[5,6]',size=13)
ytext = 1e5
# ***
#MFig.text(0.22,ytext,'Unlensed M$_{B}$ AB limit:',size=10)
## including some absolute magnitudes that correspond to magnifications
#plotmus=[-18.0,Mref,-21.0,-22.0]
#for pp in plotmus: MFig.text(getmu(pp)/1.2,ytext,'%.1f' % pp,size=10)
outdata = open('volumedata_a1689.dat','w')
for ii in np.arange(clist.size):
#for ii in [0]:
alias = clist['alias'][ii]
clusterdir = clist['clusterdir'][ii]
deflxfile = clist['deflxfile'][ii]
deflyfile = clist['deflyfile'][ii]
segfile = clist['segfile'][ii]
zcluster = clist['zcluster'][ii]
zmodel = clist['zmodel'][ii]
rescale = \
(cdad(ztarget, zcluster, **cosmo) / cdad(ztarget, **cosmo)) * \
(cdad(zmodel, **cosmo) / cdad(zmodel, zcluster, **cosmo))
# read in the deflections from Adi's lens models
axlist = pyfits.open(clusterdir+'/'+deflxfile)
aylist = pyfits.open(clusterdir+'/'+deflyfile)
ax, ay = rescale*axlist[0].data, rescale*aylist[0].data
# read in the segmentation map, which we are implicitly assuming has
# already been wregistered to the model
try:
segfile = pyfits.open(clusterdir+'/'+segfile)
segmap=segfile[0].data
segflag = 1
except:
segflag = 0
segmap=ax*0.0
# do some initializations etc
Unity = np.zeros(ax.shape)+1.0
header = axlist[0].header
try:
cdelt1, cdelt2 = header['CDELT1'], header['CDELT2']
header['CDELT1'], header['CDELT2'] = cdelt1, cdelt2
pxsc = np.abs(cdelt1)*3600.0 # in arcseconds per linear pixel dimension
except:
cd1_1, cd2_2 = header['CD1_1'], header['CD2_2']
pxsc = np.abs(cd1_1)*3600.0 # in arcseconds per linear pixel dimension
# Calculate the magnification from the Jacobian. Note that it first
# calculates the gradient with respect to the 'y' axis, and then wrt
# the 'x' axis.
axy, axx = np.gradient(ax)
ayy, ayx = np.gradient(ay)
Jxx = Unity -axx
Jxy = -axy
Jyx = -ayx
Jyy = Unity -ayy
Mu = Unity / (Jxx*Jyy - Jxy*Jyx)
AbsMu = np.abs(Mu)
# define the total wfc3ir outline mask
# regionfile = clusterdir+'/'+'wfc3ir_outline.reg'
regionfile = clusterdir+'/'+'acs_outline.reg'
rwcs=pyregion.open(regionfile)
rcoo=pyregion.open(regionfile).as_imagecoord(header)
maskboo=rwcs.get_mask(hdu=axlist[0])
# rmask=np.zeros(ax.shape)
# rmask[(maskboo)]=1.0
# The diff_comoving_volume is the differential comoving volume per
# unit redshift per unit solid angle, in units of Mpc**3 ster**-1. So
# we convert that to the Volume per (unlensed) pixel, for a source
# plane at ztarget.
VolPix = (pxsc/206265.0)**2 * cd.diff_comoving_volume(ztarget, **cosmo)
# PixMap will now be the Mpc**3 volume that each pixel corresponds to
# in the z=9-10 source plane.
PixMap = VolPix / AbsMu
# Now let's zap the areas of the mosaic that are covered by objects
# via the IR-detected segmentation map.
# /Volumes/Archive/CLASH/archive.stsci.edu/pub/clash/outgoing/macs1149/HST/catalogs/mosaicdrizzle_image_pipeline/IR_detection/SExtractor
# Now let us calculate the source-plane volume for each of the
# magnification lower limits we established.
VolarrayWithSeg = np.zeros(mu.shape)
Volarray = np.zeros(mu.shape)
for jj in np.arange(mu.size):
# VolarrayWithSeg[jj] = np.sum( PixMap[((AbsMu>mu[jj]) & (rmask==1.0) & (segmap==0) )] )
# Volarray[jj] = np.sum( PixMap[((AbsMu>mu[jj]) & (rmask==1.0))] )
VolarrayWithSeg[jj] = np.sum( PixMap[((AbsMu>mu[jj]) & (maskboo) & (segmap==0) )] )
Volarray[jj] = np.sum( PixMap[((AbsMu>mu[jj]) & (maskboo))] )
TotalVolarrayWithSeg += VolarrayWithSeg
TotalVolarray += Volarray
s=si.UnivariateSpline(np.log10(mu),np.log10(VolarrayWithSeg),s=5)
print alias,clusterdir,10**s(np.log10(muref))
outstring = '%s %s %.1f ' % (alias,clusterdir,10**s(np.log10(muref)))
outdata.write(outstring+'\n')
# need to write the mu, Volarray data to a file....
MFig.plot(mu,Volarray,label=alias)
MFig.plot(mu,VolarrayWithSeg,'--')
MFig.legend(loc=3,prop={'size':8})
# no error checking here yet...
sws = si.UnivariateSpline(np.log10(mu),np.log10(TotalVolarrayWithSeg),s=5)
s = si.UnivariateSpline(np.log10(mu),np.log10(TotalVolarray),s=5)
volwithseg = (np.asarray(10**sws(np.log10(magref)))).reshape(len(magref), 1)
volnoseg = (np.asarray(10**s(np.log10(magref)))).reshape(len(magref),1)
magref = (np.asarray(magref)).reshape(len(magref),1)
MVolArray = np.hstack((magref, volnoseg, volwithseg))
return MVolArray
def calc_dN(LF, logL0, z0, logLbinwidth, zbinwidth, N_tot, int_norm,
cosmology):
LF_val = LF(z0, logL0)
return (4*np.pi*LF_val*diff_comoving_volume(z0, **cosmology)/int_norm) * \
logLbinwidth*zbinwidth*N_tot
def volz(minmu, zmin=2.5, zmax=11.5):
clist = asciitable.read('lensmodels.lis',
names=[
'alias', 'clusterdir', 'deflxfile',
'deflyfile', 'segfile', 'zcluster', 'zmodel'
])
# Observed F160W AB magnitude is 25.7. Its restframe B-band magnitude
# is approximately -22.4, uncorrected for the magnification of ~15.5.
# So the corrected absolute magnitude is -22.4+2.5*log(15.5) = -19.4.
# target source redshift for rescaling model deflection maps
spacing = zmax - zmin + 1
ztarget = np.linspace(zmin, zmax, spacing)
# a reasonable grid of magnifications
mu = np.linspace(0.2, 120, 100)
# fiducial threshold magnification
mufiducial = minmu
mustr = '%.1f' % mufiducial
# set the anchor point of Mref <-> muref
Mref, muref = -19.5, 9.0
#Mref, muref = -19.4, 15.5
Mlim = Mref + 2.5 * np.log10(mu / muref)
def getmu(Mag):
return muref * 10**(0.4 * (Mag - Mref))
TotalVolarray = np.zeros(mu.shape)
TotalRedarray = np.zeros(ztarget.shape)
# Plot stuff
fig = plt.figure()
MFig = fig.add_subplot(111)
MFig.set_xlabel('Redshift [z]')
MFig.set_ylabel('Effective Volume ($\mu>$' + mustr + ') [Mpc$^3$]')
MFig.set_xlim(2.0, 12)
MFig.set_ylim(1.0, 2e5)
MFig.set_yscale('log')
# # some annotations
# MFig.text(30,2e4,'z=[9,10]',size=13)
# ytext = 1e5
# MFig.text(0.22,ytext,'Unlensed M$_{B}$ [AB] limit:',size=10)
# plotmus=[-18.0,Mref,-21.0,-22.0]
# for pp in plotmus: MFig.text(getmu(pp)/1.2,ytext,'%.1f' % pp,size=10)
# outdata = open('redshiftdata.dat','w')
for ii in np.arange(clist.size):
alias = clist['alias'][ii]
clusterdir = clist['clusterdir'][ii]
deflxfile = clist['deflxfile'][ii]
deflyfile = clist['deflyfile'][ii]
zcluster = clist['zcluster'][ii]
zmodel = clist['zmodel'][ii]
# read in the deflections from Adi's lens models
axlist = pyfits.open(clusterdir + '/' + deflxfile)
aylist = pyfits.open(clusterdir + '/' + deflyfile)
# ax, ay = rescale*axlist[0].data, rescale*aylist[0].data
ax, ay = axlist[0].data, aylist[0].data
# do some initializations etc
Unity = np.zeros(ax.shape) + 1.0
header = axlist[0].header
try:
cdelt1, cdelt2 = header['CDELT1'], header['CDELT2']
header['CDELT1'], header['CDELT2'] = cdelt1, cdelt2
pxsc = np.abs(
cdelt1) * 3600.0 # in arcseconds per linear pixel dimension
except:
cd1_1, cd2_2 = header['CD1_1'], header['CD2_2']
pxsc = np.abs(
cd1_1) * 3600.0 # in arcseconds per linear pixel dimension
regionfile = clusterdir + '/' + 'acs_outline.reg'
rwcs = pyregion.open(regionfile)
rcoo = pyregion.open(regionfile).as_imagecoord(header)
maskboo = rwcs.get_mask(hdu=axlist[0])
Redarray = np.zeros(ztarget.shape)
for zi in np.arange(ztarget.size):
#print alias, ztarget[zi]
rescale = \
(cdad(ztarget[zi], zcluster, **cosmo) / cdad(ztarget[zi], **cosmo)) * \
(cdad(zmodel, **cosmo) / cdad(zmodel, zcluster, **cosmo))
# Calculate the magnification from the Jacobian. Note that it first
# calculates the gradient with respect to the 'y' axis, and then wrt
# the 'x' axis.
axy, axx = np.gradient(rescale * ax)
ayy, ayx = np.gradient(rescale * ay)
Jxx = Unity - axx
Jxy = -axy
Jyx = -ayx
Jyy = Unity - ayy
Mu = Unity / (Jxx * Jyy - Jxy * Jyx)
AbsMu = np.abs(Mu)
# The diff_comoving_volume is the differential comoving volume per
# unit redshift per unit solid angle, in units of Mpc**3 ster**-1. So
# we convert that to the Volume per (unlensed) pixel, for a source
# plane at z=9-10.
VolPix = (pxsc / 206265.0)**2 * cd.diff_comoving_volume(
ztarget[zi], **cosmo)
# PixMap will now be the Mpc**3 volume that each pixel corresponds to
# in the z=9-10 source plane.
PixMap = VolPix / AbsMu
Redarray[zi] = np.sum(PixMap[((AbsMu > mufiducial) & (maskboo))])
TotalRedarray += Redarray
MFig.plot(ztarget, Redarray, label=alias)
MFig.legend(loc=3, prop={'size': 8})
MFig.plot(ztarget, TotalRedarray, linewidth=4, color='b', label='CLASH 12')
MFig.legend(loc=3, prop={'size': 10})
d1 = len(ztarget)
VolZarray = ztarget.reshape(d1, 1)
TotalRedarray = TotalRedarray.reshape(d1, 1)
VolZarray = np.hstack((VolZarray, TotalRedarray))
return VolZarray
def volwmag(z, mumin=1, mumax=100):
#if __name__ == "__main__":
if (len(sys.argv)>1):
lensmodels = sys.argv[1]
else:
# lensmodels='lensmodels.lis'
lensmodels='vp_lensmodels.lis'
if not (os.path.isfile(lensmodels)):
print 'missing startup file'
sys.exit()
clist=asciitable.read(lensmodels,
names=['alias','clusterdir','deflxfile','deflyfile','segfile','zcluster','zmodel'])
# Observed F160W AB magnitude is 25.7. Its restframe B-band magnitude
# is approximately -22.4, uncorrected for the magnification of ~15.5.
# So the corrected absolute magnitude is -22.4+2.5*log(15.5) = -19.4.
# a reasonable grid of magnifications
#mu=np.linspace(0.2,120,100)
mu=np.linspace(1,100,100)
# representative magnifications
###magref=[5.4, 8.0, 13.5, 14.5, 18.7, 57.7]
#magref=[1, 2, 3, 4, 5, 5.4, 6, 6.6, 7, 7.5, 8.0, 9, 10, 11, 12, 13, 13.5, 14, 14.5, 15, 16, 17, 18, 18.7, 20, 25, 30, 35, 40, 45, 50, 57.7, 60]
mspacing = mumax - mumin + 1
magref = np.linspace(mumin, mumax, mspacing)
# set the anchor point of Mref <-> muref
### Mref, muref = -19.5, 14.5
Mref, muref = -19.5, 9.0
Mlim = Mref+2.5*np.log10(mu/muref)
def getmu(Mag):
return muref*10**(0.4*(Mag-Mref))
TotalVolarrayWithSeg = np.zeros(mu.shape)
TotalVolarray = np.zeros(mu.shape)
# target source redshift for rescaling model deflection maps
# ***
#ztarget = 9.5
#ztarget = 9.6
#ztarget = 5.5
ztarget = z
# Plot stuff
fig=plt.figure()
MFig=fig.add_subplot(111)
MFig.set_xlabel('Magnification [$\mu$]')
MFig.set_ylabel('Effective Volume (>$\mu$) [Mpc$^3$]')
MFig.set_xlim(0.2,100)
MFig.set_ylim(1.0,2e5)
MFig.set_xscale('log')
MFig.set_yscale('log')
# some annotations
# ***
MFig.text(30,2e4,'z=[9,10]',size=13)
#MFig.text(30,2e4,'z=[5,6]',size=13)
ytext = 1e5
# ***
#MFig.text(0.22,ytext,'Unlensed M$_{B}$ AB limit:',size=10)
## including some absolute magnitudes that correspond to magnifications
#plotmus=[-18.0,Mref,-21.0,-22.0]
#for pp in plotmus: MFig.text(getmu(pp)/1.2,ytext,'%.1f' % pp,size=10)
outdata = open('volumedata_a1689.dat','w')
for ii in np.arange(clist.size):
#for ii in [0]:
alias = clist['alias'][ii]
clusterdir = clist['clusterdir'][ii]
deflxfile = clist['deflxfile'][ii]
deflyfile = clist['deflyfile'][ii]
segfile = clist['segfile'][ii]
zcluster = clist['zcluster'][ii]
zmodel = clist['zmodel'][ii]
rescale = \
(cdad(ztarget, zcluster, **cosmo) / cdad(ztarget, **cosmo)) * \
(cdad(zmodel, **cosmo) / cdad(zmodel, zcluster, **cosmo))
# read in the deflections from Adi's lens models
axlist = pyfits.open(clusterdir+'/'+deflxfile)
aylist = pyfits.open(clusterdir+'/'+deflyfile)
ax, ay = rescale*axlist[0].data, rescale*aylist[0].data
# read in the segmentation map, which we are implicitly assuming has
# already been wregistered to the model
try:
segfile = pyfits.open(clusterdir+'/'+segfile)
segmap=segfile[0].data
segflag = 1
except:
segflag = 0
segmap=ax*0.0
# do some initializations etc
Unity = np.zeros(ax.shape)+1.0
header = axlist[0].header
try:
cdelt1, cdelt2 = header['CDELT1'], header['CDELT2']
header['CDELT1'], header['CDELT2'] = cdelt1, cdelt2
pxsc = np.abs(cdelt1)*3600.0 # in arcseconds per linear pixel dimension
except:
cd1_1, cd2_2 = header['CD1_1'], header['CD2_2']
pxsc = np.abs(cd1_1)*3600.0 # in arcseconds per linear pixel dimension
# Calculate the magnification from the Jacobian. Note that it first
# calculates the gradient with respect to the 'y' axis, and then wrt
# the 'x' axis.
axy, axx = np.gradient(ax)
ayy, ayx = np.gradient(ay)
Jxx = Unity -axx
Jxy = -axy
Jyx = -ayx
Jyy = Unity -ayy
Mu = Unity / (Jxx*Jyy - Jxy*Jyx)
AbsMu = np.abs(Mu)
# define the total wfc3ir outline mask
# regionfile = clusterdir+'/'+'wfc3ir_outline.reg'
regionfile = clusterdir+'/'+'acs_outline.reg'
rwcs=pyregion.open(regionfile)
rcoo=pyregion.open(regionfile).as_imagecoord(header)
maskboo=rwcs.get_mask(hdu=axlist[0])
# rmask=np.zeros(ax.shape)
# rmask[(maskboo)]=1.0
# The diff_comoving_volume is the differential comoving volume per
# unit redshift per unit solid angle, in units of Mpc**3 ster**-1. So
# we convert that to the Volume per (unlensed) pixel, for a source
# plane at ztarget.
VolPix = (pxsc/206265.0)**2 * cd.diff_comoving_volume(ztarget, **cosmo)
# PixMap will now be the Mpc**3 volume that each pixel corresponds to
# in the z=9-10 source plane.
PixMap = VolPix / AbsMu
# Now let's zap the areas of the mosaic that are covered by objects
# via the IR-detected segmentation map.
# /Volumes/Archive/CLASH/archive.stsci.edu/pub/clash/outgoing/macs1149/HST/catalogs/mosaicdrizzle_image_pipeline/IR_detection/SExtractor
# Now let us calculate the source-plane volume for each of the
# magnification lower limits we established.
VolarrayWithSeg = np.zeros(mu.shape)
Volarray = np.zeros(mu.shape)
for jj in np.arange(mu.size):
# VolarrayWithSeg[jj] = np.sum( PixMap[((AbsMu>mu[jj]) & (rmask==1.0) & (segmap==0) )] )
# Volarray[jj] = np.sum( PixMap[((AbsMu>mu[jj]) & (rmask==1.0))] )
VolarrayWithSeg[jj] = np.sum( PixMap[((AbsMu>mu[jj]) & (maskboo) & (segmap==0) )] )
Volarray[jj] = np.sum( PixMap[((AbsMu>mu[jj]) & (maskboo))] )
TotalVolarrayWithSeg += VolarrayWithSeg
TotalVolarray += Volarray
s=si.UnivariateSpline(np.log10(mu),np.log10(VolarrayWithSeg),s=5)
print alias,clusterdir,10**s(np.log10(muref))
outstring = '%s %s %.1f ' % (alias,clusterdir,10**s(np.log10(muref)))
outdata.write(outstring+'\n')
# need to write the mu, Volarray data to a file....
MFig.plot(mu,Volarray,label=alias)
MFig.plot(mu,VolarrayWithSeg,'--')
MFig.legend(loc=3,prop={'size':8})
# no error checking here yet...
sws = si.UnivariateSpline(np.log10(mu),np.log10(TotalVolarrayWithSeg),s=5)
s = si.UnivariateSpline(np.log10(mu),np.log10(TotalVolarray),s=5)
volwithseg = (np.asarray(10**sws(np.log10(magref)))).reshape(len(magref), 1)
volnoseg = (np.asarray(10**s(np.log10(magref)))).reshape(len(magref),1)
magref = (np.asarray(magref)).reshape(len(magref),1)
MVolArray = np.hstack((magref, volnoseg, volwithseg))
return MVolArray
def volz(minmu, zmin=2.5, zmax=11.5):
clist=asciitable.read('lensmodels.lis',
names=['alias','clusterdir','deflxfile','deflyfile','segfile', 'zcluster','zmodel'])
# Observed F160W AB magnitude is 25.7. Its restframe B-band magnitude
# is approximately -22.4, uncorrected for the magnification of ~15.5.
# So the corrected absolute magnitude is -22.4+2.5*log(15.5) = -19.4.
# target source redshift for rescaling model deflection maps
spacing = zmax - zmin + 1
ztarget = np.linspace(zmin,zmax,spacing)
# a reasonable grid of magnifications
mu=np.linspace(0.2,120,100)
# fiducial threshold magnification
mufiducial = minmu
mustr = '%.1f' % mufiducial
# set the anchor point of Mref <-> muref
Mref, muref = -19.5, 9.0
#Mref, muref = -19.4, 15.5
Mlim = Mref+2.5*np.log10(mu/muref)
def getmu(Mag):
return muref*10**(0.4*(Mag-Mref))
TotalVolarray = np.zeros(mu.shape)
TotalRedarray = np.zeros(ztarget.shape)
# Plot stuff
fig=plt.figure()
MFig=fig.add_subplot(111)
MFig.set_xlabel('Redshift [z]')
MFig.set_ylabel('Effective Volume ($\mu>$'+mustr+') [Mpc$^3$]')
MFig.set_xlim(2.0,12)
MFig.set_ylim(1.0,2e5)
MFig.set_yscale('log')
# # some annotations
# MFig.text(30,2e4,'z=[9,10]',size=13)
# ytext = 1e5
# MFig.text(0.22,ytext,'Unlensed M$_{B}$ [AB] limit:',size=10)
# plotmus=[-18.0,Mref,-21.0,-22.0]
# for pp in plotmus: MFig.text(getmu(pp)/1.2,ytext,'%.1f' % pp,size=10)
# outdata = open('redshiftdata.dat','w')
for ii in np.arange(clist.size):
alias = clist['alias'][ii]
clusterdir = clist['clusterdir'][ii]
deflxfile = clist['deflxfile'][ii]
deflyfile = clist['deflyfile'][ii]
zcluster = clist['zcluster'][ii]
zmodel = clist['zmodel'][ii]
# read in the deflections from Adi's lens models
axlist = pyfits.open(clusterdir+'/'+deflxfile)
aylist = pyfits.open(clusterdir+'/'+deflyfile)
# ax, ay = rescale*axlist[0].data, rescale*aylist[0].data
ax, ay = axlist[0].data, aylist[0].data
# do some initializations etc
Unity = np.zeros(ax.shape)+1.0
header = axlist[0].header
try:
cdelt1, cdelt2 = header['CDELT1'], header['CDELT2']
header['CDELT1'], header['CDELT2'] = cdelt1, cdelt2
pxsc = np.abs(cdelt1)*3600.0 # in arcseconds per linear pixel dimension
except:
cd1_1, cd2_2 = header['CD1_1'], header['CD2_2']
pxsc = np.abs(cd1_1)*3600.0 # in arcseconds per linear pixel dimension
regionfile = clusterdir+'/'+'acs_outline.reg'
rwcs=pyregion.open(regionfile)
rcoo=pyregion.open(regionfile).as_imagecoord(header)
maskboo=rwcs.get_mask(hdu=axlist[0])
Redarray=np.zeros(ztarget.shape)
for zi in np.arange(ztarget.size):
#print alias, ztarget[zi]
rescale = \
(cdad(ztarget[zi], zcluster, **cosmo) / cdad(ztarget[zi], **cosmo)) * \
(cdad(zmodel, **cosmo) / cdad(zmodel, zcluster, **cosmo))
# Calculate the magnification from the Jacobian. Note that it first
# calculates the gradient with respect to the 'y' axis, and then wrt
# the 'x' axis.
axy, axx = np.gradient(rescale*ax)
ayy, ayx = np.gradient(rescale*ay)
Jxx = Unity -axx
Jxy = -axy
Jyx = -ayx
Jyy = Unity -ayy
Mu = Unity / (Jxx*Jyy - Jxy*Jyx)
AbsMu = np.abs(Mu)
# The diff_comoving_volume is the differential comoving volume per
# unit redshift per unit solid angle, in units of Mpc**3 ster**-1. So
# we convert that to the Volume per (unlensed) pixel, for a source
# plane at z=9-10.
VolPix = (pxsc/206265.0)**2 * cd.diff_comoving_volume(ztarget[zi], **cosmo)
# PixMap will now be the Mpc**3 volume that each pixel corresponds to
# in the z=9-10 source plane.
PixMap = VolPix / AbsMu
Redarray[zi]=np.sum(PixMap[((AbsMu>mufiducial) & (maskboo))])
TotalRedarray += Redarray
MFig.plot(ztarget,Redarray,label=alias)
MFig.legend(loc=3,prop={'size':8})
MFig.plot(ztarget,TotalRedarray,linewidth=4,color='b',label='CLASH 12')
MFig.legend(loc=3,prop={'size':10})
d1 = len(ztarget)
VolZarray = ztarget.reshape(d1, 1)
TotalRedarray = TotalRedarray.reshape(d1, 1)
VolZarray = np.hstack((VolZarray, TotalRedarray))
return VolZarray
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)
#See equation 30 of David Hogg's arXiv:astro-ph/9905116v4. Units are s.
agetl = cd.age(z[i], **Cosmology)
#Age at z is lookback time at z'->Infinity minus lookback time at z.
tH = 3.09e17 / Cosmology['h']
ez = cd.e_z(z[i], **Cosmology)
#The unitless Hubble expansion rate at redshift z.
from math import *
# the 'x' axis.
axy, axx = np.gradient(rescale * ax)
ayy, ayx = np.gradient(rescale * ay)
Jxx = Unity - axx
Jxy = -axy
Jyx = -ayx
Jyy = Unity - ayy
Mu = Unity / (Jxx * Jyy - Jxy * Jyx)
AbsMu = np.abs(Mu)
# The diff_comoving_volume is the differential comoving volume per
# unit redshift per unit solid angle, in units of Mpc**3 ster**-1. So
# we convert that to the Volume per (unlensed) pixel, for a source
# plane at z=9-10.
VolPix = (pxsc / 206265.0)**2 * cd.diff_comoving_volume(
ztarget[zi], **cosmo)
# PixMap will now be the Mpc**3 volume that each pixel corresponds to
# in the z=9-10 source plane.
PixMap = VolPix / AbsMu
Redarray[zi] = np.sum(PixMap[(AbsMu > mufiducial)])
TotalRedarray += Redarray
MFig.plot(ztarget, Redarray, label=alias)
MFig.legend(loc=3, prop={'size': 8})
# # Now let us calculate the source-plane volume for each of the
# # magnification lower limits we established.
#
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)
#See equation 30 of David Hogg's arXiv:astro-ph/9905116v4. Units are s.
agetl = cd.age(z[i],**Cosmology)
#Age at z is lookback time at z'->Infinity minus lookback time at z.
tH = 3.09e17/Cosmology['h']
ez = cd.e_z(z[i],**Cosmology)
#The unitless Hubble expansion rate at redshift z.
def Dv(z):
'''__________ Dv_________________________'''
cosmo = {'omega_M_0' : 0.24, 'omega_lambda_0' : 1.0 - 0.24, 'h' : 0.73}
cosmo = cd.set_omega_k_0(cosmo)
Dv = cd.diff_comoving_volume(z, **cosmo)
return Dv
