def compute_diag(SNe):
lens = 0.055
#c = 3e5 #km/s
sigma_lens = 0.055 * SNe['zcmb']
sigma_pecvel = 5*8.33e-4/(np.log(10) *SNe['zcmb']) # See eq. 13 in B14
sigma_coh = np.array([coh_dict[JLA.survey(sn)] for sn in SNe])
return np.column_stack((sigma_coh, sigma_lens, sigma_pecvel))
def compute_diag(SNe):
lens = 0.055
#c = 3e5 #km/s
sigma_lens = 0.055 * SNe['zcmb']
sigma_pecvel = 5*5e-4/(np.log(10) *SNe['zcmb'])
sigma_coh = np.array([coh_dict[JLA.survey(sn)] for sn in SNe])
return np.column_stack((sigma_coh, sigma_lens, sigma_pecvel))
def apply(self, SNe, to_write=False):
""" correction to SNe"""
z_value, z_err = [], []
for sn in SNe:
c = SkyCoord(sn['ra']*u.degree, sn['dec']*u.degree)
gc = c.galactic
vpec = self.lookup_velocity(sn['zhel'], gc.l.degree, gc.b.degree)
z_c = self.correct_redshift(sn['zhel'], vpec, gc.l.degree, gc.b.degree)
z_plus = self.correct_redshift(sn['zhel'], self.r_plus*vpec,
gc.l.degree, gc.b.degree)
z_minus = self.correct_redshift(sn['zhel'], self.r_minus*vpec,
gc.l.degree, gc.b.degree)
if JLA.survey(sn) == 'nearby':
z_value.append(z_c)
z_err.append(np.mean([z_plus - z_c, z_c - z_minus]))
else:
z_value.append(sn['zcmb'])
z_err.append(0)
if to_write:
np.savetxt('z_CMB_corrected.txt', np.array(z_value))
return z_value, z_err
def apply(self, SNe, to_write=False):
""" correction to SNe"""
z_value, z_err = [], []
for sn in SNe:
c = SkyCoord(sn['ra'] * u.degree, sn['dec'] * u.degree)
gc = c.galactic
vpec = self.lookup_velocity(sn['zhel'], gc.l.degree, gc.b.degree)
z_c = self.correct_redshift(sn['zhel'], vpec, gc.l.degree,
gc.b.degree)
z_plus = self.correct_redshift(sn['zhel'], self.r_plus * vpec,
gc.l.degree, gc.b.degree)
z_minus = self.correct_redshift(sn['zhel'], self.r_minus * vpec,
gc.l.degree, gc.b.degree)
if JLA.survey(sn) == 'nearby':
z_value.append(z_c)
z_err.append(np.mean([z_plus - z_c, z_c - z_minus]))
else:
z_value.append(sn['zcmb'])
z_err.append(0)
if to_write:
np.savetxt('z_CMB_corrected.txt', np.array(z_value))
return z_value, z_err
def compute_bias(options):
import numpy
import astropy.io.fits as fits
import JLA_library as JLA
from astropy.table import Table
from astropy.cosmology import FlatwCDM
from scipy.optimize import leastsq
import matplotlib.pyplot as plt
from scipy.stats import t
# ----------- Read in the configuration file ------------
params=JLA.build_dictionary(options.config)
# ----------- Read in the SN ordering ------------------------
SNeList = Table(numpy.genfromtxt(options.SNlist,
usecols=(0, 2),
dtype='S30,S200',
names=['id', 'lc']))
nSNe = len(SNeList)
for i, SN in enumerate(SNeList):
SNeList['id'][i] = SNeList['id'][i].replace('lc-', '').replace('.list', '').replace('_smp','')
lcfile = JLA.get_full_path(params[options.lcfits])
SNe = Table.read(lcfile, format='fits')
print 'There are %d SNe' % (nSNe)
indices = JLA.reindex_SNe(SNeList['id'], SNe)
SNe=SNe[indices]
# Add a column that records the error in the bias correction
SNe['e_bias'] = numpy.zeros(nSNe,'f8')
# Read in the bias correction (see, for example, Fig.5 in B14)
# Fit a polynomial to the data
# Determine the uncertainties
bias = numpy.genfromtxt(JLA.get_full_path(params['biasPolynomial']),
skip_header=4,
usecols=(0, 1, 2, 3),
dtype='S10,f8,f8,f8',
names=['sample', 'redshift', 'bias', 'e_bias'])
if options.plot:
fig=plt.figure()
ax=fig.add_subplot(111)
colour={'nearby':'b','SNLS':'r','SDSS':'g','DES':'k'}
for sample in numpy.unique(bias['sample']):
selection=(bias['sample']==sample)
guess=[0,0,0]
print bias[selection]
plsq=leastsq(residuals, guess, args=(bias[selection]['bias'],
bias[selection]['redshift'],
bias[selection]['e_bias'],
'poly'), full_output=1)
if plsq[4] in [1,2,3,4]:
print 'Solution for %s found' % (sample)
if options.plot:
ax.errorbar(bias[selection]['redshift'],
bias[selection]['bias'],
yerr=bias[selection]['e_bias'],
ecolor='k',
color=colour[sample],
fmt='o',
label=sample)
z=numpy.arange(numpy.min(bias[selection]['redshift']),numpy.max(bias[selection]['redshift']),0.001)
ax.plot(z,poly(z,plsq[0]),color=colour[sample])
# For each SNe, determine the uncerainty in the correction. We use the approach descibed in
# https://www.astro.rug.nl/software/kapteyn/kmpfittutorial.html
# Compute the chi-sq.
chisq=(((bias[selection]['bias']-poly(bias[selection]['redshift'],plsq[0]))/bias[selection]['e_bias'])**2.).sum()
dof=selection.sum()-len(guess)
print "Reduced chi-square value for sample %s is %5.2e" % (sample, chisq / dof)
alpha=0.315 # Confidence interval is 100 * (1-alpha)
# Compute the upper alpha/2 value for the student t distribution with dof
thresh=t.ppf((1-alpha/2.0), dof)
if options.plot and sample!='nearby':
# The following is only valid for polynomial fitting functions, and we do not compute it for the nearby sample
upper_curve=[]
lower_curve=[]
for x in z:
vect=numpy.matrix([1,x,x**2.])
offset=thresh * numpy.sqrt(chisq / dof * (vect*numpy.matrix(plsq[1])*vect.T)[0,0])
upper_curve.append(poly(x,plsq[0])+offset)
lower_curve.append(poly(x,plsq[0])-offset)
ax.plot(z,lower_curve,'--',color=colour[sample])
ax.plot(z,upper_curve,'--',color=colour[sample])
# Compute the error in the bias
# We increase the absolute value
# In other words, if the bias is negative, we subtract the error to make it even more negative
# This is to get the correct sign in the off diagonal elements
# We assume 100% correlation between SNe
for i,SN in enumerate(SNe):
if SN['zcmb'] > 0:
redshift = SN['zcmb']
else:
redshift = SN['zhel']
if JLA.survey(SN) == sample:
# For the nearby SNe, the uncertainty in the bias correction is the bias correction itself
if sample=='nearby':
SNe['e_bias'][i]=poly(redshift,plsq[0])
#print SN['name'],redshift, SNe['e_bias'][i]
else:
vect = numpy.matrix([1,redshift,redshift**2.])
if poly(redshift,plsq[0]) > 0:
sign = 1
else:
sign = -1
SNe['e_bias'][i] = sign * thresh * numpy.sqrt(chisq / dof * (vect*numpy.matrix(plsq[1])*vect.T)[0,0])
# We are getting some unrealistcally large values
date = JLA.get_date()
if options.plot:
ax.legend()
plt.savefig('C_bias_%s.png' % (date))
plt.close()
# Compute the bias matrix
#
Zero=numpy.zeros(nSNe)
H=numpy.concatenate((SNe['e_bias'],Zero,Zero)).reshape(3,nSNe).ravel(order='F')
C_bias = numpy.matrix(H).T * numpy.matrix(H)
fits.writeto('C_bias_%s.fits' % (date),C_bias,clobber=True)
return None
def compute_bias(options):
import numpy
import astropy.io.fits as fits
import JLA_library as JLA
from astropy.table import Table
from astropy.cosmology import FlatwCDM
from scipy.optimize import leastsq
import matplotlib.pyplot as plt
from scipy.stats import t
# ----------- Read in the configuration file ------------
params=JLA.build_dictionary(options.config)
# ----------- Read in the SN ordering ------------------------
SNeList = Table(numpy.genfromtxt(options.SNlist,
usecols=(0, 2),
dtype='S30,S200',
names=['id', 'lc']))
nSNe = len(SNeList)
for i, SN in enumerate(SNeList):
SNeList['id'][i] = SNeList['id'][i].replace('lc-', '').replace('.list', '')
lcfile = JLA.get_full_path(params[options.lcfits])
SNe = Table.read(lcfile, format='fits')
print 'There are %d SNe' % (nSNe)
indices = JLA.reindex_SNe(SNeList['id'], SNe)
SNe=SNe[indices]
# Add a column that records the error in the bias
SNe['e_bias'] = numpy.zeros(nSNe,'f8')
# Read in the points from B14 figure
# Fit a polynomial to the data
# Determine the uncertainties
bias = numpy.genfromtxt(JLA.get_full_path(params['biasPolynomial']),
skip_header=3,
usecols=(0, 1, 2, 3),
dtype='S10,f8,f8,f8',
names=['sample', 'redshift', 'bias', 'e_bias'])
if options.plot:
fig=plt.figure()
ax=fig.add_subplot(111)
colour={'nearby':'b','SNLS':'r','SDSS':'g'}
for sample in numpy.unique(bias['sample']):
selection=(bias['sample']==sample)
guess=[0,0,0]
plsq=leastsq(residuals, guess, args=(bias[selection]['bias'],
bias[selection]['redshift'],
bias[selection]['e_bias'],
'poly'), full_output=1)
if plsq[4] in [1,2,3,4]:
print 'Solution for %s found' % (sample)
if options.plot:
ax.errorbar(bias[selection]['redshift'],
bias[selection]['bias'],
yerr=bias[selection]['e_bias'],
ecolor='k',
color=colour[sample],
fmt='o',
label=sample)
z=numpy.arange(numpy.min(bias[selection]['redshift']),numpy.max(bias[selection]['redshift']),0.001)
ax.plot(z,poly(z,plsq[0]),color=colour[sample])
# For each SNe, determine the uncerainty in the correction. We use the covariance martix
# prediction bounds for the fitted curve.
# https://www.astro.rug.nl/software/kapteyn/kmpfittutorial.html
# Compute the chi-sq.
chisq=(((bias[selection]['bias']-poly(bias[selection]['redshift'],plsq[0]))/bias[selection]['e_bias'])**2.).sum()
dof=selection.sum()-len(guess)
print "Reduced chi-square value for sample %s is %5.2e" % (sample, chisq / dof)
alpha=0.315 # Confidence interval is 100 * (1-alpha)
# Compute the upper alpha/2 vallue for the student t distribution with dof
thresh=t.ppf((1-alpha/2.0), dof)
if options.plot:
# The following is only valid for polynomial fitting functions
upper_curve=[]
lower_curve=[]
for x in z:
vect=numpy.matrix([1,x,x**2.])
offset=thresh * numpy.sqrt(chisq / dof * (vect*numpy.matrix(plsq[1])*vect.T)[0,0])
upper_curve.append(poly(x,plsq[0])+offset)
lower_curve.append(poly(x,plsq[0])-offset)
ax.plot(z,lower_curve,'--',color=colour[sample])
ax.plot(z,upper_curve,'--',color=colour[sample])
# Compute the error in the bias
# We increase the absolute vlaue
# In other words, if the bias is negative, we subtract the error to make it even more negative
# We assume 100% correlation between SNe
for i,SN in enumerate(SNe):
if JLA.survey(SN) == sample:
if SN['zcmb'] > 0:
redshift = SN['zcmb']
else:
redshift = SN['zhel']
vect = numpy.matrix([1,redshift,redshift**2.])
if poly(redshift,plsq[0]) > 0:
sign = 1
else:
sign = -1
SNe['e_bias'][i] = sign * thresh * numpy.sqrt(chisq / dof * (vect*numpy.matrix(plsq[1])*vect.T)[0,0])
# We are getting some unrealistcally large values
if options.plot:
ax.legend()
plt.show()
plt.close()
# Compute the bias matrix
#
date = JLA.get_date()
Zero=numpy.zeros(nSNe)
H=numpy.concatenate((SNe['e_bias'],Zero,Zero)).reshape(3,nSNe).ravel(order='F')
C_bias = numpy.matrix(H)
fits.writeto('C_bias_%s.fits' % (date),C_bias.T*C_bias,clobber=True)
return None