def compute_model(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.interpolate import interp1d
# ----------- Read in the configuration file ------------
params=JLA.build_dictionary(options.config)
# ----------- Read in the SN ordering ------------------------
SNeList = 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]
redshift = SNe['zcmb']
replace=(redshift < 0)
# For SNe that do not have the CMB redshift
redshift[replace]=SNe[replace]['zhel']
print len(redshift)
if options.raw:
# Data from the bottom left hand figure of Mosher et al. 2014.
# This is option ii) that is descibed above
offsets=Table.read(JLA.get_full_path(params['modelOffset']),format='ascii.csv')
Delta_M=interp1d(offsets['z'], offsets['offset'], kind='linear',bounds_error=False,fill_value='extrapolate')(redshift)
else:
Om_0=0.303 # JLA value in the wCDM model
cosmo1 = FlatwCDM(name='SNLS3+WMAP7', H0=70.0, Om0=Om_0, w0=-1.0)
cosmo2 = FlatwCDM(name='SNLS3+WMAP7', H0=70.0, Om0=Om_0, w0=-1.024)
Delta_M=5*numpy.log10(cosmo1.luminosity_distance(redshift)/cosmo2.luminosity_distance(redshift))
# Build the covariance matrix. Note that only magnitudes are affected
Zero=numpy.zeros(nSNe)
H=numpy.concatenate((Delta_M,Zero,Zero)).reshape(3,nSNe).ravel(order='F')
C_model=numpy.matrix(H).T * numpy.matrix(H)
date = JLA.get_date()
fits.writeto('C_model_%s.fits' % (date),numpy.array(C_model),clobber=True)
return None
def compute_model(options):
import numpy
import astropy.io.fits as fits
import JLA_library as JLA
from astropy.table import Table
from astropy.cosmology import FlatwCDM
# ----------- Read in the configuration file ------------
params = JLA.build_dictionary(options.config)
# ----------- Read in the SN ordering ------------------------
SNeList = 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)
#z=numpy.array([])
#offset=numpy.array([])
Om_0 = 0.303 # JLA value in the wCDM model
cosmo1 = FlatwCDM(name='SNLS3+WMAP7', H0=70.0, Om0=Om_0, w0=-1.0)
cosmo2 = FlatwCDM(name='SNLS3+WMAP7', H0=70.0, Om0=Om_0, w0=-1.024)
# For the JLA SNe
redshift = SNe['zcmb']
replace = (redshift < 0)
# For the non JLA SNe
redshift[replace] = SNe[replace]['zhel']
Delta_M = 5 * numpy.log10(
cosmo1.luminosity_distance(redshift) /
cosmo2.luminosity_distance(redshift))
# Build the covariance matrix. Note that only magnitudes are affected
Zero = numpy.zeros(nSNe)
H = numpy.concatenate((Delta_M, Zero, Zero)).reshape(3,
nSNe).ravel(order='F')
C_model = numpy.matrix(H).T * numpy.matrix(H)
date = JLA.get_date()
fits.writeto('C_model_%s.fits' % (date),
numpy.array(C_model),
clobber=True)
return None
def compute_model(options):
import numpy
import astropy.io.fits as fits
import JLA_library as JLA
from astropy.table import Table
from astropy.cosmology import FlatwCDM
# ----------- Read in the configuration file ------------
params=JLA.build_dictionary(options.config)
# ----------- Read in the SN ordering ------------------------
SNeList = 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)
#z=numpy.array([])
#offset=numpy.array([])
Om_0=0.303 # JLA value in the wCDM model
cosmo1 = FlatwCDM(name='SNLS3+WMAP7', H0=70.0, Om0=Om_0, w0=-1.0)
cosmo2 = FlatwCDM(name='SNLS3+WMAP7', H0=70.0, Om0=Om_0, w0=-1.024)
# For the JLA SNe
redshift = SNe['zcmb']
replace=(redshift < 0)
# For the non JLA SNe
redshift[replace]=SNe[replace]['zhel']
Delta_M=5*numpy.log10(cosmo1.luminosity_distance(redshift)/cosmo2.luminosity_distance(redshift))
# Build the covariance matrix. Note that only magnitudes are affected
Zero=numpy.zeros(nSNe)
H=numpy.concatenate((Delta_M,Zero,Zero)).reshape(3,nSNe).ravel(order='F')
C_model=numpy.matrix(H).T * numpy.matrix(H)
date = JLA.get_date()
fits.writeto('C_model_%s.fits' % (date),numpy.array(C_model),clobber=True)
return None
def lnlike(theta, x, y, z, xerr, yerr, zerr):
alpha, beta, h0 = theta
Or = 4.153e-5 * h0**(-2)
Om = 0.3
w0 = -1.0
cosmo = FlatwCDM(H0=h0 * 100, Om0=Om, w0=w0)
#---------------------------------------------------------------------------
ixG = np.where(z > 10)
ixH = np.where(z < 10)
Mum = z * 0.0
MumErr = z * 0.0
Mum[ixG] = z[ixG]
MumErr[ixG] = zerr[ixG]
Mum[ixH] = 5.0 * np.log10(cosmo.luminosity_distance(z[ixH]).value) + 25.0
MumErr[ixH] = (5.0 / np.log(10.0)) * (zerr[ixH] / z[ixH])
Mu = 2.5 * (beta * x + alpha) - 2.5 * y - 100.195
MuErr = 2.5 * np.sqrt((yerr)**2 + beta**2 * (xerr)**2)
R = (Mu - Mum)
W = 1.0 / (MuErr**2 + MumErr**2)
xsq = np.sum(R**2 * W)
llq = -0.5 * xsq
return (llq, xsq, R, Mum)
def simulateData():
# the number of transients
nTrans = 30
# set the state of the random number generator
seed = 0
numpy.random.seed(seed)
# simulated data in the dictionary observation, including photometry at peak,
# spectroscopic redshift, and spectroscopic type.
# the convention is SNIa are '0', SNII are '1'
# the current implementation is barebones
observation = dict()
observation["specz"] = numpy.random.uniform(low=0.1, high=0.8, size=nTrans)
observation["zprob"] = numpy.zeros(nTrans) + 1.0
spectype = numpy.random.uniform(low=0, high=1, size=nTrans)
snIarate = 1.0 / (1 + inputs.rate_II_r)
observation["spectype"] = numpy.zeros(nTrans, dtype=int)
observation["spectype"][spectype > snIarate] = 1
luminosity = (1.0 - observation["spectype"]) * numpy.exp(inputs.logL_snIa) * 10 ** (
numpy.random.normal(0, inputs.sigma_snIa / 2.5, size=nTrans)
) + observation["spectype"] * numpy.exp(inputs.logL_snII) * 10 ** (
numpy.random.normal(0, inputs.sigma_snII / 2.5, size=nTrans)
)
cosmo = FlatwCDM(H0=72, Om0=inputs.Om0, w0=inputs.w0)
ld = cosmo.luminosity_distance(observation["specz"]).value
# h0 = (const.c/cosmo.H0).to(u.Mpc).value
observation["counts"] = luminosity / 4 / numpy.pi / ld / ld * 10 ** (inputs.Z / 2.5)
# plt.scatter(observation['specz'],-2.5*numpy.log10(observation['counts']))
found = observation["counts"] >= fluxthreshold
nTrans = found.sum()
observation["specz"] = numpy.reshape(observation["specz"][found], (nTrans, 1))
observation["zprob"] = numpy.reshape(observation["zprob"][found], (nTrans, 1))
observation["spectype"] = observation["spectype"][found]
# observation['spectype'][0] = -1 # case of no spectral type
observation["counts"] = observation["counts"][found]
return observation
def simulateData():
# the number of transients
nTrans = 15
# set the state of the random number generator
seed=0
numpy.random.seed(seed)
# simulated data in the dictionary observation, including photometry at peak,
# spectroscopic redshift, and spectroscopic type.
# the convention is SNIa are '0', SNII are '1'
# the current implementation is barebones
observation=dict()
observation['specz'] = numpy.random.uniform(low=0.1, high=0.8, size=nTrans)
observation['zprob'] = numpy.zeros(nTrans)+1.
spectype = numpy.random.uniform(low=0, high=1, size=nTrans)
observation['spectype'] = spectype.round().astype('int')
luminosity = (1.-observation['spectype'])*10**(numpy.random.normal(0, 0.1/2.5, size=nTrans)) \
+ observation['spectype']*.5**10**(numpy.random.normal(0, 0.4/2.5,size=nTrans))
cosmo = FlatwCDM(H0=72, Om0=0.28, w0=-1)
ld = cosmo.luminosity_distance(observation['specz']).value
h0 = (const.c/cosmo.H0).to(u.Mpc).value
observation['counts'] = luminosity / 4/numpy.pi/ld/ld*10**(0.02/2.5)
count_lim = .4e-8
found = observation['counts'] >= count_lim
nTrans = found.sum()
observation['specz'] = numpy.reshape(observation['specz'][found],(nTrans,1))
observation['zprob'] = numpy.reshape(observation['zprob'][found],(nTrans,1))
observation['spectype'] =observation['spectype'][found]
observation['spectype'][0] = -1 # case of no spectral type
observation['counts'] =observation['counts'][found]
return observation
def distance(self, z):
cosmology = FlatwCDM(**self.__par_values__)
return cosmology.luminosity_distance(z).value
def luminosity_distance(z, Om0, w0):
cosmo = FlatwCDM(H0=72, Om0=Om0, w0=w0)
return cosmo.luminosity_distance(z).value
def simulateData():
# the number of transients
nTrans = 30
# set the state of the random number generator
seed=0
numpy.random.seed(seed)
# simulated data in the dictionary observation, including photometry at peak,
# spectroscopic redshift, and spectroscopic type.
# the convention is SNIa are '0', SNII are '1'
# the current implementation is barebones
observation=dict()
observation['specz'] = numpy.random.uniform(low=0.1, high=0.8, size=nTrans)
observation['zprob'] = numpy.zeros(nTrans)+1.
spectype = numpy.random.uniform(low=0, high=1, size=nTrans)
snIarate = 1./(1+inputs.rate_II_r)
observation['spectype'] = numpy.zeros(nTrans,dtype=int)
observation['spectype'][spectype > snIarate]=1
luminosity = (1.-observation['spectype'])*numpy.exp(inputs.logL_snIa)*10**(numpy.random.normal(0, inputs.sigma_snIa/2.5, size=nTrans)) \
+ observation['spectype']*numpy.exp(inputs.logL_snII)*10**(numpy.random.normal(0, inputs.sigma_snII/2.5,size=nTrans))
cosmo = FlatwCDM(H0=72, Om0=inputs.Om0, w0=inputs.w0)
ld = cosmo.luminosity_distance(observation['specz']).value
# h0 = (const.c/cosmo.H0).to(u.Mpc).value
npts = 2
cov = numpy.zeros((2,2))
cov[0,0] = 1e-20
cov[1,1] = 1e-20
cov[0,1] = 0 #for now uncorrelated as algorithm handles that
cov[1,0] = 0 #for now uncorrelated as algorithm handles that
invcov = numpy.linalg.inv(cov)
observation['counts'] = []
observation['counts_invcov']=[]
observation['mjds']=[]
for i in xrange(nTrans):
ans = numpy.random.multivariate_normal(numpy.zeros(npts)+ luminosity[i] / 4/numpy.pi/ld[i]/ld[i]*10**(inputs.Z/2.5), cov)
observation['counts'].append(ans)
observation['counts_invcov'].append(invcov)
observation['mjds'].append(numpy.arange(2.))
#luminosity / 4/numpy.pi/ld/ld*10**(inputs.Z/2.5)
# plt.scatter(observation['specz'],-2.5*numpy.log10(observation['counts']))
#at least one must be above threshold
nthreshold = 1
found = []
# found = observation['counts'] >= fluxthreshold
for i in xrange(nTrans):
nabove = (observation['counts'][i] >= fluxthreshold).sum()
found.append(nabove >= nthreshold)
found = numpy.array(found)
nTrans = found.sum()
observation['specz'] = [numpy.array([dum]) for dum in observation['specz'][found]]
observation['zprob'] = [numpy.array([dum]) for dum in observation['zprob'][found]]
observation['spectype'] = observation['spectype'][found]
observation['spectype'][0] = -1 # case of no spectral type
observation['specz'][0] = numpy.array([observation['specz'][0][0], 0.2])
observation['zprob'][0] = numpy.array([0.6,0.4])
observation['spectype'][1] = -1 # case of no spectral type
observation['specz'][1] = numpy.array([observation['specz'][1][0], 0.8])
observation['zprob'][1] = numpy.array([0.3,0.7])
# observation['counts'] =observation['counts'][found]
# observation['counts_cov'] =observation['counts_cov'][found]
observation['counts'] =[observation['counts'][i] for i in xrange(len(found)) if found[i]]
observation['counts_invcov'] = [observation['counts_invcov'][i] for i in xrange(len(found)) if found[i]]
observation['mjds'] = [observation['mjds'][i] for i in xrange(len(found)) if found[i]]
return observation
def compute_rel_size(options):
import numpy
import astropy.io.fits as fits
from astropy.table import Table
import JLA_library as JLA
from astropy.cosmology import FlatwCDM
import os
# ----------- Read in the configuration file ------------
params = JLA.build_dictionary(options.config)
# ---------- Read in the SNe list -------------------------
SNeList = numpy.genfromtxt(options.SNlist,
usecols=(0, 2),
dtype='S30,S200',
names=['id', 'lc'])
for i, SN in enumerate(SNeList):
SNeList['id'][i] = SNeList['id'][i].replace('lc-',
'').replace('.list', '')
# ----------- Read in the data JLA --------------------------
lcfile = JLA.get_full_path(params[options.lcfits])
SNe = Table.read(lcfile, format='fits')
nSNe = len(SNe)
print 'There are %d SNe in this sample' % (nSNe)
# sort it to match the listing in options.SNlist
indices = JLA.reindex_SNe(SNeList['id'], SNe)
SNe = SNe[indices]
# ---------- Compute the Jacobian ----------------------
# The Jacobian is an m by 4 matrix, where m is the number of SNe
# The columns are ordered in terms of Om, w, alpha and beta
J = []
JLA_result = {
'Om': 0.303,
'w': -1.00,
'alpha': 0.141,
'beta': 3.102,
'M_B': -19.05
}
offset = {'Om': 0.01, 'w': 0.01, 'alpha': 0.01, 'beta': 0.01, 'M_B': 0.01}
nFit = 4
cosmo1 = FlatwCDM(name='SNLS3+WMAP7',
H0=70.0,
Om0=JLA_result['Om'],
w0=JLA_result['w'])
# Varying Om
cosmo2 = FlatwCDM(name='SNLS3+WMAP7',
H0=70.0,
Om0=JLA_result['Om'] + offset['Om'],
w0=JLA_result['w'])
J.append(5 * numpy.log10((cosmo1.luminosity_distance(SNe['zcmb']) /
cosmo2.luminosity_distance(SNe['zcmb']))[:, 0]))
# varying alpha
J.append(1.0 * offset['alpha'] * SNe['x1'][:, 0])
# varying beta
J.append(-1.0 * offset['beta'] * SNe['color'][:, 0])
# varying M_B
J.append(offset['M_B'] * numpy.ones(nSNe))
J = numpy.matrix(
numpy.concatenate((J)).reshape(nSNe, nFit, order='F') * 100.)
# Set up the covariance matrices
systematic_terms = [
'bias', 'cal', 'host', 'dust', 'model', 'nonia', 'pecvel', 'stat'
]
covmatrices = {
'bias': params['bias'],
'cal': params['cal'],
'host': params['host'],
'dust': params['dust'],
'model': params['model'],
'nonia': params['nonia'],
'pecvel': params['pecvel'],
'stat': params['stat']
}
if options.type in systematic_terms:
print "Using %s for the %s term" % (options.name, options.type)
covmatrices[options.type] = options.name
# Combine the matrices to compute the full covariance matrix, and compute its inverse
if options.all:
#read in the user provided matrix, otherwise compute it, and write it out
C = fits.getdata(JLA.get_full_path(params['all']))
else:
C = add_covar_matrices(covmatrices, params['diag'])
date = JLA.get_date()
fits.writeto('C_total_%s.fits' % (date), C, clobber=True)
Cinv = numpy.matrix(C).I
# Construct eta, a 3n vector
eta = numpy.zeros(3 * nSNe)
for i, SN in enumerate(SNe):
eta[3 * i] = SN['mb']
eta[3 * i + 1] = SN['x1']
eta[3 * i + 2] = SN['color']
# Construct A, a n x 3n matrix
A = numpy.zeros(nSNe * 3 * nSNe).reshape(nSNe, 3 * nSNe)
for i in range(nSNe):
A[i, 3 * i] = 1.0
A[i, 3 * i + 1] = JLA_result['alpha']
A[i, 3 * i + 2] = -JLA_result['beta']
# ---------- Compute W ----------------------
# W has shape m * 3n, where m is the number of fit paramaters.
W = (J.T * Cinv * J).I * J.T * Cinv * numpy.matrix(A)
# Note that (J.T * Cinv * J) is a m x m matrix, where m is the number of fit parameters
# ----------- Compute V_x, where x represents the systematic uncertainty
result = []
for term in systematic_terms:
cov = numpy.matrix(fits.getdata(JLA.get_full_path(covmatrices[term])))
if 'C_stat' in covmatrices[term]:
# Add diagonal term from Eq. 13 to the magnitude
sigma = numpy.genfromtxt(
JLA.get_full_path(params['diag']),
comments='#',
usecols=(0, 1, 2),
dtype='f8,f8,f8',
names=['sigma_coh', 'sigma_lens', 'sigma_pecvel'])
for i in range(nSNe):
cov[3 * i, 3 * i] += sigma['sigma_coh'][i]**2 + sigma[
'sigma_lens'][i]**2 + sigma['sigma_pecvel'][i]**2
V = W * cov * W.T
result.append(V[0, 0])
print '%20s\t%5s\t%5s\t%s' % ('Term', 'sigma', 'var', 'Percentage')
for i, term in enumerate(systematic_terms):
if options.type != None and term == options.type:
print '* %18s\t%5.4f\t%5.4f\t%4.1f' % (term, numpy.sqrt(
result[i]), result[i], result[i] / numpy.sum(result) * 100.)
else:
print '%20s\t%5.4f\t%5.4f\t%4.1f' % (term, numpy.sqrt(
result[i]), result[i], result[i] / numpy.sum(result) * 100.)
print '%20s\t%5.4f' % ('Total', numpy.sqrt(numpy.sum(result)))
return
def compute_rel_size(options):
import numpy
import astropy.io.fits as fits
from astropy.table import Table
import JLA_library as JLA
from astropy.cosmology import FlatwCDM
import os
# ----------- Read in the configuration file ------------
params=JLA.build_dictionary(options.config)
# ---------- Read in the SNe list -------------------------
SNeList=numpy.genfromtxt(options.SNlist,usecols=(0,2),dtype='S30,S200',names=['id','lc'])
for i,SN in enumerate(SNeList):
SNeList['id'][i]=SNeList['id'][i].replace('lc-','').replace('.list','')
# ----------- Read in the data JLA --------------------------
lcfile = JLA.get_full_path(params[options.lcfits])
SNe = Table.read(lcfile, format='fits')
nSNe=len(SNe)
print 'There are %d SNe in this sample' % (nSNe)
# sort it to match the listing in options.SNlist
indices = JLA.reindex_SNe(SNeList['id'], SNe)
SNe=SNe[indices]
# ---------- Compute the Jacobian ----------------------
# The Jacobian is an m by 4 matrix, where m is the number of SNe
# The columns are ordered in terms of Om, w, alpha and beta
J=[]
JLA_result={'Om':0.303,'w':-1.00,'alpha':0.141,'beta':3.102,'M_B':-19.05}
offset={'Om':0.01,'w':0.01,'alpha':0.01,'beta':0.01,'M_B':0.01}
nFit=4
cosmo1 = FlatwCDM(name='SNLS3+WMAP7', H0=70.0, Om0=JLA_result['Om'], w0=JLA_result['w'])
# Varying Om
cosmo2 = FlatwCDM(name='SNLS3+WMAP7', H0=70.0, Om0=JLA_result['Om']+offset['Om'], w0=JLA_result['w'])
J.append(5*numpy.log10((cosmo1.luminosity_distance(SNe['zcmb'])/cosmo2.luminosity_distance(SNe['zcmb']))[:,0]))
# varying alpha
J.append(1.0*offset['alpha']*SNe['x1'][:,0])
# varying beta
J.append(-1.0*offset['beta']*SNe['color'][:,0])
# varying M_B
J.append(offset['M_B']*numpy.ones(nSNe))
J = numpy.matrix(numpy.concatenate((J)).reshape(nSNe,nFit,order='F') * 100.)
# Set up the covariance matrices
systematic_terms = ['bias', 'cal', 'host', 'dust', 'model', 'nonia', 'pecvel', 'stat']
covmatrices = {'bias':params['bias'],
'cal':params['cal'],
'host':params['host'],
'dust':params['dust'],
'model':params['model'],
'nonia':params['nonia'],
'pecvel':params['pecvel'],
'stat':params['stat']}
if options.type in systematic_terms:
print "Using %s for the %s term" % (options.name,options.type)
covmatrices[options.type]=options.name
# Combine the matrices to compute the full covariance matrix, and compute its inverse
if options.all:
#read in the user provided matrix, otherwise compute it, and write it out
C=fits.getdata(JLA.get_full_path(params['all']))
else:
C=add_covar_matrices(covmatrices,params['diag'])
date=JLA.get_date()
fits.writeto('C_total_%s.fits' % (date), C, clobber=True)
Cinv=numpy.matrix(C).I
# Construct eta, a 3n vector
eta=numpy.zeros(3*nSNe)
for i,SN in enumerate(SNe):
eta[3*i]=SN['mb']
eta[3*i+1]=SN['x1']
eta[3*i+2]=SN['color']
# Construct A, a n x 3n matrix
A=numpy.zeros(nSNe*3*nSNe).reshape(nSNe,3*nSNe)
for i in range(nSNe):
A[i,3*i]=1.0
A[i,3*i+1]=JLA_result['alpha']
A[i,3*i+2]=-JLA_result['beta']
# ---------- Compute W ----------------------
# W has shape m * 3n, where m is the number of fit paramaters.
W=(J.T * Cinv * J).I * J.T* Cinv* numpy.matrix(A)
# Note that (J.T * Cinv * J) is a m x m matrix, where m is the number of fit parameters
# ----------- Compute V_x, where x represents the systematic uncertainty
result=[]
for term in systematic_terms:
cov=numpy.matrix(fits.getdata(JLA.get_full_path(covmatrices[term])))
if 'C_stat' in covmatrices[term]:
# Add diagonal term from Eq. 13 to the magnitude
sigma = numpy.genfromtxt(JLA.get_full_path(params['diag']),comments='#',usecols=(0,1,2),dtype='f8,f8,f8',names=['sigma_coh','sigma_lens','sigma_pecvel'])
for i in range(nSNe):
cov[3*i,3*i] += sigma['sigma_coh'][i] ** 2 + sigma['sigma_lens'][i] ** 2 + sigma['sigma_pecvel'][i] ** 2
V=W * cov * W.T
result.append(V[0,0])
print '%20s\t%5s\t%5s\t%s' % ('Term','sigma','var','Percentage')
for i,term in enumerate(systematic_terms):
if options.type!=None and term==options.type:
print '* %18s\t%5.4f\t%5.4f\t%4.1f' % (term,numpy.sqrt(result[i]),result[i],result[i]/numpy.sum(result)*100.)
else:
print '%20s\t%5.4f\t%5.4f\t%4.1f' % (term,numpy.sqrt(result[i]),result[i],result[i]/numpy.sum(result)*100.)
print '%20s\t%5.4f' % ('Total',numpy.sqrt(numpy.sum(result)))
return
