def plot_counts(self,
x,
S,
B,
logPgg,
xerr='None',
alpha=0.2,
filename='counts.pdf'):
"""
Plot the expected counts spectra of a gamma-ray observation.
Arguments
---------
S: dictionary with n-dim arrays, containing the expected signal counts
B: dictionary with n-dim arrays, containing the expected bkg counts
logPgg: Function for photon survival log(probability) versus log(energy)
kwargs
------
xerr: (n+1)-dim array, bin boundaries. If not given it will be caclulated
alpha: float, ratio of exposure between ON and OFF
"""
import matplotlib.pyplot as plt
# calculate the bin bounds
if xerr == 'None':
xerr = calc_bin_bounds(x)
xplot = 10.**np.linspace(np.log10(xerr[0]), np.log10(xerr[-1]), 200)
# plot everything
fig = plt.figure(1)
ax = plt.subplot(111)
ax.set_xscale('log')
ax.set_yscale('log')
cp = plt.cm.Dark2
marker = ['s', 'o']
for i, k in enumerate(S.keys()):
plt.errorbar(
x,
S[k],
xerr=[x - xerr[:-1], xerr[1:] - x],
ls='None',
marker='o',
lw=1.,
color=cp(i / (len(S.keys()) + 1.)),
mec=cp(i / (len(S.keys()) + 1.)),
mfc='None',
label='exp. signal {0:s}'.format(k),
)
plt.errorbar(
x,
B[k],
xerr=[x - xerr[:-1], xerr[1:] - x],
ls='None',
lw=1.,
marker='s',
color=cp(i / (len(S.keys()) + 1.)),
mec=cp(i / (len(S.keys()) + 1.)),
mfc='None',
label='exp. bkg {0:s}'.format(k),
)
plt.legend(loc=0)
plt.xlabel('Energy')
plt.ylabel('$\mathrm{d}N / \mathrm{d} E$')
v = plt.axis()
plt.axis([xerr[0] * 0.8, xerr[-1] / 0.8, v[2], v[3]])
ax2 = ax.twinx()
ax2.set_xscale('log')
ax2.set_yscale('log')
plt.plot(xplot,
np.exp(-self.tau.opt_depth_array(self.z, xplot))[0],
lw=2.,
color='0.')
plt.plot(xplot,
np.exp(logPgg(np.log(xplot * 1e3))),
lw=2.,
color='red')
v = plt.axis()
plt.axis([xerr[0] * 0.8, xerr[-1] / 0.8, v[2], v[3]])
plt.savefig(filename + '.spec', format=filename.split('.')[-1])
# histogramm with NON values
from scipy.stats import poisson
fig = plt.figure(2)
for i, k in enumerate(S.keys()):
NonExp = (S[k] + B[k])[0] * np.ones(5000)
NON = poisson.rvs(NonExp)
plt.hist(NON, label=k)
plt.legend(loc=0)
plt.savefig(filename + '.hist', format=filename.split('.')[-1])
plt.show()
return
def plot_spectrum(self,
x,
y,
s,
logPgg='None',
xerr='None',
filename='spectrum.pdf',
Emin=0.,
Emax=0.):
"""
Plot an observed gamma-ray spectrum together with it's abosrption corrected (w/ and w/o ALPs) versions.
Arguments
---------
x: n-dim array, Energy of spectrum in TeV
y: n-dim array, observed Flux of spectrum in dN / dE
s: n-dim array, dF
kwargs
------
logPgg: Function for photon survival log(probability) versus log(energy). If not given it will be calculated.
xerr: (n+1)-dim array, bin boundaries. If not given it will be caclulated
Emin: minimum plot energy in TeV
Emax: maximum plot energy in TeV
"""
import matplotlib.pyplot as plt
assert x.shape[0] == y.shape[0]
assert x.shape[0] == s.shape[0]
m = y > 0.
x = x[m]
y = y[m]
s = s[m]
stat, p, err, merr, cov, func, dfunc = {}, {}, {}, {}, {}, {}, {}
f, df = {'obs': y}, {'obs': s}
# calculate the bin bounds
if xerr == 'None':
xerr = calc_bin_bounds(x)
if not Emin:
Emin = xerr[0]
if not Emax:
Emin = xerr[-1]
xplot = 10.**np.linspace(np.log10(Emin), np.log10(Emax), 200)
# pl fit to observed spectrum
stat['obs'], p['obs'], err['obs'], merr['obs'], cov[
'obs'] = MinuitFitPL(x, y, s, full_output=True)
func['obs'] = pl
dfunc['obs'] = butterfly_pl
# calculate the average absorption correction
pggAve = self.calc_pggave_conversion(xerr * 1e3,
func=func['obs'],
pfunc=p['obs'],
logPgg=logPgg)
tauAve = self.tau.opt_depth_Ebin(self.z, xerr, func['obs'], p['obs'])
atten = np.exp(-tauAve)
f['alp'] = y / pggAve
df['alp'] = s / pggAve
f['tau'] = y / atten
df['tau'] = s / atten
# pl fit to deabs spectra
stat['alp'], p['alp'], err['alp'], merr['alp'], cov[
'alp'] = MinuitFitPL(x, y / pggAve, s / pggAve, full_output=True)
func['alp'] = pl
dfunc['alp'] = butterfly_pl
stat['tau'], p['tau'], err['tau'], merr['tau'], cov[
'tau'] = MinuitFitPL(x, y / atten, s / atten, full_output=True)
func['tau'] = pl
dfunc['tau'] = butterfly_pl
for k in stat.keys():
print '{0:s}:'.format(k)
for l in p[k].keys():
print "{0:s} = {1:.2e} +/- {2:.2e}".format(
l, p[k][l], err[k][l])
# plot everything
fig = plt.figure()
ax = plt.subplot(111)
ax.set_xscale('log')
ax.set_yscale('log')
cp = plt.cm.Dark2
marker = {'obs': 's', 'tau': 'v', 'alp': 'o'}
label = {
'obs': 'observed',
'tau': 'deabs. w/o ALPs',
'alp': 'deabs. w/ ALPs'
}
for i, k in enumerate(f.keys()):
plt.errorbar(
x,
f[k],
yerr=df[k],
xerr=[x - xerr[:-1], xerr[1:] - x],
ls='None',
marker=marker[k],
color=cp(i / (len(f.keys()) + 1.)),
label=label[k],
)
plt.plot(xplot,
func[k](p[k], xplot),
ls='-',
lw=1.,
color=cp(i / (len(f.keys()) + 1.)))
plt.fill_between(xplot,
func[k](p[k], xplot) *
(1. - dfunc[k](p[k], xplot, err[k], cov[k])),
y2=func[k](p[k], xplot) *
(1. + dfunc[k](p[k], xplot, err[k], cov[k])),
lw=1.,
facecolor='None',
edgecolor=cp(i / (len(f.keys()) + 1.)))
plt.legend(loc=0)
plt.xlabel('Energy')
plt.ylabel('$\mathrm{d}N / \mathrm{d} E$')
v = plt.axis()
plt.axis([Emin * 0.8, Emax / 0.8, v[2], v[3]])
ax2 = ax.twinx()
ax2.set_xscale('log')
ax2.set_yscale('log')
plt.plot(xplot,
np.exp(logPgg(np.log(xplot * 1e3))),
lw=2.,
color='red')
plt.plot(xplot,
np.exp(-self.tau.opt_depth_array(self.z, xplot))[0],
lw=2.,
color='0.',
ls='--')
v = plt.axis()
plt.axis([Emin * 0.8, Emax / 0.8, v[2], v[3]])
plt.savefig(filename, format=filename.split('.')[-1])
plt.show()
return
def plot_counts(self, x,S,B, logPgg, xerr = 'None',alpha = 0.2,filename = 'counts.pdf'):
"""
Plot the expected counts spectra of a gamma-ray observation.
Arguments
---------
S: dictionary with n-dim arrays, containing the expected signal counts
B: dictionary with n-dim arrays, containing the expected bkg counts
logPgg: Function for photon survival log(probability) versus log(energy)
kwargs
------
xerr: (n+1)-dim array, bin boundaries. If not given it will be caclulated
alpha: float, ratio of exposure between ON and OFF
"""
import matplotlib.pyplot as plt
# calculate the bin bounds
if xerr == 'None':
xerr = calc_bin_bounds(x)
xplot = 10.**np.linspace(np.log10(xerr[0]),np.log10(xerr[-1]),200)
# plot everything
fig = plt.figure(1)
ax = plt.subplot(111)
ax.set_xscale('log')
ax.set_yscale('log')
cp = plt.cm.Dark2
marker = ['s','o']
for i,k in enumerate(S.keys()):
plt.errorbar(x,S[k], xerr = [x - xerr[:-1], xerr[1:] - x],
ls = 'None',
marker = 'o',
lw = 1.,
color = cp(i / (len(S.keys()) + 1.)),
mec = cp(i / (len(S.keys()) + 1.)),
mfc = 'None',
label = 'exp. signal {0:s}'.format(k),
)
plt.errorbar(x,B[k], xerr = [x - xerr[:-1], xerr[1:] - x],
ls = 'None',
lw = 1.,
marker = 's',
color = cp(i / (len(S.keys()) + 1.)),
mec = cp(i / (len(S.keys()) + 1.)),
mfc = 'None',
label = 'exp. bkg {0:s}'.format(k),
)
plt.legend(loc = 0)
plt.xlabel('Energy')
plt.ylabel('$\mathrm{d}N / \mathrm{d} E$')
v = plt.axis()
plt.axis([xerr[0] * 0.8, xerr[-1] / 0.8, v[2], v[3]])
ax2 = ax.twinx()
ax2.set_xscale('log')
ax2.set_yscale('log')
plt.plot(xplot, np.exp(-self.tau.opt_depth_array(self.z,xplot))[0],
lw = 2.,
color = '0.'
)
plt.plot(xplot, np.exp(logPgg(np.log(xplot * 1e3))),
lw = 2.,
color = 'red'
)
v = plt.axis()
plt.axis([xerr[0] * 0.8, xerr[-1] / 0.8, v[2], v[3]])
plt.savefig(filename + '.spec', format = filename.split('.')[-1])
# histogramm with NON values
from scipy.stats import poisson
fig = plt.figure(2)
for i,k in enumerate(S.keys()):
NonExp = (S[k] + B[k])[0] * np.ones(5000)
NON = poisson.rvs(NonExp)
plt.hist(NON, label = k)
plt.legend(loc = 0)
plt.savefig(filename + '.hist', format = filename.split('.')[-1])
plt.show()
return
def plot_spectrum(self, x,y,s, logPgg = 'None', xerr = 'None',filename = 'spectrum.pdf',Emin = 0., Emax = 0.):
"""
Plot an observed gamma-ray spectrum together with it's abosrption corrected (w/ and w/o ALPs) versions.
Arguments
---------
x: n-dim array, Energy of spectrum in TeV
y: n-dim array, observed Flux of spectrum in dN / dE
s: n-dim array, dF
kwargs
------
logPgg: Function for photon survival log(probability) versus log(energy). If not given it will be calculated.
xerr: (n+1)-dim array, bin boundaries. If not given it will be caclulated
Emin: minimum plot energy in TeV
Emax: maximum plot energy in TeV
"""
import matplotlib.pyplot as plt
assert x.shape[0] == y.shape[0]
assert x.shape[0] == s.shape[0]
m = y > 0.
x = x[m]
y = y[m]
s = s[m]
stat,p,err,merr,cov,func,dfunc = {},{},{},{},{},{},{}
f,df = {'obs': y}, {'obs': s}
# calculate the bin bounds
if xerr == 'None':
xerr = calc_bin_bounds(x)
if not Emin:
Emin = xerr[0]
if not Emax:
Emin = xerr[-1]
xplot = 10.**np.linspace(np.log10(Emin),np.log10(Emax),200)
# pl fit to observed spectrum
stat['obs'],p['obs'], err['obs'],merr['obs'], cov['obs'] = MinuitFitPL(x,y,s , full_output = True)
func['obs'] = pl
dfunc['obs'] = butterfly_pl
# calculate the average absorption correction
pggAve = self.calc_pggave_conversion(xerr * 1e3, func=func['obs'], pfunc=p['obs'], logPgg = logPgg)
tauAve = self.tau.opt_depth_Ebin(self.z,xerr,func['obs'],p['obs'])
atten = np.exp(-tauAve)
f['alp'] = y / pggAve
df['alp'] = s / pggAve
f['tau'] = y / atten
df['tau'] = s / atten
# pl fit to deabs spectra
stat['alp'],p['alp'], err['alp'],merr['alp'], cov['alp'] = MinuitFitPL(x,y / pggAve,s / pggAve , full_output = True)
func['alp'] = pl
dfunc['alp'] = butterfly_pl
stat['tau'],p['tau'], err['tau'],merr['tau'], cov['tau'] = MinuitFitPL(x,y / atten ,s / atten, full_output = True)
func['tau'] = pl
dfunc['tau'] = butterfly_pl
for k in stat.keys():
print '{0:s}:'.format(k)
for l in p[k].keys():
print "{0:s} = {1:.2e} +/- {2:.2e}".format(l,p[k][l],err[k][l])
# plot everything
fig = plt.figure()
ax = plt.subplot(111)
ax.set_xscale('log')
ax.set_yscale('log')
cp = plt.cm.Dark2
marker = {'obs': 's', 'tau': 'v', 'alp':'o'}
label = {'obs': 'observed', 'tau': 'deabs. w/o ALPs', 'alp':'deabs. w/ ALPs'}
for i,k in enumerate(f.keys()):
plt.errorbar(x,f[k], yerr = df[k], xerr = [x - xerr[:-1], xerr[1:] - x],
ls = 'None',
marker = marker[k],
color = cp(i / (len(f.keys()) + 1.)),
label = label[k],
)
plt.plot(xplot, func[k](p[k],xplot),
ls = '-',
lw = 1.,
color = cp(i / (len(f.keys()) + 1.))
)
plt.fill_between(xplot, func[k](p[k],xplot)*(1. - dfunc[k](p[k],xplot,err[k],cov[k])),
y2 = func[k](p[k],xplot)*(1. + dfunc[k](p[k],xplot,err[k],cov[k])),
lw = 1.,
facecolor = 'None',
edgecolor = cp(i / (len(f.keys()) + 1.))
)
plt.legend(loc = 0)
plt.xlabel('Energy')
plt.ylabel('$\mathrm{d}N / \mathrm{d} E$')
v = plt.axis()
plt.axis([Emin * 0.8, Emax / 0.8, v[2], v[3]])
ax2 = ax.twinx()
ax2.set_xscale('log')
ax2.set_yscale('log')
plt.plot(xplot, np.exp(logPgg(np.log(xplot * 1e3))),
lw = 2.,
color = 'red'
)
plt.plot(xplot, np.exp(-self.tau.opt_depth_array(self.z,xplot))[0],
lw = 2.,
color = '0.',
ls = '--'
)
v = plt.axis()
plt.axis([Emin * 0.8, Emax / 0.8, v[2], v[3]])
plt.savefig(filename, format = filename.split('.')[-1])
plt.show()
return
def __init__(self,x,y,s,bins = None, **kwargs):
"""
Class to fit Powerlaw to data using minuit.migrad
Data is corrected for absorption using the B-field environments of either an AGN Jet or intracluster medium and the GMF
y(x) = p['Prefactor'] * ( x / p['Scale'] ) ** p['Index']
y_abs = < P gg > * y_obs
< P gg > is bin averaged transfer function including ALPs.
Additional fit parameters are B,g,m,Rmax,R_BLR,n
Parameters
----------
x: n-dim array containing the measured x values in TeV
y: n-dim array containing the measured y values, i.e. y = y(x)
s: n-dim array with (symmetric) measurment uncertainties on y
kwargs
------
bins: n+1 dim array with boundaries. if none, comupted from x data.
func: Function that describes the observed spectrum and takes x and pobs as parameters, y = func(x,pobs)
pobs: parameters for function
and all kwargs from PhotALPsConv.calc_conversion.Calc_Conv.
"""
# --- Set the defaults
kwargs.setdefault('func',None)
kwargs.setdefault('pobs',None)
# --------------------
kwargs.setdefault('nE',30)
kwargs.setdefault('Esteps',50)
# --------------------
for k in kwargs.keys():
if kwargs[k] == None:
raise TypeError("kwarg {0:s} cannot be None type.".format(k))
if not len(x) == len(y) or not len(x) == len(s) or not len(y) == len(s):
raise TypeError("Lists must have same length!")
super(Fit_JetICMGMF,self).__init__(**kwargs) # init the jet mixing and gmf mixing, see e.g.
# http://stackoverflow.com/questions/3277367/how-does-pythons-super-work-with-multiple-inheritance
# for a small example
self.__dict__.update(kwargs) # form instance of kwargs
self.x = np.array(x)
self.y = np.array(y)
self.yerr = np.array(s)
self.exp = floor(np.log10(y[0]))
self.y /= 10.**self.exp
self.yerr /= 10.**self.exp
if bins == None or not len(bins) == x.shape[0] + 1:
self.bins = calc_bin_bounds(x)
# --- create 2-dim energy and tau arrays to compute average mixing in each energy bin
for i,E in enumerate(self.bins):
if not i:
self.logE_array = np.linspace(np.log(E),np.log(self.bins[i+1]),self.nE)
self.t_array = self.tau.opt_depth_array(self.z,np.exp(self.logE_array))[0]
elif i == len(self.bins) - 1:
break
else:
logE = np.linspace(np.log(E),np.log(self.bins[i+1]),self.nE)
self.t_array = np.vstack((self.t_array,self.tau.opt_depth_array(self.z,np.exp(logE))[0]))
self.logE_array = np.vstack((self.logE_array,logE))
return
def __init__(self, x, y, s, bins=None, **kwargs):
"""
Class to fit Powerlaw to data using minuit.migrad
Data is corrected for absorption using the B-field environments of either an AGN Jet or intracluster medium and the GMF
y(x) = p['Prefactor'] * ( x / p['Scale'] ) ** p['Index']
y_abs = < P gg > * y_obs
< P gg > is bin averaged transfer function including ALPs.
Additional fit parameters are B,g,m,Rmax,R_BLR,n
Parameters
----------
x: n-dim array containing the measured x values in TeV
y: n-dim array containing the measured y values, i.e. y = y(x)
s: n-dim array with (symmetric) measurment uncertainties on y
kwargs
------
bins: n+1 dim array with boundaries. if none, comupted from x data.
func: Function that describes the observed spectrum and takes x and pobs as parameters, y = func(x,pobs)
pobs: parameters for function
and all kwargs from PhotALPsConv.calc_conversion.Calc_Conv.
"""
# --- Set the defaults
kwargs.setdefault('func', None)
kwargs.setdefault('pobs', None)
# --------------------
kwargs.setdefault('nE', 30)
kwargs.setdefault('Esteps', 50)
# --------------------
for k in kwargs.keys():
if kwargs[k] == None:
raise TypeError("kwarg {0:s} cannot be None type.".format(k))
if not len(x) == len(y) or not len(x) == len(s) or not len(y) == len(
s):
raise TypeError("Lists must have same length!")
super(Fit_JetICMGMF, self).__init__(
**kwargs) # init the jet mixing and gmf mixing, see e.g.
# http://stackoverflow.com/questions/3277367/how-does-pythons-super-work-with-multiple-inheritance
# for a small example
self.__dict__.update(kwargs) # form instance of kwargs
self.x = np.array(x)
self.y = np.array(y)
self.yerr = np.array(s)
self.exp = floor(np.log10(y[0]))
self.y /= 10.**self.exp
self.yerr /= 10.**self.exp
if bins == None or not len(bins) == x.shape[0] + 1:
self.bins = calc_bin_bounds(x)
# --- create 2-dim energy and tau arrays to compute average mixing in each energy bin
for i, E in enumerate(self.bins):
if not i:
self.logE_array = np.linspace(np.log(E),
np.log(self.bins[i + 1]),
self.nE)
self.t_array = self.tau.opt_depth_array(
self.z, np.exp(self.logE_array))[0]
elif i == len(self.bins) - 1:
break
else:
logE = np.linspace(np.log(E), np.log(self.bins[i + 1]),
self.nE)
self.t_array = np.vstack(
(self.t_array,
self.tau.opt_depth_array(self.z, np.exp(logE))[0]))
self.logE_array = np.vstack((self.logE_array, logE))
return