def test_drawcontour_show_sigma():
m = Minuit(f1, x=0, y=0, pedantic=False, print_level=1)
m.tol=1e-4
m.migrad()
assert_less(m.fval, 1e-6)
assert_almost_equal(m.values['x'], 1., places=3)
assert_almost_equal(m.values['y'], 1., places=3)
m.minos()
m.draw_contour('x','y',show_sigma=True)
# <codecell>
#we also provide convenience wrapper for drawing it
m.draw_profile('x');
# <codecell>
#2d contour NOT minos contour
x,y,z = m.contour('x','y',subtract_min=True)
cs = contour(x,y,z)
clabel(cs)
# <codecell>
#or a convenience wrapper
m.draw_contour('x','z');
# <markdowncell>
# ###Hesse and Minos
# <markdowncell>
# ####Hesse
# Hesse find the error by finding the inverse of second derivative matrix(hessian). The error assume parabolic shape at the minimum. Hesse error is symmetric by construct. Hesse is always called at the end of migrad to get the error. You normally don't need to call it manually.
# <codecell>
m.hesse()
# <markdowncell>
# <codecell>
ulh.show(m, parts=True)
# <codecell>
m.print_matrix()
# <codecell>
m.draw_profile('mass');#not exactly minos profile just a simple scan
# <codecell>
m.draw_contour('mass','f_0', show_sigma=False);
#not exactly minos contour though just a 2d scan
#Matt Bellis already signed up for this task.;
# <markdowncell>
# ####Note on complex PDF
# There is nothing preventing you from doing something like this:
# ```
# def mypdf(x,mass, gamma, m, c, f_0):
# return brietwigner(x, mass, gamma) + f_0*(m*x+c)/normalization
# ulh=UnbinnedLH(mypdf, data)
# m=Minuit(ulh, **initial_values)
# m.migrad()
# ```
#
def Hubble_diagram(zcmb,
zhel,
mB,
dmB,
X1,
dX1,
C,
dC,
M_stell,
IDJLA,
exp,
results,
cov_path,
sigma_mu_path,
fixe,
omgM=0.295,
alpha=0.141,
beta=3.101,
Mb=-19.05,
delta_M=-0.070):
"""
Function which make the hubble fit of the given compilation.
inputs :
-omgM: 1st free parameter to be fitted initialized to the 0.295 value if not precised
-alpha: 2nd free parameter to be fitted initialized to the 0.141 value if not precised
-beta: 3rd free parameter to be fitted initialized to the 3.101 value if not precised
-Mb: 4th free parameter to be fitted initialized to the -19.05 value if not precised
-delta_M: 5th free parameter to be fitted initialized to the -0.070 value if not precised
-fixe: when fixe=0 omgK and w are fixe, fixe = 1 w is fixe, fixe =2 omgK is fixe else all parameters are fixe
-zcmb: an array which contains the redshifts of the SNs
-mB: B band peak magnitude of the SNs
-dmB: uncertainty on mB
-X1: SALT2 shape parameter
-dX1: uncertainty on X1Cmu[N.diag_indices_from(Cmu)]
-dC: uncertainty on C
-C: colour parameter
-M_stell: the log_10 host stellar mass in units of solar mass
-IDJLA: index of the SNs from the 740 of jla used for the fit
-results : a file where some results wiil be written
- m : the iminuit object (see doc of iminuit for more information).
-ecarts5 : the residuals of the fit
"""
#check : need to have at least 2 SNe
'''f2,(test,P2,P3,P4,P5) = P.subplots(5, sharex=True, sharey=False, gridspec_kw=dict(height_ratios=[3,1,1,1,1]))'''
if len(zcmb) == 1 or len(zcmb) == 0:
results.write('Not enough data \n')
return 0
#Definition of the Chi2 object
chi2mini = Chi2(zcmb, zhel, mB, dmB, X1, dX1, C, dC, M_stell, IDJLA,
cov_path, sigma_mu_path)
#minimisation of the chi2
'''
the values of the free parameter can be initialized.
'''
# TO BE CLEANED
if fixe == 0:
m = Minuit(chi2mini.chi2,
omgM=0.295,
omgK=0,
w=-1,
alpha=0.141,
beta=3.101,
Mb=-19.05,
delta_M=-0.070,
limit_omgM=(0.2, 0.4),
limit_omgK=(-1, 1),
limit_w=(-1.4, 0.4),
limit_alpha=(0.1, 0.2),
limit_beta=(2.0, 4.0),
limit_Mb=(-20., -18.),
limit_delta_M=(-0.1, -0.0),
fix_omgM=False,
fix_omgK=True,
fix_w=True,
fix_alpha=False,
fix_beta=False,
fix_Mb=False,
fix_delta_M=False,
print_level=1)
elif fixe == 1:
# last_iter_args={u'fix_Mb': True, u'limit_w': None, u'fix_delta_M': True, u'error_omgL': 0.1672842193144214, u'error_omgM': 0.11284796124765262, 'delta_M': -0.07040462309885408, u'error_Mb': 0.02559618467415318, u'error_w': 1.0, u'error_alpha': 0.006593439955397084, u'fix_alpha': True, u'limit_alpha': None, 'Mb': -19.038807526119403, u'limit_omgM': None, u'limit_omgL': None, u'limit_Mb': None, 'beta': 3.0999314004965535, u'limit_delta_M': None, u'limit_beta': None, 'alpha': 0.14098769528058613, 'omgM': 0.20020038670359183, 'omgL': 0.561065865545341, u'fix_w': True, u'fix_beta': True, u'fix_omgM': False, u'fix_omgL': False, u'error_delta_M': 0.023111327883836057, u'error_beta': 0.08066293365248206, 'w': -1.0}
# m=Minuit(chi2mini.chi2,**last_iter_args)
# m=Minuit(chi2mini.chi2,omgM=0.2,omgL=0.55,w=-1,alpha=0.141,beta=3.101,Mb=-19.05,delta_M=-0.070,limit_omgM=(0,0.4),limit_omgL=(-1,1),limit_w=(-1.4,0.4),limit_alpha=(0.1,0.2),limit_beta=(2.0,4.0),limit_Mb=(-20.,-18.),limit_delta_M=(-0.1,-0.0),fix_omgM=False,fix_omgL=False,fix_w=True, fix_alpha=False, fix_beta=False, fix_Mb=False, fix_delta_M=False, print_level=1)
m = Minuit(chi2mini.chi2,
omgM=0.2,
omgL=0.55,
w=-1,
alpha=0.141,
beta=3.101,
Mb=-19.05,
delta_M=-0.070,
limit_omgM=(0, 0.4),
limit_omgL=(-1, 1),
limit_w=(-1.4, 0.4),
limit_alpha=(0.1, 0.2),
limit_beta=(2.0, 4.0),
limit_Mb=(-20., -18.),
limit_delta_M=(-0.1, -0.0),
fix_omgM=False,
fix_omgL=False,
fix_w=True,
fix_alpha=True,
fix_beta=True,
fix_Mb=True,
fix_delta_M=True,
print_level=1)
#m=Minuit(chi2mini.chi2,omgM=0.2,omgL=0.55,w=-1,alpha=0.141,beta=3.101,Mb=-19.05,delta_M=-0.070,fix_omgM=False,fix_omgL=False,fix_w=True, fix_alpha=False, fix_beta=False, fix_Mb=False, fix_delta_M=False, print_level=1)
elif fixe == 2:
m = Minuit(chi2mini.chi2,
omgM=0.2,
omgK=0,
w=-1,
alpha=0.141,
beta=3.101,
Mb=-19.05,
delta_M=-0.070,
limit_omgM=(0, 0.4),
limit_omgK=(-1, 1),
limit_w=(-1.4, 0.4),
limit_alpha=(0.1, 0.2),
limit_beta=(2.0, 4.0),
limit_Mb=(-20., -18.),
limit_delta_M=(-0.1, -0.0),
fix_omgM=False,
fix_omgK=True,
fix_w=False,
fix_alpha=False,
fix_beta=False,
fix_Mb=False,
fix_delta_M=False,
print_level=1)
else:
m = Minuit(chi2mini.chi2,
omgM=0.2,
omgK=0,
w=-1,
alpha=0.141,
beta=3.101,
Mb=-19.05,
delta_M=-0.070,
limit_omgM=(0, 0.4),
limit_omgK=(-1, 1),
limit_w=(-1.4, 0.4),
limit_alpha=(0.1, 0.2),
limit_beta=(2.0, 4.0),
limit_Mb=(-20., -18.),
limit_delta_M=(-0.1, -0.0),
fix_omgM=True,
fix_omgK=True,
fix_w=True,
fix_alpha=True,
fix_beta=True,
fix_Mb=True,
fix_delta_M=True,
print_level=1)
m.migrad()
return m
m.hesse()
chi2miniminuit = chi2mini.chi2tot #minimun chi2 value obtain by iminuit
#print(m.values)
#print(m.errors)
omgM = m.args[0]
omgK = m.args[1]
w = m.args[2]
alpha = m.args[3]
beta = m.args[4]
Mb = m.args[5]
delta_M = m.args[6]
#errors obtain by minuit
omgMerr = m.errors.get('omgM')
omgKerr = m.errors.get('omgL')
werr = m.errors.get('w')
alphaerr = m.errors.get('alpha')
betaerr = m.errors.get('beta')
Mberr = m.errors.get('Mb')
delta_Merr = m.errors.get('delta_M')
# cov_omg=m.hesse()
# cov_omg=m.matrix()
if fixe == 1:
# Pcov = P.plot()
# bX,bY,contourXY = m.mncontour('omgM', 'omgL', numpoints=20, sigma=1.0)
# bX,bY,contourXY = m.contour('omgM', 'omgL', bins=20, bound=2)
# contourXY -= chi2miniminuit
# Pcov=m.draw_contour('omgM', 'omgL', bins=20, bound=1)
Pcov = m.draw_mncontour('omgM', 'omgL')
# X,Y=N.meshgrid(N.linspace(0,0.3,1000),N.linspace(0,0.5,1000))
# Pcov = P.contour(bX,bY,contourXY,[1,2,9])
# P.show()
elif fixe == 2:
Pcov = P.plot()
# bins_X,bins_Y,contour_X_Y = m.contour('omgM', 'w', bins=20, bound=1)
m.draw_contour('omgM', 'w', bins=20, bound=1)
P.show()
#write some results in output
results.write('\\begin{tabular}{|c|l|}' + '\n' + '\\hline' + '\n')
results.write('chi2 / d.o.f& %.3f' %
((chi2mini.chi2tot) / (len(IDJLA) - 5)) + ' \\\\ \\hline \n')
results.write('chi2& %.3f' % (chi2mini.chi2tot) + ' \\\\ \\hline \n')
#Computation of the luminosity-distance modulus and its uncertainty for the minimized parameters
mufinal = muexp(mB, X1, C, alpha, beta, Mb, delta_M, M_stell)
dmufinal = dmuexp(dmB, dX1, dC, alpha, beta)
#Computation of the difference between the measured luminosity-distance modulus and the theorical one (residuals)
ecarts5 = ecarts(zcmb, zhel, mufinal, omgM, omgK, w)
#computation of the RMS,mean and their error of the distribution
#std5,std5err = comp_rms(N.array(ecarts5),(len(ecarts5)))
std5 = N.std(ecarts5)
std5err = RMSerr(ecarts5)
mean5 = N.mean(ecarts5)
mean5err = MEANerr(ecarts5)
results.write('mean of the residuals& %.5f' % mean5 + ' \\\\ \\hline \n')
sigma_mean5 = std5 / N.sqrt(len(ecarts5))
results.write('rms& %.4f' % (std5) + ' \\\\ \\hline \n')
#mean = N.mean(ecarts5)
#Computaion of the rms of the fit.
rms, err_rms = comp_rms(N.array(ecarts5), len(mB), err=True, variance=None)
results.write('omgM& %.4f' % (omgM) + ' +/- %.4f' % (omgMerr) +
' \\\\ \\hline \n')
results.write('omgK& %.4f' % (omgK) + ' +/- %.4f' % (omgKerr) +
' \\\\ \\hline \n')
results.write('w& %.4f' % (w) + ' +/- %.4f' % (werr) + ' \\\\ \\hline \n')
results.write('alpha& %.4f' % (alpha) + ' +/- %.4f' % (alphaerr) +
' \\\\ \\hline \n')
results.write('beta& %.4f' % (beta) + ' +/- %.4f' % (betaerr) +
' \\\\ \\hline \n')
results.write('Mb& %.4f' % (Mb) + ' +/- %.4f' % (Mberr) +
' \\\\ \\hline \n')
results.write('delta-M& %.4f' % (delta_M) + ' +/- %.4f' % (delta_Merr) +
' \\\\ \\hline \n')
results.write('\\end{tabular}')
return m
