def run_minuit():
from minuit import Minuit
m = Minuit(chi2, b=5, a=10)
m.migrad()
m.hesse()
popt = m.values.values()
perr = np.array(m.errors.values())
# In scipy.optimize.curve_fit, the following factor is applied
# cov = cov * sum_sqr / self.nfree
factor = m.fval / (len(x) - 2)
perr *= np.sqrt(factor)
print ('minuit')
print('popt: {0}'.format(popt))
print('perr: {0}'.format(perr))
# Load data
x, y, y_err = load_data()
# Define model
def power_law(x, norm, gamma):
return norm * x ** -gamma
# Define fit statistic
def chi2(norm, gamma):
model = power_law(x, norm, gamma)
chi = (y - model) / y_err
return (chi ** 2).sum()
# Perform fit
m = Minuit(chi2, norm=1e-12, gamma=2)
m.migrad()
m.hesse()
#m.minos()
#print 'matrix:\n', m.matrix()
#print 'errors: ', m.errors
#print 'merrors:', m.merrors
# Report results
package = 'minuit'
gamma, norm = m.values.values()
gamma_err, norm_err = m.errors.values()
chi2 = m.fval
cov = m.covariance[('norm', 'gamma')]
corr = m.matrix(correlation=True)[0][1]
report_results(package, norm, norm_err, gamma, gamma_err,
phess = approx_hess(popt, chi2)
def approx_covar(hess, red_chi2):
return red_chi2 * inv(phess / 2.)
red_chi2 = chi2(popt) / (len(x) - len(p0))
pcov = approx_covar(popt, red_chi2)
print 'fmin and approx_hess results:'
print 'values:', popt
print 'errors:', np.sqrt(pcov.diagonal())
"""Just to check, here is what Minuit has to say"""
from minuit import Minuit
def chi2(a, b, c):
chi = yn - func(x, a, b, c)
return (chi ** 2).sum()
m = Minuit(chi2, a=2.5, b=1.3, c=0.5)
m.migrad()
m.hesse()
pcov = red_chi2 * np.array(m.matrix())
popt = np.array(m.args)
print 'minuit results'
print 'values:', popt
print 'errors:', np.sqrt(pcov.diagonal())
try:
raise
import matplotlib.pyplot as plt
plt.plot(x, yn, label='data')
yfit = func(x, *popt)
plt.plot(x, yfit, label='fit')
plt.show()