def test_chichi():
magic_residuals = mock.MagicMock()
parameters = []
magic_residuals.residuals_fn.return_value = np.array([0, 1, 50])
parameters2 = [0, 6, 5]
chichi = microltoolbox.chichi(magic_residuals.residuals_fn, parameters2)
assert chichi == 2501
def lmarquardt(self):
"""The LM method. This is based on the Levenberg-Marquardt algorithm:
"A Method for the Solution of Certain Problems in Least Squares"
Levenberg, K. Quart. Appl. Math. 2, 1944, p. 164-168
"An Algorithm for Least-Squares Estimation of Nonlinear Parameters"
Marquardt, D. SIAM J. Appl. Math. 11, 1963, p. 431-441
Based on scipy.optimize.leastsq python routine, which is based on MINPACK's lmdif and
lmder
algorithms (fortran based).
The objective function is :func:`residuals_LM`.
The starting point parameters are self.guess.
the Jacobian is given by :func:`LM_Jacobian`.
The fit is performed on all parameters : Paczynski parameters and telescopes fluxes.
:return: a tuple containing (fit_results, covariance_matrix, computation_time)
:rtype: tuple
**WARNING**:
ftol (relative error desired in the sum of square) is set to 10^-6
maxfev (maximum number of function call) is set to 50000
These limits can avoid the fit to properly converge (expected to be rare :))
"""
starting_time = python_time.time()
# use the analytical Jacobian (faster) if no second order are present, else let the
# algorithm find it.
if self.guess == []:
self.guess = self.initial_guess()
if self.model.Jacobian_flag == 'OK':
lmarquardt_fit = scipy.optimize.leastsq(self.residuals_LM,
self.guess,
maxfev=50000,
Dfun=self.LM_Jacobian,
col_deriv=0,
full_output=1,
ftol=10**-6,
xtol=10**-10,
gtol=10**-5)
else:
lmarquardt_fit = scipy.optimize.leastsq(self.residuals_LM,
self.guess,
maxfev=50000,
full_output=1,
ftol=10**-6,
xtol=10**-10,
gtol=10**-5,
factor=0.1)
# import pdb;
# pdb.set_trace()
computation_time = python_time.time() - starting_time
fit_result = lmarquardt_fit[0].tolist()
fit_result.append(
microltoolbox.chichi(self.residuals_LM, lmarquardt_fit[0]))
n_data = 0.0
for telescope in self.event.telescopes:
n_data = n_data + telescope.n_data('flux')
n_parameters = len(self.model.model_dictionnary)
try:
# Try to extract the covariance matrix from the lmarquard_fit output
if np.all(lmarquardt_fit[1].diagonal() > 0) & (lmarquardt_fit[1]
is not None):
# Normalise the output by the reduced chichi
covariance_matrix = lmarquardt_fit[1] * fit_result[-1] / (
n_data - n_parameters)
# Try to do it "manually"
else:
print(' Attempt to construct a rough covariance matrix')
jacobian = self.LM_Jacobian(fit_result)
covariance_matrix = np.linalg.inv(np.dot(jacobian.T, jacobian))
# Normalise the output by the reduced chichi
covariance_matrix = covariance_matrix * fit_result[-1] / (
n_data - n_parameters)
# Construct a dummy covariance matrix
if np.any(lmarquardt_fit[1].diagonal() > 0):
print('Bad covariance covariance matrix')
covariance_matrix = np.zeros(
(len(self.model.model_dictionnary),
len(self.model.model_dictionnary)))
# Construct a dummy covariance matrix
except:
print('Bad covariance covariance matrix')
covariance_matrix = np.zeros((len(self.model.model_dictionnary),
len(self.model.model_dictionnary)))
# import pdb; pdb.set_trace()
print(sys._getframe().f_code.co_name,
' : Levenberg_marquardt fit SUCCESS')
print(fit_result)
return fit_result, covariance_matrix, computation_time