import numpy as np
"""
This module contains functions for computing log(likelihood).
"""
[docs]def chi2_lnlike(data, errors, model, seppa_indices):
"""Compute Log of the chi2 Likelihood
Args:
data (np.array): Nobsx2 array of data, where data[:,0] = sep/RA/RV
for every epoch, and data[:,1] = corresponding pa/DEC/np.nan
errors (np.array): Nobsx2 array of errors for each data point. Same
format as ``data``
model (np.array): Nobsx2xM array of model predictions, where M is the \
number of orbits being compared against the data. If M is 1, \
``model`` can be 2 dimensional.
seppa_indices (list): list of epoch numbers whose observations are
given in sep/PA. This list is located in System.seppa.
Returns:
np.array: Nobsx2xM array of chi-squared values.
.. note::
**Example**: We have 8 epochs of data for a system. OFTI returns an
array of 10,000 sets of orbital parameters. The ``model`` input for
this function should be an array of dimension 8 x 2 x 10,000.
"""
if np.ndim(model) == 3:
# move M dimension to the primary axis, so that numpy knows to iterate over it
model = np.rollaxis(model, 2, 0) # now MxNobsx2 in dimensions
third_dim = True
elif np.ndim(model) == 2:
model.shape = (1,) + model.shape
third_dim = False
residual = (data - model)
# if there are PA values, we should take the difference modulo angle wrapping
if np.size(seppa_indices) > 0:
residual[:, seppa_indices, 1] = (residual[:, seppa_indices, 1] + 180.) % 360. - 180.
chi2 = -0.5 * residual**2 / errors**2
if third_dim:
# move M dimension back to the last axis
model = np.rollaxis(model, 0, 3) # now MxNobsx2 in dimensions
chi2 = np.rollaxis(chi2, 0, 3) # same with chi2
else:
model.shape = model.shape[1:]
chi2.shape = chi2.shape[1:]
return chi2