orientation_mlem

anri.index.orientation_mlem(d, U, B, rings, geom, bins, etacut=0.2, n_iter=20, qc=256, log=<built-in function print>, censor=0.0, return_model=False)

Fit one occupancy per orientation to a row-summed histogram by MLEM, and score each orientation.

The predictions of each orientation are computed afresh in every pass, so memory stays at a chunk of qc orientations whatever the number of orientations.

Parameters:

• d (Array | ndarray | bool | number | bool | int | float | complex) – [n_rings * n_e * n_o] histogram with the dty rows summed (e.g. the voxel fit’s histogram, summed over rows)

• U (Array | ndarray | bool | number | bool | int | float | complex) – [Nq, 3, 3] orientations, e.g. the grid orientations above chance completeness

• B (Array | ndarray | bool | number | bool | int | float | complex) – [3, 3] B matrix

• rings (dict) – From anri.index.ring_table() (“hkls”, “ring_j” and, optionally, “F2”)

• geom (dict) – Geometry dict, see anri.index.predict()

• bins (tuple) – (b_e, b_o, n_e, n_o, om0): the histogram’s eta and omega bin widths (degrees) and counts, and its first omega bin edge

• etacut (float, default: 0.2) – Reflections with |sin eta| at or below this are not used

• n_iter (int, default: 20) – MLEM iterations

• qc (int, default: 256) – Orientations per chunk

• log (Callable, default: <built-in function print>) – Progress messages

• censor (float, default: 0.0) – Empty bins censored above this many counts per bin, in the fit and in the likelihood ratio (anri.index.censored_ratio()); 0: plain Poisson

• return_model (bool, default: False) – Also return the fitted histogram, e.g. for its deviance (anri.index.deviance())

Returns:

• occupancy (np.ndarray) – [Nq] global occupancy of each orientation (in the units of d over Lorentz x polarisation x F^2)

• likelihood_ratio (np.ndarray) – [Nq] increase in the Poisson deviance if that orientation alone were removed, the others fixed: 2 sum_b [d_b log(mu_b / (mu_b - g a_b)) - g a_b] over observed bins (empty bins: the change in max(mu_b - censor, 0)). About chi-square with one degree of freedom for an orientation that is not there, so ~25 is 5 sigma.

• model (np.ndarray) – [n_cells] the fitted histogram, if return_model