def test_sample_to_event(dim, max_count_per_mode):
"""Test if function ``similarity.sample_to_event`` gives the correct set of events when
applied to all orbits with a fixed number of photons ``dim``. This test ensures that orbits
exceeding the ``max_count_per_mode`` value are attributed the ``None`` event and that orbits
not exceeding the ``max_count_per_mode`` are attributed the event ``dim``."""
orb = all_orbits[dim]
target_events = all_events[(dim, max_count_per_mode)]
ev = [similarity.sample_to_event(o, max_count_per_mode) for o in orb]
assert ev == target_events
# statistically more likely to be observed. However, we are interested in coarse-graining further
# into *events*, which correspond to a combination of orbits with the same photon number such
# that the number of photons counted in each mode does not exceed a fixed value
# ``max_count_per_mode``. To understand this, let's look at all of the orbits with a photon
# number of 5:
print(list(similarity.orbits(5)))
##############################################################################
# All 5-photon samples belong to one of the orbits above. A 5-photon event with
# ``max_count_per_mode = 3`` means that we include the orbits: ``[[1, 1, 1, 1, 1], [2, 1, 1, 1],
# [3, 1, 1], [2, 2, 1], [3, 2]]`` and ignore the orbits ``[[4, 1], [5]]``. For example,
# the sample ``[0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0]`` is a 5-photon event:
print(
similarity.sample_to_event(
[0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0], 3))
##############################################################################
# Samples with more than ``max_count_per_mode`` in any mode are not counted as part of the event:
print(
similarity.sample_to_event(
[0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 3))
##############################################################################
# Now that we have mastered orbits and events, how can we make a feature vector? It was shown in
# :cite:`schuld2019quantum` that one way of making a feature vector of a graph is through the
# frequencies of events. Specifically, for a :math:`k` photon event :math:`E_{k, n_{\max}}`
# with maximum count per mode :math:`n_{\max}` and corresponding probability :math:`p_{k,
# n_{\max}}:=p_{E_{k, n_{\max}}}(G)` with respect to a graph :math:`G`, a feature vector can be
# written as