def count_pairs(assignments, v1, v2, M):
"""Construct sufficient statistics for (v1, v2) pairs.
Args:
assignments: An _ x V assignment matrix with values in range(M).
v1, v2: Column ids of the assignments matrix.
M: The number of possible assignment bins.
Returns:
An M x M array of counts.
"""
assert v1 != v2
pairs = assignments[:, v1].astype(np.int32) * M + assignments[:, v2]
return np.bincount(pairs, minlength=M * M).reshape((M, M))
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