This module contains a few python functions to run Brute-force scans for rectangular cut optimization.

To install ahoi run

python3 -m pip install [--user] ahoi

Use --user if not in a virtual environment or conda environment.

It's recommended to use python3, but currently python2 is also supported.

The basic functionality uses a masks_list which is a list of lists or a list of 2D numpy arrays that represent pass flags for selection criteria.

For example, the following represents pass flags for the criteria >0, >0.1, >0.2, ..., >0.9 for 5 random uniform variables in 10000 events:

import numpy as np
np.random.seed(42)
x = np.random.rand(10000, 5)
masks_list = [[x[:,i] > v for v in np.linspace(0, 0.9, 10)] for i in range(x.shape[1])]

To count all matching combinations for all criteria on each variable run

import ahoi
counts = ahoi.scan(masks_list)

The entry [0, 1, 2, 3, 4] of counts will contain the number of matching events where the first column of x is >0, the second one >0.1, the third one >0.2 etc.

>>> counts[0, 1, 2, 3, 4]
3032
>>> np.count_nonzero((x[:,0] > 0) & (x[:,1] > 0.1) & (x[:,2] > 0.2) & (x[:,3] > 0.3) & (x[:,4] > 0.4))
3032

You can also pass weights

weights = np.random.normal(loc=1, size=len(x))
counts, sumw, sumw2 = ahoi.scan(masks_list, weights=weights)

The arrays sumw and sumw2 will contain the sum of weights and sum of squares of weights for matching combinations. The sum of squares of weights can be used to estimate the statistical uncertainty on the sum of weights ($\sigma = \sqrt{\sum w_i^2}$).

>>> sumw[0, 1, 2, 3, 4]
3094.2191136427627
>>> np.dot(
...     (x[:,0] > 0) & (x[:,1] > 0.1) & (x[:,2] > 0.2) & (x[:,3] > 0.3) & (x[:,4] > 0.4),
...     weights
... )
3094.219113642755
>>> np.sqrt(sumw2[0, 1, 2, 3, 4])
78.5528532026876
>>> np.sqrt(
...     np.dot(
...         (x[:,0] > 0) & (x[:,1] > 0.1) & (x[:,2] > 0.2) & (x[:,3] > 0.3) & (x[:,4] > 0.4),
...         weights ** 2
...     )
... )
78.55285320268761

Have a look at the examples for a tutorial that explains how to use this for solving a classification problem.

Run the tests and coverage report inside the project directory with

python3 -m pytest --cov=ahoi --doctest-modules
coverage html