intdistribute.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# intdistribute.py
# Created by K. Sriram on 2018-10-29
#
# MIT License
#
# Copyright (c) 2018 Sriram Krishna
#
# Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated
# documentation files (the "Software"), to deal in the Software without restriction, including without limitation the
# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit
# persons to whom the Software is furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in all copies or substantial portions of the
# Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
# WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
# COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
# OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

import numpy as np

EPSILON = 1e-4

def intdistribute(total, distribution, epsilon=EPSILON):
    """
    Function to distribute a given integer into several bins so that they roughly follow a given ratio.

    Parameters
    ----------
    total : int
        The number to be divided into bins.
    distribution : array_like
        The ratios into which the number is to be divided. This should add up to 1.
    epsilon : float, optional
        Threshold used by the algorithm to differentiate between ints and non-ints.
    
    Returns
    -------
    ndarray(dtype=int)
        The integers which add up to total and are roughly in the ratio given by distribution.
    
    Notes
    -----
    The algorithm tries to minimize the sum of deviations from the real numbers in the requisite ratios.
    
    Examples
    --------
    >>> intdistribute(5,[0.25,0.75])
    array([1, 4])
    """
    if not isinstance(distribution, np.ndarray):
        distribution = np.array(distribution)
    if np.absolute(np.around(total) - total) > epsilon:
        raise TypeError('Total not integer: {:.2f}'.format(total))
    if np.absolute(distribution.sum() - 1) > epsilon:
        raise TypeError('Distribution not proper. Sum = {:.2f}'.format(np.absolute(distribution.sum() - 1)))
    if len(distribution.shape) != 1:
        raise ValueError('Multi-dimensional arrays are not (yet) supported as distribution.')
    total = int(total+0.5)
    rem,base = np.modf(total*distribution)
    base = base.astype(int)
    extraneed = int(round((base.sum() - total)))
    for i in rem.argsort()[-extraneed:]:
        base[i] += 1
    assert base.sum() == total, ('intdistribute didn\'t function as expected. mismatch between final sum and initial '
                                 'value. {} != {}').format(base.sum(),total)
    return base

if __name__ == '__main__':
    assert np.all(intdistribute(5,[0.25,0.75]) == np.array([1, 4]))