wquantiles.py

"""
Library to compute weighted quantiles, including the weighted median, of
numpy arrays.
"""
from __future__ import print_function
import numpy as np

__version__ = "0.4"


def quantile_1D(data, weights, quantile):
    """
    Compute the weighted quantile of a 1D numpy array.

    Parameters
    ----------
    data : ndarray
        Input array (one dimension).
    weights : ndarray
        Array with the weights of the same size of `data`.
    quantile : float
        Quantile to compute. It must have a value between 0 and 1.

    Returns
    -------
    quantile_1D : float
        The output value.
    """
    # Check the data
    if not isinstance(data, np.matrix):
        data = np.asarray(data)
    if not isinstance(weights, np.matrix):
        weights = np.asarray(weights)
    nd = data.ndim
    if nd != 1:
        raise TypeError("data must be a one dimensional array")
    ndw = weights.ndim
    if ndw != 1:
        raise TypeError("weights must be a one dimensional array")
    if data.shape != weights.shape:
        raise TypeError("the length of data and weights must be the same")
    if ((quantile > 1.) or (quantile < 0.)):
        raise ValueError("quantile must have a value between 0. and 1.")
    # Sort the data
    ind_sorted = np.argsort(data)
    sorted_data = data[ind_sorted]
    sorted_weights = weights[ind_sorted]
    # Compute the auxiliary arrays
    Sn = np.cumsum(sorted_weights)
    # TODO: Check that the weights do not sum zero
    #assert Sn != 0, "The sum of the weights must not be zero"
    Pn = (Sn-0.5*sorted_weights)/np.sum(sorted_weights)
    # Get the value of the weighted median
    return np.interp(quantile, Pn, sorted_data)


def quantile(data, weights, quantile):
    """
    Weighted quantile of an array with respect to the last axis.

    Parameters
    ----------
    data : ndarray
        Input array.
    weights : ndarray
        Array with the weights. It must have the same size of the last 
        axis of `data`.
    quantile : float
        Quantile to compute. It must have a value between 0 and 1.

    Returns
    -------
    quantile : float
        The output value.
    """
    # TODO: Allow to specify the axis
    nd = data.ndim
    if nd == 0:
        TypeError("data must have at least one dimension")
    elif nd == 1:
        return quantile_1D(data, weights, quantile)
    elif nd > 1:
        n = data.shape
        imr = data.reshape((np.prod(n[:-1]), n[-1]))
        result = np.apply_along_axis(quantile_1D, -1, imr, weights, quantile)
        return result.reshape(n[:-1])


def median(data, weights):
    """
    Weighted median of an array with respect to the last axis.

    Alias for `quantile(data, weights, 0.5)`.
    """
    return quantile(data, weights, 0.5)