numpy.histogram:检索每个垃圾箱中的权重平方和

Question

在numpy (或scipy)中，是否有可能检索直方图每个框中的权重平方之和？我想要在我的直方图中的每个垃圾箱高度上有一个错误。对于未称重的数据，每个仓高的统计误差应该是sqrt(N)，其中N是仓高。但对于加权数据，我需要加权平方和。numpy.histogram无法做到这一点，但是在numpy或can中是否还有其他功能可以根据不同的数组(例如，我正在进行直方图的值数组)来存储数组(例如权重数组)？我仔细看过文件，但什么也没找到。

Answer 1

正如亚历克斯所建议的，numpy.digitize是你想要的。该函数返回x数组的条目所属的回收站。然后，可以使用此信息访问w的正确元素。

x = np.array([2,9,4,8])
w = np.array([0.1,0.2,0.3,0.4])

bins = np.digitize(x, [0,5,10])

# access elements for first bin
first_bin_ws = w[np.where(bins==1)[0]]

# error of fist bin
error = np.sqrt(np.sum(first_bin_ws**2.))

最后一行计算第一个bin的错误。请注意，np.digitize从1开始计数。

Answer 2

如果我可以在@obachtos的答案中添加一个补语，我将其扩展为一个函数，然后演示完整的直方图：

def hist_bin_uncertainty(data, weights, bin_edges):
    """
    The statistical uncertainity per bin of the binned data.
    If there are weights then the uncertainity will be the root of the
    sum of the weights squared.
    If there are no weights (weights = 1) this reduces to the root of
    the number of events.

    Args:
        data: `array`, the data being histogrammed.
        weights: `array`, the associated weights of the `data`.
        bin_edges: `array`, the edges of the bins of the histogram.

    Returns:
        bin_uncertainties: `array`, the statistical uncertainity on the bins.

    Example:
    >>> x = np.array([2,9,4,8])
    >>> w = np.array([0.1,0.2,0.3,0.4])
    >>> edges = [0,5,10]
    >>> hist_bin_uncertainty(x, w, edges)
    array([ 0.31622777,  0.4472136 ])
    >>> hist_bin_uncertainty(x, None, edges)
    array([ 1.41421356,  1.41421356])
    >>> hist_bin_uncertainty(x, np.ones(len(x)), edges)
    array([ 1.41421356,  1.41421356])
    """
    import numpy as np
    # Bound the data and weights to be within the bin edges
    in_range_index = [idx for idx in range(len(data))
                      if data[idx] > min(bin_edges) and data[idx] < max(bin_edges)]
    in_range_data = np.asarray([data[idx] for idx in in_range_index])

    if weights is None or np.array_equal(weights, np.ones(len(weights))):
        # Default to weights of 1 and thus uncertainty = sqrt(N)
        in_range_weights = np.ones(len(in_range_data))
    else:
        in_range_weights = np.asarray([weights[idx] for idx in in_range_index])

    # Bin the weights with the same binning as the data
    bin_index = np.digitize(in_range_data, bin_edges)
    # N.B.: range(1, bin_edges.size) is used instead of set(bin_index) as if
    # there is a gap in the data such that a bin is skipped no index would appear
    # for it in the set
    binned_weights = np.asarray(
        [in_range_weights[np.where(bin_index == idx)[0]] for idx in range(1, len(bin_edges))])
    bin_uncertainties = np.asarray(
        [np.sqrt(np.sum(np.square(w))) for w in binned_weights])
    return bin_uncertainties