在Python中创建直方图

Question

我在Python里写了一个函数，用来计算数据的直方图。这个函数有一个参数bins，它用来指定分成多少个部分。

我把我的代码放在下面，数据可以在这个链接找到：https://gist.github.com/mesarvagya/11367012

import numpy as np
def histogram_using_numpy(filename, bins=10):
    datas =  np.loadtxt(filename, delimiter=" ", usecols=(0,))
    hist,bin_edges = np.histogram(datas, bins)
    return hist
print "from numpy %s" % histogram_using_numpy("ex.txt", bins=10)

def histogram_using_list(filename, bins=10, take_col=0):
    f = open(filename,"r")
    data = []
    for item in f.readlines():
        data.append(float(item.split()[take_col]))
    f.close()
    mi,ma = min(data), max(data)
    bin_length = (ma-mi)/bins
    def get_count(lis,low,diff):
        count = 0
        for item in lis:
            if item >= low and item < low + diff:
                count += 1
        return count
    tot = []    
    for i in np.arange(mi, ma, bin_length):
        tot.append(get_count(data,i, bin_length))
    return tot    
print "From my function %s " % histogram_using_list("ex.txt", bins=10)

现在，当bins = 10时，两个函数的结果是：

from numpy [10 19 20 28 15 16 14 11  5 12]
From my function [10, 19, 20, 28, 16, 15, 14, 11, 5, 12] 

这个结果是不对的。而当bins = 15时，我得到的结果是：

from numpy [ 7  4 18 19  5 24  8 10 13  6 13  6  5  1 11]
From my function [7, 4, 18, 19, 10, 19, 8, 10, 13, 10, 9, 6, 5, 1, 11] 

这个结果也不对。假设Numpy是正确的，那我的代码里有没有什么问题呢？

Answer 1

看起来你代码里缺少的部分是，numpy的直方图最后一个区间是闭合的，也就是说它包括了两个端点，而前面的区间是半开区间。你所有的区间都是半开的。 (来源，见“说明”)

如果一个区间是由它的边界定义的，binmin 和 binmax，那么一个值 x 会被分配到这个区间，如果满足以下条件：

对于前面的 n-1 个区间： binmin <= x < binmax

对于最后一个区间： binmin <= x <= binmax

同样，np.arange() 也期望使用半开区间，所以在接下来的代码中我用了np.linspace()。

考虑以下内容：

import numpy as np
def histogram_using_numpy(filename, bins=10):
    datas =  np.loadtxt(filename, delimiter=" ", usecols=(0,))
    hist, bin_edges = np.histogram(datas, bins)

    return hist, bin_edges


def histogram_using_list(filename, bins=10, take_col=0):
    f = open(filename,"r")
    data = []
    for item in f.readlines():
        data.append(float(item.split()[take_col]))
    f.close()
    mi,ma = min(data), max(data)

    def get_count(lis,binmin,binmax,inclusive_endpoint=False):
        count = 0
        for item in lis:
            if item >= binmin and item < binmax:
                count += 1
            elif inclusive_endpoint and item == binmax:
                count += 1
        return count

    bin_edges = np.linspace(mi, ma, bins+1)

    tot = []
    binlims = zip(bin_edges[0:-1], bin_edges[1:])
    for i,(binmin,binmax) in enumerate(binlims):
        inclusive = (i == (len(binlims) - 1))
        tot.append(get_count(data, binmin, binmax, inclusive))

    return tot, bin_edges

nump_hist, nump_bin_edges = histogram_using_numpy("ex.txt", bins=15)
func_hist, func_bin_edges = histogram_using_list("ex.txt", bins=15)

print "Histogram:"
print "  From numpy:      %s" % list(nump_hist)
print "  From my function %s" % list(func_hist)
print ""
print "Bin Edges:"
print "  From numpy:      %s" % nump_bin_edges
print "  From my function %s" % func_bin_edges

对于 bins=10，输出结果是：

Histogram:
  From numpy:      [10, 19, 20, 28, 15, 16, 14, 11, 5, 12]
  From my function [10, 19, 20, 28, 15, 16, 14, 11, 5, 12]

Bin Edges:
  From numpy:      [ 4.3   4.66  5.02  5.38  5.74  6.1   6.46  6.82  7.18  7.54  7.9 ]
  From my function [ 4.3   4.66  5.02  5.38  5.74  6.1   6.46  6.82  7.18  7.54  7.9 ]

对于 bins=15，输出结果是：

Histogram:
  From numpy:      [7, 4, 18, 19, 5, 24, 8, 10, 13, 6, 13, 6, 5, 1, 11]
  From my function [7, 4, 18, 19, 5, 24, 8, 10, 13, 6, 13, 6, 5, 1, 11]

Bin Edges:
  From numpy:      [ 4.3   4.54  4.78  5.02  5.26  5.5   5.74  5.98  6.22  6.46  6.7   6.94  7.18  7.42  7.66  7.9 ]
  From my function [ 4.3   4.54  4.78  5.02  5.26  5.5   5.74  5.98  6.22  6.46  6.7   6.94  7.18  7.42  7.66  7.9 ]