Creating a histogram for the data in Python

Question

I have created a function in Python that computes the histogram of data. It has parameter bins that specifies no. of division.

I have given my code below and data is at link 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)

Now for bins = 10 for both function. the result is:

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] 

which is incorrect. and for bins = 15 I get:

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] 

which is incorrect too. Assuming Numpy is correct is there anything wrong in my code?

Answer 1

It looks like the only thing missing in your code was that (unlike the leading bins which are half-open) the last bin in the numpy histogram is closed (includes both endpoints), whereas all of your bins were half-open. (Source, see "Notes")

If a bin is defined by it's edges, binmin and binmax, a value x is assigned to that bin if:

For the first n-1 bins: binmin <= x < binmax

For the last bin: binmin <= x <= binmax

Similarly, np.arange() also expects a half-open interval, so in the code that follows I used np.linspace().

Consider the following:

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

Which, for bins=10, outputs:

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 ]

And for bins=15, outputs:

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 ]