How to get data in a histogram bin

Question

I want to get a list of the data contained in a histogram bin. I am using numpy, and Matplotlib. I know how to traverse the data and check the bin edges. However, I want to do this for a 2D histogram and the code to do this is rather ugly. Does numpy have any constructs to make this easier?

For the 1D case, I can use searchsorted(). But the logic is not that much better, and I don’t really want to do a binary search on each data point when I don’t have to.

Most of the nasty logic is due to the bin boundary regions. All regions have boundaries like this: [left edge, right edge). Except the last bin, which has a region like this: [left edge, right edge].

Here is some sample code for the 1D case:

import numpy as np

data = [0, 0.5, 1.5, 1.5, 1.5, 2.5, 2.5, 2.5, 3]

hist, edges = np.histogram(data, bins=3)

print 'data =', data
print 'histogram =', hist
print 'edges =', edges

getbin = 2  #0, 1, or 2

print '---'
print 'alg 1:'

#for i in range(len(data)):
for d in data:
    if d >= edges[getbin]:
        if (getbin == len(edges)-2) or d < edges[getbin+1]:
            print 'found:', d
        #end if
    #end if
#end for

print '---'
print 'alg 2:'

for d in data:
    val = np.searchsorted(edges, d, side='right')-1
    if val == getbin or val == len(edges)-1:
        print 'found:', d
    #end if
#end for

Here is some sample code for the 2D case:

import numpy as np

xdata = [0, 1.5, 1.5, 2.5, 2.5, 2.5, \
         0.5, 0.5, 0.5, 0.5, 1.5, 1.5, 1.5, 1.5, 1.5, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5, \
         0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5, 3]
ydata = [0, 5,5, 5, 5, 5, \
         15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, \
         25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 30]

xbins = 3
ybins = 3
hist2d, xedges, yedges = np.histogram2d(xdata, ydata, bins=(xbins, ybins))

print 'data2d =', zip(xdata, ydata)
print 'hist2d ='
print hist2d
print 'xedges =', xedges
print 'yedges =', yedges

getbin2d = 5  #0 through 8

print 'find data in bin #', getbin2d

xedge_i = getbin2d % xbins
yedge_i = int(getbin2d / xbins) #IMPORTANT: this is xbins

for x, y in zip(xdata, ydata):
    # x and y left edges
    if x >= xedges[xedge_i] and y >= yedges[yedge_i]:
        #x right edge
        if xedge_i == xbins-1 or x < xedges[xedge_i + 1]:
            #y right edge
            if yedge_i == ybins-1 or y < yedges[yedge_i + 1]:
                print 'found:', x, y
            #end if
        #end if
    #end if
#end for

Is there a cleaner / more efficient way to do this? It seems like numpy would have something for this.

Answer 1

digitize, from core NumPy, will give you the index of the bin to which each value in your histogram belongs:

import numpy as NP
A = NP.random.randint(0, 10, 100)

bins = NP.array([0., 20., 40., 60., 80., 100.])

# d is an index array holding the bin id for each point in A
d = NP.digitize(A, bins)