Finding the row with the highest average in a numpy array

Question

Given the following array:

complete_matrix = numpy.array([
    [0, 1, 2, 4],
    [1, 0, 3, 5],
    [2, 3, 0, 6],
    [4, 5, 6, 0]])

I would like to identify the row with the highest average, excluding the diagonal zeros. So, in this case, I would be able to identify complete_matrix[:,3] as being the row with the highest average.

Answer 1

Note that the presence of the zeros doesn't affect which row has the highest mean because all rows have the same number of elements. Therefore, we just take the mean of each row, and then ask for the index of the largest element.

#Take the mean along the 1st index, ie collapse into a Nx1 array of means
means = np.mean(complete_matrix, 1)
#Now just get the index of the largest mean
idx = np.argmax(means)

idx is now the index of the row with the highest mean!

Answer 2

You don't need to worry about the 0s, they shouldn't effect how the averages compare since there will presumably be one in each row. Hence, you can do something like this to get the index of the row with the highest average:

>>> import numpy as np 
>>> complete_matrix = np.array([
...     [0, 1, 2, 4],
...     [1, 0, 3, 5],
...     [2, 3, 0, 6],
...     [4, 5, 6, 0]])
>>> np.argmax(np.mean(complete_matrix, axis=1))
3

---

Reference:

• numpy.mean
• numpy.argmax

Answer 3

As pointed out by a lot of people, presence of zeros isn't an issue as long as you have the same number of zeros in each column. Just in case your intention was to ignore all the zeros, preventing them from participating in the average computation, you could use weights to suppress the contribution of the zeros. The following solution assigns 0 weight to zero entries, 1 otherwise:

numpy.argmax(numpy.average(complete_matrix,axis=0, weights=complete_matrix!=0))

You can always create a weight matrix where the weight is 0 for diagonal entries, and 1 otherwise.

Answer 4

You will see that this answer actually would fit better to your other question that was marked as duplicated to this one (and don't know why because it is not the same question...)

The presence of zeros can indeed affect the columns' or rows' average, for instance:

a = np.array([[  0, 1, 0.9,   1],
              [0.9, 0,   1,   1],
              [  1, 1,   0, 0.5]])

Without eliminating the diagonals, it would tell that the column 3 has the highest average, but eliminating the diagonals the highest average belongs to column 1 and now column 3 has the least average of all columns!

You can correct the calculated mean using the lcm (least common multiple) of the number of lines with and without the diagonals, by guaranteeing that where a diagonal element does not exist the correction is not applied:

correction = column_sum/lcm(len(column), len(column)-1)
new_mean = mean + correction

I copied the algorithm for lcm from this answer and proposed a solution for your case:

import numpy as np

def gcd(a, b):
    """Return greatest common divisor using Euclid's Algorithm."""
    while b:
        a, b = b, a % b
    return a

def lcm(a, b):
    """Return lowest common multiple."""
    return a * b // gcd(a, b)

def mymean(a):
    if len(a.diagonal()) < a.shape[1]:
        tmp = np.hstack((a.diagonal()*0+1,0))
    else:
        tmp = a.diagonal()*0+1
    return np.mean(a, axis=0) + np.sum(a,axis=0)*tmp/lcm(a.shape[0],a.shape[0]-1)

Testing with the a given above:

mymean(a)
#array([ 0.95      ,  1.        ,  0.95      ,  0.83333333])

With another example:

b = np.array([[  0, 1, 0.9,   0],
              [0.9, 0,   1,   1],
              [  1, 1,   0, 0.5],
              [0.9, 0.2,   1,   0],
              [  1, 1,   0.7, 0.5]])

mymean(b)
#array([ 0.95,  0.8 ,  0.9 ,  0.5 ])

With the corrected average you just use np.argmax() to get the column index with the highest average. Similarly, np.argmin() to get the index of the column with the least average:

np.argmin(mymean(a))