Sorting lists with multiple tie breakers

I have data in an array like so:

array([[ 5,  5,  5,  6,  9,  6,  6],
       [10,  4, 10,  3,  5,  3,  3],
       [10,  3, 10,  4,  5,  3,  4],
       [ 9,  6,  8,  8, 10,  6,  9],
       [10, 10, 10,  7, 10,  4,  4],
       [10,  6, 10,  5,  9,  7,  5],
       [ 9,  7, 10,  7, 10,  8, 10],
       [ 8,  5, 10,  7, 10,  7, 10],
       [ 7, 10, 10,  9, 10,  7,  8]])

I want to sort it by the amount of non-10 values, and I also want to sort it in ascending order for rows, and in descending order of number of 10s:

arr = np.sort(arr, axis=1)
arr = arr[(arr==10).sum(axis=1).argsort()][::-1]

Output:

array([[ 4,  4,  7, 10, 10, 10, 10],
       [ 7,  7,  8,  9, 10, 10, 10],
       [ 5,  7,  7,  8, 10, 10, 10],
       [ 7,  7,  8,  9, 10, 10, 10],
       [ 5,  5,  6,  7,  9, 10, 10],
       [ 3,  3,  4,  4,  5, 10, 10],
       [ 3,  3,  3,  4,  5, 10, 10],
       [ 6,  6,  8,  8,  9,  9, 10],
       [ 5,  5,  5,  6,  6,  6,  9]])

I want to implement a tie breaker system so that if the amount of 10s the same, it now orders by amount of 9s, then 8s, and so on. Expected output:

array([[ 4,  4,  7, 10, 10, 10, 10],
       [ 7,  7,  8,  9, 10, 10, 10],
       [ 7,  7,  8,  9, 10, 10, 10],
       [ 5,  7,  7,  8, 10, 10, 10],
       [ 5,  5,  6,  7,  9, 10, 10],
       [ 3,  3,  4,  4,  5, 10, 10],
       [ 3,  3,  3,  4,  5, 10, 10],
       [ 6,  6,  8,  8,  9,  9, 10],
       [ 5,  5,  5,  6,  6,  6,  9]])

Answer

You can achieve it with numpy.frompyfunc.

The basic idea is to construct an array with the same rows, each element of which is a tuple containing the number of 10s, 9s, etc. Then apply numpy.argsort to this array and get the result.

import numpy as np

arr = np.array([[ 5,  5,  5,  6,  9,  6,  6],
                [10,  4, 10,  3,  5,  3,  3],
                [10,  3, 10,  4,  5,  3,  4],
                [ 9,  6,  8,  8, 10,  6,  9],
                [10, 10, 10,  7, 10,  4,  4],
                [10,  6, 10,  5,  9,  7,  5],
                [ 9,  7, 10,  7, 10,  8, 10],
                [ 8,  5, 10,  7, 10,  7, 10],
                [ 7, 10, 10,  9, 10,  7,  8]])
arr = np.sort(arr, 1)

keys = sorted(set(arr.ravel()), reverse=True)

def make_tuple(*argv):
    return tuple(argv)
ufunc = np.frompyfunc(make_tuple, len(keys), 1)

cnt_array = ufunc(*[(arr == k).sum(1) for k in keys])
result = arr[cnt_array.argsort()[::-1]]
print(result)
# [[ 4  4  7 10 10 10 10]
#  [ 7  7  8  9 10 10 10]
#  [ 7  7  8  9 10 10 10]
#  [ 5  7  7  8 10 10 10]
#  [ 5  5  6  7  9 10 10]
#  [ 3  3  4  4  5 10 10]
#  [ 3  3  3  4  5 10 10]
#  [ 6  6  8  8  9  9 10]
#  [ 5  5  5  6  6  6  9]]