Question

I have a function that returns a comparison matrix from a given list:

def compare(a, b):
    if b > a:
        return 1
    elif b < a:
        return -1
    else:
        return 0

def matrix(data):
    return [[compare(a, b) for b in data] for a in data]

I use this function in this way:

>>> matrix([0, 4, 5, 2, 1, 3])
[[0, 1, 1, 1, 1, 1],
 [-1, 0, 1, -1, -1, -1],
 [-1, -1, 0, -1, -1, -1],
 [-1, 1, 1, 0, -1, 1],
 [-1, 1, 1, 1, 0, 1],
 [-1, 1, 1, -1, -1, 0]]

I need a function to return data from a given matrix, like the code below, but I don’t know how to do.

>>> data_from_matrix([[0, 1, 1, 1, 1, 1],
                      [-1, 0, 1, -1, -1, -1],
                      [-1, -1, 0, -1, -1, -1],
                      [-1, 1, 1, 0, -1, 1],
                      [-1, 1, 1, 1, 0, 1],
                      [-1, 1, 1, -1, -1, 0]])
[0, 4, 5, 2, 1, 3]

Answer 1

A simple hack would be to compute the sums over every row of the matrix:

def data_from_matrix(m):
    return [(len(m) - 1 - sum(row)) // 2 for row in m]

This assumes that the matrix actually defines a total ordering and does not check the consistency of the matrix. Another assumption is that the set the total ordering is supposed to be defined on is range(len(m)).

Example:

>>> data_from_matrix([[ 0,  1,  1,  1,  1,  1],
...                   [-1,  0,  1, -1, -1, -1],
...                   [-1, -1,  0, -1, -1, -1],
...                   [-1,  1,  1,  0, -1,  1],
...                   [-1,  1,  1,  1,  0,  1],
...                   [-1,  1,  1, -1, -1,  0]])
[0, 4, 5, 2, 1, 3]