First gist for Hungarian post.

hungarian1.py

# First gist for Hungarian post.
# Brute force estimation of optimal assignment for given preference. 
%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns
sns.set_context('talk')
sns.set_style('white')
import itertools
import numpy as np

preferences = np.array([[99, 99, 13, 41],
                        [14, 99, 21, 11],
                        [31, 95, 21, 51],
                        [52, 50, 51, 11]])


maxsums, colixs = [], []
group_size = np.shape(preferences)[0]
np.random.seed(0)
rowix = list(range(group_size)) # rows don't need to be permuted
# Permute choice of columns. 
for colix in itertools.permutations(range(group_size)):
    _sum = np.sum(preferences[rowix,colix])
    maxsums.append(_sum)
    colixs.append(colix)
maxsum = np.max(maxsums)
maxcolix = colixs[np.argmax(maxsums)]
print("Total preference:", maxsum)
print("Row:",rowix, "Col:", maxcolix)

f,ax = plt.subplots(figsize=(10,5))
ax.bar(range(len(maxsums)),np.sort(maxsums)[::-1])
ax.set(xlabel='Permutations',ylabel='Combined Group Preference', title="Preferences for every assignment combination")
plt.show()