How to make permutation matrix for two lists of str, Python3

问题

I have two lists.

a_num = [1, 3, 2, 4]
b_num = [1, 2, 3, 4]

I want to find a permutation matrix to convert a to b. Mathematically, a permutation matrix is a square matrix, whose elements are either 1 or 0. It can change the sequence of elements in a vector, by multiplying it. In this particular example, the permutation matrix is:

p = [[1,0,0,0],
     [0,0,1,0],
     [0,1,0,0],
     [0,0,0,1]]
# check whether p is correct.
b_num == np.dot(np.array(p), np.array(a_num).reshape(4,1))

Could you please show me how to make that matrix p? In my real application, there can be tens of elements in the lists with arbitrary sequence. And the two lists always contain str instead of int. And how to make p when the a and b are lists of str?

a_str = ['c1', 'c2', 's1', 's2']
b_str = ['c1', 's1', 'c2', 's2']

回答1:

In pure Python you can do:

a_str = ['c1', 'c2', 's1', 's2']
b_str = ['c1', 's1', 'c2', 's2']

from collections import defaultdict

dd = defaultdict(lambda: [0, []])
for i, x in enumerate(b_str):  # collect indexes of target chars
    dd[x][1].append(i)

matrix = [[0]*len(a_str) for x in b_str]

for i, a in enumerate(a_str):
    # set cell at row (src index) and col (next tgt index) to 1
    matrix[i][dd[a][1][dd[a][0]]] = 1  
    # increment index for looking up next tgt index
    dd[a][0] += 1

matrix
# [[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]]

This assumes that a_str and b_str are in fact respective permutations.

回答2:

Edit: works only with numbers.

For arrays with the same length using NumPy:

import numpy as np

a_num = [1, 3, 2, 4]
b_num = [4, 2, 3, 1]
a = np.array(a_num)
b = np.array(b_num)
len_v = len(a)  # = len(b)

A = np.zeros((len_v, len_v))
A[np.argsort(a), np.arange(len_v)] = 1

B = np.zeros((len_v, len_v))
B[np.argsort(b), np.arange(len_v)] = 1

np.dot(np.linalg.inv(B), np.dot(A, a))  # array([4., 2., 3., 1.])

来源：https://stackoverflow.com/questions/53079668/how-to-make-permutation-matrix-for-two-lists-of-str-python3

标签

string

python-3.x

permutation