如何将矩阵（嵌套列表）逆时针旋转90度

Question

I'm trying to rotate a matrix counter clockwise by 90 degrees. For example, if:

m = [[1,2,3],
     [2,3,3],
     [5,4,3]]

then the result should be

m = [[3,3,3],
     [2,3,4],
     [1,2,5]]

So far, I found:

rez = [[m[j][i] for j in range(len(m))] for i in range(len(m[0]))]
    for row in rez:
        print(row)

This gives me

[1, 2, 5]
[2, 3, 4]
[3, 3, 3]

This is close, but the rows would need to be reverses. Does anyone know a simple way to rotate this matrix counter clockwise by 90 degrees?

Answer 1

You could do the following:

m = [[1, 2, 3],
     [2, 3, 3],
     [5, 4, 3]]

result = list(map(list, zip(*m)))[::-1]

print(result)

Output

[[3, 3, 3],
 [2, 3, 4],
 [1, 2, 5]]

With map(list, zip(*m)) you create an iterable of the columns, and with the expression list(...)[::-1] you convert that iterable into a list and reverse it.

Answer 2

What you here basically do is map a matrix A to a matrix B such that:

B _ij =A _ji

In case you rotate elements, that means that if you rotate an n×m -matrix, then that means that:

B _ij =A _{j ni}

So we can calculate this as:

rez = [[m[j][] for j in range(len(m))] for  in ]

which is thus the transpose, but than "reversed". Using indices is however typically not how you do such processing in Python, since now it works only for items that are subscriptable, so I advice you to look for a more elegant solution.

But that being said, numpy offers a numpy.rot90 function to rotate matrices:

>>> np.rot90(m)
array([[3, 3, 3],
       [2, 3, 4],
       [1, 2, 5]])

Answer 3

Other option is to use scipy.ndimage.rotate

Rotate an array.

The array is rotated in the plane defined by the two axes given by the axes parameter using spline interpolation of the requested order.

import numpy as np
from  scipy import ndimage

m = np.matrix([[1,2,3],
               [2,3,3],
               [5,4,3]])

ndimage.rotate(m, 90.0) #angle as float.

 Out: array([[3, 3, 3], [2, 3, 4], [1, 2, 5]]) 

---

Same result you can get by using the zip() function to transpose rows and columns of a 5.1.4. Nested List then reverse the nested list with [::-1] + put in a np.matrix :

matrix = [[1, 2, 3],
          [2, 3, 3],
          [5, 4, 3]]

np.matrix(list(zip(*matrix)))[::-1]

 Out: matrix([[3, 3, 3], [2, 3, 4], [1, 2, 5]])