Making rows in a matrix vertical-CodePudding

I am trying to take the input of this (4x4) matrix:

1.0 2.0 3.0 4.0

5.0 6.0 7.0 8.0

9.0 10.0 11.0 12.0

13.0 14.0 15.0 16.0

and make it appear as:

1.0 5.0 9.0 13.0

2.0 6.0 10.0 14.0

3.0 7.0 11.0 15.0

4.0 8.0 12.0 16.0

I need to write the code in such a way that it only works for an NxN matrix. I thought I may have to do a nested for in loop but I'm confused on exactly how to make it work correctly. If you could help me that would be great!

CodePudding user response：

What you are trying to do is to take the transpose of the matrix. Transposing a matrix means changing all columns into rows (or equivalently, rows into columns). It is easily achieved with numpy:

>>> import numpy as np
>>> a = np.random.randint(10, size=(5, 5))
>>> a
array([[3, 3, 4, 9, 8],
       [9, 0, 0, 5, 6],
       [4, 1, 2, 4, 5],
       [2, 9, 0, 8, 0],
       [9, 9, 2, 3, 0]])
>>> a.T
array([[3, 9, 4, 2, 9],
       [3, 0, 1, 9, 9],
       [4, 0, 2, 0, 2],
       [9, 5, 4, 8, 3],
       [8, 6, 5, 0, 0]])
>>> np.transpose(a)
array([[3, 9, 4, 2, 9],
       [3, 0, 1, 9, 9],
       [4, 0, 2, 0, 2],
       [9, 5, 4, 8, 3],
       [8, 6, 5, 0, 0]])

To do it with more manually, for example

>>> import numpy as np
>>> matrix = np.array([
        [1, 2, 3],
        [4, 5, 6],
        [7, 8, 9],
    ])
>>> transposed_matrix = np.empty((3, 3))
>>> for i in range(3):
...     transposed_matrix[:, i] = matrix[i, :]
>>> transposed_matrix
array([[1. 4. 7.]
       [2. 5. 8.]
       [3. 6. 9.]])

or completely without numpy (probably many ways to do this, and probably more clever ways than I did too! =)):

>>> matrix = [
        [1, 2, 3],
        [4, 5, 6],
        [7, 8, 9],
    ]
>>> transposed_matrix = []
>>> for i in range(3):
...     tmp = []
...     for j in range(3):
...         tmp.append(matrix[j][i])
...     transposed_matrix.append(tmp)
>>> transposed_matrix
[[1, 4, 7], [2, 5, 8], [3, 6, 9]]