Interpret the transfer() function in numpy in detail (with examples to help understand)

stay Numpy In transposing a matrix , We can use transpose() Function to handle .

The operation of this function is very counterintuitive , It may lead people to think wrong .

I just feel difficult to understand in the process of learning , Fortunately, I have consulted many materials , Finally, I understand a little .

Two dimensional array

Let's take a look at the two-dimensional array first :

import numpy as np
X=np.arange(6).reshape((2,3))
print(X)

[[0 1 2]
 [3 4 5]]

We use transpose() Function to handle ：

print(X.transpose())

[[0 3]
 [1 4]
 [2 5]]

Does the result look familiar ？ Yes , Is our usual transpose , It is also very convenient to understand :

transpose() The function is to exchange the index value of the row and column value of the array , Similar to finding the transpose of a matrix .

print(X.T)

[[0 3]
 [1 4]
 [2 5]]

We can see directly , The row and column index values of the array are swapped ,1 From x(0,1) Run to x(1,0).

Three dimensional array

We continue to generate a three-dimensional array ：

x=np.arange(16).reshape((2,2,4))
print(x)

[[[ 0  1  2  3]
  [ 4  5  6  7]]

 [[ 8  9 10 11]
  [12 13 14 15]]]

Our usual idea is

from x Look at the axis ,0, 1 ,2 ,3

from y Look at the axis ,0,4

from z Look at the axis ,0, 8

This expression may be clearer .

The subscripts are arranged as [x, y, z]

in fact , The above axis is wrong , We can test by subscript ：

print(x[0,0,0],x[1,0,0])

0 8

But when we continue to change the value of the first index :

print(x[2,0,0])

IndexError: index 2 is out of bounds for axis 0 with size 2

We continue to test :

print(x[0,1,0],x[1,1,0])

4 12

print(x[0,0,1],x[0,0,2])

1 2

It can be seen that , By changing the first subscript , Our actual change is what we usually think z, instead of x,x[1, 0, 0] The number obtained is 8 instead of 1; By changing the third subscript , Our actual change is what we usually think x, instead of z,x[0, 0, 1] The number obtained is 1 instead of 8.

therefore , The subscript of a number is [z, y, x]

transpose Use of functions

First , We make use of transpose Original output ：

print(x.transpose((0,1,2))) #z,y,x

[[[ 0  1  2  3]
  [ 4  5  6  7]]

 [[ 8  9 10 11]
  [12 13 14 15]]]

ad locum ,transpose() Functional (0, 1, 2) Corresponding (z, y, x) Axis

When we type in x.transpose((0, 2, 1)) when , Produce the following results ：

[[[ 0  4]
  [ 1  5]
  [ 2  6]
  [ 3  7]]

 [[ 8 12]
  [ 9 13]
  [10 14]
  [11 15]]]

We can see , When we change 1 and 2 The location of ,x and y Transposed .

When we type in x.transpose((1,0,2)) when , Produce the following results ：

[[[ 0  1  2  3]
  [ 8  9 10 11]]

 [[ 4  5  6  7]
  [12 13 14 15]]]

We can see , When we change 1 and 0 The location of ,z and y Transposed .

My understanding is that ：x、y、z Can be understood as —— dimension ( Number of channels or superposition of several two-dimensional planes （ high ））—— Rows of two-dimensional matrix —— The number of columns of a two-dimensional matrix .224 The matrix of is 2 individual 2*4 The superposition of the plane matrix of .

summary ：

The point is to understand , The subscript of the three-dimensional array is [z, y, x], transpose() The default number for it is 0=z, y=1, x=2.