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NumPy - 06 Transposing Arrays
Transposing is a special form of reshaping that returns a view of the underlying data without making a copy. Transposing an array swaps its rows and columns.
Arrays can be transposed using the .T attribute or the transpose() method.
’ arr.T ’ - Using the ’ .T ’ Attribute for Transposing
The .T attribute returns the transpose of an array, swapping its rows and columns.
>>> import numpy as np
>>> arr = np.array([[2, 3, 4, 5], [5, 2, 4, 5]])
>>> arr.T
array([[2, 5],
[3, 2],
[4, 4],
[5, 5]])- The original array’s rows and columns are swapped.
Transposing a 2D Array
>>> arr = np.arange(15).reshape((3, 5))
>>> arr
array([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14]])
>>> arr.T
array([[ 0, 5, 10],
[ 1, 6, 11],
[ 2, 7, 12],
[ 3, 8, 13],
[ 4, 9, 14]])Matrix Multiplication using Transpose
Matrix multiplication can be performed using the transposed array with np.dot() or the @ infix operator.
>>> arr
array([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14]])
>>> np.dot(arr.T, arr)
array([[125, 140, 155, 170, 185],
[140, 158, 176, 194, 212],
[155, 176, 197, 218, 239],
[170, 194, 218, 242, 266],
[185, 212, 239, 266, 293]])
>>> arr.T @ arr
array([[125, 140, 155, 170, 185],
[140, 158, 176, 194, 212],
[155, 176, 197, 218, 239],
[170, 194, 218, 242, 266],
[185, 212, 239, 266, 293]])- Both
np.dot(arr.T, arr)andarr.T @ arrperform the same matrix multiplication.
’ swapaxes() ’ - Swapping Array Axes
The swapaxes() method allows you to swap any two axes of an array. This rearranges the data and returns a view on the data without copying.
>>> arr = np.arange(24).reshape((6, 4))
>>> arr
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]])
>>> arr.swapaxes(0, 1)
array([[ 0, 4, 8, 12, 16, 20],
[ 1, 5, 9, 13, 17, 21],
[ 2, 6, 10, 14, 18, 22],
[ 3, 7, 11, 15, 19, 23]])- The
swapaxes(0, 1)swaps the first and second axes of the array.
Swapping Axes Without Changing the Original Array
>>> arr
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]])
>>> arr.T
array([[ 0, 4, 8, 12, 16, 20],
[ 1, 5, 9, 13, 17, 21],
[ 2, 6, 10, 14, 18, 22],
[ 3, 7, 11, 15, 19, 23]])- After calling
.T, the result is the same as after usingswapaxes(0, 1).
Summary of Key Functions
arr.T: Returns the transpose of the array, swapping rows and columns.np.dot(): Performs matrix multiplication using the transpose.@operator: Another way to perform matrix multiplication with the transpose.swapaxes(): Swaps two axes of the array, returning a view without copying data.