Python:NumPy .diagonal()

The .diagonal() method returns the specified diagonal elements of a NumPy array. For 2D arrays, the diagonal consists of elements where the row index equals the column index (or with an offset). For multi-dimensional arrays, the axes specified by axis1 and axis2 define the matrix dimensions from which to extract the diagonal.

Unlike .trace(), which returns the sum of diagonal elements, .diagonal() returns the actual diagonal elements as an array. This method typically returns a view rather than a copy, making it memory-efficient for large arrays.

Syntax

ndarray.diagonal(offset=0, axis1=0, axis2=1)

Parameters:

• offset (Optional): The diagonal offset from the main diagonal. A positive value selects a diagonal above the main diagonal, while a negative value selects one below. Default is 0 (main diagonal).
• axis1 (Optional): The axis to be used as the first axis of the 2D sub-arrays from which the diagonals should be taken. Default is 0.
• axis2 (Optional): The axis to be used as the second axis of the 2D sub-arrays from which the diagonals should be taken. Default is 1.

Return value:

Returns an array containing the diagonal elements. For 2D arrays, this is a 1D array. For higher-dimensional arrays, the result has one fewer dimension than the input.

Example 1: Extracting Diagonals from 2D and Rectangular Arrays

This example demonstrates how to extract diagonals from both square and rectangular arrays using different offset values:

import numpy as np

# Create a 3×3 square array
square = np.array([[1, 2, 3],
                   [4, 5, 6],
                   [7, 8, 9]])

print("Square array:")
print(square)

print("\nMain diagonal:", square.diagonal())
print("Upper diagonal (offset=1):", square.diagonal(offset=1))
print("Lower diagonal (offset=-1):", square.diagonal(offset=-1))

# Create a 4×3 rectangular array
rectangular = np.array([[1, 2, 3],
                        [4, 5, 6],
                        [7, 8, 9],
                        [10, 11, 12]])

print("\nRectangular array:")
print(rectangular)

print("\nMain diagonal:", rectangular.diagonal())
print("Upper diagonal (offset=1):", rectangular.diagonal(offset=1))
print("Lower diagonal (offset=-2):", rectangular.diagonal(offset=-2))

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The output produced by this code is:

Square array:
[[1 2 3]
 [4 5 6]
 [7 8 9]]

Main diagonal: [1 5 9]
Upper diagonal (offset=1): [2 6]
Lower diagonal (offset=-1): [4 8]

Rectangular array:
[[ 1  2  3]
 [ 4  5  6]
 [ 7  8  9]
 [10 11 12]]

Main diagonal: [1 5 9]
Upper diagonal (offset=1): [2 6]
Lower diagonal (offset=-2): [7 11]

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For rectangular matrices, the diagonal length is determined by the smaller dimension, and different offsets extract parallel diagonals above or below the main one.

Example 2: Using .diagonal() with Multi-Dimensional Arrays

This example demonstrates how to extract diagonals from higher-dimensional arrays by specifying axes:

import numpy as np

# Create a 3D array (2x3x3)
array_3d = np.array([[[1, 2, 3], [4, 5, 6], [7, 8, 9]],
                     [[10, 11, 12], [13, 14, 15], [16, 17, 18]]])
print("3D array shape:", array_3d.shape)
print("3D array:")
print(array_3d)

# Extract diagonal from the last two dimensions
diag_default = array_3d.diagonal()
print("\nDiagonal (axis1=0, axis2=1):")
print(diag_default)

# Extract diagonal with different axes
diag_12 = array_3d.diagonal(axis1=1, axis2=2)
print("\nDiagonal (axis1=1, axis2=2):")
print(diag_12)

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The output produced by this code is:

3D array shape: (2, 3, 3)
3D array:
[[[ 1  2  3]
  [ 4  5  6]
  [ 7  8  9]]

 [[10 11 12]
  [13 14 15]
  [16 17 18]]]

Diagonal (axis1=0, axis2=1):
[[ 1 13]
 [ 2 14]
 [ 3 15]]

Diagonal (axis1=1, axis2=2):
[[ 1  5  9]
 [10 14 18]]

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For 3D arrays, .diagonal() extracts diagonal elements from 2D slices defined by the specified axes, resulting in an array with one fewer dimension.

Codebyte Example

Run the following codebyte example to understand the usage of the .diagonal() method:

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