Python:NumPy .trace()

The .trace() method returns the sum of the elements along the diagonal of a NumPy array. For 2D arrays, the diagonal consists of elements where the row index equals the column index. For multi-dimensional arrays, the axes specified by axis1 and axis2 define the matrix dimensions for diagonal summation.

The .trace() method supports optional parameters to select a diagonal offset or specify axes, making it versatile for arrays of different shapes and orientations.

Syntax

ndarray.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)

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.
• dtype (Optional): The data type of the returned array. If not specified, it is determined from the input array.
• out (Optional): An alternative output array to place the result. It must have the same shape as the expected output.

Return value:

Returns the sum of the diagonal elements as a scalar or array, depending on the input array’s dimensions and the specified parameters.

Example

This example demonstrates how to use .trace() to calculate the sum of the main diagonal elements of a 2D array:

import numpy as np

# Create a 2D array
array_2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
print("Original array:")
print(array_2d)

# Calculate the trace (sum of main diagonal)
trace_value = array_2d.trace()
print("\nTrace (sum of diagonal elements):", trace_value)

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The output produced by this code is:

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

Trace (sum of diagonal elements): 15

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This code creates a 3×3 array and calculates the trace by summing the diagonal elements (1 + 5 + 9 = 15).

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