.trace()

The .trace() function returns the sum of the elements along the main diagonal of an array. The array must have at least two dimensions. If the array used has more than two dimensions then axes need to be specified to determine the 2D sub-array whose traces are returned.

Syntax

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

• a: An array for which the sum of elements along the main diagonal is calculated.
• offset: An optional parameter can be both negative and positive. It is offset of diagonal from the main diagonal. The default is 0.
• axis1: An optional parameter used as the first axis of the 2D sub-arrays from which the diagonals should be taken. The default is 0.
• axis2: An optional parameter used as the second axis of the 2D sub-arrays from which the diagonals should be taken. The default is 1.
• dtype: An optional parameter used as the return type of sum returned if not provided then data type of the input array a is used.
• out: An optional parameter specifying an array where the result will be stored. If not provided, a new array is created.

Example

The below example shows how .trace() works on a 2D array:

import numpy as np

# Creating a 2D array
arr = np.array([[1, 2, 3, 4],
                [5, 6, 7, 8],
                [9, 10, 11, 12],
                [13, 14, 15, 16]])

# Computing the trace of the main diagonal
sum1 = np.trace(arr,0)

# Computing the trace of the diagonal above the main diagonal.
sum2 = np.trace(arr,1)

# Computing the trace of the diagonal below the main diagonal.
sum3 = np.trace(arr,-1)

print("The sum when offset is 0:", sum1)
print("The sum when offset is 1:", sum2)
print("The sum when offset is -1:", sum3)

The output would be:

The sum when offset is 0: 34
The sum when offset is 1: 21
The sum when offset is -1: 30

Codebyte Example

Run the following code to understand how the .trace() function works:

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