[Python] How do the SoftMax partial derivatives map to my Python code?

The SoftMax function partial derivatives are defined as follows:

S_ij * delta_jk - S_ij * S_ik


Where S is the SoftMax function, i is the 0th axis index, j is the 1st axis index, and k is the corrected label.

But how does this relate to the bellow Python code?

import numpy as np

softmax_output = np.array([0.7, 0.1, 0.2]).reshape(-1, 1)
jacobian_matrix = np.diagflat(softmax_output)
right = np.dot(softmax_output, softmax_output.T)
result = jacobian_matrix - right

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