Numerical implementation of a matrix derivative

[Sophia Clark]

Homework Statement

Hi all!

I'm having trouble understanding the implementation of some derivatives in the expression (1) of this article:
https://www.ncbi.nlm.nih.gov/pubmed/26248210

How do I implement ∑_(ij) ∂_ijw ?

Thank you all in advance.

Homework Equations

w is a square matrix(120x120) with periodic boundary conditions.

The Attempt at a Solution

I understood it as the second derivative of the matrix w, but it doesn't seem to be correct.

 

[DrClaude]

I understood it as the second derivative of the matrix w, but it doesn't seem to be correct.

It is not exactly the derivative of a matrix, but of a scalar field, which computationally is represented as a matrix.

Why do you say this is not correct?

 

[Sophia Clark]

It is not exactly the derivative of a matrix, but of a scalar field, which computationally is represented as a matrix.

Why do you say this is not correct?

Because the obtained results don't have any physical meaning considering the problem, so I'm not sure that the implementation is correct.
How would you implement that equation ?

Thank you very much for your attention!