DOC: integrate: Add complex matrix DE solution to examples

[topolskikevin]

Reference issue

Closes #13437

What does this implement/fix?

Added examples to solve complex matrix differential equations to docstring

Additional information

First commit, welcome to any feedback and changes I can follow up.

[tupuinui]

Thank you for your first PR @topolskikevin! Nice example.

On my side (as I don't know these functions) I just have a few cosmetic comments. Let see as well if the doctests pass.

[tupui]

Sorry about the mess, I used the wrong account... (Believe me, I hate to have this setup but I don't have the choice...)

[tupui]

Thanks for the update. You still have issues with the CI. These suggestions should fix them.

[tupui]

The following example should be placed above as the exponential_decay function is defined above. The examples are linked.

[tupui]

Already imported above.

Suggested change

>>> from scipy.integrate import solve_ivp

[tupui]

@nmayorov could you have a look at the example itself? I am not a user of this so I would not know if this makes sense TBH.

[Patol75]

@tupui The idea of this PR is to provide an example of how to use solve_ivp when the variable y is a matrix-valued function. In other words, how to solve an ordinary differential equation that involves a matrix-valued function through solve_ivp. The motivation behind this PR is this SO question that I have answered in which the author is confused about how to proceed in the aforementioned scenario. Indeed, throughout the documentation, it is mentioned that y is a vector. However, the confusion comes from the fact that the author assumed it was necessary to pass a 2-D NumPy array to solve_ivp, while the way to proceed is to provide solve_ivp with the flattened array and reshape y within fun to perform matrix operations before flattening again the returned array. Following my answer on SO, the question's author opened #13437 to ask for a similar example to be included in the documentation. The present PR simply reproduces my answer to the author's question on SO. The ordinary differential equation used does not have anything special. Instead, the idea is to show the flatten/reshape procedure to allow for execution through solve_ivp. I guess that the question here is whether SciPy developers consider this scenario should be documented, and if yes, whether the proposed approach is satisfying.

[mdhaber]

@nmayorov Do you have a moment to check out this new example? Rendered documentation is here.

[nitin-pandita]

Can i work on it

[tupui]

Hi @nitin-pandita, I am afraid there is no simple way to work on someone else's PR. I would suggest you look at other issues.

[nitin-pandita]

Hi @nitin-pandita, I am afraid there is no simple way to work on someone else's PR. I would suggest you look at other issues.

Ok Sure

[j-bowhay]

Thanks @topolskikevin