DOC: Add explanation of a sparse mesh grid

[timhoffm]

See #19561 (comment).

I've also changed np.arange(-5, 5, 0.1) to np.linspace(-5, 5, 101) in the example because arange for non-integer steps is generally not recommended.

https://numpy.org/doc/stable/reference/generated/numpy.arange.html:

When using a non-integer step, such as 0.1, the results will often not be consistent. It is better to use numpy.linspace for these cases.

[charris]

@timhoffm @rossbar Ping.

[rossbar]

I don't think this is correct. There's both the squaring and addition operations to consider: doesn't the addition require 101**2 operations?

In any case, my two cents is that this could benefit from less detail as it's easy to lose the forest through the trees here. I'd advocate for chopping out the text from Here,: IMO the best way to provide more detail would be to add a reference to the 2011 NumPy paper, which has an excellent detailed example of broadcasting with "sparse" arrays.

Just my two cents though - leaving the detail is also fine, but we should double check to make sure the numbers are correct.

[timhoffm]

I was only referring to the square operations. I anticipated that the square operation was more expensive than addition, but that doesn't seem to be the case. So the overall gain is theoretically just a factor 3 (beacuse the sparse sqares can be neglected compared to the addition). A bit more testing also shows that a real gain only appears when x, y have order of 1000 elements or larger, which I find surprisingly high.

Anyway, it's not within my scope to discuss performance characteristics. I've removed everything from "Here" as suggested.

[charris]

close/reopen

[rossbar]

Oops - I only meant that the text about performance should be removed, not the example. I think the clearest way to demonstrate what the sparse kwarg does is to show it:

>>> xx, yy = np.meshgrid(x, y)
>>> xx.shape, yy.shape
((101, 101), (101, 101))
>>> xs, ys = np.meshgrid(x, y, sparse=True)
>>> xs.shape, ys.shape
((1, 101), (101, 1))
>>> zs = np.sin(xs**2 + ys**2) / (xs**2 + ys**2)
>>> np.array_equal(z, zs, equal_nan=True)
True
>>> zs.shape
(101, 101)

Also, it seems that sparse keeps getting replaced with spare in the pushes.

[timhoffm]

@rossbar Thanks, I've taken your example suggestion and adapted:

• have separate sections for full and sparse arrays. - This example shows how to use a meshgrid to evaluate a function. Having first a complete "full" example is serves this primary purpose without already mixing in spare logic.
• simplified the function to evaluate.
• removed the plot. - While it is nice for illustration of "evaluate a function", the plotting code and the need for a more complex function would make the example longer and harder to read.

[rossbar]

removed the plot. - While it is nice for illustration of "evaluate a function", the plotting code and the need for a more complex function would make the example longer and harder to read.

Personally I'm -1 on this change. This is an example of a very common use-case that demonstrates how these two fundamental packages (numpy and matplotlib) are used together. It'd be a shame to lose that, and I don't really think the 4 extra lines for matplotlib make the example difficult to follow.

If you feel strongly about removing it, I'd recommend opening a separate PR for it.

[timhoffm]

I've reverted the plot removal, Instead I've moved it to a separate block and added a colorbar.

[rossbar]

Thanks @timhoffm !