Improve Strided Arrays interface documentation with "user-defined" example

[JeffFessler]

The documentation for Strided Array interfaces needs a "user-defined" example.
https://docs.julialang.org/en/latest/manual/interfaces/#man-interface-strided-arrays-1

(Updated url: https://docs.julialang.org/en/v1/manual/interfaces/#man-interface-strided-arrays)

The text there says "A typical example of a user-defined strided array is one that wraps a standard Array with additional structure." But the only examples given are pre-existing data types. I made my own attempt at a strided array and it works, but matrix multiplication operations with it seem to be no faster than for a generic AbstractArray leaving me wondering what was the benefit of endowing my data type with a strides() method. Having a "typical example" where adding strides() is beneficial would be very useful in the manual, even if just a URL pointing to some package that uses it.

This is especially subtle here because "user-defined" might be read as meaning that one can define a subtype of a StridedArray, but I found out the hard way that one cannot because it is a Union type. (Mentioning that limitation explicitly in the manual would be good.)

I realize there is ongoing work to improve the docstring here #28144 and to improve the reference section of the manual here #26150.
And there are many open topics related to improving the stride interface #30432 JuliaLang/LinearAlgebra.jl#186 and general discussions about the array hierarchy #987.
I am also aware of the Strided.jl package, but its documentation also does not give any examples of user-defined strided arrays, only wrappers around preexisting array types.

I would have submitted PR instead of a new issue if I had a compelling example.

[cmichelenstrofer]

I am reading through the manual (it is great! :) ) and this is the first time I got stumped. I don't get it, at all. It says the strides are in memory, but then in the example the strides are in the values. The benefit is not clear at all either.

[JeffFessler]

the strides are in the value

What is the URL of that example?

[cmichelenstrofer]

The link is the one you shared above. I am probably misunderstanding the whole concept tbh (I don't have a CS background). The example is:

1:5   # not strided (there is no storage associated with this array.)
Vector(1:5)  # is strided with strides (1,)
A = [1 5; 2 6; 3 7; 4 8]  # is strided with strides (1,4)
V = view(A, 1:2, :)   # is strided with strides (1,4)
V = view(A, 1:2:3, 1:2)   # is strided with strides (2,4)
V = view(A, [1,2,4], :)   # is not strided, as the spacing between rows is not fixed.

[JeffFessler]

The strides documented there are the related to the spacings of elements in memory:
https://en.wikipedia.org/wiki/Stride_of_an_array
It has nothing to do with the actual values stored in memory.
Vector(5:10:25) is also strided with strides (1,) and probably the example should be changed to something like that to make it more clear.

[cmichelenstrofer]

That example helps a lot! Since the "stride" in values is different from the stride (in memory). Thanks, I finally get it! I think an example where the values have no obvious pattern (e.g. using randn) would also be beneficial.

The other thing I realize now and I was missing is that view is a wrapper array. Giving a preview of how view is defined would be extremely helpful and make it more clear what the stride is.

I think those two changes would go a long way to help people who are seeing this concept for the first time (like me). And then, as you mention, a real example of how this is useful would be good.