iter::Sum for DMatrix

[jswrenn]

This is one potential way to address #514. It tackles the problem in three steps:

1. The foundation of this approach is to introduce a notion of Default for dimensions. Statically known dimensions default to their value (this is already the behavior of the Default implementation provided by typenum). The Default of a Dynamic dimension is 0.
2. Using this, we can then lift DimName requirements on Matrix constructors that required them; any dynamic dimensions simply default to zero size.
3. Finally, we can lift the DimName requirements on functions that used these constructors, like the implementation of iter::Sum.

This PR only lifts the DimName requirement on iter::Sum, but the approach is broadly applicable and we can use it to lift DimName requirements in many parts of nalgebra.

[grtlr]

That was a really quick response, thank you very much!

I have not found any test cases for the implementation of Sum in the current code base. If you want, I could write up some tests for the static and the dynamic case (as well as DVector)?

[jswrenn]

@grtlr That would be great! In the interest of killing two birds with one stone, perhaps implement these as doctests on the sum functions?

If you fork and file a PR on my more-generic-sum branch, I'll merge them so they're included with this PR!

[grtlr]

@jswrenn I have created a PR on your branch. If you have any comments regarding the formatting, feel free to let me know.

[vadixidav]

Was literally just wanting this now. You solved it in the past. Awesome!

[sebcrozet]

Thanks @jswrenn and @grtlr and very sorry for the late answer.

For a first implementation of this, we should just panic if the provided matrix iterator is empty. Indeed, this implementation of Zero for dynamic matrices does not really comply with what the Zero trait is intended to do. In particular, the returned matrix is not a valid zero element for any non-empty dynamically-sized matrix thus code like the following won't work as the user would expect:

let zero = DMatrix::zero();
let m = DMatrix::from_diagonal(2, 2, 1.0);
assert_eq!(m + zero, m)

[jswrenn]

I've opened a separate pull request implementing the panic-on-empty behavior: #552.

Sorry for the slow response; I've been recovering from some medical issues.

[sebcrozet]

@jswrenn No worry. Take care!