array comparison

[JeffBezanson]

At this point most of us want .== for elementwise comparison. There are many reasons for this. Forming boolean arrays is often unnecessary and inefficient. More importantly, in mathematics when equality is extended to matrices it is still boolean, i.e. A=I denotes that A is everywhere equal to the identity matrix; it does not denote another matrix (of booleans).

== should be extended to containers by giving true iff it is true for all parts. This handles nested arrays, etc. with no problem.

A.==B should be equivalent to map(==, A, B). That way it always gives a container of booleans, and still uses == for all comparisons.

.< can be defined for arrays in the same way, but I'm not sure whether < should be.

[ViralBShah]

As per IRC discussion

We will have == and != doing all() by default and giving a boolean. All other operations such as <, <=, >, >= remain undefined for arrays.

[pao]

And the dotted operators will be array-of-booleans as Jeff proposes above? Sounds good to me.

[StefanKarpinski]

Yep. That's the plan. It's tempting to define A < B to mean all(A .< B) but faster too, but maybe dangerous.

[JeffBezanson]

In progress on the array_comparison branch: https://github.com/JuliaLang/julia/tree/array_comparison

Other library maintainers @ViralBShah @carlobaldassi please update your array implementations.

Everybody else please try to find comparisons that need to be changed.

[carlobaldassi]

The bitarray comparisons are now fixed in the array_comparison branch.
The sparse comparisons work already, via the AbstractArray version, but they could be optimized. It may also make sense to return a sparse matrix of Bools in some cases (e.g. when doing A .!= B with A and B sparse matrices the result is likely to be sparse), but not in others (e.g. A .== B). I'm not sure it's a good idea though: on one hand, it doesn't seem to break any convention; on the other hand, having .== and .!= return different types seems a bit weird.

[JeffBezanson]

Branch merged by 3040405.