Specify behaviour of map for sparse matrices

[jumutc]

We need a solid and unambiguous behaviour of map for sparse matrices which would preserve sparse structure and keep the memory and computational burden small. Please consider conversation related to issue: #6918.

[nalimilan]

If pure declarations were supported (#414), map could be restricted to pure functions when applied to sparse arrays, which would allow assuming that f(0) returns always the same value, and thus checking only once that f(0) == 0 (else error out).

[johnmyleswhite]

As long as pure implies deterministic, I agree that the relevant restriction is that map needs to be restricted to pure functions.

[tkelman]

This seems like a lot of extra checking and special-casing for something that's not all that hard to do manually. Rather than trying to enforce extra requirements on the general-purpose map for sparse matrices, why not put in a helper function spmap or something that operates only on (structural) nonzeros, returns an output with the same sparsity pattern, but doesn't impose any extra checks or requirements on the function. This would be quite simple to write by hand, just a few lines of code, if it's something you find yourself doing often.

[StefanKarpinski]

Excellent idea.

[jumutc]

I would consider operations over non-zero entries of SparseMatrixCSC as a common use case which shouldn't be duplicated over and over again. May be something like spmap is a good idea but it should belong to sparse.jl.

[ViralBShah]

Closing as dup of #7010