array recycling/bsxfun-like operator

[shabbychef]

Having some kind of array recycling (as e.g. in R) for some (all?) binary operators can aid vectorized computation. (Rather, it allows one to write code without thinking too much about vectorization.) I am not sure that R's version of this Does The Right Thing, however:

1. Without fair warning, new users may silently be using this 'feature' without knowing it.
2. Turning it on by default in the core language is an extra complication in the compiler at least, and in the language definition.
3. My preference, at least, is to recycle as Matlab's bsxfun, instead of considering a multidimensional array as a single vector and recycling modulo its length. For example, I often deal with multidimensional (5d or higher) arrays; to compute a Z-score 'along' dimension dim, in Matlab I can write x_zscore = bsxfun(@rdivide,bsxfun(@minus,x,mean(x,dim)),std(x,1,dim)). While this is agnostic to the dimensionality of x and the value in dim, it is a right PITA to read. It would be preferrable to have, instead, x_zscore = (x - mean(x,dim)) / std(x,1,dim).

Perhaps there should be some way to 'turn on' this kind of recycling in a given scope, which would result in overloading of the binary operators. (And perhaps this mechanism could support other kinds of recycling, e.g. R style.)

[JeffBezanson]

bsxfun would be an uncontroversial addition to the library even if not ideal.

Another alternative is to define a type like ExpandedArray that virtually replicates an array or vector. Then you could write something like x - expand(mean(x,dim)). Other naming ideas welcome.

[JeffBezanson]

bsxfun is now implemented.