Real part of complex dot product

[antoine-levitt]

A common enough operation when dealing with complex vectors is taking the real part of the inner product, ie dotr(a,b) = re(dot(a,b)) = sum_i re(ai) re(bi) + im(ai) im(bi). This turns up when evaluating Taylor series of complex-to-real maps, when evaluating quadratic forms (z* A z where A is Hermitian), etc. It is not trivial enough that one can easily define a one-liner that computes this in an optimal way (ie not real(dot(a,b))). Would it be a good idea to add a "dotr" function to base Julia or is this considered namespace pollution?

[andreasnoack]

I feel that this falls under our usual "modulizing Julia" discussion. I think it would be ok to export this from the LinAlg module but it is probably not a sufficiently common operation to become a Base exported function.

Update: The comment above was a bit too brief. I don't think it makes much sense in the current situation to add exports to LinAlg that are not exported from Base. In a possible future world where we don't export a lot of linear algebra symbols from Base by default, I think it would make sense to be more liberal about adding exports to LinAlg.

[stevengj]

This should work for Vector, at least:

dotr{T}(a::Vector{Complex{T}}, b::Vector{Complex{T}}) = dot(reinterpret(T, a), reinterpret(T, b))

[antoine-levitt]

If anybody is interested I did some benchmarking on this. On a single thread, the reinterpret version is consistently slower than real(dot()), even for large-ish arrays (which is surprising to me). A dot product of length 2N is faster for small arrays (<~= 1000), but at that point switching to static arrays is much more beneficial anyway. So the benefit in introducing a realdot is pretty marginal.

However, OpenBLAS does not multithread the complex dot product, and so even the reinterpret version is better for large arrays. I guess this should rather be fixed in OpenBLAS (opened an issue here: OpenMathLib/OpenBLAS#2221). I'm closing this issue.