New complex bridges are very inefficient

[araujoms]

I've been benchmarking the new complex cone of SCS, and I've noticed that there is a problem with the bridges. For a very large problem the time spent pre-processing went from 15s to 295s. Profiling shows that all of this time is spent in the function set_dot:

SCS.jl/src/MOI_wrapper/hermitian_complex_psd_cone_bridge.jl

Lines 37 to 57 in d266483

	function MOI.Utilities.set_dot(
	x::AbstractVector{S},
	y::AbstractVector{T},
	set::ComplexPositiveSemidefiniteConeTriangle,
	) where {S,T}
	U = MA.promote_operation(MA.add_mul, S, T)
	result = zero(U)
	d = set.side_dimension
	k = 0
	for j in 1:d
	for i in 1:j-1
	k += 1
	result = MA.add_mul!!(result, 2, x[k], y[k])
	k += 1
	result = MA.add_mul!!(result, 2, x[k], y[k])
	end
	k += 1
	result = MA.add_mul!!(result, x[k], y[k])
	end
	return result
	end

Perhaps is it obvious to you what is wrong with it?

[odow]

What are the arguments that it is called with?

What is a reproducible benchmark?

[blegat]

The typical case is that set_dot is called with a CanonicalVector and you don't have a specialized method for that. Do you have the stacktrace of the bottleneck ?

[araujoms]

That was indeed the problem! Making a PR now.