Add dot for complex matrices

[dalum]

This fixes the bug mentioned in #22220 where dot is undefined for complex matrices.

[fredrikekre]

Perhaps add a test? For instance here:

julia/test/blas.jl

Lines 53 to 67 in 5aa15ff

	@testset "dot products" begin
	if elty <: Real
	x1 = convert(Vector{elty}, randn(n))
	x2 = convert(Vector{elty}, randn(n))
	@test BLAS.dot(x1,x2) ≈ sum(x1.*x2)
	@test_throws DimensionMismatch BLAS.dot(x1,rand(elty, n + 1))
	else
	z1 = convert(Vector{elty}, complex.(randn(n),randn(n)))
	z2 = convert(Vector{elty}, complex.(randn(n),randn(n)))
	@test BLAS.dotc(z1,z2) ≈ sum(conj(z1).*z2)
	@test BLAS.dotu(z1,z2) ≈ sum(z1.*z2)
	@test_throws DimensionMismatch BLAS.dotc(z1,rand(elty, n + 1))
	@test_throws DimensionMismatch BLAS.dotu(z1,rand(elty, n + 1))
	end
	end

I did not find any tests for dot(A::Matrix{Real}, B::Matrix{Real}) either, perhaps you can add that in the same block while you're at it?

[andreasnoack]

Sorry. I should have mentioned in #22220 that dot(Matrix,Matrix) working in the real case is a bug introduced in befbcec. See also #11067 (comment). I think we should deprecate the method in BLAS. You can get that behavior with vecdot.

[fredrikekre]

That explains the missing tests then.

[stevengj]

Alternatively, we could define dot for arbitrary AbstractArray arguments (of matching size), using the ordinary (Euclidean) inner product and add a test.

The main problem with this, however, is that it is inconsistent with the default norm. Of course, we could change the default norm too (which would have the advantage of making the default norm much faster!) but this would be a subtly breaking change.

[dalum]

Closing this in light of #22374.

[StefanKarpinski]

Thanks for opening the PR, @eveydee!