Fix issue #249

[bvdmitri]

This PR fixes #249 . The underlying issue happens to be related to ForwardDiff.jl. JuliaDiff/ForwardDiff.jl#622 JuliaDiff/ForwardDiff.jl#481

[bartvanerp]

I think the PR looks good and gets rid of the ForwardDiff bug (at least for the 3 argument dot product). However, I am a bit hesitant of renaming all dot operations to xT_A_y for readability/simplicity sake. Would it be possible to instead use Julia multiple dispatch feature that only uses this new dot operation if we are processing dual numbers as:

function dot(x::AbstractVector, A::AbstractMatrix, y::AbstractVector{<:DualNumber})
    (axes(x)..., axes(y)...) == axes(A) || throw(DimensionMismatch())
    T = typeof(dot(first(x), first(A), first(y)))
    s = zero(T)
    i₁ = first(eachindex(x))
    x₁ = first(x)
    @inbounds for j in eachindex(y)
        yj = y[j]
        temp = zero(adjoint(A[i₁,j]) * x₁)
        @simd for i in eachindex(x)
            temp += adjoint(A[i,j]) * x[i]
        end
        s += dot(temp, yj)
    end
    return s
end

[bvdmitri]

@bartvanerp Agreed, I've changed the PR to use multiple dispatch instead. Let's see if all tests are passing on CI.

[codecov-commenter]

Codecov Report

Base: 61.61% // Head: 61.69% // Increases project coverage by +0.07% 🎉

Coverage data is based on head (f5f42b3) compared to base (f9d83ac).
Patch coverage: 94.73% of modified lines in pull request are covered.

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Additional details and impacted files

@@            Coverage Diff             @@
##           master     #250      +/-   ##
==========================================
+ Coverage   61.61%   61.69%   +0.07%     
==========================================
  Files         194      195       +1     
  Lines        7183     7200      +17     
==========================================
+ Hits         4426     4442      +16     
- Misses       2757     2758       +1     

Impacted Files	Coverage Δ
src/ReactiveMP.jl	75.86% <ø> (ø)
src/nodes/autoregressive.jl	20.00% <ø> (ø)
src/fixes.jl	93.33% <93.33%> (ø)
src/distributions/mv_normal_mean_precision.jl	91.93% <100.00%> (ø)
...distributions/mv_normal_weighted_mean_precision.jl	98.00% <100.00%> (ø)
src/distributions/normal.jl	90.00% <100.00%> (+0.06%)	⬆️

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[Nimrais]

Thanks @bvdmitri! Well Done!