Fix dot(::Adjoint, ::Adjoint) for numbers that don't commute under mu…

…ltiplication (#44219)

Co-authored-by: Fredrik Ekre <[email protected]>

stdlib/LinearAlgebra/src/generic.jl

@@ -886,7 +886,9 @@ function dot(x::AbstractArray, y::AbstractArray)
     s
 end
 
-dot(x::Adjoint, y::Adjoint) = conj(dot(parent(x), parent(y)))
+function dot(x::Adjoint{<:Union{Real,Complex}}, y::Adjoint{<:Union{Real,Complex}})
+    return conj(dot(parent(x), parent(y)))
+end
 dot(x::Transpose, y::Transpose) = dot(parent(x), parent(y))
 
 """

stdlib/LinearAlgebra/test/generic.jl

@@ -497,20 +497,21 @@ end
 end
 
 @testset "adjtrans dot" begin
-    for t in (transpose, adjoint)
-        x, y = t(rand(ComplexF64, 10)), t(rand(ComplexF64, 10))
+    for t in (transpose, adjoint), T in (ComplexF64, Quaternion{Float64})
+        x, y = t(rand(T, 10)), t(rand(T, 10))
         X, Y = copy(x), copy(y)
         @test dot(x, y) ≈ dot(X, Y)
-        x, y = t([rand(ComplexF64, 2, 2) for _ in 1:5]), t([rand(ComplexF64, 2, 2) for _ in 1:5])
+        x, y = t([rand(T, 2, 2) for _ in 1:5]), t([rand(T, 2, 2) for _ in 1:5])
         X, Y = copy(x), copy(y)
         @test dot(x, y) ≈ dot(X, Y)
-        x, y = t(rand(ComplexF64, 10, 5)), t(rand(ComplexF64, 10, 5))
+        x, y = t(rand(T, 10, 5)), t(rand(T, 10, 5))
         X, Y = copy(x), copy(y)
         @test dot(x, y) ≈ dot(X, Y)
-        x = t([rand(ComplexF64, 2, 2) for _ in 1:5, _ in 1:5])
-        y = t([rand(ComplexF64, 2, 2) for _ in 1:5, _ in 1:5])
+        x = t([rand(T, 2, 2) for _ in 1:5, _ in 1:5])
+        y = t([rand(T, 2, 2) for _ in 1:5, _ in 1:5])
         X, Y = copy(x), copy(y)
         @test dot(x, y) ≈ dot(X, Y)
+        x, y = t([rand(T, 2, 2) for _ in 1:5]), t([rand(T, 2, 2) for _ in 1:5])
     end
 end
 

test/testhelpers/Quaternions.jl

@@ -1,6 +1,7 @@
 # This file is a part of Julia. License is MIT: https://julialang.org/license
 
 module Quaternions
+using Random
 
 export Quaternion
 
@@ -36,4 +37,17 @@ Base.:(*)(q::Quaternion, b::Bool) = b * q # remove method ambiguity
 Base.:(/)(q::Quaternion, w::Quaternion) = q * conj(w) * (1.0 / abs2(w))
 Base.:(\)(q::Quaternion, w::Quaternion) = conj(q) * w * (1.0 / abs2(q))
 
+# adapted from https://github.com/JuliaGeometry/Quaternions.jl/pull/42
+function Base.rand(rng::AbstractRNG, ::Random.SamplerType{Quaternion{T}}) where {T<:Real}
+    return Quaternion{T}(rand(rng, T), rand(rng, T), rand(rng, T), rand(rng, T))
+end
+function Base.randn(rng::AbstractRNG, ::Type{Quaternion{T}}) where {T<:AbstractFloat}
+    return Quaternion{T}(
+        randn(rng, T) / 2,
+        randn(rng, T) / 2,
+        randn(rng, T) / 2,
+        randn(rng, T) / 2,
+    )
+end
+
 end