Improve AbstractQ coverage

src/abstractq.jl

@@ -277,6 +277,7 @@ QRPackedQ(factors::AbstractMatrix{T}, τ::AbstractVector{T}) where {T} =
     QRPackedQ{T,typeof(factors),typeof(τ)}(factors, τ)
 QRPackedQ{T}(factors::AbstractMatrix, τ::AbstractVector) where {T} =
     QRPackedQ(convert(AbstractMatrix{T}, factors), convert(AbstractVector{T}, τ))
+QRPackedQ{T}(Q::QRPackedQ) where {T} = QRPackedQ{T}(Q.factors, Q.τ)
 # backwards-compatible constructors (remove with Julia 2.0)
 @deprecate(QRPackedQ{T,S}(factors::AbstractMatrix{T}, τ::AbstractVector{T}) where {T,S},
            QRPackedQ{T,S,typeof(τ)}(factors, τ), false)
@@ -300,12 +301,11 @@ QRCompactWYQ(factors::AbstractMatrix{S}, T::AbstractMatrix{S}) where {S} =
     QRCompactWYQ{S,typeof(factors),typeof(T)}(factors, T)
 QRCompactWYQ{S}(factors::AbstractMatrix, T::AbstractMatrix) where {S} =
     QRCompactWYQ(convert(AbstractMatrix{S}, factors), convert(AbstractMatrix{S}, T))
+QRCompactWYQ{S}(Q::QRCompactWYQ) where {S} = QRCompactWYQ{S}(Q.factors, Q.T)
 # backwards-compatible constructors (remove with Julia 2.0)
 @deprecate(QRCompactWYQ{S,M}(factors::AbstractMatrix{S}, T::AbstractMatrix{S}) where {S,M},
            QRCompactWYQ{S,M,typeof(T)}(factors, T), false)
 
-QRPackedQ{T}(Q::QRPackedQ) where {T} = QRPackedQ(convert(AbstractMatrix{T}, Q.factors), convert(AbstractVector{T}, Q.τ))
-QRCompactWYQ{S}(Q::QRCompactWYQ) where {S} = QRCompactWYQ(convert(AbstractMatrix{S}, Q.factors), convert(AbstractMatrix{S}, Q.T))
 
 # override generic square fallback
 Matrix{T}(Q::Union{QRCompactWYQ{S},QRPackedQ{S}}) where {T,S} =

test/abstractq.jl

@@ -30,10 +30,13 @@ n = 5
         F = qr(A)
         Q = MyQ(F.Q)
         @test ndims(Q) == 2
+        @test eltype([A, Q]) == Union{AbstractQ{T}, AbstractMatrix{T}} # promotion
         T <: Real && @test transpose(Q) == adjoint(Q)
         T <: Complex && @test_throws ErrorException transpose(Q)
         @test convert(AbstractQ{complex(T)}, Q) isa MyQ{complex(T)}
         @test convert(AbstractQ{complex(T)}, Q') isa AdjointQ{<:complex(T),<:MyQ{complex(T)}}
+        @test Q == Matrix(Q) == Q
+        @test Q ≈ Matrix(Q) ≈ Q
         @test *(Q) == Q
         @test Q*I ≈ Q.Q*I rtol=2eps(real(T))
         @test Q'*I ≈ Q.Q'*I rtol=2eps(real(T))
@@ -47,6 +50,7 @@ n = 5
         @test (Q')^2 ≈ Q'*Q'
         @test abs(det(Q)) ≈ 1
         @test logabsdet(Q)[1] ≈ 0 atol=2n*eps(real(T))
+        @test logdet(Q) ≈ log(sign(det(Q)))
         y = rand(T, n)
         @test Q * y ≈ Q.Q * y ≈ Q' \ y ≈ ldiv!(Q', copy(y)) ≈ ldiv!(zero(y), Q', y)
         @test Q'y ≈ Q.Q' * y ≈ Q \ y ≈ ldiv!(Q, copy(y)) ≈ ldiv!(zero(y), Q, y)

test/hessenberg.jl

@@ -305,4 +305,12 @@ end
     end
 end
 
+@testset "Hessenberg factorization of Q" begin
+    for T in (Float32, Float64, ComplexF32, ComplexF64)
+        Q1, H1 = hessenberg(randn(T,5,5))
+        Q2, H2 = hessenberg(Q1)
+        @test Q2'Q2 ≈ I
+    end
+end
+
 end # module TestHessenberg

test/lq.jl

@@ -234,4 +234,13 @@ end
 
 end
 
+@testset "LQ factorization of Q" begin
+    for T in (Float32, Float64, ComplexF32, ComplexF64)
+        L1, Q1 = lq(randn(T, 5, 5))
+        L2, Q2 = lq(Q1)
+        @test Matrix(Q1) ≈ Matrix(Q2)
+        @test L2 ≈ I
+    end
+end
+
 end # module TestLQ