Add transpose/adjoint specializations for block Bidiagonal (#1231)

With this, the adjoint of a block `Bidiagonal` will also be a
`Bidiagonal`, following the behavior of a `Diagonal`.
```julia
julia> m = rand(Int8, 2, 2)
2×2 Matrix{Int8}:
 -50  -123
 -11    18

julia> B = Bidiagonal(fill(m,4), fill(m,3), :U)
4×4 Bidiagonal{Matrix{Int8}, Vector{Matrix{Int8}}}:
 [-50 -123; -11 18]  [-50 -123; -11 18]  …      ⋅     
     ⋅               [-50 -123; -11 18]         ⋅     
     ⋅                   ⋅                  [-50 -123; -11 18]
     ⋅                   ⋅                  [-50 -123; -11 18]

julia> B'
4×4 Bidiagonal{Adjoint{Int8, Matrix{Int8}}, Vector{Adjoint{Int8, Matrix{Int8}}}}:
 [-50 -11; -123 18]        ⋅             …        ⋅       
 [-50 -11; -123 18]  [-50 -11; -123 18]           ⋅       
       ⋅             [-50 -11; -123 18]           ⋅       
       ⋅                   ⋅                [-50 -11; -123 18]

julia> B''
4×4 Bidiagonal{Matrix{Int8}, Vector{Matrix{Int8}}}:
 [-50 -123; -11 18]  [-50 -123; -11 18]  …      ⋅     
     ⋅               [-50 -123; -11 18]         ⋅     
     ⋅                   ⋅                  [-50 -123; -11 18]
     ⋅                   ⋅                  [-50 -123; -11 18]
```

---------

Co-authored-by: Daniel Karrasch <daniel.karrasch@posteo.de>

Author: jishnub

src/bidiag.jl

@@ -311,20 +311,14 @@ isreal(M::Bidiagonal) = isreal(M.dv) && isreal(M.ev)
 adjoint(B::Bidiagonal{<:Number}) = Bidiagonal(vec(adjoint(B.dv)), vec(adjoint(B.ev)), B.uplo == 'U' ? :L : :U)
 adjoint(B::Bidiagonal{<:Number, <:Base.ReshapedArray{<:Number,1,<:Adjoint}}) =
     Bidiagonal(adjoint(parent(B.dv)), adjoint(parent(B.ev)), B.uplo == 'U' ? :L : :U)
+adjoint(B::Bidiagonal) = Bidiagonal(adjoint.(B.dv), adjoint.(B.ev), B.uplo == 'U' ? :L : :U)
 transpose(B::Bidiagonal{<:Number}) = Bidiagonal(B.dv, B.ev, B.uplo == 'U' ? :L : :U)
+transpose(B::Bidiagonal) = Bidiagonal(transpose.(B.dv), transpose.(B.ev), B.uplo == 'U' ? :L : :U)
 permutedims(B::Bidiagonal) = Bidiagonal(B.dv, B.ev, B.uplo == 'U' ? 'L' : 'U')
 function permutedims(B::Bidiagonal, perm)
     Base.checkdims_perm(axes(B), axes(B), perm)
     NTuple{2}(perm) == (2, 1) ? permutedims(B) : B
 end
-function Base.copy(aB::Adjoint{<:Any,<:Bidiagonal})
-    B = aB.parent
-    return Bidiagonal(map(x -> copy.(adjoint.(x)), (B.dv, B.ev))..., B.uplo == 'U' ? :L : :U)
-end
-function Base.copy(tB::Transpose{<:Any,<:Bidiagonal})
-    B = tB.parent
-    return Bidiagonal(map(x -> copy.(transpose.(x)), (B.dv, B.ev))..., B.uplo == 'U' ? :L : :U)
-end
 
 @noinline function throw_zeroband_error(A)
     uplo = A.uplo
@@ -1362,14 +1356,10 @@ function ldiv!(c::AbstractVecOrMat, A::Bidiagonal, b::AbstractVecOrMat)
     end
     return c
 end
-ldiv!(A::AdjOrTrans{<:Any,<:Bidiagonal}, b::AbstractVecOrMat) = @inline ldiv!(b, A, b)
-ldiv!(c::AbstractVecOrMat, A::AdjOrTrans{<:Any,<:Bidiagonal}, b::AbstractVecOrMat) =
-    (t = wrapperop(A); _rdiv!(t(c), t(b), t(A)); return c)
 
 ### Generic promotion methods and fallbacks
 \(A::Bidiagonal, B::AbstractVecOrMat) =
     ldiv!(matprod_dest(A, B, promote_op(\, eltype(A), eltype(B))), A, B)
-\(xA::AdjOrTrans{<:Any,<:Bidiagonal}, B::AbstractVecOrMat) = copy(xA) \ B
 
 ### Triangular specializations
 for tri in (:UpperTriangular, :UnitUpperTriangular)
@@ -1441,9 +1431,6 @@ function _rdiv!(C::AbstractMatrix, A::AbstractMatrix, B::Bidiagonal)
     C
 end
 rdiv!(A::AbstractMatrix, B::Bidiagonal) = @inline _rdiv!(A, A, B)
-rdiv!(A::AbstractMatrix, B::AdjOrTrans{<:Any,<:Bidiagonal}) = @inline _rdiv!(A, A, B)
-_rdiv!(C::AbstractMatrix, A::AbstractMatrix, B::AdjOrTrans{<:Any,<:Bidiagonal}) =
-    (t = wrapperop(B); ldiv!(t(C), t(B), t(A)); return C)
 
 /(A::AbstractMatrix, B::Bidiagonal) =
     _rdiv!(similar(A, promote_op(/, eltype(A), eltype(B)), size(A)), A, B)
@@ -1476,15 +1463,9 @@ function /(D::Diagonal, B::Bidiagonal)
     return B.uplo == 'U' ? UpperTriangular(A) : LowerTriangular(A)
 end
 
-/(A::AbstractMatrix, B::Transpose{<:Any,<:Bidiagonal}) = A / copy(B)
-/(A::AbstractMatrix, B::Adjoint{<:Any,<:Bidiagonal}) = A / copy(B)
 # disambiguation
 /(A::AdjointAbsVec, B::Bidiagonal) = adjoint(adjoint(B) \ parent(A))
 /(A::TransposeAbsVec, B::Bidiagonal) = transpose(transpose(B) \ parent(A))
-/(A::AdjointAbsVec, B::Transpose{<:Any,<:Bidiagonal}) = adjoint(adjoint(B) \ parent(A))
-/(A::TransposeAbsVec, B::Transpose{<:Any,<:Bidiagonal}) = transpose(transpose(B) \ parent(A))
-/(A::AdjointAbsVec, B::Adjoint{<:Any,<:Bidiagonal}) = adjoint(adjoint(B) \ parent(A))
-/(A::TransposeAbsVec, B::Adjoint{<:Any,<:Bidiagonal}) = transpose(transpose(B) \ parent(A))
 
 factorize(A::Bidiagonal) = A
 function inv(B::Bidiagonal{T}) where T

test/bidiag.jl

@@ -807,7 +807,7 @@ end
     @test convert(AbstractMatrix{Float64}, Bl)::Bidiagonal{Float64,ImmutableArray{Float64,1,Array{Float64,1}}} == Bl
 end
 
-@testset "block-bidiagonal matrix indexing" begin
+@testset "block-bidiagonal matrix" begin
     dv = [ones(4,3), ones(2,2).*2, ones(2,3).*3, ones(4,4).*4]
     evu = [ones(4,2), ones(2,3).*2, ones(2,4).*3]
     evl = [ones(2,3), ones(2,2).*2, ones(4,3).*3]
@@ -847,6 +847,18 @@ end
         @test @inferred(B[2,1]) isa typeof(s)
         @test all(iszero, B[2,1])
     end
+
+    @testset "adjoint/transpose" begin
+        m = rand(Int, 2, 2)
+        for uplo in [:U, :L]
+            B = Bidiagonal(fill(m,4), fill(m,3), uplo)
+            A = Array{Matrix{Int}}(B)
+            @testset for f in (adjoint, transpose)
+                @test f(B) == f(A)
+                @test f(f(B)) == B
+            end
+        end
+    end
 end
 
 @testset "copyto!" begin