fixed symtridiagonal +/- bidiagonal

[mcognetta]

SymTridiagonal + Bidiagonal matrices fail because the output is forced to Symtridiagonal. Now it correctly promotes to Tridiagonal matrices. This does not consider the case where the Bidiagonal matrix is diagonal.

Before:

julia> S = SymTridiagonal(rand(10), rand(9))
julia> B = Bidiagonal(rand(10), rand(9), :U)
julia> S+B # same with B+S, S-B, B-S
ERROR: ArgumentError: matrix cannot be represented as SymTridiagonal

Now:

julia> S = SymTridiagonal(rand(10), rand(9))
julia> B = Bidiagonal(rand(10), rand(9), :U)
julia> S+B # returns10×10 Tridiagonal{Float64,Array{Float64,1}}

[mbauman]

Thanks so much for tackling this! Here's an alternate patch that passes both the existing tests and the new ones you added:

diff --git a/stdlib/LinearAlgebra/src/special.jl b/stdlib/LinearAlgebra/src/special.jl
index 70014837e0..984c9271df 100644
--- a/stdlib/LinearAlgebra/src/special.jl
+++ b/stdlib/LinearAlgebra/src/special.jl
@@ -79,54 +79,6 @@ macro commutative(myexpr)
     esc(Expr(:block, myexpr, reversed_call))
 end

-for op in (:+, :-)
-    SpecialMatrices = [:Diagonal, :Bidiagonal, :Tridiagonal, :Matrix]
-    for (idx, matrixtype1) in enumerate(SpecialMatrices) # matrixtype1 is the sparser matrix type
-        for matrixtype2 in SpecialMatrices[idx+1:end] # matrixtype2 is the denser matrix type
-            @eval begin # TODO quite a few of these conversions are NOT defined
-                ($op)(A::($matrixtype1), B::($matrixtype2)) = ($op)(convert(($matrixtype2), A), B)
-                ($op)(A::($matrixtype2), B::($matrixtype1)) = ($op)(A, convert(($matrixtype2), B))
-            end
-        end
-    end
-
-    for  matrixtype1 in (:SymTridiagonal,)                      # matrixtype1 is the sparser matrix type
-        for matrixtype2 in (:Tridiagonal, :Matrix) # matrixtype2 is the denser matrix type
-            @eval begin
-                ($op)(A::($matrixtype1), B::($matrixtype2)) = ($op)(convert(($matrixtype2), A), B)
-                ($op)(A::($matrixtype2), B::($matrixtype1)) = ($op)(A, convert(($matrixtype2), B))
-            end
-        end
-    end
-
-    for matrixtype1 in (:Diagonal, :Bidiagonal) # matrixtype1 is the sparser matrix type
-        for matrixtype2 in (:SymTridiagonal,)   # matrixtype2 is the denser matrix type
-            @eval begin
-                ($op)(A::($matrixtype1), B::($matrixtype2)) = ($op)(convert(($matrixtype2), A), B)
-                ($op)(A::($matrixtype2), B::($matrixtype1)) = ($op)(A, convert(($matrixtype2), B))
-            end
-        end
-    end
-
-    for matrixtype1 in (:Diagonal,)
-        for (matrixtype2,matrixtype3) in ((:UpperTriangular,:UpperTriangular),
-                                          (:UnitUpperTriangular,:UpperTriangular),
-                                          (:LowerTriangular,:LowerTriangular),
-                                          (:UnitLowerTriangular,:LowerTriangular))
-            @eval begin
-                ($op)(A::($matrixtype1), B::($matrixtype2)) = ($op)(($matrixtype3)(A), B)
-                ($op)(A::($matrixtype2), B::($matrixtype1)) = ($op)(A, ($matrixtype3)(B))
-            end
-        end
-    end
-    for matrixtype in (:SymTridiagonal,:Tridiagonal,:Bidiagonal,:Matrix)
-        @eval begin
-            ($op)(A::AbstractTriangular, B::($matrixtype)) = ($op)(copyto!(similar(parent(A)), A), B)
-            ($op)(A::($matrixtype), B::AbstractTriangular) = ($op)(A, copyto!(similar(parent(B)), B))
-        end
-    end
-end
-
 rmul!(A::AbstractTriangular, adjB::Adjoint{<:Any,<:Union{QRCompactWYQ,QRPackedQ}}) =
     (B = adjB.parent; rmul!(full!(A), adjoint(B)))
 *(A::AbstractTriangular, adjB::Adjoint{<:Any,<:Union{QRCompactWYQ,QRPackedQ}}) =

[mbauman]

In other words: the fallback definitions for array + and - simply assert the sizes are correct and then use broadcasting… and while I've not put together nearly as complete a table as you have in #28883, I think broadcasting mostly does the right thing.

[mcognetta]

Well... how about that. Nice find haha. I am going to add a few more tests and then push these changes to #28883.

[mcognetta]

@mbauman Your fix worked in all cases except Bidiagonal since there is an input parameter and not a special type for upper and lower.

[mcognetta]

I still need to update this for UnitUpperTriangular/UnitLowerTriangular and add tests for the correct types.

[mcognetta]

I am moving all development of this to #28883.