Remove kludgy VectorStyle and MatrixStyle (#26430)

* Remove kludgy VectorStyle and MatrixStyle

These broadcast styles were introduced in response to JuliaLang/julia#23939 (comment) as a way to limit the "greediness" of Sparse's broadcasting implementation -- sparse only wanted to allow known combinations of array types (including Array but not any AbstractArray). The idea was to allow us to gradually improve the sparse broadcast implementation over 1.x in a non-breaking manner.  Unfortunately, these special styles for Array make defining new styles in the heirarchy a bit of a pain (ref. JuliaLang/julia#23939 (comment)), and it was making my life harder in getting the 1.0 breaking changes in.

This commit removes these special broadcast styles in favor of just having Sparse identify the cases itself and re-dispatch back into the default implementation in the cases it doesn't know how to handle.

* Add a graceful deprecation

src/higherorderfns.jl

@@ -973,35 +973,39 @@ broadcast(f::Tf, A::SparseMatrixCSC, ::Type{T}) where {Tf,T} = broadcast(x -> f(
 # and rebroadcast. otherwise, divert to generic AbstractArray broadcast code.
 
 struct PromoteToSparse <: Broadcast.AbstractArrayStyle{2} end
-const StructuredMatrix = Union{Diagonal,Bidiagonal,Tridiagonal,SymTridiagonal}
-Broadcast.BroadcastStyle(::Type{<:StructuredMatrix}) = PromoteToSparse()
-
 PromoteToSparse(::Val{0}) = PromoteToSparse()
 PromoteToSparse(::Val{1}) = PromoteToSparse()
 PromoteToSparse(::Val{2}) = PromoteToSparse()
 PromoteToSparse(::Val{N}) where N = Broadcast.DefaultArrayStyle{N}()
 
-Broadcast.BroadcastStyle(::PromoteToSparse, ::SPVM) = PromoteToSparse()
-Broadcast.BroadcastStyle(::PromoteToSparse, ::Broadcast.Style{Tuple}) = Broadcast.DefaultArrayStyle{2}()
-
-# FIXME: switch to DefaultArrayStyle once we can delete VectorStyle and MatrixStyle
-# Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{0}) = PromoteToSparse()
-# Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{1}) = PromoteToSparse()
-# Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{2}) = PromoteToSparse()
-Broadcast.BroadcastStyle(::Type{<:Adjoint{T,<:Vector} where T}) = Broadcast.MatrixStyle() # Adjoint not yet defined when broadcast.jl loaded
-Broadcast.BroadcastStyle(::Type{<:Transpose{T,<:Vector} where T}) = Broadcast.MatrixStyle() # Transpose not yet defined when broadcast.jl loaded
+const StructuredMatrix = Union{Diagonal,Bidiagonal,Tridiagonal,SymTridiagonal}
+Broadcast.BroadcastStyle(::Type{<:StructuredMatrix}) = PromoteToSparse()
 Broadcast.BroadcastStyle(::Type{<:Adjoint{T,<:Union{SparseVector,SparseMatrixCSC}} where T}) = PromoteToSparse()
 Broadcast.BroadcastStyle(::Type{<:Transpose{T,<:Union{SparseVector,SparseMatrixCSC}} where T}) = PromoteToSparse()
-Broadcast.BroadcastStyle(::SPVM, ::Broadcast.VectorStyle) = PromoteToSparse()
-Broadcast.BroadcastStyle(::SPVM, ::Broadcast.MatrixStyle) = PromoteToSparse()
-Broadcast.BroadcastStyle(::SparseVecStyle, ::Broadcast.DefaultArrayStyle{N}) where N =
-    Broadcast.DefaultArrayStyle(Broadcast._max(Val(N), Val(1)))
-Broadcast.BroadcastStyle(::SparseMatStyle, ::Broadcast.DefaultArrayStyle{N}) where N =
-    Broadcast.DefaultArrayStyle(Broadcast._max(Val(N), Val(2)))
-# end FIXME
 
-broadcast(f, ::PromoteToSparse, ::Nothing, ::Nothing, As::Vararg{Any,N}) where {N} =
-    broadcast(f, map(_sparsifystructured, As)...)
+Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{0}) = PromoteToSparse()
+Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{1}) = PromoteToSparse()
+Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{2}) = PromoteToSparse()
+Broadcast.BroadcastStyle(::PromoteToSparse, ::SPVM) = PromoteToSparse()
+Broadcast.BroadcastStyle(::PromoteToSparse, ::Broadcast.Style{Tuple}) = Broadcast.DefaultArrayStyle{2}()
+
+# FIXME: currently sparse broadcasts are only well-tested on known array types, while any AbstractArray
+# could report itself as a DefaultArrayStyle().
+# See https://github.com/JuliaLang/julia/pull/23939#pullrequestreview-72075382 for more details
+is_supported_sparse_broadcast() = true
+is_supported_sparse_broadcast(::AbstractArray, rest...) = false
+is_supported_sparse_broadcast(::AbstractSparseArray, rest...) = is_supported_sparse_broadcast(rest...)
+is_supported_sparse_broadcast(::StructuredMatrix, rest...) = is_supported_sparse_broadcast(rest...)
+is_supported_sparse_broadcast(::Array, rest...) = is_supported_sparse_broadcast(rest...)
+is_supported_sparse_broadcast(t::Union{Transpose, Adjoint}, rest...) = is_supported_sparse_broadcast(t.parent, rest...)
+is_supported_sparse_broadcast(x, rest...) = BroadcastStyle(typeof(x)) === Broadcast.Scalar() && is_supported_sparse_broadcast(rest...)
+function broadcast(f, s::PromoteToSparse, ::Nothing, ::Nothing, As::Vararg{Any,N}) where {N}
+    if is_supported_sparse_broadcast(As...)
+        return broadcast(f, map(_sparsifystructured, As)...)
+    else
+        return broadcast(f, Broadcast.ArrayConflict(), nothing, nothing, As...)
+    end
+end
 
 # For broadcast! with ::Any inputs, we need a layer of indirection to determine whether
 # the inputs can be promoted to SparseVecOrMat. If it's just SparseVecOrMat and scalars,