improve cat design / performance (#49322)

This used to make a lot of references to design issues with the
SparseArrays package (JuliaLang/julia#2326 /
JuliaLang/julia#20815), which result in a
non-sensical dispatch arrangement, and contribute to a slow loading
experience do to the nonsense Unions that must be checked by subtyping.

(cherry picked from commit 5a922fadfef083b83d983ac84f49a4460baa42ab)
(cherry picked from commit 8fd5f279c8c81a8e59dec3852235c7dd5c88b143)

src/special.jl

@@ -330,27 +330,11 @@ end
 ==(A::Bidiagonal, B::SymTridiagonal) = iszero(_evview(B)) && iszero(A.ev) && A.dv == B.dv
 ==(B::SymTridiagonal, A::Bidiagonal) = A == B
 
-# concatenation
-const _SpecialArrays = Union{Diagonal, Bidiagonal, Tridiagonal, SymTridiagonal}
-const _Symmetric_DenseArrays{T,A<:Matrix} = Symmetric{T,A}
-const _Hermitian_DenseArrays{T,A<:Matrix} = Hermitian{T,A}
-const _Triangular_DenseArrays{T,A<:Matrix} = AbstractTriangular{T,A}
-const _Annotated_DenseArrays = Union{_SpecialArrays, _Triangular_DenseArrays, _Symmetric_DenseArrays, _Hermitian_DenseArrays}
-const _Annotated_Typed_DenseArrays{T} = Union{_Triangular_DenseArrays{T}, _Symmetric_DenseArrays{T}, _Hermitian_DenseArrays{T}}
-const _DenseConcatGroup = Union{Number, Vector, Adjoint{<:Any,<:Vector}, Transpose{<:Any,<:Vector}, Matrix, _Annotated_DenseArrays}
-const _TypedDenseConcatGroup{T} = Union{Vector{T}, Adjoint{T,Vector{T}}, Transpose{T,Vector{T}}, Matrix{T}, _Annotated_Typed_DenseArrays{T}}
-
-promote_to_array_type(::Tuple{Vararg{Union{_DenseConcatGroup,UniformScaling}}}) = Matrix
-
-Base._cat(dims, xs::_DenseConcatGroup...) = Base._cat_t(dims, promote_eltype(xs...), xs...)
-vcat(A::_DenseConcatGroup...) = Base.typed_vcat(promote_eltype(A...), A...)
-hcat(A::_DenseConcatGroup...) = Base.typed_hcat(promote_eltype(A...), A...)
-hvcat(rows::Tuple{Vararg{Int}}, xs::_DenseConcatGroup...) = Base.typed_hvcat(promote_eltype(xs...), rows, xs...)
-# For performance, specially handle the case where the matrices/vectors have homogeneous eltype
-Base._cat(dims, xs::_TypedDenseConcatGroup{T}...) where {T} = Base._cat_t(dims, T, xs...)
-vcat(A::_TypedDenseConcatGroup{T}...) where {T} = Base.typed_vcat(T, A...)
-hcat(A::_TypedDenseConcatGroup{T}...) where {T} = Base.typed_hcat(T, A...)
-hvcat(rows::Tuple{Vararg{Int}}, xs::_TypedDenseConcatGroup{T}...) where {T} = Base.typed_hvcat(T, rows, xs...)
+# TODO: remove these deprecations (used by SparseArrays in the past)
+const _DenseConcatGroup = Union{}
+const _SpecialArrays = Union{}
+
+promote_to_array_type(::Tuple) = Matrix
 
 # factorizations
 function cholesky(S::RealHermSymComplexHerm{<:Real,<:SymTridiagonal}, ::NoPivot = NoPivot(); check::Bool = true)

src/uniformscaling.jl

@@ -408,7 +408,7 @@ end
 # so that we can re-use this code for sparse-matrix hcat etcetera.
 promote_to_arrays_(n::Int, ::Type, a::Number) = a
 promote_to_arrays_(n::Int, ::Type{Matrix}, J::UniformScaling{T}) where {T} = Matrix(J, n, n)
-promote_to_arrays_(n::Int, ::Type, A::AbstractVecOrMat) = A
+promote_to_arrays_(n::Int, ::Type, A::AbstractArray) = A
 promote_to_arrays(n,k, ::Type) = ()
 promote_to_arrays(n,k, ::Type{T}, A) where {T} = (promote_to_arrays_(n[k], T, A),)
 promote_to_arrays(n,k, ::Type{T}, A, B) where {T} =
@@ -417,17 +417,16 @@ promote_to_arrays(n,k, ::Type{T}, A, B, C) where {T} =
     (promote_to_arrays_(n[k], T, A), promote_to_arrays_(n[k+1], T, B), promote_to_arrays_(n[k+2], T, C))
 promote_to_arrays(n,k, ::Type{T}, A, B, Cs...) where {T} =
     (promote_to_arrays_(n[k], T, A), promote_to_arrays_(n[k+1], T, B), promote_to_arrays(n,k+2, T, Cs...)...)
-promote_to_array_type(A::Tuple{Vararg{Union{AbstractVecOrMat,UniformScaling,Number}}}) = Matrix
 
 _us2number(A) = A
 _us2number(J::UniformScaling) = J.λ
 
 for (f, _f, dim, name) in ((:hcat, :_hcat, 1, "rows"), (:vcat, :_vcat, 2, "cols"))
     @eval begin
-        @inline $f(A::Union{AbstractVecOrMat,UniformScaling}...) = $_f(A...)
+        @inline $f(A::Union{AbstractArray,UniformScaling}...) = $_f(A...)
         # if there's a Number present, J::UniformScaling must be 1x1-dimensional
-        @inline $f(A::Union{AbstractVecOrMat,UniformScaling,Number}...) = $f(map(_us2number, A)...)
-        function $_f(A::Union{AbstractVecOrMat,UniformScaling,Number}...; array_type = promote_to_array_type(A))
+        @inline $f(A::Union{AbstractArray,UniformScaling,Number}...) = $f(map(_us2number, A)...)
+        function $_f(A::Union{AbstractArray,UniformScaling,Number}...; array_type = promote_to_array_type(A))
             n = -1
             for a in A
                 if !isa(a, UniformScaling)
@@ -445,9 +444,8 @@ for (f, _f, dim, name) in ((:hcat, :_hcat, 1, "rows"), (:vcat, :_vcat, 2, "cols"
     end
 end
 
-hvcat(rows::Tuple{Vararg{Int}}, A::Union{AbstractVecOrMat,UniformScaling}...) = _hvcat(rows, A...)
-hvcat(rows::Tuple{Vararg{Int}}, A::Union{AbstractVecOrMat,UniformScaling,Number}...) = _hvcat(rows, A...)
-function _hvcat(rows::Tuple{Vararg{Int}}, A::Union{AbstractVecOrMat,UniformScaling,Number}...; array_type = promote_to_array_type(A))
+hvcat(rows::Tuple{Vararg{Int}}, A::Union{AbstractArray,UniformScaling,Number}...) = _hvcat(rows, A...)
+function _hvcat(rows::Tuple{Vararg{Int}}, A::Union{AbstractArray,UniformScaling,Number}...; array_type = promote_to_array_type(A))
     require_one_based_indexing(A...)
     nr = length(rows)
     sum(rows) == length(A) || throw(ArgumentError("mismatch between row sizes and number of arguments"))