Merge pull request #48933 from JuliaLang/dk/cat_array_number

Let Base handle concatenation of arrays and numbers

base/abstractarray.jl

@@ -1985,12 +1985,16 @@ julia> cat(1, [2], [3;;]; dims=Val(2))
 
 # The specializations for 1 and 2 inputs are important
 # especially when running with --inline=no, see #11158
+# The specializations for Union{AbstractVecOrMat,Number} are necessary
+# to have more specialized methods here than in LinearAlgebra/uniformscaling.jl
 vcat(A::AbstractArray) = cat(A; dims=Val(1))
 vcat(A::AbstractArray, B::AbstractArray) = cat(A, B; dims=Val(1))
 vcat(A::AbstractArray...) = cat(A...; dims=Val(1))
+vcat(A::Union{AbstractVecOrMat,Number}...) = cat(A...; dims=Val(1))
 hcat(A::AbstractArray) = cat(A; dims=Val(2))
 hcat(A::AbstractArray, B::AbstractArray) = cat(A, B; dims=Val(2))
 hcat(A::AbstractArray...) = cat(A...; dims=Val(2))
+hcat(A::Union{AbstractVecOrMat,Number}...) = cat(A...; dims=Val(2))
 
 typed_vcat(T::Type, A::AbstractArray) = _cat_t(Val(1), T, A)
 typed_vcat(T::Type, A::AbstractArray, B::AbstractArray) = _cat_t(Val(1), T, A, B)
@@ -2140,6 +2144,8 @@ end
 
 hvcat(rows::Tuple{Vararg{Int}}, xs::Number...) = typed_hvcat(promote_typeof(xs...), rows, xs...)
 hvcat(rows::Tuple{Vararg{Int}}, xs...) = typed_hvcat(promote_eltypeof(xs...), rows, xs...)
+# the following method is needed to provide a more specific one compared to LinearAlgebra/uniformscaling.jl
+hvcat(rows::Tuple{Vararg{Int}}, xs::Union{AbstractVecOrMat,Number}...) = typed_hvcat(promote_eltypeof(xs...), rows, xs...)
 
 function typed_hvcat(::Type{T}, rows::Tuple{Vararg{Int}}, xs::Number...) where T
     nr = length(rows)

base/array.jl

@@ -1916,7 +1916,7 @@ function reverse!(v::AbstractVector, start::Integer, stop::Integer=lastindex(v))
     return v
 end
 
-# concatenations of homogeneous combinations of vectors, horizontal and vertical
+# concatenations of (in)homogeneous combinations of vectors, horizontal and vertical
 
 vcat() = Vector{Any}()
 hcat() = Vector{Any}()
@@ -1930,6 +1930,7 @@ function hcat(V::Vector{T}...) where T
     end
     return [ V[j][i]::T for i=1:length(V[1]), j=1:length(V) ]
 end
+hcat(A::Vector...) = cat(A...; dims=Val(2)) # more special than SparseArrays's hcat
 
 function vcat(arrays::Vector{T}...) where T
     n = 0
@@ -1946,6 +1947,19 @@ function vcat(arrays::Vector{T}...) where T
     end
     return arr
 end
+vcat(A::Vector...) = cat(A...; dims=Val(1)) # more special than SparseArrays's vcat
+
+# disambiguation with LinAlg/special.jl
+# Union{Number,Vector,Matrix} is for LinearAlgebra._DenseConcatGroup
+# VecOrMat{T} is for LinearAlgebra._TypedDenseConcatGroup
+hcat(A::Union{Number,Vector,Matrix}...) = cat(A...; dims=Val(2))
+hcat(A::VecOrMat{T}...) where {T} = typed_hcat(T, A...)
+vcat(A::Union{Number,Vector,Matrix}...) = cat(A...; dims=Val(1))
+vcat(A::VecOrMat{T}...) where {T} = typed_vcat(T, A...)
+hvcat(rows::Tuple{Vararg{Int}}, xs::Union{Number,Vector,Matrix}...) =
+    typed_hvcat(promote_eltypeof(xs...), rows, xs...)
+hvcat(rows::Tuple{Vararg{Int}}, xs::VecOrMat{T}...) where {T} =
+    typed_hvcat(T, rows, xs...)
 
 _cat(n::Integer, x::Integer...) = reshape([x...], (ntuple(Returns(1), n-1)..., length(x)))
 

stdlib/LinearAlgebra/src/special.jl

@@ -335,9 +335,7 @@ const _TypedDenseConcatGroup{T} = Union{Vector{T}, Adjoint{T,Vector{T}}, Transpo
 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::Vector...) = Base.typed_vcat(promote_eltype(A...), A...)
 vcat(A::_DenseConcatGroup...) = Base.typed_vcat(promote_eltype(A...), A...)
-hcat(A::Vector...) = Base.typed_hcat(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

stdlib/LinearAlgebra/src/uniformscaling.jl

@@ -419,10 +419,14 @@ 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{AbstractVecOrMat,UniformScaling,Number}...) = $_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))
             n = -1
             for a in A