Concatenation with UniformScaling and numbers (JuliaLang#41394)

Co-authored-by: Jameson Nash <vtjnash@gmail.com>

stdlib/LinearAlgebra/src/LinearAlgebra.jl

@@ -15,8 +15,8 @@ import Base: USE_BLAS64, abs, acos, acosh, acot, acoth, acsc, acsch, adjoint, as
     oneunit, parent, power_by_squaring, print_matrix, promote_rule, real, round, sec, sech,
     setindex!, show, similar, sin, sincos, sinh, size, sqrt,
     strides, stride, tan, tanh, transpose, trunc, typed_hcat, vec
-using Base: IndexLinear, promote_op, promote_typeof,
-    @propagate_inbounds, @pure, reduce, typed_vcat, require_one_based_indexing,
+using Base: IndexLinear, promote_eltype, promote_op, promote_typeof,
+    @propagate_inbounds, @pure, reduce, typed_hvcat, typed_vcat, require_one_based_indexing,
     splat
 using Base.Broadcast: Broadcasted, broadcasted
 import Libdl

stdlib/LinearAlgebra/src/uniformscaling.jl

@@ -391,6 +391,7 @@ end
 # in A to matrices of type T and sizes given by n[k:end].  n is an array
 # so that the same promotion code can be used for hvcat.  We pass the type T
 # 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} = copyto!(Matrix{T}(undef, n,n), J)
 promote_to_arrays_(n::Int, ::Type, A::AbstractVecOrMat) = A
 promote_to_arrays(n,k, ::Type) = ()
@@ -401,11 +402,11 @@ 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}}}) = Matrix
+promote_to_array_type(A::Tuple{Vararg{Union{AbstractVecOrMat,UniformScaling,Number}}}) = Matrix
 
 for (f,dim,name) in ((:hcat,1,"rows"), (:vcat,2,"cols"))
     @eval begin
-        function $f(A::Union{AbstractVecOrMat,UniformScaling}...)
+        function $f(A::Union{AbstractVecOrMat,UniformScaling,Number}...)
             n = -1
             for a in A
                 if !isa(a, UniformScaling)
@@ -418,13 +419,13 @@ for (f,dim,name) in ((:hcat,1,"rows"), (:vcat,2,"cols"))
                 end
             end
             n == -1 && throw(ArgumentError($("$f of only UniformScaling objects cannot determine the matrix size")))
-            return $f(promote_to_arrays(fill(n,length(A)),1, promote_to_array_type(A), A...)...)
+            return cat(promote_to_arrays(fill(n, length(A)), 1, promote_to_array_type(A), A...)..., dims=Val(3-$dim))
         end
     end
 end
 
 
-function hvcat(rows::Tuple{Vararg{Int}}, A::Union{AbstractVecOrMat,UniformScaling}...)
+function hvcat(rows::Tuple{Vararg{Int}}, A::Union{AbstractVecOrMat,UniformScaling,Number}...)
     require_one_based_indexing(A...)
     nr = length(rows)
     sum(rows) == length(A) || throw(ArgumentError("mismatch between row sizes and number of arguments"))
@@ -467,16 +468,27 @@ function hvcat(rows::Tuple{Vararg{Int}}, A::Union{AbstractVecOrMat,UniformScalin
         j = 0
         for i = 1:nr
             if rows[i] > 0 && n[j+1] == -1 # this row consists entirely of UniformScalings
-                nci = nc ÷ rows[i]
-                nci * rows[i] != nc && throw(DimensionMismatch("indivisible UniformScaling sizes"))
+                nci, r = divrem(nc, rows[i])
+                r != 0 && throw(DimensionMismatch("indivisible UniformScaling sizes"))
                 for k = 1:rows[i]
                     n[j+k] = nci
                 end
             end
             j += rows[i]
         end
     end
-    return hvcat(rows, promote_to_arrays(n,1, promote_to_array_type(A), A...)...)
+    Atyp = promote_to_array_type(A)
+    Amat = promote_to_arrays(n, 1, Atyp, A...)
+    # We have two methods for promote_to_array_type, one returning Matrix and
+    # another one returning SparseMatrixCSC (in SparseArrays.jl). In the dense
+    # case, we cannot call hvcat for the promoted UniformScalings because this
+    # causes a stack overflow. In the sparse case, however, we cannot call
+    # typed_hvcat because we need a sparse output.
+    if Atyp == Matrix
+        return typed_hvcat(promote_eltype(Amat...), rows, Amat...)
+    else
+        return hvcat(rows, Amat...)
+    end
 end
 
 ## Matrix construction from UniformScaling

stdlib/LinearAlgebra/test/uniformscaling.jl

@@ -335,10 +335,19 @@ end
         B = T(rand(3,3))
         C = T(rand(0,3))
         D = T(rand(2,0))
+        E = T(rand(1,3))
+        F = T(rand(3,1))
+        α = rand()
         @test (hcat(A, 2I))::T == hcat(A, Matrix(2I, 3, 3))
+        @test (hcat(E, α))::T == hcat(E, [α])
+        @test (hcat(E, α, 2I))::T == hcat(E, [α], fill(2, 1, 1))
         @test (vcat(A, 2I))::T == vcat(A, Matrix(2I, 4, 4))
+        @test (vcat(F, α))::T == vcat(F, [α])
+        @test (vcat(F, α, 2I))::T == vcat(F, [α], fill(2, 1, 1))
         @test (hcat(C, 2I))::T == C
+        @test_throws DimensionMismatch hcat(C, α)
         @test (vcat(D, 2I))::T == D
+        @test_throws DimensionMismatch vcat(D, α)
         @test (hcat(I, 3I, A, 2I))::T == hcat(Matrix(I, 3, 3), Matrix(3I, 3, 3), A, Matrix(2I, 3, 3))
         @test (vcat(I, 3I, A, 2I))::T == vcat(Matrix(I, 4, 4), Matrix(3I, 4, 4), A, Matrix(2I, 4, 4))
         @test (hvcat((2,1,2), B, 2I, I, 3I, 4I))::T ==
@@ -353,6 +362,9 @@ end
             hvcat((2,2,2), B, Matrix(2I, 3, 3), C, C, Matrix(3I, 3, 3), Matrix(4I, 3, 3))
         @test hvcat((3,2,1), C, C, I, B ,3I, 2I)::T ==
             hvcat((2,2,1), C, C, B, Matrix(3I,3,3), Matrix(2I,6,6))
+        @test (hvcat((1,2), A, E, α))::T == hvcat((1,2), A, E, [α]) == hvcat((1,2), A, E, α*I)
+        @test (hvcat((2,2), α, E, F, 3I))::T == hvcat((2,2), [α], E, F, Matrix(3I, 3, 3))
+        @test (hvcat((2,2), 3I, F, E, α))::T == hvcat((2,2), Matrix(3I, 3, 3), F, E, [α])
     end
 end
 

stdlib/SparseArrays/src/sparsevector.jl

@@ -1083,23 +1083,26 @@ const _Triangular_DenseArrays{T,A<:Matrix} = LinearAlgebra.AbstractTriangular{T,
 const _Annotated_DenseArrays = Union{_Triangular_DenseArrays, _Symmetric_DenseArrays, _Hermitian_DenseArrays}
 const _Annotated_Typed_DenseArrays{T} = Union{_Triangular_DenseArrays{T}, _Symmetric_DenseArrays{T}, _Hermitian_DenseArrays{T}}
 
-const _SparseConcatGroup = Union{Vector, Adjoint{<:Any,<:Vector}, Transpose{<:Any,<:Vector}, Matrix, _SparseConcatArrays, _Annotated_SparseConcatArrays, _Annotated_DenseArrays}
-const _DenseConcatGroup = Union{Vector, Adjoint{<:Any,<:Vector}, Transpose{<:Any,<:Vector}, Matrix, _Annotated_DenseArrays}
+const _SparseConcatGroup = Union{Number, Vector, Adjoint{<:Any,<:Vector}, Transpose{<:Any,<:Vector}, Matrix, _SparseConcatArrays, _Annotated_SparseConcatArrays, _Annotated_DenseArrays}
+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}}
 
 # Concatenations involving un/annotated sparse/special matrices/vectors should yield sparse arrays
+_makesparse(x::Number) = x
+_makesparse(x::AbstractArray) = SparseMatrixCSC(issparse(x) ? x : sparse(x))
+
 function Base._cat(dims, Xin::_SparseConcatGroup...)
-    X = map(x -> SparseMatrixCSC(issparse(x) ? x : sparse(x)), Xin)
+    X = map(_makesparse, Xin)
     T = promote_eltype(Xin...)
     Base.cat_t(T, X...; dims=dims)
 end
 function hcat(Xin::_SparseConcatGroup...)
-    X = map(x -> SparseMatrixCSC(issparse(x) ? x : sparse(x)), Xin)
-    hcat(X...)
+    X = map(_makesparse, Xin)
+    return cat(X..., dims=Val(2))
 end
 function vcat(Xin::_SparseConcatGroup...)
-    X = map(x -> SparseMatrixCSC(issparse(x) ? x : sparse(x)), Xin)
-    vcat(X...)
+    X = map(_makesparse, Xin)
+    return cat(X..., dims=Val(1))
 end
 hvcat(rows::Tuple{Vararg{Int}}, X::_SparseConcatGroup...) =
     vcat(_hvcat_rows(rows, X...)...)