Fix vcat of sparse vectors with numbers

src/sparsevector.jl

@@ -1143,21 +1143,28 @@ const _Annotated_SparseConcatArrays = Union{_Triangular_SparseConcatArrays, _Sym
 const _SparseConcatGroup = Union{_DenseConcatGroup, _SparseConcatArrays, _Annotated_SparseConcatArrays}
 
 # Concatenations involving un/annotated sparse/special matrices/vectors should yield sparse arrays
+
+# the output array type is determined by the first element of the to be concatenated objects
+# if this is a Number, the output would be dense by the fallback abstractarray.jl code (see cat_similar)
+# so make sure that if that happens, the "array" is sparse (if more sparse arrays are involved, of course)
+_sparse(x::Number) = sparsevec([1], [x], 1)
+_sparse(A) = _makesparse(A)
 _makesparse(x::Number) = x
-_makesparse(x::AbstractArray) = SparseMatrixCSC(issparse(x) ? x : sparse(x))
+_makesparse(x::AbstractVector) = convert(SparseVector, issparse(x) ? x : sparse(x))::SparseVector
+_makesparse(x::AbstractMatrix) = convert(SparseMatrixCSC, issparse(x) ? x : sparse(x))::SparseMatrixCSC
 
 # `@constprop :aggressive` allows `dims` to be propagated as constant improving return type inference
 Base.@constprop :aggressive function Base._cat(dims, Xin::_SparseConcatGroup...)
-    X = map(_makesparse, Xin)
+    X = (_sparse(first(Xin)), map(_makesparse, Base.tail(Xin))...)
     T = promote_eltype(Xin...)
     return Base._cat_t(dims, T, X...)
 end
 function hcat(Xin::_SparseConcatGroup...)
-    X = map(_makesparse, Xin)
+    X = (_sparse(first(Xin)), map(_makesparse, Base.tail(Xin))...)
     return cat(X..., dims=Val(2))
 end
 function vcat(Xin::_SparseConcatGroup...)
-    X = map(_makesparse, Xin)
+    X = (_sparse(first(Xin)), map(_makesparse, Base.tail(Xin))...)
     return cat(X..., dims=Val(1))
 end
 hvcat(rows::Tuple{Vararg{Int}}, X::_SparseConcatGroup...) =
@@ -1191,9 +1198,9 @@ Concatenate along dimension 2. Return a SparseMatrixCSC object.
     the concatenation with specialized "sparse" matrix types from LinearAlgebra.jl
     automatically yielded sparse output even in the absence of any SparseArray argument.
 """
-sparse_hcat(Xin::Union{AbstractVecOrMat,Number}...) = cat(map(_makesparse, Xin)..., dims=Val(2))
+sparse_hcat(Xin::Union{AbstractVecOrMat,Number}...) = cat(_sparse(first(Xin)), map(_makesparse, Base.tail(Xin))..., dims=Val(2))
 function sparse_hcat(X::Union{AbstractVecOrMat,UniformScaling,Number}...)
-    LinearAlgebra._hcat(X...; array_type = SparseMatrixCSC)
+    LinearAlgebra._hcat(_sparse(first(X)), map(_makesparse, Base.tail(X))...; array_type = SparseMatrixCSC)
 end
 
 """
@@ -1206,9 +1213,9 @@ Concatenate along dimension 1. Return a SparseMatrixCSC object.
     the concatenation with specialized "sparse" matrix types from LinearAlgebra.jl
     automatically yielded sparse output even in the absence of any SparseArray argument.
 """
-sparse_vcat(Xin::Union{AbstractVecOrMat,Number}...) = cat(map(_makesparse, Xin)..., dims=Val(1))
+sparse_vcat(Xin::Union{AbstractVecOrMat,Number}...) = cat(_sparse(first(Xin)), map(_makesparse, Base.tail(Xin))..., dims=Val(1))
 function sparse_vcat(X::Union{AbstractVecOrMat,UniformScaling,Number}...)
-    LinearAlgebra._vcat(X...; array_type = SparseMatrixCSC)
+    LinearAlgebra._vcat(_sparse(first(X)), map(_makesparse, Base.tail(X))...; array_type = SparseMatrixCSC)
 end
 
 """
@@ -1224,10 +1231,10 @@ arguments to concatenate in each block row.
     automatically yielded sparse output even in the absence of any SparseArray argument.
 """
 function sparse_hvcat(rows::Tuple{Vararg{Int}}, Xin::Union{AbstractVecOrMat,Number}...)
-    hvcat(rows, map(_makesparse, Xin)...)
+    hvcat(rows, _sparse(first(Xin)), map(_makesparse, Base.tail(Xin))...)
 end
 function sparse_hvcat(rows::Tuple{Vararg{Int}}, X::Union{AbstractVecOrMat,UniformScaling,Number}...)
-    LinearAlgebra._hvcat(rows, X...; array_type = SparseMatrixCSC)
+    LinearAlgebra._hvcat(rows, _sparse(first(X)), map(_makesparse, Base.tail(X))...; array_type = SparseMatrixCSC)
 end
 
 ### math functions

test/sparsevector.jl

@@ -544,6 +544,22 @@ end
         @test length(V) == m * n
         Vr = vec(Hr)
         @test Array(V) == Vr
+        Vnum = vcat(A..., zero(Float64))
+        Vnum2 = sparse_vcat(map(Array, A)..., zero(Float64))
+        @test Vnum isa SparseVector{Float64,Int}
+        @test Vnum2 isa SparseVector{Float64,Int}
+        @test length(Vnum) == length(Vnum2) == m*n + 1
+        @test Array(Vnum) == Array(Vnum2) == [Vr; 0]
+        Vnum = vcat(zero(Float64), A...)
+        Vnum2 = sparse_vcat(zero(Float64), map(Array, A)...)
+        @test Vnum isa SparseVector{Float64,Int}
+        @test Vnum2 isa SparseVector{Float64,Int}
+        @test length(Vnum) == length(Vnum2) == m*n + 1
+        @test Array(Vnum) == Array(Vnum2) == [0; Vr]
+        # case with rowwise a Number as first element, should still yield a sparse matrix
+        x = sparsevec([1], [3.0], 1)
+        X = [3.0 x; 3.0 x]
+        @test issparse(X)
     end
 
     @testset "concatenation of sparse vectors with other types" begin