cat: ensure vararg is more inferrable

Ensures that Union{} is not part of the output possibilities after type-piracy of Base.cat methods.

Refs JuliaLang/julia#50550

Author: vtjnash

src/sparsevector.jl

@@ -1194,13 +1194,14 @@ anysparse() = false
 anysparse(X) = X isa AbstractArray && issparse(X)
 anysparse(X, Xs...) = anysparse(X) || anysparse(Xs...)
 
-function hcat(X::Union{Vector, AbstractSparseVector}...)
+const _SparseVecConcatGroup = Union{Vector, AbstractSparseVector}
+function hcat(X::_SparseVecConcatGroup...)
     if anysparse(X...)
         X = map(sparse, X)
     end
     return cat(X...; dims=Val(2))
 end
-function vcat(X::Union{Vector, AbstractSparseVector}...)
+function vcat(X::_SparseVecConcatGroup...)
     if anysparse(X...)
         X = map(sparse, X)
     end
@@ -1213,30 +1214,30 @@ end
 const _SparseConcatGroup = Union{AbstractVecOrMat{<:Number},Number}
 
 # `@constprop :aggressive` allows `dims` to be propagated as constant improving return type inference
-Base.@constprop :aggressive function Base._cat(dims, X::_SparseConcatGroup...)
-    T = promote_eltype(X...)
-    if anysparse(X...)
-        X = (_sparse(first(X)), map(_makesparse, Base.tail(X))...)
+Base.@constprop :aggressive function Base._cat(dims, X1::_SparseConcatGroup, X::_SparseConcatGroup...)
+    T = promote_eltype(X1, X...)
+    if anysparse(X1) || anysparse(X...)
+        X1, X = _sparse(X1), map(_makesparse, X)
     end
-    return Base._cat_t(dims, T, X...)
+    return Base._cat_t(dims, T, X1, X...)
 end
-function hcat(X::_SparseConcatGroup...)
-    if anysparse(X...)
-        X = (_sparse(first(X)), map(_makesparse, Base.tail(X))...)
+function hcat(X1::_SparseConcatGroup, X::_SparseConcatGroup...)
+    if anysparse(X1) || anysparse(X...)
+        X1, X = _sparse(X1), map(_makesparse, X)
     end
-    return cat(X..., dims=Val(2))
+    return cat(X1, X..., dims=Val(2))
 end
-function vcat(X::_SparseConcatGroup...)
-    if anysparse(X...)
-        X = (_sparse(first(X)), map(_makesparse, Base.tail(X))...)
+function vcat(X1::_SparseConcatGroup, X::_SparseConcatGroup...)
+    if anysparse(X1) || anysparse(X...)
+        X1, X = _sparse(X1), map(_makesparse, X)
     end
-    return cat(X..., dims=Val(1))
+    return cat(X1, X..., dims=Val(1))
 end
-function hvcat(rows::Tuple{Vararg{Int}}, X::_SparseConcatGroup...)
-    if anysparse(X...)
-        vcat(_hvcat_rows(rows, X...)...)
+function hvcat(rows::Tuple{Vararg{Int}}, X1::_SparseConcatGroup, X::_SparseConcatGroup...)
+    if anysparse(X1) || anysparse(X...)
+        vcat(_hvcat_rows(rows, X1, X...)...)
     else
-        Base.typed_hvcat(Base.promote_eltypeof(X...), rows, X...)
+        Base.typed_hvcat(Base.promote_eltypeof(X1, X...), rows, X1, X...)
     end
 end
 function _hvcat_rows((row1, rows...)::Tuple{Vararg{Int}}, X::_SparseConcatGroup...)
@@ -1254,6 +1255,15 @@ function _hvcat_rows((row1, rows...)::Tuple{Vararg{Int}}, X::_SparseConcatGroup.
 end
 _hvcat_rows(::Tuple{}, X::_SparseConcatGroup...) = ()
 
+# disambiguation for type-piracy problems created above
+hcat(n1::Number, ns::Vararg{Number}) = invoke(hcat, Tuple{Vararg{Number}}, n1, ns...)
+vcat(n1::Number, ns::Vararg{Number}) = invoke(vcat, Tuple{Vararg{Number}}, n1, ns...)
+hcat(n1::Type{N}, ns::Vararg{N}) where {N<:Number} = invoke(hcat, Tuple{Vararg{Number}}, n1, ns...)
+vcat(n1::Type{N}, ns::Vararg{N}) where {N<:Number} = invoke(vcat, Tuple{Vararg{Number}}, n1, ns...)
+hvcat(rows::Tuple{Vararg{Int}}, n1::Number, ns::Vararg{Number}) = invoke(hvcat, Tuple{typeof(rows), Vararg{Number}}, rows, n1, ns...)
+hvcat(rows::Tuple{Vararg{Int}}, n1::N, ns::Vararg{N}) where {N<:Number} = invoke(hvcat, Tuple{typeof(rows), Vararg{N}}, rows, n1, ns...)
+
+
 # make sure UniformScaling objects are converted to sparse matrices for concatenation
 promote_to_array_type(A::Tuple{Vararg{Union{_SparseConcatGroup,UniformScaling}}}) = anysparse(A...) ? SparseMatrixCSC : Matrix
 promote_to_arrays_(n::Int, ::Type{SparseMatrixCSC}, J::UniformScaling) = sparse(J, n, n)