Fix Matrix on diagonal and triangular matrices for types without zero

stdlib/LinearAlgebra/src/bidiag.jl

@@ -163,7 +163,7 @@ function Matrix{T}(A::Bidiagonal) where T
     B[n,n] = A.dv[n]
     return B
 end
-Matrix(A::Bidiagonal{T}) where {T} = Matrix{T}(A)
+Matrix(A::Bidiagonal{T}) where {T} = Matrix{promote_with_zero(T)}(A)
 Array(A::Bidiagonal) = Matrix(A)
 promote_rule(::Type{Matrix{T}}, ::Type{<:Bidiagonal{S}}) where {T,S} =
     @isdefined(T) && @isdefined(S) ? Matrix{promote_type(T,S)} : Matrix

stdlib/LinearAlgebra/src/dense.jl

@@ -299,11 +299,15 @@ function diagm_size(size::Tuple{Int,Int}, kv::Pair{<:Integer,<:AbstractVector}..
     (m ≥ mmax && n ≥ nmax) || throw(DimensionMismatch("invalid size=$size"))
     return m, n
 end
+# For some type `T`, `zero(T)` is not a `T` and `zeros(T, ...)` fails.
+# `zero_type(T::Type) = typeof(zero(T))` would not work for types such
+# as `Array` for which `zero(::T)` is defined but not `zero(::Type{T})`
+# so we use `promote_op` instead.
+zero_type(T::Type) = promote_op(zero, T)
+promote_with_zero(T::Type) = promote_type(T, zero_type(T))
 function diagm_container(size, kv::Pair{<:Integer,<:AbstractVector}...)
     T = promote_type(map(x -> eltype(x.second), kv)...)
-    # For some type `T`, `zero(T)` is not a `T` and `zeros(T, ...)` fails.
-    U = promote_type(T, typeof(zero(T)))
-    return zeros(U, diagm_size(size, kv...)...)
+    return zeros(promote_with_zero(T), diagm_size(size, kv...)...)
 end
 diagm_container(size, kv::Pair{<:Integer,<:BitVector}...) =
     falses(diagm_size(size, kv...)...)

stdlib/LinearAlgebra/src/triangular.jl

@@ -31,7 +31,7 @@ for t in (:LowerTriangular, :UnitLowerTriangular, :UpperTriangular,
             Anew = convert(AbstractMatrix{T}, A.data)
             $t(Anew)
         end
-        Matrix(A::$t{T}) where {T} = Matrix{T}(A)
+        Matrix(A::$t{T}) where {T} = Matrix{promote_with_zero(T)}(A)
 
         size(A::$t, d) = size(A.data, d)
         size(A::$t) = size(A.data)

stdlib/LinearAlgebra/src/tridiag.jl

@@ -138,7 +138,7 @@ function Matrix{T}(M::SymTridiagonal) where T
     end
     return Mf
 end
-Matrix(M::SymTridiagonal{T}) where {T} = Matrix{T}(M)
+Matrix(M::SymTridiagonal{T}) where {T} = Matrix{promote_with_zero(T)}(M)
 Array(M::SymTridiagonal) = Matrix(M)
 
 size(A::SymTridiagonal) = (length(A.dv), length(A.dv))
@@ -579,7 +579,7 @@ function Matrix{T}(M::Tridiagonal{T}) where T
     end
     A
 end
-Matrix(M::Tridiagonal{T}) where {T} = Matrix{T}(M)
+Matrix(M::Tridiagonal{T}) where {T} = Matrix{promote_with_zero(T)}(M)
 Array(M::Tridiagonal) = Matrix(M)
 
 # For M<:Tridiagonal, similar(M[, neweltype]) should yield a Tridiagonal matrix.

stdlib/LinearAlgebra/test/dense.jl

@@ -940,14 +940,29 @@ end
 end
 
 struct TypeWithoutZero end
-Base.zero(::Type{TypeWithoutZero}) = TypeWithZero()
+Base.zero(::Union{TypeWithoutZero, Type{TypeWithoutZero}}) = TypeWithZero()
 struct TypeWithZero end
 Base.promote_rule(::Type{TypeWithoutZero}, ::Type{TypeWithZero}) = TypeWithZero
-Base.zero(::Type{<:Union{TypeWithoutZero, TypeWithZero}}) = TypeWithZero()
+Base.convert(::Type{TypeWithZero}, ::TypeWithoutZero) = TypeWithZero()
+Base.zero(::Union{TypeWithZero, Type{<:Union{TypeWithoutZero, TypeWithZero}}}) = TypeWithZero()
 Base.:+(x::TypeWithZero, ::TypeWithoutZero) = x
 
-@testset "diagm for type with no zero" begin
-    @test diagm(0 => [TypeWithoutZero()]) isa Matrix{TypeWithZero}
+@testset "diagm and Matrix for type with no zero" begin
+    x = TypeWithoutZero()
+    @test (@inferred diagm(0 => [x])) isa Matrix{TypeWithZero}
+    diag = [x, x, x]
+    offdiag = [x, x]
+    X = [x x
+         x x]
+    for A in [
+        Bidiagonal(diag, offdiag, :U),
+        Tridiagonal(offdiag, diag, offdiag),
+        SymTridiagonal(diag, offdiag),
+        LowerTriangular(X),
+        UpperTriangular(X)
+    ]
+        @test (@inferred Matrix(A)) isa Matrix{TypeWithZero}
+    end
 end
 
 end # module TestDense