Fix copy for partly initialized unit triangular (#1350)

Currently, we forward copy for unit triangular matrices to the parents.
This also copies the diagonal, which may not be initialized in the
parent. This PR fixes this.
After this, the following works again
```julia
julia> M = Matrix{BigFloat}(undef,2,2);

julia> M[2,1] = 3;

julia> M'
2×2 adjoint(::Matrix{BigFloat}) with eltype BigFloat:
 #undef    3.0
 #undef  #undef

julia> U = UnitUpperTriangular(M')
2×2 UnitUpperTriangular{BigFloat, Adjoint{BigFloat, Matrix{BigFloat}}}:
 1.0  3.0
  ⋅   1.0

julia> copyto!(similar(M), U)
2×2 Matrix{BigFloat}:
 1.0  3.0
 0.0  1.0
```

Author: jishnub

src/triangular.jl

@@ -599,14 +599,15 @@ end
     copytrito!(dest, U, U isa UpperOrUnitUpperTriangular ? 'L' : 'U')
     return dest
 end
-@propagate_inbounds function _copyto!(dest::StridedMatrix, U::UpperOrLowerTriangular{<:Any, <:StridedMatrix})
+@propagate_inbounds function _copyto!(dest::StridedMatrix,
+    U::Union{UnitUpperOrUnitLowerTriangular, UpperOrLowerTriangular{<:Any, <:StridedMatrix}})
     U2 = Base.unalias(dest, U)
     copyto_unaliased!(dest, U2)
     return dest
 end
 # for strided matrices, we explicitly loop over the arrays to improve cache locality
 # This fuses the copytrito! for the two halves
-@inline function copyto_unaliased!(dest::StridedMatrix, U::UpperOrUnitUpperTriangular{<:Any, <:StridedMatrix})
+@inline function copyto_unaliased!(dest::StridedMatrix, U::UpperOrUnitUpperTriangular)
     @boundscheck checkbounds(dest, axes(U)...)
     isunit = U isa UnitUpperTriangular
     for col in axes(dest,2)
@@ -619,7 +620,7 @@ end
     end
     return dest
 end
-@inline function copyto_unaliased!(dest::StridedMatrix, L::LowerOrUnitLowerTriangular{<:Any, <:StridedMatrix})
+@inline function copyto_unaliased!(dest::StridedMatrix, L::LowerOrUnitLowerTriangular)
     @boundscheck checkbounds(dest, axes(L)...)
     isunit = L isa UnitLowerTriangular
     for col in axes(dest,2)

test/triangular.jl

@@ -6,6 +6,7 @@ isdefined(Main, :pruned_old_LA) || @eval Main include("prune_old_LA.jl")
 
 using Test, LinearAlgebra, Random
 using LinearAlgebra: errorbounds, transpose!, BandIndex
+using Test: GenericArray
 
 const BASE_TEST_PATH = joinpath(Sys.BINDIR, "..", "share", "julia", "test")
 
@@ -650,6 +651,16 @@ end
             @test_throws "cannot set index in the upper triangular part" copyto!(A, B)
         end
     end
+
+    @testset "partly initialized unit triangular" begin
+        for T in (UnitUpperTriangular, UnitLowerTriangular)
+            isupper = T == UnitUpperTriangular
+            M = Matrix{BigFloat}(undef, 2, 2)
+            M[1+!isupper,1+isupper] = 3
+            U = T(GenericArray(M))
+            @test copyto!(similar(M), U) == U
+        end
+    end
 end
 
 @testset "getindex with Integers" begin