Scaling for partly initialized unit triangular (#1351)

After this, scaling unit triangular matrices with parents that don't
have the diagonal initialized works.
```julia
julia> M = Matrix{BigFloat}(undef,2,2);
  
julia> M[1,2] = 3;

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

julia> U * 2
2×2 UpperTriangular{BigFloat, Matrix{BigFloat}}:
 2.0  6.0
  ⋅   2.0
```
Probably needs #1350
for tests to pass.

Author: jishnub

src/triangular.jl

@@ -1324,15 +1324,6 @@ end
 # Generic routines #
 ####################
 
-function _set_diag!(B::UpperOrLowerTriangular, x)
-    # get a mutable array to modify the diagonal
-    Bm = parent(B) isa StridedArray ? B : copy!(similar(B), B)
-    for i in diagind(Bm.data, IndexStyle(Bm.data))
-        Bm.data[i] = x
-    end
-    Bm
-end
-
 for (t, unitt) in ((UpperTriangular, UnitUpperTriangular),
                    (LowerTriangular, UnitLowerTriangular))
     tstrided = t{<:Any, <:StridedMaybeAdjOrTransMat}
@@ -1345,8 +1336,8 @@ for (t, unitt) in ((UpperTriangular, UnitUpperTriangular),
         end
 
         function (*)(A::$unitt, x::Number)
-            B = $t(A.data)*x
-            _set_diag!(B, oneunit(eltype(A)) * x)
+            B = copy!(similar($t(A.data)), A)
+            B * x
         end
 
         (*)(x::Number, A::$t) = $t(x*A.data)
@@ -1357,8 +1348,8 @@ for (t, unitt) in ((UpperTriangular, UnitUpperTriangular),
         end
 
         function (*)(x::Number, A::$unitt)
-            B = x*$t(A.data)
-            _set_diag!(B, x * oneunit(eltype(A)))
+            B = copy!(similar($t(A.data)), A)
+            x * B
         end
 
         (/)(A::$t, x::Number) = $t(A.data/x)
@@ -1369,8 +1360,8 @@ for (t, unitt) in ((UpperTriangular, UnitUpperTriangular),
         end
 
         function (/)(A::$unitt, x::Number)
-            B = $t(A.data)/x
-            _set_diag!(B, oneunit(eltype(A)) / x)
+            B = copy!(similar($t(A.data)), A)
+            B / x
         end
 
         (\)(x::Number, A::$t) = $t(x\A.data)
@@ -1381,8 +1372,8 @@ for (t, unitt) in ((UpperTriangular, UnitUpperTriangular),
         end
 
         function (\)(x::Number, A::$unitt)
-            B = x\$t(A.data)
-            _set_diag!(B, x \ oneunit(eltype(A)))
+            B = copy!(similar($t(A.data)), A)
+            x \ B
         end
     end
 end

test/triangular.jl

@@ -955,4 +955,18 @@ end
     @test 2*U == 2*M
 end
 
+@testset "scaling 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(M)
+        C = Matrix(U)
+        @test U * 2 == C * 2
+        @test 2 * U == 2 * C
+        @test U / 2 == C / 2
+        @test 2 \ U == 2 \ C
+    end
+end
+
 end # module TestTriangular