Forward istriu/istril for triangular to parent

stdlib/LinearAlgebra/src/special.jl

@@ -567,3 +567,7 @@ function cholesky(S::RealHermSymComplexHerm{<:Real,<:SymTridiagonal}, ::NoPivot
     B = Bidiagonal{T}(diag(S, 0), diag(S, S.uplo == 'U' ? 1 : -1), sym_uplo(S.uplo))
     cholesky!(Hermitian(B, sym_uplo(S.uplo)), NoPivot(); check = check)
 end
+
+# istriu/istril for triangular wrappers of structured matrices
+_istril(A::LowerTriangular{<:Any, <:BandedMatrix}, k) = istril(parent(A), k)
+_istriu(A::UpperTriangular{<:Any, <:BandedMatrix}, k) = istriu(parent(A), k)

stdlib/LinearAlgebra/src/triangular.jl

@@ -330,14 +330,32 @@ function Base.replace_in_print_matrix(A::Union{LowerTriangular,UnitLowerTriangul
     return i >= j ? s : Base.replace_with_centered_mark(s)
 end
 
-Base.@constprop :aggressive function istril(A::Union{LowerTriangular,UnitLowerTriangular}, k::Integer=0)
+istril(A::UnitLowerTriangular, k::Integer=0) = k >= 0
+istriu(A::UnitUpperTriangular, k::Integer=0) = k <= 0
+Base.@constprop :aggressive function istril(A::LowerTriangular, k::Integer=0)
     k >= 0 && return true
     return _istril(A, k)
 end
-Base.@constprop :aggressive function istriu(A::Union{UpperTriangular,UnitUpperTriangular}, k::Integer=0)
+@inline function _istril(A::LowerTriangular, k)
+    P = parent(A)
+    m = size(A, 1)
+    for j in max(1, k + 2):m
+        all(iszero, view(P, j:min(j - k - 1, m), j)) || return false
+    end
+    return true
+end
+Base.@constprop :aggressive function istriu(A::UpperTriangular, k::Integer=0)
     k <= 0 && return true
     return _istriu(A, k)
 end
+@inline function _istriu(A::UpperTriangular, k)
+    P = parent(A)
+    m = size(A, 1)
+    for j in 1:min(m, m + k - 1)
+        all(iszero, view(P, max(1, j - k + 1):j, j)) || return false
+    end
+    return true
+end
 istril(A::Adjoint, k::Integer=0) = istriu(A.parent, -k)
 istril(A::Transpose, k::Integer=0) = istriu(A.parent, -k)
 istriu(A::Adjoint, k::Integer=0) = istril(A.parent, -k)

stdlib/LinearAlgebra/test/triangular.jl

@@ -1228,4 +1228,32 @@ end
     end
 end
 
+@testset "istriu/istril forwards to parent" begin
+    @testset "$(nameof(typeof(M)))" for M in [Tridiagonal(rand(n-1), rand(n), rand(n-1)),
+                Tridiagonal(zeros(n-1), zeros(n), zeros(n-1)),
+                Diagonal(randn(n)),
+                Diagonal(zeros(n)),
+                ]
+        @testset for TriT in (UpperTriangular, UnitUpperTriangular, LowerTriangular, UnitLowerTriangular)
+            U = TriT(M)
+            A = Array(U)
+            for k in -n:n
+                @test istriu(U, k) == istriu(A, k)
+                @test istril(U, k) == istril(A, k)
+            end
+        end
+    end
+    z = zeros(n,n)
+    @testset for TriT in (UpperTriangular, UnitUpperTriangular, LowerTriangular, UnitLowerTriangular)
+        P = Matrix{BigFloat}(undef, n, n)
+        copytrito!(P, z, TriT <: Union{UpperTriangular, UnitUpperTriangular} ? 'U' : 'L')
+        U = TriT(P)
+        A = Array(U)
+        @testset for k in -n:n
+            @test istriu(U, k) == istriu(A, k)
+            @test istril(U, k) == istril(A, k)
+        end
+    end
+end
+
 end # module TestTriangular