eigen for triangular (#125)

JuliaLinearAlgebra · Jan 10, 2024 · 465d37a · 465d37a
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diff --git a/src/linearalgebra.jl b/src/linearalgebra.jl
@@ -433,3 +433,9 @@ function factorize(A::UpperTriangularToeplitz)
     dft = plan_fft!(tmp)
     return ToeplitzFactorization{T,typeof(A),S,typeof(dft)}(dft * tmp, similar(tmp), dft)
 end
+
+# triangular
+eigvals(T::TriangularToeplitz) = diag(T)
+eigvecs(U::UpperTriangularToeplitz) = eigvecs(UpperTriangular(Matrix(U)))
+eigvecs(L::LowerTriangularToeplitz) = eigvecs(LowerTriangular(Matrix(L)))
+eigen(U::TriangularToeplitz) = Eigen(eigvals(U), eigvecs(U))
diff --git a/test/runtests.jl b/test/runtests.jl
@@ -634,6 +634,16 @@ end
         @test_broken inv(TU)::TriangularToeplitz ≈ inv(Matrix(TU))
         @test inv(TL)::TriangularToeplitz ≈ inv(Matrix(TL))
     end
+
+    @testset "eigen" begin
+        for T in (UpperTriangularToeplitz, LowerTriangularToeplitz)
+            for p in ([1:6;], rand(ComplexF64, 5))
+                M = T(p)
+                λ, V = eigen(M)
+                @test M * V ≈ V * Diagonal(λ)
+            end
+        end
+    end
 end
 
 @testset "Cholesky" begin