From a1a0a324a546f1eb42e6ec42bb65695acb80f06d Mon Sep 17 00:00:00 2001
From: "John F. Gibson" <johnfgibson@gmail.com>
Date: Tue, 7 Sep 2021 09:48:25 -0400
Subject: [PATCH] Add wrapper function eigen(Matrix A) where A is hermitian by
 value but not by type

---
 src/eigenSelfAdjoint.jl |  7 ++++++-
 test/eigengeneral.jl    | 10 +++++++++-
 2 files changed, 15 insertions(+), 2 deletions(-)

diff --git a/src/eigenSelfAdjoint.jl b/src/eigenSelfAdjoint.jl
index 0b6dd3c..52f3970 100644
--- a/src/eigenSelfAdjoint.jl
+++ b/src/eigenSelfAdjoint.jl
@@ -593,7 +593,6 @@ LinearAlgebra.eigen!(A::Hermitian;
                      tol = eps(real(eltype(A))),
                      debug = false) = _eigen!(A, tol = tol, debug = debug)
 
-
 function eigen2!(A::SymmetricTridiagonalFactorization;
                  tol = eps(real(float(one(eltype(A))))),
                  debug = false)
@@ -649,6 +648,12 @@ function LinearAlgebra.eigen(A::Hermitian)
     T = typeof(sqrt(zero(eltype(A))))
     return eigen!(LinearAlgebra.copy_oftype(A, T))
 end
+function LinearAlgebra.eigen(A::Matrix)
+    if !ishermitian(A)
+         throw(ArgumentError("eigen not implement for non-Hermitian matrices of generic type (e.g. Matrix{BigFloat})"))
+    end
+    return eigen(Hermitian(A))
+end
 
 # Aux (should go somewhere else at some point)
 function LinearAlgebra.givensAlgorithm(f::Real, g::Real)
diff --git a/test/eigengeneral.jl b/test/eigengeneral.jl
index 91ae90b..f8d0613 100644
--- a/test/eigengeneral.jl
+++ b/test/eigengeneral.jl
@@ -150,4 +150,12 @@ end
     @test sort(imag(vals)) ≈ sort(imag(λs)) atol=1e-25
 end
 
-end
\ No newline at end of file
+@testset "Wrapper function for eigen(Matrix A) where A is hermitian by value but not by type" begin
+    # just need to verify that the wrapper function correctly calls eigen(Hermitian(A))
+    # so no need for multiple numeric tests
+    a = big(2.0);
+    A = [1 a; a 0] # A == A^*, but type is Matrix{BigFloat}, not Hermitian{BigFloat, Matrix{BigFloat}}
+    λs = [(1 - √(1+4a^2))/2 ; (1 + √(1+4a^2))/2]
+    vals = eigvals(A)
+    @test sort(vals) ≈ sort(λs) atol=1e-25
+end