issymmetric/ishermitian for Circulant (#95)

* issymmetric and ishermitian for Circulant

* import ishermitian

* don't use begin in indexing

src/ToeplitzMatrices.jl

@@ -11,7 +11,9 @@ import LinearAlgebra: ldiv!, factorize, lmul!, pinv, eigvals, eigvecs, eigen, Ei
 import LinearAlgebra: cholesky!, cholesky, tril!, triu!, checksquare, rmul!, dot, mul!, tril, triu
 import LinearAlgebra: istriu, istril, isdiag
 import LinearAlgebra: UpperTriangular, LowerTriangular, Symmetric, Adjoint
+import LinearAlgebra: issymmetric, ishermitian
 import LinearAlgebra: eigvals, eigvecs, eigen
+
 import AbstractFFTs: Plan, plan_fft!
 import StatsBase
 

src/linearalgebra.jl

@@ -329,6 +329,23 @@ function sqrt(C::CirculantFactorization)
     return Circulant(maybereal(eltype(C), vc))
 end
 
+function _vc_first_rest_rev(C::Circulant)
+    v = _vc(C)
+    v1 = first(v)
+    vrest = @view v[firstindex(v)+1:lastindex(v)]
+    vrestrev = view(vrest, reverse(eachindex(vrest)))
+    v1, vrest, vrestrev
+end
+
+function issymmetric(C::Circulant)
+    v1, vrest, vrestrev = _vc_first_rest_rev(C)
+    issymmetric(v1) && all(((a,b),) -> a == transpose(b), zip(vrest, vrestrev))
+end
+function ishermitian(C::Circulant)
+    v1, vrest, vrestrev = _vc_first_rest_rev(C)
+    ishermitian(v1) && all(((a,b),) -> a == adjoint(b), zip(vrest, vrestrev))
+end
+
 # Triangular
 
 # NB! only valid for lower triangular

test/runtests.jl

@@ -510,6 +510,33 @@ end
 
     D = Diagonal(axes(C1,2))
     @test mul!(similar(C1), C1, D) ≈ C1 * D
+
+    @testset "issymmetric/ishermitian" begin
+        C = Circulant([1,2,3,0,3,2])
+        @test issymmetric(C)
+        @test ishermitian(C)
+        C = Circulant([1,2])
+        @test issymmetric(C)
+        @test ishermitian(C)
+        C = Circulant([1,2,3])
+        @test !issymmetric(C)
+        @test !ishermitian(C)
+
+        C = Circulant([1,im,2-3im,0,2+3im,-im])
+        @test ishermitian(C)
+        @test !issymmetric(C)
+        C = Circulant([1,im])
+        @test !ishermitian(C)
+        @test issymmetric(C)
+
+        C = Circulant([2])
+        @test issymmetric(C)
+        @test ishermitian(C)
+
+        C = Circulant([NaN])
+        @test !issymmetric(C)
+        @test !ishermitian(C)
+    end
 end
 
 @testset "TriangularToeplitz" begin