add more degenerate tests for 2x2 eigen

Author: tfgast

test/eigen.jl

@@ -75,13 +75,25 @@ using StaticArrays, Test, LinearAlgebra
         @test vals::SVector ≈ sort(m_d)
         @test eigvals(m_c) ≈ sort(m_d)
         @test eigvals(Hermitian(m_c)) ≈ sort(m_d)
+    end
 
-        # issue #523
-        for (i, j) in ((1, 2), (2, 1)), uplo in (:U, :L)
-            A = SMatrix{2,2,Float64}((i, 0, 0, j))
-            E = eigen(Symmetric(A, uplo))
-            @test eigvecs(E) * SDiagonal(eigvals(E)) * eigvecs(E)' ≈ A
-        end
+    # issue #523
+    @testset "2×2 degenerate cases" for (i, j) in ((1 , 1), (1, 2), (2, 1)), uplo in (:U, :L)
+        fmin = floatmin(Float64)
+        pfmin = prevfloat(fmin)
+        nfmin = nextfloat(fmin)
+        A = SMatrix{2,2,Float64}((i, 0, 0, j))
+        E = eigen(Symmetric(A, uplo))
+        @test eigvecs(E) * SDiagonal(eigvals(E)) * eigvecs(E)' ≈ A
+        A = SMatrix{2,2,Float64}((i, pfmin, pfmin, j))
+        E = eigen(Symmetric(A, uplo))
+        @test eigvecs(E) * SDiagonal(eigvals(E)) * eigvecs(E)' ≈ A
+        A = SMatrix{2,2,Float64}((i, fmin, fmin, j))
+        E = eigen(Symmetric(A, uplo))
+        @test eigvecs(E) * SDiagonal(eigvals(E)) * eigvecs(E)' ≈ A
+        A = SMatrix{2,2,Float64}((i, nfmin, nfmin, j))
+        E = eigen(Symmetric(A, uplo))
+        @test eigvecs(E) * SDiagonal(eigvals(E)) * eigvecs(E)' ≈ A
     end
 
     @testset "3×3" for i = 1:100