Clarify comment on default_algorithm ambiguity more, make eig test more general

Author: mtfishman

src/algorithms.jl

@@ -201,7 +201,13 @@ macro functiondef(f)
         # define default algorithm fallbacks for out-of-place functions
         # in terms of the corresponding in-place function for types,
         # in principle this is covered by the definition above but
-        # it is necessary to avoid ambiguity errors
+        # it is necessary to avoid ambiguity errors with the generic definitions:
+        # ```julia
+        # default_algorithm(f::F, A; kwargs...) where {F} = default_algorithm(f, typeof(A); kwargs...)
+        # function default_algorithm(f::F, ::Type{T}; kwargs...) where {F,T}
+        #     throw(MethodError(default_algorithm, (f, T)))
+        # end
+        # ```
         @inline function default_algorithm(::typeof($f), ::Type{A}; kwargs...) where {A}
             return default_algorithm($f!, A; kwargs...)
         end

test/eig.jl

@@ -63,9 +63,9 @@ end
                                                                ComplexF64)
     rng = StableRNG(123)
     m = 4
-    V = qr_compact(randn(rng, T, m, m))[1]
+    V = randn(rng, T, m, m)
     D = Diagonal([0.9, 0.3, 0.1, 0.01])
-    A = V * D * V'
+    A = V * D * inv(V)
     alg = TruncatedAlgorithm(LAPACK_Simple(), truncrank(2))
     D2, V2 = @constinferred eig_trunc(A; alg)
     @test diagview(D2) ≈ diagview(D)[1:2] rtol = sqrt(eps(real(T)))