Generalized eigenvalues of two static matrices (#693)

Support generalized `eigvals` of two `StaticMatrixLike` arguments.

Author: mateuszbaran

src/eigen.jl

@@ -13,6 +13,19 @@ end
     end
 end
 
+function eigvals(A::StaticMatrixLike, B::StaticMatrixLike; kwargs...)
+    SA = Size(A)
+    if SA != Size(B)
+        throw(DimensionMismatch("Generalized eigenvalues can only be calculated for matrices of equal sizes: dimensions are $SA and $(Size(B))"))
+    end
+    checksquare(A)
+    return _eigvals(SA, A, B; kwargs...)
+end
+
+@inline function _eigvals(s::Size, A::StaticMatrixLike, B::StaticMatrixLike; kwargs...)
+    return SVector{s[1]}(eigvals(Array(A), Array(B); kwargs...))
+end
+
 @inline _eigvals(::Size{(1,1)}, a, permute, scale) = @inbounds return SVector(Tuple(a))
 @inline _eigvals(::Size{(1, 1)}, a::LinearAlgebra.RealHermSymComplexHerm{T}, permute, scale) where {T <: Real} = @inbounds return SVector(real(parent(a).data[1]))
 

test/eigen.jl

@@ -82,8 +82,20 @@ using StaticArrays, Test, LinearAlgebra
             E = eigen(Symmetric(A, uplo))
             @test eigvecs(E) * SDiagonal(eigvals(E)) * eigvecs(E)' ≈ A
         end
+
+        m1_a = randn(2,2)
+        m1_a = m1_a*m1_a'
+        m1 = SMatrix{2,2}(m1_a)
+        m2_a = randn(2,2)
+        m2_a = m2_a*m2_a'
+        m2 = SMatrix{2,2}(m2_a)
+        @test (@inferred_maybe_allow SVector{2,ComplexF64} eigvals(m1, m2)) ≈ eigvals(m1_a, m2_a)
+        @test (@inferred_maybe_allow SVector{2,ComplexF64} eigvals(Symmetric(m1), Symmetric(m2))) ≈ eigvals(Symmetric(m1_a), Symmetric(m2_a))
     end
 
+    @test_throws DimensionMismatch eigvals(SA[1 2 3; 4 5 6], SA[1 2 3; 4 5 5])
+    @test_throws DimensionMismatch eigvals(SA[1 2; 4 5], SA[1 2 3; 4 5 5; 3 4 5])
+
     @testset "3×3" for i = 1:100
         m_a = randn(3,3)
         m_a = m_a*m_a'
@@ -112,6 +124,14 @@ using StaticArrays, Test, LinearAlgebra
         @test vals::SVector ≈ sort(m_d)
         @test eigvals(m) ≈ sort(m_d)
         @test eigvals(Hermitian(m)) ≈ sort(m_d)
+
+        m1_a = randn(3,3)
+        m1_a = m1_a*m1_a'
+        m1 = SMatrix{3,3}(m1_a)
+        m2_a = randn(3,3)
+        m2_a = m2_a*m2_a'
+        m2 = SMatrix{3,3}(m2_a)
+        @test (@inferred_maybe_allow SVector{3,ComplexF64} eigvals(m1, m2)) ≈ eigvals(m1_a, m2_a)
     end
 
     @testset "3x3 degenerate cases" begin

test/testutil.jl

@@ -95,3 +95,17 @@ should_not_be_inlined(x) = _should_not_be_inlined(x)
     @test ts.errorcount == 0 && ts.failcount == 2 && ts.passcount == 0
 end
 
+
+"""
+    @inferred_maybe_allow allow ex
+
+Expands to `@inferred allow ex` on Julia 1.2 and newer and
+`ex` on Julia 1.0 and 1.1.
+"""
+macro inferred_maybe_allow(allow, ex)
+    if VERSION < v"1.2"
+        return esc(:($ex))
+    else
+        return esc(:(@inferred $allow $ex))
+    end
+end