Merge pull request #24380 from Sacha0/equalsI

fix and specialize equality comparison with UniformScaling

base/linalg/uniformscaling.jl

@@ -211,6 +211,24 @@ broadcast(::typeof(/), J::UniformScaling,x::Number) = UniformScaling(J.λ/x)
 
 ==(J1::UniformScaling,J2::UniformScaling) = (J1.λ == J2.λ)
 
+## equality comparison with UniformScaling
+==(J::UniformScaling, A::AbstractMatrix) = A == J
+function ==(A::AbstractMatrix, J::UniformScaling)
+    size(A, 1) == size(A, 2) || return false
+    iszero(J.λ) && return iszero(A)
+    isone(J.λ) && return isone(A)
+    return A == J.λ*one(A)
+end
+function ==(A::StridedMatrix, J::UniformScaling)
+    size(A, 1) == size(A, 2) || return false
+    iszero(J.λ) && return iszero(A)
+    isone(J.λ) && return isone(A)
+    for j in indices(A, 2), i in indices(A, 1)
+        ifelse(i == j, A[i, j] == J.λ, iszero(A[i, j])) || return false
+    end
+    return true
+end
+
 function isapprox(J1::UniformScaling{T}, J2::UniformScaling{S};
             atol::Real=0, rtol::Real=Base.rtoldefault(T,S,atol), nans::Bool=false) where {T<:Number,S<:Number}
     isapprox(J1.λ, J2.λ, rtol=rtol, atol=atol, nans=nans)

test/linalg/uniformscaling.jl

@@ -189,3 +189,30 @@ end
         @test_throws LinAlg.PosDefException chol(-λ*I)
     end
 end
+
+@testset "equality comparison of matrices with UniformScaling" begin
+    # AbstractMatrix methods
+    diagI = Diagonal(fill(1, 3))
+    rdiagI = view(diagI, 1:2, 1:3)
+    bidiag = Bidiagonal(fill(2, 3), fill(2, 2), :U)
+    @test diagI  ==  I == diagI  # test isone(I) path / equality
+    @test 2diagI !=  I != 2diagI # test isone(I) path / inequality
+    @test 0diagI == 0I == 0diagI # test iszero(I) path / equality
+    @test 2diagI != 0I != 2diagI # test iszero(I) path / inequality
+    @test 2diagI == 2I == 2diagI # test generic path / equality
+    @test 0diagI != 2I != 0diagI # test generic path / inequality on diag
+    @test bidiag != 2I != bidiag # test generic path / inequality off diag
+    @test rdiagI !=  I != rdiagI # test square matrix check
+    # StridedMatrix specialization
+    denseI = eye(3)
+    rdenseI = eye(3, 4)
+    alltwos = fill(2, (3, 3))
+    @test denseI  ==  I == denseI  # test isone(I) path / equality
+    @test 2denseI !=  I != 2denseI # test isone(I) path / inequality
+    @test 0denseI == 0I == 0denseI # test iszero(I) path / equality
+    @test 2denseI != 0I != 2denseI # test iszero(I) path / inequality
+    @test 2denseI == 2I == 2denseI # test generic path / equality
+    @test 0denseI != 2I != 0denseI # test generic path / inequality on diag
+    @test alltwos != 2I != alltwos # test generic path / inequality off diag
+    @test rdenseI !=  I != rdenseI # test square matrix check
+end