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[LinearAlgebra] Add isdiag/isposdef for Diagonal and UniformScaling #29638

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Oct 16, 2018
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[LinearAlgebra] Add isdiag/isposdef for Diagonal and UniformScaling #29638

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6d1efa9
add isdiag(::Diagonal)
dkarrasch Oct 14, 2018
d281128
add test for isdiag(::Diagonal)
dkarrasch Oct 14, 2018
79315b1
add isdiag/isposdef(::UniformScaling)
dkarrasch Oct 15, 2018
c582998
add tests for isdiag/isposdef(::UniformScaling)
dkarrasch Oct 15, 2018
b53c3a5
correct isposdef(::UniformScaling)
dkarrasch Oct 15, 2018
aeb2b56
add more tests for isposdef(::UniformScaling)
dkarrasch Oct 15, 2018
b614442
fix isdiag(::Diagonal) for non-Number eltypes
dkarrasch Oct 15, 2018
ffe7cf3
add isdiag tests for non-Number diagonal matrices
dkarrasch Oct 15, 2018
e68c778
add isposdef(::Diagonal) for complex/non-number eltype
dkarrasch Oct 15, 2018
7dcd568
add tests for isposdef(::Diagonal) w/ cmplx/non-number eltype
dkarrasch Oct 15, 2018
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1 change: 1 addition & 0 deletions stdlib/LinearAlgebra/src/diagonal.jl
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Expand Up @@ -123,6 +123,7 @@ factorize(D::Diagonal) = D
real(D::Diagonal) = Diagonal(real(D.diag))
imag(D::Diagonal) = Diagonal(imag(D.diag))

isdiag(D::Diagonal) = true
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@mcognetta mcognetta Oct 15, 2018 •
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Sorry, one more thing. This fails when we have a block diagonal matrix in which not all blocks are diagonal.

MWE:

julia> D=Diagonal([[1 0; 0 1], [1 0; 1 1]])
2×2 Diagonal{Array{Int64,2},Array{Array{Int64,2},1}}:
 [1 0; 0 1]      ⋅     
     ⋅       [1 0; 1 1]

julia> isdiag(D)
true

I believe it should be
isdiag(D::Diagonal) = all(isdiag, D.diag)
isdiag(D::Diagonal{<:Number}) = true

But I am not so sure on what it means to be a matrix of matrices so maybe @fredrikekre can correct me.

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I see, I only had the Number case in mind. I'll fix this.

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... and add a test.

istriu(D::Diagonal) = true
istril(D::Diagonal) = true
function triu!(D::Diagonal,k::Integer=0)
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2 changes: 2 additions & 0 deletions stdlib/LinearAlgebra/src/uniformscaling.jl
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Expand Up @@ -74,10 +74,12 @@ oneunit(J::UniformScaling{T}) where {T} = oneunit(UniformScaling{T})
zero(::Type{UniformScaling{T}}) where {T} = UniformScaling(zero(T))
zero(J::UniformScaling{T}) where {T} = zero(UniformScaling{T})

isdiag(::UniformScaling) = true
istriu(::UniformScaling) = true
istril(::UniformScaling) = true
issymmetric(::UniformScaling) = true
ishermitian(J::UniformScaling) = isreal(J.λ)
isposdef(J::UniformScaling) = J.λ > zero(J.λ)
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This fails when J.λ is complex with imaginary part 0 (since there is no comparison operator).

You can simply do isposdef(J::UniformScaling) = isposdef(J.λ).


(+)(J::UniformScaling, x::Number) = J.λ + x
(+)(x::Number, J::UniformScaling) = x + J.λ
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1 change: 1 addition & 0 deletions stdlib/LinearAlgebra/test/diagonal.jl
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Expand Up @@ -50,6 +50,7 @@ Random.seed!(1)
@test D[1,2] == 0

@test issymmetric(D)
@test isdiag(D)
@test istriu(D)
@test istril(D)
if elty <: Real
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5 changes: 4 additions & 1 deletion stdlib/LinearAlgebra/test/uniformscaling.jl
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Expand Up @@ -30,13 +30,16 @@ end
@test conj(UniformScaling(1.0+1.0im))::UniformScaling{Complex{Float64}} == UniformScaling(1.0-1.0im)
end

@testset "istriu, istril, issymmetric, ishermitian, isapprox" begin
@testset "isdiag, istriu, istril, issymmetric, ishermitian, isposdef, isapprox" begin
@test isdiag(I)
@test istriu(I)
@test istril(I)
@test issymmetric(I)
@test issymmetric(UniformScaling(complex(1.0,1.0)))
@test ishermitian(I)
@test !ishermitian(UniformScaling(complex(1.0,1.0)))
@test isposdef(I)
@test !isposdef(-I)
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Maybe test these for complex-valued UniformScalings as well?

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Yes, I think that's what @mcognetta's suggestion above does, I believe. This is now included.

@test UniformScaling(4.00000000000001) ≈ UniformScaling(4.0)
@test UniformScaling(4.32) ≈ UniformScaling(4.3) rtol=0.1 atol=0.01
@test UniformScaling(4.32) ≈ 4.3 * [1 0; 0 1] rtol=0.1 atol=0.01
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