[LinearAlgebra] Add isdiag/isposdef for Diagonal and UniformScaling #29638
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There should probably be the same for Edit: Also |
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Thanks @mcognetta for your suggestions. I think I found the right spot to put those methods and went ahead to include them. I hope you don't mind. |
dkarrasch
changed the title
| 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).
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@dkarrasch No problem. I had two other tests that might be useful as well (for the case I mentioned in the comment). |
| @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.
stdlib/LinearAlgebra/src/diagonal.jl
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| @@ -123,6 +123,7 @@ factorize(D::Diagonal) = D | |||
| real(D::Diagonal) = Diagonal(real(D.diag)) | |||
| imag(D::Diagonal) = Diagonal(imag(D.diag)) | |||
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| isdiag(D::Diagonal) = true | |||
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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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Cool, I'll include them. Thanks! |
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While you are at it, you might as well correct
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That wasn't me. :-))) Indeed, I included it and will add tests. |
dkarrasch
changed the title
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This is looking good. Is it ready to go from your perspective, @dkarrasch? |
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Thanks. I think so, yes. |
changes between Julia 1.0 and 1.1, including: - Custom .css-style for compat admonitions. - Information about compat annotations to CONTRIBUTING.md. - NEWS.md entry for PRs #30090, #30035, #30022, #29978, #29969, #29858, #29845, #29754, #29638, #29636, #29615, #29600, #29506, #29469, #29316, #29259, #29178, #29153, #29033, #28902, #28761, #28745, #28708, #28696, #29997, #28790, #29092, #29108, #29782 - Compat annotation for PRs #30090, #30013, #29978, #29890, #29858, #29827, #29754, #29679, #29636, #29623, #29600, #29440, #29316, #29259, #29178, #29157, #29153, #29033, #28902, #28878, #28761, #28708, #28156, #29733, #29670, #29997, #28790, #29092, #29108, #29782, #25278 - Documentation for broadcasting CartesianIndices (#30230). - Documentation for Base.julia_cmd(). - Documentation for colon constructor of CartesianIndices (#29440). - Documentation for ^(::Matrix, ::Number) and ^(::Number, ::Matrix). - Run NEWS-update.jl. Co-authored-by: Morten Piibeleht <[email protected]> Co-authored-by: Fredrik Ekre <[email protected]>
changes between Julia 1.0 and 1.1, including: - Custom .css-style for compat admonitions. - Information about compat annotations to CONTRIBUTING.md. - NEWS.md entry for PRs #30090, #30035, #30022, #29978, #29969, #29858, #29845, #29754, #29638, #29636, #29615, #29600, #29506, #29469, #29316, #29259, #29178, #29153, #29033, #28902, #28761, #28745, #28708, #28696, #29997, #28790, #29092, #29108, #29782 - Compat annotation for PRs #30090, #30013, #29978, #29890, #29858, #29827, #29754, #29679, #29636, #29623, #29600, #29440, #29316, #29259, #29178, #29157, #29153, #29033, #28902, #28878, #28761, #28708, #28156, #29733, #29670, #29997, #28790, #29092, #29108, #29782, #25278 - Documentation for broadcasting CartesianIndices (#30230). - Documentation for Base.julia_cmd(). - Documentation for colon constructor of CartesianIndices (#29440). - Documentation for ^(::Matrix, ::Number) and ^(::Number, ::Matrix). - Run NEWS-update.jl. Co-authored-by: Morten Piibeleht <[email protected]> Co-authored-by: Fredrik Ekre <[email protected]>
Addition of NEWS and compat admonitions for important changes between Julia 1.0 and 1.1, including: - Custom .css-style for compat admonitions. - Information about compat annotations to CONTRIBUTING.md. - NEWS.md entry for PRs #30090, #30035, #30022, #29978, #29969, #29858, #29845, #29754, #29638, #29636, #29615, #29600, #29506, #29469, #29316, #29259, #29178, #29153, #29033, #28902, #28761, #28745, #28708, #28696, #29997, #28790, #29092, #29108, #29782 - Compat annotation for PRs #30090, #30013, #29978, #29890, #29858, #29827, #29754, #29679, #29636, #29623, #29600, #29440, #29316, #29259, #29178, #29157, #29153, #29033, #28902, #28878, #28761, #28708, #28156, #29733, #29670, #29997, #28790, #29092, #29108, #29782, #25278 - Documentation for broadcasting CartesianIndices (#30230). - Documentation for Base.julia_cmd(). - Documentation for colon constructor of CartesianIndices (#29440). - Documentation for ^(::Matrix, ::Number) and ^(::Number, ::Matrix). - Run NEWS-update.jl. Co-authored-by: Morten Piibeleht <[email protected]> Co-authored-by: Fredrik Ekre <[email protected]>
I found a tiny tiny gap, a noop test for diagonality of
Diagonalmatrices. It seems that all other matrix structure tests have specializedDiagonal-methods:istriu,istril,issymmetric, andisposdef.Edit: Based on @mcognetta's suggestion, this now also includes
isdiagandisposdefforUniformScalings (title changed accordingly).