inv of Symmetric/Hermitian with more eltypes than BlasFloat #22882
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this makes #22686 (comment) more of an issue |
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I find it unlikely that a matrix which is a result of Lines 317 to 318 in 8cd3c3f |
test/linalg/symmetric.jl
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| @test inv(Symmetric(asym))::Symmetric ≈ inv(asym) | ||
| @test inv(Hermitian(aherm))::Hermitian ≈ inv(aherm) | ||
| for uplo in (:U, :L) | ||
| @test inv(Symmetric(asym, uplo))::Symmetric ≈ inv(full(Symmetric(asym, uplo))) |
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Perhaps Array instead of full? :)
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The previous fallback assumes that the inverse will have the same element type as the factorization, so this should not be a problem. |
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Do you still think this is problematic @tkelman, or anyone else? |
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Main concern for me is whether this requires additional methods to be defined for it to work on inv of symmetric/hermitian wrappers of user defined array and/or element types |
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Okay, yea, I did some testing, and for a user defined number type, this does not change anything; if you define all that's needed for |
| @@ -364,8 +364,8 @@ function _inv(A::HermOrSym) | |||
| end | |||
| B | |||
| end | |||
| inv(A::Hermitian{T,S}) where {T<:BlasFloat,S<:StridedMatrix} = Hermitian{T,S}(_inv(A), A.uplo) | |||
| inv(A::Symmetric{T,S}) where {T<:BlasFloat,S<:StridedMatrix} = Symmetric{T,S}(_inv(A), A.uplo) | |||
| inv(A::Hermitian{<:Any,<:StridedMatrix}) = Hermitian(_inv(A), Symbol(A.uplo)) | |||
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Re my comment above regarding user define array types, should this be changed to:
inv(A::Hermitian{<:Any,S}) where {S<:StridedMatrix} = (Ai = _inv(A); Hermitian{eltype(Ai), S}(Ai, A.uplo)such that we enforce a conversion back to the same array type? I noticed that if you don't implement getindex to return your user defined array you get back an Array from the backsolve.
Edit: No, this does not work, it is not always possible to convert back to the same type, e.g. with Ints. So I think the current implementation is the best.
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Restarting Travis since there was some time this went through. Hoping to get more than 0 out of 3 this time |
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Nope. None your fault though. |
#22686 and #22767 implemented the infrastructure to invert
Symmetric/Hermitianmatrices with any element type that supports LU factorization (and backsolve). The relaxations here are necessary as well. For instance, before thisinv(::Symmetric{Int})returned aMatrixrather thanSymmetricandinv(::Symmetric{Int})MethodErrord.