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Define chol for UniformScaling's #22633

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Jul 18, 2017
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Define chol for UniformScaling's #22633

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46b53ef
Define chol for UniformScaling's
mschauer Jun 30, 2017
6138c66
Move test for chol(lambda*I) to test/linalg/uniformscaling.jl
mschauer Jul 7, 2017
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24 changes: 24 additions & 0 deletions base/linalg/uniformscaling.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -313,3 +313,27 @@ function hvcat(rows::Tuple{Vararg{Int}}, A::Union{AbstractVecOrMat,UniformScalin
end
return hvcat(rows, promote_to_arrays(n,1, promote_to_array_type(A), A...)...)
end


## Cholesky
function _chol!(J::UniformScaling, uplo)
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is this mutating?

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@mschauer mschauer Jun 30, 2017 •
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This is following verbatim the chol(::Number) implementation.

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It is a trick to allow a recursive definition of chol. See

julia/base/linalg/cholesky.jl

Line 75 in 71d7c16

Akk, info = _chol!(A[k,k], UpperTriangular)
. The outer structures will typically be mutable but not the inner. I think it is fine because ! is not saying "will mutate", just "be aware, might mutate".

c, info = _chol!(J.λ, uplo)
UniformScaling(c), info
end

chol!(J::UniformScaling, uplo) = ((J, info) = _chol!(J, uplo); @assertposdef J info)
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@fredrikekre fredrikekre Nov 9, 2017 •
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What is the motivation for this method? Should fall in the same category as the now deprecated chol(::Number) IIUC, see #24498

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The function chol! is a chainable modifying array function and should do the right thing to immutable arrays. If !-versions of chainable array functions are defined for immutable arrays, then f!(g!(h!(copy(A())))) is a good way to write efficient and generic code which works for immutables and mutables (here ! allows f, g, h to use the copy of A as workspace where appropriate). In the same fashion, copy pushes through immutables and is defined for UniformScalings.


"""
chol(J::UniformScaling) -> C

Compute the square root of a non-negative UniformScaling `J`.

# Examples
```jldoctest
julia> chol(16I)
UniformScaling{Float64}
4.0*I
```
"""
chol(J::UniformScaling, args...) = ((C, info) = _chol!(J, nothing); @assertposdef C info)

8 changes: 8 additions & 0 deletions test/linalg/uniformscaling.jl
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Expand Up @@ -173,3 +173,11 @@ end
hvcat((2,1,2),B,2eye(3,3),eye(6,6),3eye(3,3),4eye(3,3))
end
end

@testset "chol" begin
for T in (Float64, Complex64, BigFloat, Int)
λ = T(4)
@test chol(λ*I) ≈ √λ*I
@test_throws LinAlg.PosDefException chol(-λ*I)
end
end