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implements a rank(::SVD) method and adds unit tests. fixes #1126 #1127

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Merged
merged 3 commits into from
Dec 3, 2024
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implements a rank(::SVD) method and adds unit tests. fixes #1126 #1127

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9cf5df3
added rank method for SVD object alongwith unit tests for the method.…
ajinkya-k Nov 29, 2024
aec0135
simplified DOCSTRING for rank(::SVD)
ajinkya-k Nov 30, 2024
743b94d
simplified rank(::SVD) implementation
ajinkya-k Dec 1, 2024
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18 changes: 18 additions & 0 deletions src/svd.jl
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Expand Up @@ -245,6 +245,24 @@ svdvals(A::AbstractVector{T}) where {T} = [convert(eigtype(T), norm(A))]
svdvals(x::Number) = abs(x)
svdvals(S::SVD{<:Any,T}) where {T} = (S.S)::Vector{T}

"""
rank(S::SVD{<:Any, T}; atol::Real=0, rtol::Real=min(n,m)*ϵ) where {T}

Compute the numerical rank of given an SVD object by counting how many singular values are greater
than `max(atol, rtol*σ₁)` where `σ₁` is the largest calculated singular value.
`atol` and `rtol` are the absolute and relative tolerances, respectively.
The default relative tolerance is `n*ϵ`, where `n` is the size of the smallest dimension of UΣV'
and `ϵ` is the [`eps`](@ref) of the element type of `S`.

!!! compat "Julia 1.12"
The `rank(::SVD)` method requires at least Julia 1.12.
"""
function rank(S::SVD{<:Any,T}; atol::Real = 0.0, rtol::Real = (min(size(S)...)*eps(real(float(one(eltype(S))))))) where {T}
svals = getfield(S, :S)
tol = max(atol, rtol*svals[1])
count(>(tol), svals)
end

### SVD least squares ###
function ldiv!(A::SVD{T}, B::AbstractVecOrMat) where T
m, n = size(A)
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12 changes: 12 additions & 0 deletions test/svd.jl
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Expand Up @@ -294,4 +294,16 @@ end
@test F.S ≈ F32.S
end

@testset "rank svd" begin
# Test that the rank of an svd is computed correctly
@test rank(svd([1.0 0.0; 0.0 1.0])) == 2
@test rank(svd([1.0 0.0; 0.0 0.9]), rtol=0.95) == 1
@test rank(svd([1.0 0.0; 0.0 0.9]), atol=0.95) == 1
@test rank(svd([1.0 0.0; 0.0 1.0]), rtol=1.01) == 0
@test rank(svd([1.0 0.0; 0.0 1.0]), atol=1.01) == 0

@test rank(svd([1.0 2.0; 2.0 4.0])) == 1
@test rank(svd([1.0 2.0 3.0; 4.0 5.0 6.0 ; 7.0 8.0 9.0])) == 2
end

end # module TestSVD