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Add tests to ensure SVD error decreases monotonically with rank #564

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Merged
nefrathenrici merged 1 commit into from
Jun 3, 2026
Merged

Add tests to ensure SVD error decreases monotonically with rank #564

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19 changes: 19 additions & 0 deletions test/Observations/runtests.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -290,7 +290,26 @@ end
tall = Dinv * U * S * cholT.L
@test norm(get_diag_cov(DmT) - Dinv) < 1e-12
@test norm(get_tall_cov(DmT) - tall) < 1e-12
end

@testset "tsvd_cov_from_samples monotonic error vs. rank" begin
rng = Random.MersenneTwister(42)
X = randn(rng, 80, 30)
Σ = cov(X; dims = 2)
σ = svd((X .- mean(X, dims = 2)) ./ sqrt(size(X, 2) - 1)).S
full_rank = length(σ)

errs_fro = Float64[]
for r in 1:full_rank
cov_r = Matrix(tsvd_cov_from_samples(X, r))
push!(errs_fro, norm(Σ - cov_r))
@test isapprox(errs_fro[end], sqrt(sum(σ[(r + 1):end] .^ 4)); atol = 1e-10)
end
# Monotonic non-increase
@test all(diff(errs_fro) .<= 1e-12)
# Strict decrease where the discarded singular value is nonzero
nontrivial = findall(>(1e-8), σ[2:end])
@test all(errs_fro[nontrivial] .> errs_fro[nontrivial .+ 1])
end


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