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Avoid testing condition number of random matrices against hard coded numbers #42361

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Sep 23, 2021
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Avoid testing condition number of random matrices against hard coded numbers #42361

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30 changes: 21 additions & 9 deletions stdlib/LinearAlgebra/test/dense.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -18,27 +18,39 @@ n2 = 2*n1
Random.seed!(1234323)

@testset "Matrix condition number" begin
ainit = rand(n,n)
ainit = rand(n, n)
@testset "for $elty" for elty in (Float32, Float64, ComplexF32, ComplexF64)
ainit = convert(Matrix{elty}, ainit)
for a in (copy(ainit), view(ainit, 1:n, 1:n))
@test cond(a,1) ≈ 198.3324294531168 atol=0.5
@test cond(a,2) ≈ 85.93920079319506 atol=0.5
@test cond(a,Inf) ≈ 149.7523084803039 atol=0.4
@test cond(a[:,1:5]) ≈ 8.319279144493297 atol=0.01
ainv = inv(a)
@test cond(a, 1) == opnorm(a, 1) *opnorm(ainv, 1)
@test cond(a, Inf) == opnorm(a, Inf)*opnorm(ainv, Inf)
@test cond(a[:, 1:5]) == (\)(extrema(svdvals(a[:, 1:5]))...)
@test_throws ArgumentError cond(a,3)
end
end
@testset "Singular matrices" for p in (1, 2, Inf)
@test cond(zeros(Int, 2, 2), p) == Inf
@test cond(zeros(2, 2), p) == Inf
@test cond([0 0; 1 1], p) == Inf
@test cond([0. 0.; 1. 1.], p) == Inf
@test cond(zeros(2, 2), p) == Inf
@test cond([0 0; 1 1], p) == Inf
@test cond([0. 0.; 1. 1.], p) == Inf
end
@testset "Issue #33547, condition number of 2x2 matrix" begin
M = [1.0 -2.0; -2.0 -1.5]
M = [1.0 -2.0
-2.0 -1.5]
@test cond(M, 1) ≈ 2.227272727272727
end
@testset "Condition numbers of a non-random matrix" begin
# To ensure that we detect any regressions in the underlying functions
Mars= [11 24 7 20 3
4 12 25 8 16
17 5 13 21 9
10 18 1 14 22
23 6 19 2 15]
@test cond(Mars, 1) ≈ 7.1
@test cond(Mars, 2) ≈ 6.181867355918493
@test cond(Mars, Inf) ≈ 7.1
end
end

areal = randn(n,n)/2
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