Full-rank SVD has high error

[PythonNut]

I am not exactly sure if this is correct, but I would expect the result to be close to zero.

using TSVD, LinearAlgebra
A = randn(10, 10)
U, S, V = tsvd(A, 10);
@show norm(U * Diagonal(S) * V' - A)

instead I get

julia> @show norm(U * Diagonal(S) * V' - A)
norm(U * Diagonal(S) * V' - A) = 9.224320184306517
9.224320184306517

I do realize a full-rank SVD is probably not the intended use-case of this package. If this really can't be handled by this algorithm, then maybe it should throw an error?

[adrilow]

I can report the same issue:

B = rand(100,100)
nvals = 55
U, s, V  = tsvd(B,nvals)
Δ = norm(U * Diagonal(s) * transpose(V) - B)

returns an error of 7.99, but increasing to 56 returns an error of 402.63. I don't see how there is a distinction between these two values. For reference, the 55th and 56th singular values are 2.09 and 2.06.

I am using Julia v1.6.4 and TSVD v0.4.3

[jmbeckers]

using TSVD, LinearAlgebra
A = randn(10, 10)
U, S, V = tsvd(A, 10;tolreorth=0.0);
@show U * Diagonal(S) * V'-A 

does provide the correct expansion, but how to be sure one takes a good value for tolreorth in a more general case ?