When doing linear algebra procedures such as
A\b or pinv(A),
where A is a square matrix, is there a way to check for singularity of A ? Otherwise I keep getting errors such as SingularException(3) or LAPACKException(1).
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pretty new to julia, but I think this would work:
is_singular = A → rank(A) == max(size(A)…)
#only true for matrix A when square and no dependent columns (full rank) = singular
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Numerically, this question is a bit ill-defined, because roundoff errors make it hard to distinguish between a matrix that is exactly singular and a matrix that is nearly singular. Moreover, as a practical matter it is rarely a good idea to try to make this distinction — matrices that are nearly singular are in many ways just as “bad” as matrices that are singular.
If you find yourself solving a lot of systems that are nearly singular, that it is a good sign that you need to re-think what you are doing. (e.g. perhaps you need some regularization in your equations)
Where are these matrices coming from? Why are they sometimes singular or nearly so?
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Just adding that checking the condition number of a matrix can be done with:
julia> using LinearAlgebra
julia> M = rand(4,4)
4×4 Matrix{Float64}:
0.596334 0.699729 0.632193 0.931758
0.910922 0.150834 0.605005 0.90234
0.640964 0.0686345 0.0811358 0.372114
0.67283 0.458002 0.346649 0.485548
julia> cond(M)
23.45879906432043
julia> cond(zeros(4,4)) # zero matrix is singular
Inf
and for any singular matrix, the condition number would be Inf. A smaller condition number is better.
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Very nice point. I shall follow it.
Thank you, that is quite handy