Eigenvalues not sorted for almost perfectly symmetric matrix #343
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Description
I'm not sure whether this qualifies as a bug, though the behavior seems undesirable. Below A is a matrix that is almost exactly symmetric. eigvals(A) returns the singular values without sorting them. For perfectly symmetric matrices (e.g., B below), the eigenvalues are always sorted. It seems like eigvals(A) should sort them too, since due to numerical issues, even symmetric matrices are often not exactly symmetric.
julia> A = [2.319564160285209 20.613046913136856 -0.5068584177942504
20.613046913136856 201.80977596527438 -1.2031203195074227
-0.5068584177942503 -1.203120319507423 11.188307566885028];
julia> eigvals(A) # these singular values are not sorted
3-element Array{Float64,1}:
203.926
0.198637
11.1935
julia> norm(A - A') # though A is almost perfectly symmetric
2.482534153247273e-16
julia> B = (A + A') / 2. # but if A is symmetrized
3x3 Array{Float64,2}:
2.31956 20.613 -0.506858
20.613 201.81 -1.20312
-0.506858 -1.20312 11.1883
julia> eigvals(B) # then they are sorted
3-element Array{Float64,1}:
0.198637
11.1935
203.926
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