don't check approximate equality elementwise

[stevengj]

In #109, you added an isapproxskewhermitian that checks A[i,j] ≈ -A[j,i]' elementwise. This is generally a bad way to compare arrays. Instead, you generally want to compare whole-array norms, e.g. compare ‖A+A'‖ to ‖A‖. For example, this result makes little sense:

julia> A = [0 1 1e-16; -1 0 1; 0 -1 0]
3×3 Matrix{Float64}:
  0.0   1.0  1.0e-16
 -1.0   0.0  1.0
  0.0  -1.0  0.0

julia> isapproxskewhermitian(A)
false

julia> norm(A+A') / norm(A)
7.071067811865474e-17

Since this function is only used for testing, it makes more sense to just define isapproxskewhermitian(A) = A ≈ -A' (where ≈ on arrays compares whole-array norms) in runtests.jl, rather than trying to export something.

I also removed the export for to_symtridiagonal, which is mostly an internal implementation detail and is not documented. If there is some need for this we could always document it and export it. (It would make sense to add documentation for it and other internal functions anyway, of course.)

[codecov]

Codecov Report

Base: 88.81% // Head: 88.74% // Decreases project coverage by -0.06% ⚠️

Coverage data is based on head (7739f0b) compared to base (9f7fa85).
Patch has no changes to coverable lines.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #110      +/-   ##
==========================================
- Coverage   88.81%   88.74%   -0.07%     
==========================================
  Files           9        9              
  Lines        1430     1422       -8     
==========================================
- Hits         1270     1262       -8     
  Misses        160      160              

Impacted Files	Coverage Δ
src/skewhermitian.jl	83.72% <ø> (-0.96%)	⬇️

Help us with your feedback. Take ten seconds to tell us how you rate us. Have a feature suggestion? Share it here.

☔ View full report at Codecov.
📢 Do you have feedback about the report comment? Let us know in this issue.