How to compare vectors?

[nilshg]

See for one of the more recent ones:

History of `isapprox` in languages

Does anyone know why the de-facto standard definition of isapprox intentionally fails when one of the arguments is zero? isapprox(0.0, 0.0 + 1e-10) # false isapprox(1.0, 1.0 + 1e-10) # true It is clear from the formula why this is happening: ||x - y|| \le max(atol, rtol*max(||x||, ||y||)) If we set y=0, we get: ||x|| \le max(atol, rtol*||x||) The default atol = 0 then makes it: ||x|| \le rtol * ||x|| and the default rtol = \sqrt\epsilon leads to: ||x|| \le \sqrt\epsilon ||x|| which…