[Python-ideas] Way to check for floating point "closeness"?

[Neil Girdhar]

You almost always want to use either an absolute tolerance or a relative
tolerance.  Here's why:  Consider your estimated value a and your actual
value b.  If the estimate is taken to be the mean of a standard Gaussian
distribution (the minimum assumptive distribution for a given mean and
variance over the reals), then using an absolute tolerance is equivalent to
verifying that the probability of observing b is within a interval with
sufficient probability.  Similarly, if the estimate is taken to be the mean
of an standard exponential distribution (the minimum
assumptive distribution for a given mean over the positive reals), then
using a relative tolerance is equivalent to verifying the same thing.

You almost always want one or the other.  The symmetric error that people
are proposing in this thread has no intuitive meaning to me.

Best,

Neil

On Thu, Jan 15, 2015 at 6:47 PM, Chris Barker - NOAA Federal <
chris.barker at noaa.gov> wrote:

>
>
> On Jan 15, 2015, at 3:31 PM, Neil Girdhar <mistersheik at gmail.com> wrote:
> absolute(*a* - *b*) <= (*atol* + *rtol* * absolute(*b*))
> Oh, and if the numbers are small, then adding the absolute tolerance
> changes the tolerance significantly -- so you don't get what you expect
> there, either.
>
> Chris
>
>
>
>
>>> where atol is an absolute tolerance and rtol is a relative tolerance
>>> (relative to the actual value b).  This subsumes most of the proposals here.
>>>
>>
>> adding atol  in there "takes care of" the near zero and straddleing zero
>> issue ( I suspect that's why it's done that way), but it is fatally wrong
>> for values much less than 1.0 --  the atol totally overwhelms the rtol.
>>
>> See my post earlier today.
>>
>> -Chris
>>
>>
>> --
>>
>> Christopher Barker, Ph.D.
>> Oceanographer
>>
>> Emergency Response Division
>> NOAA/NOS/OR&R            (206) 526-6959   voice
>> 7600 Sand Point Way NE   (206) 526-6329   fax
>> Seattle, WA  98115       (206) 526-6317   main reception
>>
>> Chris.Barker at noaa.gov
>>
>
>
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