[Numpy-discussion] Testing for close to zero?

[Charles R Harris]

On Mon, Jan 19, 2009 at 9:17 PM, Robert Kern <robert.kern at gmail.com> wrote:

> On Mon, Jan 19, 2009 at 22:09, Charles R Harris
> <charlesr.harris at gmail.com> wrote:
> >
> >
> > On Mon, Jan 19, 2009 at 7:23 PM, Jonathan Taylor
> > <jonathan.taylor at utoronto.ca> wrote:
> >>
> >> Interesting.  That makes sense and I suppose that also explains why
> >> there is no function to do this sort of thing for you.
> >
> > A combination of relative and absolute errors is another common solution,
> > i.e., test against relerr*max(abs(array_of_inputs)) + abserr. In cases
> like
> > this relerr is typically eps and abserr tends to be something like 1e-12,
> > which keeps you from descending towards zero any further than you need
> to.
>
> I don't think the absolute error term is appropriate in this case. If
> all of my inputs are of the size 1e-12, I would expect a result of
> 1e-14 to be significantly far from 0.
>

Sure, that's why you *chose* constants appropriate to the problem. As to
this case, I don't know what the quadratic is or what methods are being used
to solve it, or even if the methods are appropriate. So the comment was
general and I think many numeric methods for solving equations use some
variant of the combination. For instance, the 1D zero finders in Scipy use
it.

Chuck
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