[SciPy-User] Default tolerances for scipy.integrate.quadrature

[Warren Weckesser]

On Wed, Apr 24, 2013 at 9:21 AM, Andrew Nelson <andyfaff at gmail.com> wrote:

> Dear list,
> I am using scipy.integrate.quadrature to do some adaptive gaussian
> quadrature.  I am wondering about the default options for the
> tolerances:
>
> tol=1.49e-8, rtol=1.49e-8
>
> I was wondering where these numbers come from?  Are they related to
> some sort of hardware feature (e.g. related to machine precision)?
>


Yes.  Those values are the square root of numpy.finfo(numpy.float64).eps.
eps is  the smallest representable positive number such that 1.0 + eps !=
1.0.

Warren



>
> Whilst I'm on this topic, I've noticed that a minimum number of
> adaption iterations for my problem using this function is
> approximately 10.  I was wondering if it would be possible to add a
> 'startingOrder' keyword, so that the iteration could start from a 10th
> order integration?  I don't mind trying to add this myself, if it
> would prove useful for scipy.
> --
> _____________________________________
> Dr. Andrew Nelson
>
>
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