#20127: zetaderiv: numerically unstable
-------------------------------------+-------------------------------------
Reporter: behackl | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-7.1
Component: numerical | Resolution:
Keywords: | Merged in:
Authors: Benjamin Hackl | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/behackl/symbolic/test_relation/noconvergence|
4ddf10c1c65acabc21bae40d80b51735cf26be24
Dependencies: | Stopgaps:
-------------------------------------+-------------------------------------
Changes (by behackl):
* component: symbolics => numerical
Old description:
> Testing the following expression for zero randomly results in a
> `NoConvergence` error being thrown from `mpmath`:
>
> {{{
> sage: var('k')
> k
> sage: bool(gamma(k*pi) * zetaderiv(1, k*pi*I)/log(2)^2 == 0)
> False
> }}}
>
> or
>
> {{{
> sage: bool(gamma(k*pi) * zetaderiv(1, k*pi*I)/log(2)^2 == 0)
> Traceback (most recent call last):
> ...
> NoConvergence: zeta: too much cancellation
> }}}
>
> This ticket adds this error to the list of caught errors in
> `test_relation`.
New description:
The implementation of the derivative of the zeta function `zetaderiv` is
numerically unstable and very slow (for large negative values):
{{{
sage: zetaderiv(1, CIF(-600))
Traceback (most recent call last):
...
NoConvergence: zeta: too much cancellation
}}}
{{{
sage: timeit('zetaderiv(1, CIF(-500))')
5 loops, best of 3: 3.08 s per loop
}}}
Could either the current implementation be improved or an alternative
numerical implementation be used?
---
This also causes errors when testing relations like
{{{
sage: bool(gamma(k*pi) * zetaderiv(1, k*pi*I)/log(2)^2 == 0)
Traceback (most recent call last):
...
NoConvergence: zeta: too much cancellation
}}}
--
--
Ticket URL: <http://trac.sagemath.org/ticket/20127#comment:13>
Sage <http://www.sagemath.org>
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