The three major non-graphical components are fast_eval, numpy, and cython.
Cython seems an unlikely culprit--though who knows. More likely it's either
fast_eval or numpy. I know that different builds get minorly different
answers due to differences in the numpy/lapack matrix computation routines
that get called under the hood. Those errors, however, are nowhere near the
scale of the ones you are observing and are properly caught by the ...'s in
the test cases. Could it be that your builds are miscompiling some
numerical linear algebra routines? Otherwise it might be due to fast_eval
and fast_callable which Riemann uses in evaluating collocation points for
the map. I have no idea how the fast libraries work under the hood, so I
won't be any help there.
Ethan
On Thursday, January 17, 2013 8:22:33 AM UTC-8, kcrisman wrote:
>
>
>
> On Thursday, January 17, 2013 10:57:14 AM UTC-5, Jeroen Demeyer wrote:
>>
>> On 2013-01-17 15:59, kcrisman wrote:
>> > These are weird. This code is (documented to be) only accurate up to a
>> > point, because of the inherent craziness of computing such things, but
>> > it's good for what it does. But these errors are very different. I'm
>> > cc:ing the author in case he can think of any build-time issues like
>> env
>> > vars or things in PATH that might make a difference.
>> It would be interesting to know which Sage components this uses, such
>> that I can rebuild selected parts which might be the cause.
>>
>
> sage: ps = polygon_spline([(-1, -1), (1, -1), (1, 1), (-1, 1)])
> sage: f = lambda t: ps.value(real(t))
> sage: fprime = lambda t: ps.derivative(real(t))
> sage: get_systems('m = Riemann_Map([f], [fprime], 0.25, ncorners=4)')
> ['numpy', 'MPFR']
> sage: m = Riemann_Map([f], [fprime], 0.25, ncorners=4)
> sage: x = 0.75
> sage: get_systems('print "error =",
> m.inverse_riemann_map(m.riemann_map(x)) - x ')
> error = (-0.000291742263558+0.00160874617676j)
> []
> sage: print "error =", m.inverse_riemann_map(m.riemann_map(x)) - x
> error = (-0.000291742263558+0.00160874617676j)
>
> I really think that's it, too; it's heavily numerical code in Cython and
> numpy.
>
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