#8321: numerical integration with arbitrary precision
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Reporter: burcin | Owner: burcin
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.5.3
Component: symbolics | Keywords: numerics,integration
Author: Stefan Reiterer | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by newvalueoldvalue):
* cc: fredrik.johansson (added)
* keywords: => numerics,integration
* author: => Stefan Reiterer
Comment:
Thank you for the patch Stefan. This was much needed for quite a while
now.
Replying to [comment:10 maldun]:
> Replying to [comment:8 kcrisman]:
> > Thanks, Maldun, this is a good addition to have. I don't have time to
review this immediately, but it would be helpful to know if you detected
any errors, compared this with symbolic integrals and their evaluation,
etc. Basically, that the results from this really are as accurate as
advertised.
I agree. I like how the patch looks overall. It would be good to see
comparisons on
* error margins
* speed
Maybe Fredrik can comment on this as well.
Using `fast_callable()` for `mp_f` could help improve the speed.
Does anyone know of good examples to add as tests for numerical
integration?
> > Also, you might as well leave the GSL stuff in as comments, as in the
patch you posted above, or even as an optional argument, though that may
not be compatible with `_evalf_` elsewhere...
Unfortunately, ATM, the numerical evaluation framework for symbolic
expressions doesn't support specifying different methods. This could
(probably, I didn't check the code) be done by changing the interpretation
of the python object we pass around to keep the algorithm parameter and
the parent, instead of just the parent. Is this a desirable change? Shall
we open a ticket for this?
> I will consider this, but hopefully it is not necessary, and mpmath will
do the whole thing.
> If I understood that right, burcin wants to change the numerical
evaluation completly to mpmath, because it supports arbitrary prescision.
I guess this is based on a comment I made in the context of orthogonal
polynomials and scipy vs. mpmath. Instead of a general policy, I'd like to
consider each function separately.
Overall, I'd lean toward using `mpfr` if it supports the given function.
Otherwise, choosing between `pari`, `mpmath`, etc. can be difficult, since
on many examples one implementation doesn't beat the other uniformly for
different precision or domains.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8321#comment:12>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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