Opened 8 years ago
Last modified 5 years ago
#14274 new defect
Numerical approximation of a divergent integral
Reported by: | eviatarbach | Owned by: | burcin |
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Priority: | major | Milestone: | sage-6.4 |
Component: | calculus | Keywords: | |
Cc: | Merged in: | ||
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
Sage is numerically approximating this integral, even though it's divergent:
sage: integrate(x^3/sqrt(x^7+1), x, 1, oo).n() -2.0585298599983344
It seems that if we don't allow Maxima to detect its divergence (numerical_integral
passes it directly to GSL), GSL will also fail on simpler divergent integrals:
sage: numerical_integral(1/x, 1, oo) (65.94931131932763, 8.156214940519742) sage: numerical_integral(x,1,oo) (-0.4999999993521234, 1.3615531480049015e-09)
See also this ask question:
sage: numerical_integral(e^(-x)/x,0,oo) (37.191280375549404, 6.239196965189217)
Change History (11)
comment:1 Changed 8 years ago by
- Description modified (diff)
comment:2 Changed 8 years ago by
comment:3 Changed 8 years ago by
Maybe the options being passed to GSL could be changed? It seems absurd that it should give a numerical answer for numerical_integral(x^3,1,oo)
, for example. It apparently has an error for divergence (http://www.gnu.org/software/gsl/manual/html_node/Numerical-integration-error-codes.html).
comment:4 Changed 8 years ago by
In fact, with the code at http://www.physics.ohio-state.edu/~ntg/780/gsl_examples/qagiu_test.cpp, it returns errors for all these integrals.
comment:5 Changed 8 years ago by
If you present a patch, I think we'd be very interested in reviewing it. Silly to return nonsense in these cases.
comment:6 Changed 8 years ago by
- Milestone changed from sage-5.11 to sage-5.12
comment:7 Changed 7 years ago by
- Milestone changed from sage-6.1 to sage-6.2
comment:8 Changed 7 years ago by
- Milestone changed from sage-6.2 to sage-6.3
comment:9 Changed 7 years ago by
- Milestone changed from sage-6.3 to sage-6.4
comment:10 Changed 6 years ago by
Edit: sorry wrong ticket
comment:11 Changed 5 years ago by
- Description modified (diff)
Regarding the first one; basically, when we return a noun form
and call
n
we dobecause we do
So these are both manifestations of the same thing.
So... is it user error to numerically integrate a divergent integral? I certainly don't know that we should be checking every numerical integral for divergence, particularly since Maxima apparently can't (yet) do the first one in any case!