#10952: better numerical accuracy testing
-----------------------------------------+----------------------------------
Reporter: robertwb | Owner: mvngu
Type: enhancement | Status: needs_review
Priority: critical | Milestone: sage-4.7.2
Component: doctest | Keywords:
Work_issues: | Upstream: N/A
Reviewer: Jason Grout, Mariah Lenox | Author: Robert Bradshaw
Merged: | Dependencies:
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Old description:
> If a line contains ``tol`` or ``tolerance, numerical results are only
> verified to the given tolerance. This may be prefixed by ``abs[olute``
> or ``rel[ative]`` to specify whether to measure absolute or relative
> error; defaults to relative error except when the expected value is
> exactly zero:
>
> {{{
> sage: RDF(pi) # abs tol 1e-5
> 3.14159
> sage: [10^n for n in [0.0 .. 4]] # rel tol 2e-4
> [0.9999, 10.001, 100.01, 999.9, 10001]
> }}}
>
> This can be useful when the exact output is subject to rounding error
> and/or processor floating point arithmetic variation.
>
> '''Apply''':
> 1. [attachment:10952-tol-bin.patch]
> 1. [attachment:10952-tol-doc.2.patch]
> 1. [attachment:trac_10952-reviewer-docs.patch]
New description:
If a line contains ``tol`` or ``tolerance, numerical results are only
verified to the given tolerance. This may be prefixed by ``abs[olute``
or ``rel[ative]`` to specify whether to measure absolute or relative
error; defaults to relative error except when the expected value is
exactly zero:
{{{
sage: RDF(pi) # abs tol 1e-5
3.14159
sage: [10^n for n in [0.0 .. 4]] # rel tol 2e-4
[0.9999, 10.001, 100.01, 999.9, 10001]
}}}
This can be useful when the exact output is subject to rounding error
and/or processor floating point arithmetic variation.
'''Apply''':
1. [attachment:10952-tol-bin.patch] - to the local/bin repo
1. [attachment:10952-tol-doc.2.patch] - to the devel/sage repo
1. [attachment:trac_10952-reviewer-docs.patch] - to the devel/sage repo
--
Comment(by was):
This ticket is pretty amazing.
Rob, this doctest you added seems very wrong:
{{{
A relative tolerance on a root of a polynomial.
::
sage: p = (y - 10^16)*(y-10^(-13))*(y-2); p
y^3 + (-1e+16)*y^2 + (2e+16)*y - 2000.0
sage: p.roots()
sage: p.roots(multiplicities=False)[2] # relative tol 1e-10
10^16
}}}
In particular,
* it seems that y isn't defined
* the output of {{{p.roots()}}} is missing
* I get an output of {{{1e16}}} instead of {{{10^16}}}.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10952#comment:22>
Sage <http://www.sagemath.org>
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