#2607: find_minimum_on_interval() uses the wrong scipy function
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Reporter: AlexGhitza | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-4.7.1
Component: calculus | Keywords: sd31
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Comment(by kcrisman):
Answering the question first...
Sure, but it would be nice if we at least got the 'right' answer for
'easy' functions. That's all I'm looking for here, not things like
finding a minimum on a set of measure zero...
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I think we can fix Brent to use this. Compare:
{{{
sage: optimize.fminbound(h._fast_float_(x),0,6,full_output=True)
(3.8298366870225147, -1.327181022449951, 0, 10)
sage: optimize.fminbound(h._fast_float_(x),0,3,full_output=True)
(0.86667541098916612, -2.7358151040622416, 0, 9)
sage: optimize.brent(h._fast_float_(x),brack=(0,6),full_output=True)
(0.86667608708813437, -2.73581510406422, 11, 12)
}}}
This shows that brent does give the 'right' answer in this case. So when
does it give a 'wrong' answer?
{{{
sage: j(x) = sin(x)
sage: optimize.brent(j._fast_float_(x),brack=(0,6),full_output=True)
(10.995574367047061, -0.99999999999999689, 10, 11)
sage: 3.5*pi.n()
10.9955742875643
}}}
Well, of course - there IS no calculus-style minimum of sin between 0 and
pi! Only a minimum relative to the interval itself. Interesting that it
goes all the way to 7/2*pi, rather than 3/2*pi, but oh well!
So the fix is to switch to Brent, and then if it gives an answer outside
the interval, pick the 'lower' endpoint. This would need lots of testing
with well-behaved functions to make sure they actually work correctly.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/2607#comment:11>
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