[R] Finding Infimum in R

[Boris Steipe]

Analytically speaking. But we are (presumably) looking for a numerical algorithm, and that is constrained by numerical accuracy, and in that realm we have  0.3333333333333333148296 on the left, and 0.3333333333333333703408 on the right.

And the left-side representable number is what gets returned for x <- 1/3. Whether this number, which is less than the defined discontinuity, is a correct solution depends on aspects of the problem that have not been disclosed.

No?



B.




> On Apr 10, 2017, at 1:15 PM, Peter Dalgaard <pdalgd at gmail.com> wrote:
> 
> Er, 1/3, of course? (assuming that F is f). The infimum of a set is not necessarily a member of the set.
> 
> -pd
> 
>> On 10 Apr 2017, at 16:56 , Boris Steipe <boris.steipe at utoronto.ca> wrote:
>> 
>> Well - the _procedure_ will give a result.
>> 
>> But think of f(x) = {-1; x <= 1/3 and 1; x > 1/3 
>> 
>> What should inf{x| F(x) >= 0} be?
>> What should the procedure return?
>> 
>> 
>> 
>> 
>> 
>>> On Apr 10, 2017, at 10:38 AM, Bert Gunter <bgunter.4567 at gmail.com> wrote:
>>> 
>>> Given what she said, how does the procedure I suggested fail?
>>> 
>>> (Always happy to be corrected).
>>> 
>>> -- Bert
>>> Bert Gunter
>>> 
>>> "The trouble with having an open mind is that people keep coming along
>>> and sticking things into it."
>>> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
>>> 
>>> 
>>> On Mon, Apr 10, 2017 at 1:57 AM, Boris Steipe <boris.steipe at utoronto.ca> wrote:
>>>> Are you sure this is trivial? I have the impression the combination of an ill-posed problem and digital representation of numbers might just create the illusion that is so.
>>>> 
>>>> B.
>>>> 
>>>> 
>>>> 
>>>> 
>>>>> On Apr 10, 2017, at 12:34 AM, Bert Gunter <bgunter.4567 at gmail.com> wrote:
>>>>> 
>>>>> Then it's trivial. Check values at the discontinuities and find the
>>>>> first where it's <0 at the left discontinuity and >0 at the right, if
>>>>> such exists. Then just use zero finding on that interval (or fit a
>>>>> line if everything's linear). If none exists, then just find the first
>>>>> discontinuity where it's > 0.
>>>>> 
>>>>> Cheers,
>>>>> Bert
>>>>> 
>>>>> 
>>>>> Bert Gunter
>>>>> 
>>>>> "The trouble with having an open mind is that people keep coming along
>>>>> and sticking things into it."
>>>>> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
>>>>> 
>>>>> 
>>>>> On Sun, Apr 9, 2017 at 5:38 PM, li li <hannah.hlx at gmail.com> wrote:
>>>>>> Hi Burt,
>>>>>> Yes, the function is monotone increasing and points of discontinuity are
>>>>>> all known.
>>>>>> They are all numbers between 0 and 1.  Thanks very much!
>>>>>> Hanna
>>>>>> 
>>>>>> 
>>>>>> 2017-04-09 16:55 GMT-04:00 Bert Gunter <bgunter.4567 at gmail.com>:
>>>>>>> 
>>>>>>> Details matter!
>>>>>>> 
>>>>>>> 1. Are the points of discontinuity known? This is critical.
>>>>>>> 
>>>>>>> 2. Can we assume monotonic increasing, as is shown?
>>>>>>> 
>>>>>>> 
>>>>>>> -- Bert
>>>>>>> 
>>>>>>> 
>>>>>>> 
>>>>>>> 
>>>>>>> Bert Gunter
>>>>>>> 
>>>>>>> "The trouble with having an open mind is that people keep coming along
>>>>>>> and sticking things into it."
>>>>>>> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
>>>>>>> 
>>>>>>> 
>>>>>>> On Sun, Apr 9, 2017 at 1:28 PM, li li <hannah.hlx at gmail.com> wrote:
>>>>>>>> Dear all,
>>>>>>>> For a piecewise function F similar to the attached graph, I would like
>>>>>>>> to
>>>>>>>> find
>>>>>>>>                                     inf{x| F(x) >=0}.
>>>>>>>> 
>>>>>>>> 
>>>>>>>> I tried to uniroot. It does not seem to work. Any suggestions?
>>>>>>>> Thank you very much!!
>>>>>>>> Hanna
>>>>>>>> 
>>>>>>>> ______________________________________________
>>>>>>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>>>>>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>>>>>> PLEASE do read the posting guide
>>>>>>>> http://www.R-project.org/posting-guide.html
>>>>>>>> and provide commented, minimal, self-contained, reproducible code.
>>>>>> 
>>>>>> 
>>>>> 
>>>>> ______________________________________________
>>>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>>>>> and provide commented, minimal, self-contained, reproducible code.
>>>> 
>> 
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
> 
> -- 
> Peter Dalgaard, Professor,
> Center for Statistics, Copenhagen Business School
> Solbjerg Plads 3, 2000 Frederiksberg, Denmark
> Phone: (+45)38153501
> Office: A 4.23
> Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com
> 
> 
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