[R] find inflexion point of discrete value list with R

[Ben Bolker]

On 12-01-02 04:09 PM, David Winsemius wrote:
> 
> On Jan 2, 2012, at 11:49 AM, Ben Bolker wrote:
> 
>> Jonas Stein <news <at> jonasstein.de> writes:
>>
>>>
>>> i have a list of values like this
>>>
>>> x y
>>> 1 3
>>> 2 2
>>
>>  [snip]
>>
>>>
>>> and need the inflexion [sic] points (and all max and min).
>>> Is there a nice way to get the local max, min and inflexion points?
>>
>>  diff(y) gives you the first difference, the analogue of the gradient
>>  diff(diff(y)) gives the second difference, the analogue of the second
>> derivative.
>>
>>  dy <- diff(y)
>>  d2y <- diff(dy)
>>  which(dy==0)  ## critical values
>>  sign(s2y)[which(dy==0)]  ## test for max/min/saddle
>>  which(d2y==0)   ## inflection points
> 
> I would think that testing for d2y==0 would be akin to the error in
> numeric analysis warned about in FAQ 7.31. Seems unlikely that in real
> data that there would always be three points in a row with equal
> differences at a "true" inflection and even then, many of the ones you
> did find satisfying that criterion would not be in fact inflection
> points. Wouldn't it be better to fit a spline and then do your testing
> on the spline approximation?
> 
> Counter-example:
>  x=1:10
>> y=c(1,2,3,5,7,10,13,16,20,24)
>>  dy <- diff(y)
>>  d2y <- diff(dy)
>> which(d2y==0)
> [1] 1 3 5 6 8
> 
> And actually the original data was a pretty good counter-example as well.


  The original post wasn't entirely clear, but I thought the data were
indeed integers and that the discrete-state version of
min/max/inflection point was indeed what was wanted.  Yes, if the
underlying variable is continuous you might want to use splinefun(),
with its deriv= argument, and uniroot(), to find maxima and minima.
Might be a little tricky in general, although with an interpolation
spline between a finite set of points you can at least deal with it
exhaustively.

  Ben