R help - Sep 2015 - Find Crossover Points of Two Spline Functions

Good day,

I have two probability densities, each with a function determined by
splinefun(densityResult[['x']], densityResult[['y']],
"natural"), where densityResult is the output of the density function
in stats. How can I determine all of the x values at which the densities cross ?

--------------------------------------
Dario Strbenac
PhD Student
University of Sydney
Camperdown NSW 2050
Australia

Dario Strbenac <dstr7320 <at> uni.sydney.edu.au> writes:
> 
> Good day,
> 
> I have two probability densities, each with a function determined
> by splinefun(densityResult[['x']],
> densityResult[['y']], "natural"), where densityResult is
the
> output of the density function in stats.
> How can I determine all of the x values at which the densities cross ?
> 
  My initial thought was this is non-trivial, because the two densities could
cross (or nearly-but-not-quite cross) at an unlimited number of points.
I thought it would essentially boils down to "how do I find all 
the roots of an arbitrary (continuous, smooth) function?

  However, after thinking about it for a few more seconds I realize
that at least the functions are piecewise cubic.  I still don't see
a *convenient* way to do it ... if the knots were all coincident between
the two densities (maybe you could constrain them to be so?) then you
just have a difference of cubics within each segment, and you can use
polyroot() to find the roots (and throw out any that are complex or
don't fall within the segment).
  If the knots are not coincident it's more of a pain but you should
still be able to do it by considering overlapping segments ...

Use ?uniroot to do it numerically instead of polyroot()?

Cheers,
Bert
Bert Gunter

"Data is not information. Information is not knowledge. And knowledge
is certainly not wisdom."
   -- Clifford Stoll


On Mon, Sep 28, 2015 at 9:17 AM, Ben Bolker <bbolker at gmail.com>
wrote:
> Dario Strbenac <dstr7320 <at> uni.sydney.edu.au> writes:
>
>>
>> Good day,
>>
>> I have two probability densities, each with a function determined
>> by splinefun(densityResult[['x']],
>> densityResult[['y']], "natural"), where densityResult
is the
>> output of the density function in stats.
>> How can I determine all of the x values at which the densities cross ?
>>
>
>   My initial thought was this is non-trivial, because the two densities
could
> cross (or nearly-but-not-quite cross) at an unlimited number of points.
> I thought it would essentially boils down to "how do I find all
> the roots of an arbitrary (continuous, smooth) function?
>
>   However, after thinking about it for a few more seconds I realize
> that at least the functions are piecewise cubic.  I still don't see
> a *convenient* way to do it ... if the knots were all coincident between
> the two densities (maybe you could constrain them to be so?) then you
> just have a difference of cubics within each segment, and you can use
> polyroot() to find the roots (and throw out any that are complex or
> don't fall within the segment).
>   If the knots are not coincident it's more of a pain but you should
> still be able to do it by considering overlapping segments ...
>
> ______________________________________________
> 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.