Feng
thanks for this. The problem you report is
reproducible; it originates from simplex()
of the boot packge.
It is ultimately due to
the fact that x_i is precisely *on* the convex hull,
which is evidently causing problems. I'll
investigate it.
In the short term, you can break the degeneracy:
> isin.chull(X[1,]+1e-10,X)
[1] FALSE
>
but I don't know if that is acceptable to you.
best
rksh
On 24/09/10 13:17, Feng Li wrote:
> Thanks. I agree with you that the speed and memory issues might be
> (actually is) a big problem for big dimensions. It is interesting to
> know to solve this by using linear programming. Buy the way, it seems
> a potential bug in your function if you try this
>
>
>
>> X <- matrix(rnorm(50), 10, 5)
>> x_i<-X[1,,drop=FALSE]
>> isin.chull(x_i,X)
>>
> Error in A.out[, basic] <- iden(M) : subscript out of bounds
>
> Or I must be wrong somewhere.
>
>
> Feng
>
>
> On Sep 24, 12:39 pm, Robin Hankin <rk...@cam.ac.uk> wrote:
>
>> Hello
>>
>> convex hulls in large numbers of dimensions are hard.
>>
>> For your problem, though, one can tell whether a given
>> point is inside or outside by using linear programming:
>>
>>
>>> X <- matrix(rnorm(50), 10, 5)
>>> x_i <- matrix(rnorm(5), 1, 5)
>>> isin.chull
>>>
>> function(candidate,p,plot=FALSE,give.answers=FALSE,
>> ...){
>> if(plot){
>> plot(p,...)
>> p(candidate[1],candidate[2], pch=16)
>> }
>> n <- nrow(p) # number of points
>> d <- ncol(p) # number of dimensions
>>
>> p <- t(sweep(p,2,candidate))
>> jj <- simplex(a=rep(1,n),A3=rbind(p,1),b3=c(0*candidate,1))
>> if(give.answers){
>> return(jj)
>> } else {
>> return((jj$solved >= 0) & all(jj$soln<1))
>> }
>>
>> }
>>
>>> isin.chull(x_i,X)
>>>
>> [1] FALSE
>>
>> (we can discuss offline; I'll summarize)
>>
>> HTH
>>
>> rksh
>>
>> On 24/09/10 10:44, Feng Li wrote:
>>
>>
>>
>>
>>> Dear R,
>>>
>>
>>> I have a covariates matrix with 10 observations, e.g.
>>>
>>
>>>> X <- matrix(rnorm(50), 10, 5)
>>>> X
>>>>
>>
>>> [,1] [,2] [,3] [,4] [,5]
>>> [1,] 0.24857135 0.30880745 -1.44118657 1.10229027 1.0526010
>>> [2,] 1.24316806 0.36275370 -0.40096866 -0.24387888 -1.5324384
>>> [3,] -0.33504014 0.42996246 0.03902479 -0.84778875 -2.4754644
>>> [4,] 0.06710229 1.01950917 -0.09325091 -0.03222811 0.4127816
>>> [5,] -0.13619141 1.33143821 -0.79958805 2.08274102 0.6901768
>>> [6,] -0.45060357 0.19348831 -1.23793647 -0.72440163 0.5057326
>>> [7,] -1.20740516 0.20231086 1.15584485 0.81777770 -1.2719855
>>> [8,] -1.81166284 -0.07913113 -0.91080581 -0.34774436 0.9552182
>>> [9,] 0.19131383 0.14980569 -0.37458224 -0.09371273 -1.7667203
>>> [10,] -0.85159276 -0.66679528 1.63019340 0.56920196 -2.4049600
>>>
>>
>>> And I define a boundary of X: The smallest "ball" that nests all the
>>> observations of X. I wish to check if a particular point x_i
>>>
>>
>>>> x_i <- matrix(rnorm(5), 1, 5)
>>>> x_i
>>>>
>>
>>> [,1] [,2] [,3] [,4] [,5]
>>> [1,] -0.1525543 0.4606419 -0.1011011 -1.557225 -1.035694
>>>
>>
>>> is inside the boundary of X or not. I know it's easy to do it with 1-D or
>>> 2-D, but I don't knot how to manage it when the dimension is large.
>>>
>>
>>> Can someone give a hint? Thanks in advance!
>>>
>>
>>> Feng
>>>
>> --
>> Robin K. S. Hankin
>> Uncertainty Analyst
>> University of Cambridge
>> 19 Silver Street
>> Cambridge CB3 9EP
>> 01223-764877
>>
>> ______________________________________________
>> r-h...@r-project.org mailing listhttps://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guidehttp://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
--
Robin K. S. Hankin
Uncertainty Analyst
University of Cambridge
19 Silver Street
Cambridge CB3 9EP
01223-764877
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