[R] boundary check

[Robin Hankin]

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