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Andrew Criswell

2001-Nov-20 04:42 UTC

[R] Sampling from a population

Hi ALL:

Suppose you have a population of N <- 5 observations, x <- c(43, 28, 7,
61, 39). From that you can draw a maximum of 10 samples without replacement of
size n <- 3. (Command choose(N,n) yields 10). For instance the samples I seek
are

    43, 61, 7
    39, 7, 28  ...etc

How can I get R to do that for me, to get an exhaustive list of samples of size
n drawn without replacement from a population of size N?  The command, sample(x,
3, replace=FALSE), works well for one draw. Is there a package that will handle
multiple draws?

Thanks and best wishes,
ANDREW

    
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Prof Brian Ripley

2001-Nov-20 09:05 UTC

head link

[R] Sampling from a population

On Tue, 20 Nov 2001, Andrew Criswell wrote:
> Hi ALL:
>
> Suppose you have a population of N <- 5 observations, x <- c(43, 28,
7, 61, 39). From that you can draw a maximum of 10 samples without replacement
of size n <- 3. (Command choose(N,n) yields 10). For instance the samples I
seek are
>
>     43, 61, 7
>     39, 7, 28  ...etc
>
> How can I get R to do that for me, to get an exhaustive list of samples of
size n drawn without replacement from a population of size N?  The command,
sample(x, 3, replace=FALSE), works well for one draw. Is there a package that
will handle multiple draws?
This is a question about drawing subsets, as covered in the Programmer's
Niche articles in Rnews.  You want all subsets (not subvectors, as order
does not matter) of size n=3 from N=5 items.

There is some C code to so it in package lqs, where it is used for
exhaustive searching, but that doesn't currently have an R interface (it
did once).

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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Mario Sendra Pina

2001-Nov-20 16:44 UTC

head link

[R] Sampling from a population

Suppose you have a population of N <- 5 observations, x <- c(43, 28, 7,
61, 39). From that you can draw a maximum of 10 samples without replacement of
size n <- 3. (Command choose(N,n) yields 10). For instance the samples I seek
are

      43, 61, 7
      39, 7, 28  ...etc

  How can I get R to do that for me, to get an exhaustive list of samples of
size n drawn without replacement from a population of size N?  The command,
sample(x, 3, replace=FALSE), works well for one draw. Is there a package that
will handle multiple draws?


  # First solution

  combix<-function(x,r) {
  n<-length(x)
  total<-choose(n,r)
  a<-matrix(0,total,r)
  ind<-c(1:r)
  for (i in 1:total){
     for (j in 1:r){a[i,j]<-x[ind[j]]}
     for (j in r:1){
          miro<-j
          ind[j]<-ind[j]+1
     if (ind[j]<n-r+j+1) break()
  }
     while(miro<r) {
     ind[miro+1]<-ind[miro]+1
      miro<-miro+1
        }
  }
  return(a)
  }

  print(combix(x=1:5,r=3))


  x<-c(8,3,1,11,4,7)
  print(mean(x))


  medias<- apply(combix(x,2),1,mean)
  print(mean(medias))



  #With-Replacement

  combixr<-function(x,r) {
  n<-length(x)
  total<-n**r
  a<-matrix(0,total,r)
  ind<-rep(1,r)
  for (i in 1:total){
     for (j in 1:r){a[i,j]<-x[ind[j]]}
     for (j in r:1){
          miro<-j
          ind[j]<-ind[j]+1
     if (ind[j]<n+1) break()
  }
     while(miro<r) {
     ind[miro+1]<-1
      miro<-miro+1
        }
  }
  return(a)
  }
  print(combixr(x=1:5,r=3))


  x<-c(8,3,1,11,4,7)
  print(mean(x))


  medias<- apply(combixr(x,2),1,mean)
  mean(medias)





  #Other form


  darcombi<- function(N,n,caso){
  vecpeq<-rep(0,n)
  ante<-0
  ante1<-0
  for(i in 1:n){
  N1<- N-(ante1+1)
  n1<- n-i
  v1<-cumsum(choose(N1:n1,n1))
  ante<-min(which(caso<=v1))
  vecpeq[i]<-ante+ante1
  resta<-0
  if (ante>1) resta<-v1[ante-1]
  caso<-caso-resta
  ante1<-vecpeq[i]
  }
  return(vecpeq)
  }

  N<-5
  n<-3

  for (i in 1:choose(N,n)){
  print(darcombi(N=N,n=n,i))
  }



  x <- c(43, 28, 7, 61, 39)
  N<-length(x)
  n<-3

  for (i in 1:choose(N,n)){
  print(x[darcombi(N=N,n=n,i)])
  }
      
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Ravi Varadhan

2001-Nov-20 23:51 UTC

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[R] Sampling from a population

There is a recursive function called "subsets" in the S-Programming
book by V&R, that lets you generate all unique combinations of n objects
taken k at a time.  Tim Hesterberg also has a non-recursive function called
"combinations", which may also be used.  Note that the recursive
function uses a lot more memory. You can use any of these functions to generate
unique, exhaustive samples.

Hope this helps,
Ravi.

Here is the non-recursive function (courtesy: Tim Hesterberg):

combinations _ function(n, k){
  # Compute all n choose k combinations of size k from 1:n
  # Return matrix with k rows and choose(n,k) columns.
  # Avoids recursion.
  if(!is.numeric(n) || length(n) != 1 || n%%1) stop("'n' must be an
integer")
  if(!is.numeric(k) || length(k) != 1 || k%%1) stop("'k' must be an
integer")
  if(k > n || k <= 0) return(numeric(0))
  rowMatrix _ function(n) structure(1:n, dim=c(1,n))
  colMatrix _ function(n) structure(1:n, dim=c(n,1))
  if(k == n) return(colMatrix(n))
  if(k == 1) return(rowMatrix(n))
  L _ vector("list", k)
  # L[[j]] will contain combinations(N, j) for N = 2:n
  L[[1]] _ rowMatrix(2)
  L[[2]] _ colMatrix(2)
  Diff _ n-k
  for(N in seq(3, n, by=1)){
    # loop over j in reverse order, to avoid overwriting
    for(j in seq(min(k, N-1), max(2, N-Diff), by= -1))
      L[[j]] _ cbind(L[[j]], rbind(L[[j-1]], N, deparse.level=0))
    if(N <= Diff+1) L[[1]] _ rowMatrix(N)
    else L[[N-(Diff+1)]] _ numeric(0)
    if(N <= k) L[[N]] _ colMatrix(N)
  }
  L[[k]]
}


    -----Original Message-----
    From: Andrew Criswell <arc at arcriswell.com>
    To: r-help at stat.math.ethz.ch <r-help at stat.math.ethz.ch>
    Date: Tuesday, November 20, 2001 12:52 AM
    Subject: [R] Sampling from a population
    
    
    Hi ALL:
    
    Suppose you have a population of N <- 5 observations, x <- c(43, 28,
7, 61, 39). From that you can draw a maximum of 10 samples without replacement
of size n <- 3. (Command choose(N,n) yields 10). For instance the samples I
seek are
    
        43, 61, 7
        39, 7, 28  ...etc
    
    How can I get R to do that for me, to get an exhaustive list of samples of
size n drawn without replacement from a population of size N?  The command,
sample(x, 3, replace=FALSE), works well for one draw. Is there a package that
will handle multiple draws?
    
    Thanks and best wishes,
    ANDREW
    
        
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