[R] Elementary Symmetric Polynomials

[davidr at rhotrading.com]

How's this?

f2 <- function(v) {
  n <- length(v)
  s <- matrix(0,n,n)
  for(i in 1:n)
    for(j in 1:i)
      s[j,i] <- ifelse(i>1, s[j,i-1]+v[i]*ifelse(j>1, s[j-1,i-1], 1),
v[i])
  c(1,s[,n])
}

> system.time(f2.result <- f2(1:20))
   user  system elapsed 
      0       0       0 
> system.time(f.result <- f(1:20))
   user  system elapsed 
  29.50    0.04   29.58 
> all.equal(f.result, f2.result)
[1] TRUE


-- David Reiner


-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On Behalf Of Austin H. Jones
Sent: Tuesday, July 21, 2009 5:11 PM
To: r-help at r-project.org
Subject: [R] Elementary Symmetric Polynomials

We are interested in obtaining an efficient function that for a given 
vector of length t will output a vector of length t+1 that contains the 
associated values of the elementary symmetric polynomials in t 
variables. Below is what we have at the moment, but it is a little slow 
for our needs. Any suggestions?

Thanks ahead of time for any help you can offer,

Austin H. Jones
Department of Mathematics
Wake Forest University



f<-function(v)
{
prodsub<-function(v,q){prod(v[q])}
t<-length(v)
C<-vector("list",t)
for (i in 1:t)
{C[[i]]<-combn(1:t,i)}
e<-rep(0,t)
for (i in 1:(t))
{
e[i]<-sum(apply(C[[i]],2,prodsub,v=v))
}
e<-c(1,e)
e
}

Examples:


 > f(c(1,2,3))
[1]  1  6 11  6


 > f(c(4,6,3,1,9))
[1]    1   23  193  729 1206  648

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