Test for equality among all elements of a single numeric vector

Question

Why not simply using the variance:

var(x) == 0

If all the elements of x are equal, you will get a variance of 0.

If they're all numeric values then if tol is your tolerance then...

all( abs(y - mean(y)) < tol ) 

is the solution to your problem.

EDIT:

After looking at this, and other answers, and benchmarking a few things the following comes out over twice as fast as the DWin answer.

abs(max(x) - min(x)) < tol

This is a bit surprisingly faster than diff(range(x)) since diff shouldn't be much different than - and abs with two numbers. Requesting the range should optimize getting the minimum and maximum. Both diff and range are primitive functions. But the timing doesn't lie.

I use this method, which compares the min and the max, after dividing by the mean:

# Determine if range of vector is FP 0.
zero_range <- function(x, tol = .Machine$double.eps ^ 0.5) {
  if (length(x) == 1) return(TRUE)
  x <- range(x) / mean(x)
  isTRUE(all.equal(x[1], x[2], tolerance = tol))
}

If you were using this more seriously, you'd probably want to remove missing values before computing the range and mean.

You can just check all(v==v[1])

> isTRUE(all.equal( max(y) ,min(y)) )
[1] TRUE
> isTRUE(all.equal( max(x) ,min(x)) )
[1] FALSE

Another along the same lines:

> diff(range(x)) < .Machine$double.eps ^ 0.5
[1] FALSE
> diff(range(y)) < .Machine$double.eps ^ 0.5
[1] TRUE

You can use identical() and all.equal() by comparing the first element to all others, effectively sweeping the comparison across:

R> compare <- function(v) all(sapply( as.list(v[-1]), 
+                         FUN=function(z) {identical(z, v[1])}))
R> compare(x)
[1] FALSE
R> compare(y)
[1] TRUE
R> 

That way you can add any epsilon to identical() as needed.

Since I keep coming back to this question over and over, here's an Rcpp solution that will generally be much much faster than any of the R solutions if the answer is actually FALSE (because it will stop the moment it encounters a mismatch) and will have the same speed as the fastest R solution if the answer is TRUE. For example for the OP benchmark, system.time clocks in at exactly 0 using this function.

library(inline)
library(Rcpp)

fast_equal = cxxfunction(signature(x = 'numeric', y = 'numeric'), '
  NumericVector var(x);
  double precision = as<double>(y);

  for (int i = 0, size = var.size(); i < size; ++i) {
    if (var[i] - var[0] > precision || var[0] - var[i] > precision)
      return Rcpp::wrap(false);
  }

  return Rcpp::wrap(true);
', plugin = 'Rcpp')

fast_equal(c(1,2,3), 0.1)
#[1] FALSE
fast_equal(c(1,2,3), 2)
#[2] TRUE