################################################################################
##  Function: pass <- garp (p, x, e)
##  Inputs: p >> 0 is a (k by t) matrix of prices, x >= 0 is a (k by t) matrix
##  of consumption bundles, 0 << e <= 1 is a (1 by t) vector of efficiency
##  levels, k >= 2 is the number of goods, t >= 1 is the number of observations
##  Outputs: pass = 0, 1 is a pass/fail indicator
##  Description: returns a pass/fail indicator which represents the outcome of a
##  GARP test at some efficiency vector
################################################################################

garp <- function (p, x, e) {

  #  number of observations
  t <- length (e)

  #  construct direct revealed preference relations
  e.p.x.i <- matrix (e * apply (p * x, 2, sum), t, t)
  p.x.j <- t(p) %*% x
  R0 <- 1 * (e.p.x.i >= p.x.j)
  P0 <- 1 * (e.p.x.i > p.x.j)

  #  compute transitive closure
  R <- warshall (R0)

  #  check for strict cycles
  cycles <- 1 * all (R + t(P0) < 2)

  #  clean and return result
  result <- cycles
  remove (cycles, e, e.p.x.i, p, p.x.j, P0, R, R0, t, x)
  return (result)

}