################################################################################
##  Function:     pass <- garp (p, x, e)
##  Inputs:       p >> 0 [(k by t) matrix of prices]
##                x >= 0 [(k by t) matrix of consumption bundles]
##                0 << e <= 1 [(1 by t) vector of efficiency levels]
##                k >= 2 [number of goods]
##                t >= 1 [number of observations]
##  Outputs:      pass = 0, 1 [pass/fail indicator]
##  Libraries:    none
##  Calls:        warshall
##  Description:  returns a pass/fail indicator representing 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 <- crossprod (p, x)
  R0 <- 1 * (p.x.j <= e.p.x.i)
  P0 <- 1 * (p.x.j <= e.p.x.i - 1e-12)
  
  #  compute transitive closure
  R <- warshall (R0)
  
  #  check for strict cycles
  cycles <- 1 * any (R + t(P0) == 2)
  
  #  clean and return result
  result <- 1 - cycles
  remove (cycles, e, e.p.x.i, p, p.x.j, P0, R, R0, t, x)
  return (result)
  
}