################################################################################
##  Function:     pass <- garp(p, x, e)
##  Parameters:   k [number of goods]
##                n [number of observations]
##  Inputs:       p [(k by n) matrix of prices]
##                x [(k by n) matrix of consumption amounts]
##                e [(1 by n) vector of efficiency levels]
##  Outputs:      pass [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
  n <- length(e)
  
  #  construct direct revealed preference relations
  e.p.x.i <- matrix(e * apply(p * x, 2, sum), n, n)
  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, n, p, p.x.j, P0, R, R0, x)
  return(result)
  
}