test_that("on input of sufficient size, beta/||beta|| is estimated accurately enough",
{
  set.seed(42)
  n <- 100000
  d <- 2
  K <- 2
  p <- 1/2

  betas_ref <- array( c(1,0,0,1 , 1,-2,3,1), dim=c(d,K,2) )
  for (i in 1:(dim(betas_ref)[3]))
  {
    mu_ref <- normalize(betas_ref[,,i])
    for (link in c("logit","probit"))
    {
      cat("\n\n",link," :\n",sep="")

      io <- generateSampleIO(n, p, betas_ref[,,i], rep(0,K), link)
      mu <- computeMu(io$X, io$Y, list(K=K))
      mu_aligned <- alignMatrices(list(mu), ref=mu_ref, ls_mode="exact")[[1]]

      #Some traces: 0 is not well estimated, but others are OK
      cat("Reference normalized matrix:\n")
      print(mu_ref)
      cat("Estimated normalized matrix:\n")
      print(mu_aligned)
      cat("Difference norm (Matrix norm ||.||_1, max. abs. sum on a column)\n")
      diff_norm <- norm(mu_ref - mu_aligned)
      cat(diff_norm,"\n")

      # NOTE: 0.5 is loose threshold, but values around 0.3 are expected...
      expect_lt( diff_norm, 0.5 )
    }
  }
})