cgr.R

dans.rng = function(N_samp, n_eff, planck_length) {
  pnorm(rnorm(N_samp, sd=1 + runif(N_samp, -1/sqrt(n_eff), 1/sqrt(n_eff))))
}
discrete.dan = function(N_samp, n_eff, pl) {
  round(pnorm(rnorm(N_samp, sd=1 + runif(N_samp, -1/sqrt(n_eff), 1/sqrt(n_eff)))) * pl) / pl
}

linear_neff_plots = function(xlab, gen_data, n_samp, n_eff, planck_length) {
  data = gen_data(n_samp, n_eff, planck_length)
  bins <- n_eff * c(0.5, 1, 2, 3, 10, 50)
  par(mfrow=c(3, 2))
  #par(mar=c(4,2,2,1)+0.1)
  for (num_bins in bins) {
    label = paste0(#"N_samp: ", n_samp,
                   " n_eff:", n_eff,
                   " bins: n_eff*", num_bins / n_eff)
    hist(data, breaks = num_bins, main=label, xlab=xlab)
  }
}

sqrt_neff_plots = function(xlab, gen_data, n_samp, n_eff, planck_length) {
  data = gen_data(n_samp, n_eff, planck_length)
  bins <- sqrt(n_eff) * c(1, 2, 3, 5, 10, 20)
  bins = bins[bins > 1]
  par(mfrow=c(3, 2))
  #par(mar=c(4,2,2,1)+0.1)
  for (num_bins in bins) {
    label = paste0(#"N_samp: ", n_samp,
                   ", n_eff:", n_eff,
                   ", bins: sqrt(n_eff)*", num_bins / sqrt(n_eff),
                   ", pl: ", planck_length)
    hist(data, breaks = num_bins, main=label, xlab=xlab)
  }
}

pdf("linear_n_eff.pdf")
linear_neff_plots("Dan's RNG", dans.rng, 1e5, 26, 1000)
for (i in c(1e3, 1e4, 1e5)) {
  linear_neff_plots("Discretized Dan RNG", discrete.dan, 1e5, 26, i)
}
for (i in c(100, 1e3, 1e4)) {
  linear_neff_plots("Discretized Dan RNG", discrete.dan, 1e5, i, 1000)
}
dev.off()

pdf("sqrt_n_eff.pdf")
sqrt_neff_plots("Dan's RNG", dans.rng, 1e5, 26, 1000)
for (i in c(1e3, 1e4, 1e5)) {
  sqrt_neff_plots("Discretized Dan RNG", discrete.dan, 1e5, 26, i)
}
for (i in c(100, 1e3, 1e4)) {
  sqrt_neff_plots("Discretized Dan RNG", discrete.dan, 1e5, i, 1000)
}

dev.off()