# We'll bootstrap the monk data, consider those to somewhat legit representations of 'real'
# graphs, and run those through the prob calculating function, then compare the prob of our
# random graph to the resulting distribution of probabilities.

# we can use the probability of the non bootstrapped, actual Monk graph data to possibly
# slightly change the distribution of the probabitlies, if the bootstrapped calced probs
# seem a bit skewed.

# would this have implications regarding the theta involved?

# first, we need a random graph.
p = .28
rand.grph <- matrix(sample( c(1, 0), size = 18*18, prob = c(p, (1-p)), replace = TRUE), nrow = 18)

theta.mle <- c(-1.9, 1.89, .098)
acc.trials.kappa = 700
burn = 300


prob.of.graph = function(graph.test, theta.mle, acc.trials.kappa, burn){
  kappa.test <- mean(mcmc.kappa(graph, theta = theta.mle,
                  acc.trials = acc.trials.kappa)$kappa[burn:(acc.trials.kappa-1)])
  return(exp( Theta.vector %*% c(g1(graph.test), g2(graph.test), g3(graph.test)) / kappa.test))
}

# now, we want to retain certain charecteristics of the monk graph, so we wont randomly select
# cells from the graph. We could do rows, we could to columns, the idea is to be random and
# different while still keeping certain info from the graph, that is specifically different
# than only the total number of ones in the graph.

# we'll chose some by column, some by rown, and some by mixing up different grids, mxn, from
# the monk graph
bootsrap.graph = function(graph){
  r.comp <- runif(1)
  if(r.comp < .34){
    smp <- sample(1:18, size = 18, replace = TRUE)
    graph.new <- graph[,smp]}
  else #(r.comp < .67)
  {
    smp <- sample(1:18, size = 18, replace = TRUE)
    graph.new <- graph[,smp]}
  #   else{
  #     smp.col <- sample(2:17, size = 1, replace = TRUE)
  #     smp.row <- sample(2:17, size = 1, replace = TRUE)
  #     graph.new <- as.matrix(rbind( cbind( graph[smp.row:18,1:smp.col], graph[smp.row:18,(smp.col+1):18]),
  #                         cbind( graph[1:(smp.row-1),smp.col:18], graph[1:(smp.row-1),1:(smp.col-1)]) ),
  #                         nrow = 18)
  #     colnames(graph.new) <- colnames(graph)
  #     rownames(graph.new) <- rownames(1:18)
  #   }

  return(graph.new)
}

# Yup, we're staying
View(bootsrap.graph(graph))


prob.dist.func = function(iter, graph.initial, theta.mle, acc.trials.kappa, burn){
  prob.store <- rep(0, iter)
  for(i in 1:iter){
    graph.test <- bootsrap.graph(graph.initial)
    prob.store <- prob.of.graph(graph.test, theta.mle, acc.trials.kappa, burn)
  }
  return(prob.store)
}

prob.dist.func = function(iter, graph.initial, theta.mle, acc.trials.kappa, burn){
  prob.store <- rep(0, iter)
  for(i in 1:iter){
    graph.test <- bootsrap.graph(graph.initial)
    prob.store [i] <- prob.of.graph(graph.test, theta.mle, acc.trials.kappa, burn)
  }
  return(prob.store)
}