/* 

  BDA3 in Picat.

  https://github.com/probmods/ppaml2016/blob/gh-pages/chapters/5-data.md
  """
  Part 2: Making predictions from data

  Some times, we're more interested in getting model predictions than, say, 
  analyzing learned model parameters. Uncertain and reversible financial models

  Estimating Amazon hosting costs for a fictional video streaming company:
  """

  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import ppl_distributions, ppl_utils.
import util.
% import ordset.

main => go.

/*

  var : costs
  Probabilities (truncated):
  370.005444000000011: 0.0018000000000000
  370.005443999999898: 0.0003000000000000
  440.005451999999991: 0.0002000000000000
  370.005443999999329: 0.0002000000000000
  .........
  320.280085231682051: 0.0001000000000000
  320.276078484776576: 0.0001000000000000
  320.257426728734458: 0.0001000000000000
  320.035484638337493: 0.0001000000000000
  mean = 388.644
  HPD intervals:
  HPD interval (0.84): 363.58838872165870..440.05646521316555

  var : requests B
  Probabilities (truncated):
  50000.0: 0.0265000000000000
  49999.999999999985448: 0.0019000000000000
  49999.999999999992724: 0.0016000000000000
  49999.999999999970896: 0.0012000000000000
  .........
  40050.376649444326176: 0.0001000000000000
  40026.46967375400709: 0.0001000000000000
  40022.815373369805457: 0.0001000000000000
  40004.186124653446313: 0.0001000000000000
  mean = 48805.9
  HPD intervals:
  HPD interval (0.84): 47134.66165441452176..50000.00000000000000

  var : requests
  Probabilities (truncated):
  110000.0: 0.0019000000000000
  109999.999999999970896: 0.0002000000000000
  149999.999999930092599: 0.0001000000000000
  149999.993778331321664: 0.0001000000000000
  .........
  100054.94154527792125: 0.0001000000000000
  100054.127692625203053: 0.0001000000000000
  100050.406209830136504: 0.0001000000000000
  100006.790128183216439: 0.0001000000000000
  mean = 117377.0
  HPD intervals:
  HPD interval (0.84): 108395.90268973856291..130037.36189517741150

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,
                           % show_simple_stats % ,
                           % show_percentiles,
                           show_hpd_intervals,hpd_intervals=[0.84],
                           % show_histogram,
                           min_accepted_samples=10000 % ,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  Resources = [["a", 1, beta_dist(0.01,0.1) * 20000 + 30000],
               ["b",10, beta_dist(0.02,0.1) * 20000 + 30000],
               ["c", 7, beta_dist(0.05,0.1) * 20000 + 30000]
               ],
  N = Resources.len,

  [_Name,Storage1,Requests1] = Resources.transpose,  
  Storage = Storage1.sum,
  Requests = Requests1.sum,

  Transfer1 = [ Storage1[I]*Requests1[I] : I in 1..N],
  Transfer = Transfer1.sum,

  
  % B goes viral
  % Requests of B > 40000
  observe(Requests1[2] > 40_000),

  Requests2 = 0.004 * Requests / 100_000,
  Storage2 = 0.03 * Storage,
  Transfer2 = Transfer * cases([[Transfer <= 1, 0],
                               [Transfer <= 10_000, 0.09],
                               [Transfer <= 40_000, 0.085],
                               [Transfer <= 100_000,0.07],
                               [true,0.05]]),
  Costs = (Requests2 + Storage2 + Transfer2) / 100,
  
  if observed_ok then
    add("costs",Costs),
    add("requests B",Requests1[2]),    
    add("requests",Requests),

  end.