/* 

  True skill (R2)  in Picat.

  This is a port of the R2 model TrueSkillSimple.cs
  (via the WebPPL model true_skill_simple.wppl)

  With the datafiles from R2
  - true_skill_simple_r2_players.csv
  - true_skill_simple_r2_games.csv
  
  Output from the R2 model (skills):
  ```
  [0] Mean: 107.265          skills[0]
  [0] Variance: 72.9736
  
  [1] Mean: 100.541          skills[1]
  [1] Variance: 86.9287
  
  [2] Mean: 95.7907          skills[2]
  [2] Variance: 84.9168
  ```

  This is a port of my Gamble model gamble_true_skill_simple.rkt.

  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.

main => go.

/*

  var : skills(1)
  Probabilities (truncated):
  138.686139436927988: 0.00072833211944647 (1 / 1373)
  136.757251361663805: 0.00072833211944647 (1 / 1373)
  134.013434306172314: 0.00072833211944647 (1 / 1373)
  132.285538348591729: 0.00072833211944647 (1 / 1373)
  .........
  78.330023251134151: 0.00072833211944647 (1 / 1373)
  77.813016341809544: 0.00072833211944647 (1 / 1373)
  76.566771465466573: 0.00072833211944647 (1 / 1373)
  75.690773344358348: 0.00072833211944647 (1 / 1373)
  mean = 105.889

  var : skills(2)
  Probabilities (truncated):
  131.861086373999512: 0.00072833211944647 (1 / 1373)
  125.810415902656374: 0.00072833211944647 (1 / 1373)
  125.682242386650842: 0.00072833211944647 (1 / 1373)
  125.178968678568623: 0.00072833211944647 (1 / 1373)
  .........
  75.973924186634576: 0.00072833211944647 (1 / 1373)
  74.950523654757546: 0.00072833211944647 (1 / 1373)
  73.147176472007203: 0.00072833211944647 (1 / 1373)
  71.380761935993803: 0.00072833211944647 (1 / 1373)
  mean = 100.031

  var : skills(3)
  Probabilities (truncated):
  126.581905164488447: 0.00072833211944647 (1 / 1373)
  123.92761107341876: 0.00072833211944647 (1 / 1373)
  121.052452615963603: 0.00072833211944647 (1 / 1373)
  120.92548531654927: 0.00072833211944647 (1 / 1373)
  .........
  67.084769087573619: 0.00072833211944647 (1 / 1373)
  66.634845302911799: 0.00072833211944647 (1 / 1373)
  64.74638887494325: 0.00072833211944647 (1 / 1373)
  61.673338758581863: 0.00072833211944647 (1 / 1373)
  mean = 94.2245

  var : performance(1,1)
  Probabilities (truncated):
  162.039255948868259: 0.00072833211944647 (1 / 1373)
  157.309234515905075: 0.00072833211944647 (1 / 1373)
  156.583991227424747: 0.00072833211944647 (1 / 1373)
  156.268379240276346: 0.00072833211944647 (1 / 1373)
  .........
  72.408076623962515: 0.00072833211944647 (1 / 1373)
  71.996520937841481: 0.00072833211944647 (1 / 1373)
  71.706065300321754: 0.00072833211944647 (1 / 1373)
  71.091948335819197: 0.00072833211944647 (1 / 1373)
  mean = 112.854

  var : performance(1,2)
  Probabilities (truncated):
  143.187670581721875: 0.00072833211944647 (1 / 1373)
  140.324944717946579: 0.00072833211944647 (1 / 1373)
  136.38214608332072: 0.00072833211944647 (1 / 1373)
  134.969675128992151: 0.00072833211944647 (1 / 1373)
  .........
  48.272482947567767: 0.00072833211944647 (1 / 1373)
  46.805747685678256: 0.00072833211944647 (1 / 1373)
  45.419846968809438: 0.00072833211944647 (1 / 1373)
  45.241518084482166: 0.00072833211944647 (1 / 1373)
  mean = 92.3863

  var : performance(2,1)
  Probabilities (truncated):
  153.854361597780922: 0.00072833211944647 (1 / 1373)
  151.438797973070649: 0.00072833211944647 (1 / 1373)
  150.609051373411376: 0.00072833211944647 (1 / 1373)
  148.349611765145767: 0.00072833211944647 (1 / 1373)
  .........
  68.353575316656546: 0.00072833211944647 (1 / 1373)
  67.814881837291892: 0.00072833211944647 (1 / 1373)
  66.794056500731827: 0.00072833211944647 (1 / 1373)
  52.709799375863568: 0.00072833211944647 (1 / 1373)
  mean = 106.741

  var : performance(2,2)
  Probabilities (truncated):
  138.540559501767916: 0.00072833211944647 (1 / 1373)
  135.21284998948812: 0.00072833211944647 (1 / 1373)
  132.065703232713958: 0.00072833211944647 (1 / 1373)
  131.660580527630458: 0.00072833211944647 (1 / 1373)
  .........
  43.998947964774288: 0.00072833211944647 (1 / 1373)
  41.483487675358397: 0.00072833211944647 (1 / 1373)
  35.978536763046634: 0.00072833211944647 (1 / 1373)
  14.720861479960277: 0.00072833211944647 (1 / 1373)
  mean = 87.0699

  var : performance(3,1)
  Probabilities (truncated):
  166.132104855562602: 0.00072833211944647 (1 / 1373)
  160.942598080274593: 0.00072833211944647 (1 / 1373)
  159.914506112392331: 0.00072833211944647 (1 / 1373)
  151.368479582586417: 0.00072833211944647 (1 / 1373)
  .........
  71.720259159422113: 0.00072833211944647 (1 / 1373)
  70.759354033259712: 0.00072833211944647 (1 / 1373)
  70.39748583845406: 0.00072833211944647 (1 / 1373)
  66.16352978102671: 0.00072833211944647 (1 / 1373)
  mean = 110.915

  var : performance(3,2)
  Probabilities (truncated):
  126.732228396474369: 0.00072833211944647 (1 / 1373)
  126.360441234179973: 0.00072833211944647 (1 / 1373)
  125.598501848325768: 0.00072833211944647 (1 / 1373)
  125.151327558334145: 0.00072833211944647 (1 / 1373)
  .........
  50.359352171811395: 0.00072833211944647 (1 / 1373)
  48.189165212324589: 0.00072833211944647 (1 / 1373)
  44.644197613792983: 0.00072833211944647 (1 / 1373)
  39.006327746160402: 0.00072833211944647 (1 / 1373)
  mean = 87.9911


*/
go ?=>
  reset_store(),
  time2(run_model(10_000,$model,[show_probs_rat_trunc,mean])),
  fail,
  nl.
go => true.


model() =>
  % From the Gamble model (0 based)
  % Players = 0..2,
  % Games:
  % p1 p2 result (1:won 0:tie, -1:lost)
  % Games = [ [0,1,1], % player 0 won over player 1
  %           [1,2,1], % player 1 won over player 2
  %           [0,2,1]],% player 0 won over player 2
  
  % 1 based
  Players = 1..3,
  Games =   [ [1,2,1], % player 1 won over player 2
              [2,3,1], % player 2 won over player 3
              [1,3,1]],% player 1 won over player 3

  NumPlayers = Players.len,
  NumGames = Games.len,
  
  % Each player has some fixed skill
  Skills = normal_dist_n(100,10,NumPlayers),

  % Performances per game
  % The performance per game is - however - depending on the skill
  % but might vary.
  Performance = [ [normal_dist(Skills[G[P]],15) :
                  P in 1..2] :
                  G in Games],

  foreach(G in 1..NumGames)
    if Games[G,3] == 1 then
      observe(Performance[G,1] > Performance[G,2])
    elseif Games[G,3] == -1 then
      observe(Performance[G,1] < Performance[G,2])
    else
      observe(abs(Performance[G,1]-Performance[G,2])<= 0.1)
    end
  end,

  if observed_ok then  
    add("skills(1)",Skills[1]),
    add("skills(2)",Skills[2]),
    add("skills(3)",Skills[3]),
    % Peformance for each game
    add("performance(1,1)",Performance[1,1]),
    add("performance(1,2)",Performance[1,2]),
    add("performance(2,1)",Performance[2,1]),
    add("performance(2,2)",Performance[2,2]),
    add("performance(3,1)",Performance[3,1]),
    add("performance(3,2)",Performance[3,2])
  end.