/* 

  Piecewise transformation in Picat.

  Based on the SPPL model piecewise_transformation.pynb

  Cf my Gamble model gamble_piecewise_transformation.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.
import util.

main => go.

/*

  var : x
  Probabilities (truncated):
  7.647218862214786: 0.0001000000000000
  7.554555696250038: 0.0001000000000000
  6.646156885333496: 0.0001000000000000
  6.590823373466852: 0.0001000000000000
  .........
  -6.620771551812407: 0.0001000000000000
  -6.929920769946673: 0.0001000000000000
  -7.030719947463972: 0.0001000000000000
  -7.125806862650598: 0.0001000000000000
  mean = 0.00387121
  HPD intervals:
  HPD interval (0.94): -3.81289631050185..3.69824915528616

  var : z
  Probabilities (truncated):
  369.850256969369639: 0.0001000000000000
  354.782382581584272: 0.0001000000000000
  339.245419342400794: 0.0001000000000000
  294.328964839119351: 0.0001000000000000
  .........
  -4.060670527426659: 0.0001000000000000
  -4.060671380795453: 0.0001000000000000
  -4.060671500108283: 0.0001000000000000
  -4.060672060988497: 0.0001000000000000
  mean = 5.29927
  HPD intervals:
  HPD interval (0.94): -4.06067206098850..21.93914838105016


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,show_hpd_intervals,hpd_intervals=[0.94]]),
  nl,
  % show_store_lengths,
  % fail,
  nl.
go => true.
  
  
model() =>
  X = normal_dist(0,2),

  Z = cond(X < 1,
           pow(-X,3) + pow(X,2) + 6*X,
           (-5)*sqrt(X) + 11),
  
  add("x",X),  
  add("z",Z).