/* 

  Curve fitting in Picat.

  From GLPK example cf12a.mod:
  """
  Curve fitting problem 12.11(a) H P Williams "Model Building in 
  Mathematical Programming"
  """

  The answer should be 
     y = 0.6375x + 0.581

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

*/


import mip.


main => go.


go =>
  
  N = 19,
  X = [0.0, 0.5,1.0,1.5,1.9,2.5,3.0,3.5,4.0,4.5,5.0,5.5,6.0,6.6,7.0,7.6,8.5,9.0,10.0],
  Y =  [1.0,0.9,0.7,1.5,2.0,2.4,3.2,2.0,2.7,3.5,1.0,4.0,3.6,2.7,5.7,4.6,6.0,6.8,7.3],

  A :: 0.0..1.0,
  B :: 0.0..1.0,

  U = new_list(N),
  U :: 0.0..3.0,

  V = new_list(N),
  V :: 0.0..3.0,

  Z #=  sum(U) + sum(V),

  foreach(I in 1..N)
     B * X[I] + A + U[I] - V[I] #= Y[I]
  end,


  solve($[min(Z)], X ++ Y ++ U ++ V),

  println(z=Z),
  println(a=A),
  println(b=B),
  % println(u=U),
  % println(v=V),


  nl.