/*
  From 
  http://www.mapleprimes.com/forum/howcanidononlinearfitsomedata
  """
  I am trying to fit  this function with some data
  F:= M*(  (1 -  ( 1 - a)*e^(-k*q*t)) /q)^(1/(1-q)) ;
  where a:= (No/M)^(1-q). I need to know the values
  of k, q and M, I do have No (initial condition)

  ...
  
  I did try to do this but it does not work
  with(Optimization):
  f:= x -> M*(  (1 -  ( 1 - q*(0.0012/M)^(1-q))*exp(-k*q*t)) /q)^(1/(1-q)) :
   
  residuals := map(p -> (f(p[1])-p[2]), DATA):
  R:= LSSolve(residuals);
  Error, (in Optimization:-LSSolve) complex value encountered
  
  Please let me know How can I solve  this problem. 
  """
  


  Cf maple_test.conf

*/
import util.
data(maple_test,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-  
  Data = [ [[X],Y] : [X,Y] in  chunks_of([
13.2621,0.0012,
14.0740,0.0017,
15.4272,0.0031,
16.7803,0.0063,
18.1335,0.0174,
19.2161,0.0317,
20.5692,0.0598,
21.6518,0.0821,
23.0049,0.1501,
24.0875,0.2061,
25.1700,0.2742,
26.5232,0.3534,
27.3351,0.4852,
28.6883,0.5337,
29.2295,0.6059,
30.5827,0.7565,
32.4772,1.0723,
34.1010,1.1068,
34.6422,1.2173  
  ],2)],
  Vars = ['X'],
  Unknown = [21.6518],
  Ops = [+,*,/,-,pow2,pow3,pow4],
  Constants = [frand(-100,100) : I in 1..10],  
  Params = new_map([approx = 0.01,
                    % total_approx=1,
                    % num_gens=30,
                    init_size=100,
                    % show_only_improvements=false,
                    % mutate_rate=0.3,
                    % crossover_rate=0.8,
                    debug=false,
                    % stop_criteria=at_least_one_solution,
                    % , stop_criteria=loops                    
                    % pick_from_pct=0.2,
                    show_best=2,
                    remove_dups=true
                    % , random_seed=1
                    % keep_programs_pct=0.1
                    ]),
  MaxSize = 41.