#*************************************************************
# Test Problem 3 from Chapter 11, section 3.5  
# Catalytic Cracking of Gas Oil 
#*************************************************************

OPTION {{
  FTOL = 1e-8;
  OTOL = 1e-8;
  NLP = "SNOPT";

}}

DECLARATION {{
  INDEX {m,i,p};
  SET M = |1:20|;  # Number of Data sets
  SET I = |1:2|;   # Number of Variables
  SET P = |1:3|;   # Number of Parameters


  XVAR {x(M,I), # Fitted data variables
        a(P)    # Parameters
       };

  ZVAR {z(I)};
  ISPE {z(I)};
  ZINC {1,0};
  TIME {0,0.025,0.05,0.075,0.10,0.125,0.150,0.175,0.20,0.225,
        0.25,0.30,0.35,0.40,0.45,0.50,0.55,0.65,0.75,0.85,0.95};
        

# Observed data 
  PARA xe(M,I) = {0.7307,0.1954,0.5982,0.2808,0.4678,0.3175,0.4267,0.3047,
                  0.3436,0.2991,0.3126,0.2619,0.2808,0.2391,0.2692,0.2210,
                  0.2210,0.1898,0.2122,0.1801,0.1903,0.1503,0.1735,0.1030,
                  0.1615,0.0964,0.1240,0.0581,0.1190,0.0471,0.1109,0.0413,
                  0.0890,0.0367,0.0820,0.0219,0.0745,0.0124,0.0639,0.0089};

# Variable Bounds
  LBDS x(M,I) = < m E M | < i E I | 0 > >;
  UBDS x(M,I) = < m E M | < i E I | 1 > >;

  LBDS a(P) = < p E P | 0>; 
  UBDS a(P) = < p E P | 20>;
  
}}

MODEL {{
  MIN:  <<m E M | <<i E I | (xe(m,i) - x(m,i))^2 >> >>;

  dae1: z'(1) =e= -(a(1) + a(3))*z(1)^2; 
  dae2: z'(2) =e= a(1)*z(1)^2 - a(2)*z(2); 

  err(m E M,i E I)[m]:  z(i) - x(m,i) =e= 0;

}}