#*************************************************************
# Test Problem 2 from Chapter 11, section 3.4  
# Simple First Order Reversible Reaction
#*************************************************************

OPTION {{
  FTOL = 1e-10;
  OTOL = 1e-10;
  NLP = "SNOPT";

}}

DECLARATION {{
  INDEX {m,i,p};
  SET M = |1:20|;  # Number of Data sets
  SET I = |1:3|;   # Number of Variables
  SET P = |1:4|;   # Number of Parameters


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

  ZVAR {z(I)};
  ISPE {z(I)};
  ZINC {1,0,0};
  TIME {0,0.05,0.1,0.15,0.2,0.25,0.3,0.35,0.4,0.45,0.5,0.55,
        0.6,0.65,0.7,0.75,0.8,0.85,0.9,0.95,1.0};

# Observed data 
  PARA xe(M,I) = {0.8241,   0.0937,   0.0821,
                  0.6852,   0.1345,   0.1802,
                  0.5747,   0.1654,   0.2598,
                  0.4867,   0.1899,   0.3233,
                  0.4166,   0.2094,   0.3738,
                  0.3608,   0.2249,   0.4141,
                  0.3164,   0.2373,   0.4461,
                  0.2810,   0.2472,   0.4717,
                  0.2529,   0.2550,   0.4920,
                  0.2304,   0.2613,   0.5082,
                  0.2126,   0.2662,   0.5210,
                  0.1984,   0.2702,   0.5313,
                  0.1870,   0.2733,   0.5395,
                  0.1780,   0.2759,   0.5460,
                  0.1709,   0.2779,   0.5511,
                  0.1651,   0.2794,   0.5553,
                  0.1606,   0.2807,   0.5585,
                  0.1570,   0.2817,   0.5612,
                  0.1541,   0.2825,   0.5632,
                  0.1518,   0.2832,   0.5649};


# 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) = {0,0,10,10}; 
  UBDS a(P) = {10,10,50,50};
  
}}

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

  dae1: z'(1) =e= -a(1)*z(1) + a(2)*z(2);
  dae2: z'(2) =e=  a(1)*z(1) - (a(2) + a(3))*z(2) + a(4)*z(3);
  dae3: z'(3) =e=  -a(4)*z(3) + a(3)*z(2);

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

}}