//
//Dynamic planning command
//

//Syntax with parameters only.
dynmp g1 - 3 by x;

//Options
kind:max    //kind of plan value max or min 
            //max:maximum value  min:minmum value
method:plus //method about integration of functions 
            //plus : ġ func[i]   mult: Ĩfunc[i]
//
//Quation
//This Algorithm is based on discrete funcions value.
//This command needs table which is composed by discrete function value.
//Example is below.
//  x    func1   func2   func3 
//  10   f1(10)  f2(10)  f3(10)
//  20   f1(20)  f2(20)  f3(20)
//  30   f1(30)  f3(30)  f3(30)

//
//Exsample 1
// Problem  max volume of rectangular (X1*X2*X3) by constraint X1+X2+X3 <= 10.
// Variable inclease by 0.1 pich from 0 to 10.
// �Å“K‰»ƒAƒ‹ƒSƒŠƒYƒ€ ’·”ö’q�° P41
//

/* Generate function table */  
clear;
vector g[3];
for(i=0;i<=100;i++) {
  for(n=1;n<=3;n++) {
    x=i*0.1;
    g[n]=x;
  }
  outrec;
}
select g_1-3 x;

/* dynamic plan */
dynmp g_1-3 by x/
kind=max
method=mult
;

//
//Exsample 2
// Valuable is X1 X2 X3 that are integer
//   0<=X1<=4 0<=X2<=4 0<=X3<=4
// functions are defined as follow.
//   func1:-2X1**2+8X1-5
//   func2: 3X2**2-18X2+29
//   func3: -X3**2+5
// constraction
//   0<= X1+X2+X3 <= 4
// Ref
// �Å“K‰»ƒAƒ‹ƒSƒŠƒYƒ€ ’·”ö’q�° P48
//

/* Generate function table */  
clear;
vector g[3];
for(i=1;i<=5;i++) {
  for(n=1;n<=3;n++) {
    x=i-1;
    if(n == 1) {g[n]=-2*x**2+8*x-5;}
    if(n == 2) {g[n]= 3*x**2-18*x+29;}
    if(n == 3) {g[n]= -1*x**2+5;}
  }
  outrec;
}
select g_1-3 x;

/* dynamic plan */
dynmp g_1-3 by x;