(*
*  BISECTON ALGORITHM 2.1
*
*  To find a solution to f(x)=0 given the continuous function
*  f on the interval [a,b], where f(a) and f(b) have 
*  opposite signs
*
*  INPUT: endpoints a,b; tolerance TOL;
*      maximum number of iterations NO.
*
*  OUTPUT: approximate solution p or a message that the
*      algorithm fails.
*)
TEMP = Input["This is the Bisection Method.\n
              Input the function F(X) in terms of x.\n"];
F[x_] := Evaluate[TEMP];
OK = 0;
While[OK == 0,
   A = Input["Input endpoint a\n"];
   B = Input["Input endpoint b\n"];
   If[A > B,
      X = A;
      A = B;
      B = X;
   ];
   If[A == B,
      Input["A cannot equal B.\n
      Enter 1 [enter] to continue\n"],
      FA = F[A];    
      FB = F[B];
      If[FA*FB > 0,
         Input["F(A) and F(B) have the same sign.\n
         Enter 1 [enter] to continue\n"],
         OK = 1;
      ];
   ];
];
OK = 0;
While[OK == 0,
TOL = Input["Input the tolerance\n"];
   If[TOL<=0,
      Input["Tolerance must be positive.\n
      Enter 1 [enter] to continue\n"],
      OK = 1;
   ];
];
OK = 0;
While[OK == 0,
NO = Input["Input maximum number of iterations\n
        no decimal points\n"];
   If[NO<=0,
      Input["Must be a positive integer.\n
      Enter 1 [enter] to continue\n"],OK = 1
   ];
]; 
If[OK == 1,
   FLAG = Input["Select output destination\n
                 1. Screen\n
                 2. Text file\n
                 Enter 1 or 2\n"];
   If[FLAG == 2,
      NAME = InputString["Input the file name\n
                    For example:   output.dta\n"];
      OUP = OpenWrite[NAME,FormatType->OutputForm],
      OUP = "stdout";
   ];
   Write[OUP,"Bisection Method\n"];
   FLAG = Input["Select amount of output.\n
       Enter '1' for answer only\n
       Enter '2' for all intermediate approximations\n"];
   If[FLAG == 2,
      Write[OUP," i      P      F(P)\n"];
   ];
(*STEP 1*)
   i = 1;
(*STEP 2*)
   OK = 1;
   While[i <= NO && OK == 1,
(*STEP 3, compute P(i)*)
      CC = (B-A)/2;
      P = N[A+CC];
(*STEP 4*)
      FP = F[P];
      If[FLAG == 2,
         Write[OUP,"",i,"    ",SetPrecision[P,10],"    ",SetPrecision[FP,10]];
      ];
      If[(Abs[FP]<10^-20) || (CC<TOL),
(*procedure completed successfully*)
         Write[OUP,"Approximate solution P = \n",SetPrecision[P,10]];
         Write[OUP,"with F(P) = \n",SetPrecision[FP,10]];
         Write[OUP,"Number of iterations = \n",i];
         Write[OUP,"Tolerance = \n",SetPrecision[TOL,10]];
         OK = 0,
(*STEP 5*)
         i = i+1;
(*STEP 6, compute A(i) and B(i) *)
         If[(FA*FP > 0.00),
            A = P;
            FA = FP,
            B = P;
            FB = FP; 
         ]; 
      ];
   ];
   If[OK == 1,
(*STEP 7, procedure completed successfully *)
      Write[OUP,"Iteration number  ",NO];
      Write[OUP,"gave approximation  ",SetPrecision[P,10]];  
      Write[OUP,"F(P)= ",SetPrecision[FP,10]," not within tolerance: \n",SetPrecision[TOL,10]];
   ];
   If[OUP == "OutputStream[",NAME," 3]",
      Print["Output file: ",NAME," created successfully\n"];
      Close[OUP]
   ];
];
Quit[];