(*
*  NEWTON-RAPHSON ALGORITHM 2.3
*
*  To find a solution to F(X) = 0 given an 
*  initial approximation P0
*
*  INPUT: initial approximation P0; tolerance TOL;
*      maximum number of iterations n0.
*
*  OUTPUT: approximate solution p or a message that the
*      method fails.
*)
TEMP = Input["This is Newton's Method.\n
              Input the function F(X) in terms of x.\n\n
              For example: Cos[x]\n"];
F[x_] := Evaluate[TEMP]
DER = D[TEMP,x];
FP[x_] := Evaluate[DER] 
P0 = Input["Input initial approximation"];
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,
   n0 = Input["Input maximum number of iterations\n
            no decimal points\n"];
      If[n0 <= 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"
   ];
   FLAG = Input["Select amount of output.\n
      Enter '1' for answer only\n
      Enter '2' for all intermediate approximations\n"];
   Write[OUP,"Newton's Method\n"];
   If[FLAG == 2,
      Write[OUP," i      P      F(P)\n"],
   ];
   F0 = N[F[P0]];
(*STEP 1*)
   i = 1;
   OK = 1;
(*STEP 2*)
   While[i <= n0 && OK == 1,
(*STEP 3, Compute P(i)*)
      FP0 = N[FP[P0]];
      d = F0/FP0;
(*STEP 6*)
      P0 = P0-d;
      F0 = N[F[P0]];
      If[FLAG == 2,
      Write[OUP,i,"   ",SetPrecision[P0,10],"   ",SetPrecision[F0,10]]
      ];
(*STEP 4*)
      If[Abs[d] < TOL,
(*Procedure completed successfully*)
         Write[OUP,"Approximate solution = \n",SetPrecision[P0,10]];
         Write[OUP,"with F(P) = \n",SetPrecision[F0,10]];
         Write[OUP,"Number of iterations = \n",i];   
         Write[OUP,"Tolerance = \n",SetPrecision[TOL,10]];
         OK = 0,
(*STEP 5*)
         i = i+1;
      ];
   ];
   If[OK == 1,
(*STEP 7, Procedure completed unsuccessfully*)
      Write[OUP,"Iteration number ",n0];
      Write[OUP,"gave approximation \n",SetPrecision[P0,10]]; 
      Write[OUP,"with F(P) = ",SetPrecision[F0,10]];
      Write[OUP," not within tolerance \n",SetPrecision[TOL,10]];
   ];
   If[OUP == "OutputStream[",NAME," 3]",
      Print["Output file: ",NAME," created successfully\n"];
      Close[OUP];
   ];
];
Quit[];