/*
*   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 NO.
*
*   OUTPUT:  approximate solution p or a message of failure
*/

#include <stdio.h>
#include <math.h>
#include <iostream>

#define true    1
#define false   0
#define PI      3.1415926535897932384626433832795

static   double absval(double);
static   double F(double);
static   double FP(double);
static   void INPUT(int *, double *, double *, int *);
static   void OUTPUT(FILE **, int *);

int main()
{
      double TOL,P0,D,F0,FP0;
      int OK,I,NO,FLAG;
      FILE *OUP[1];

      P0 = PI/4.0;
      TOL = 1.0e-13;
      NO = 200;

      OUTPUT(OUP, &FLAG);
      F0 = F(P0);

      /* STEP 1 */ 
      I = 1;      
      OK = true;        
      /* STEP 2 */ 
      while ((I<=NO) && true == OK) 
      {  
	 /* STEP 3 */ 
	 /* compute P(I) */ 
	 FP0 = FP(P0);
	 D = F0/FP0;
	 /* STEP 6 */ 
	 P0 = P0 - D;  
	 F0 = F(P0);
	 if (FLAG == 2) fprintf(*OUP,"%3d   %14.8e   %14.7e\n",I,P0,F0); 
	 /* STEP 4 */ 
	 if (absval(D) < TOL) { 
	    /* procedure completed successfully */
	    fprintf(*OUP,"\nNewton's method successed\n");
	    fprintf(*OUP,"\nApproximate solution = %.10e\n",P0);
	    fprintf(*OUP,"with F(P) = %.10e\n",F0);
	    fprintf(*OUP,"Number of iterations = %d\n",I);
	    fprintf(*OUP,"Tolerance = %.10e\n",TOL);
	    OK = false;
	 }
	 /* STEP 5 */ 
	 else I++;      
      }
      if (true == OK) {
	 /* STEP 7 */ 
	 /* procedure completed unsuccessfully */
	 fprintf(*OUP,"\nNewton's method failed\n");
	 fprintf(*OUP,"\nIteration number %d",NO);
	 fprintf(*OUP," gave approximation %.10e\n",P0);
	 fprintf(*OUP,"with F(P) = %.10e not within tolerance  %.10e\n",F0,TOL);
      }
      fclose(*OUP);
      return 0;
}

/* Change functions F and FP for a new problem */
static double F(double X)
{
   double f; 

   f = cos(X) - X;
   return f;
}
/*  FP is the derivative of F */
static double FP(double X)
{
   double fp; 

   fp = -sin(X) - 1;
   return fp;
}

static void OUTPUT(FILE **OUP, int *FLAG)
{
   char NAME[30];

   printf("Select output destination\n");
   printf("1. Screen\n");
   printf("2. Text file\n");
   printf("Enter 1 or 2: ");
   scanf("%d", FLAG);
   if (*FLAG == 2) {
      printf("Input the file name in the form - drive:name.ext\n");
      printf("For example:   A:OUTPUT.DTA\n");
      scanf("%s", NAME);
      *OUP = fopen(NAME, "w");
   }
   else *OUP = stdout;
   printf("Select amount of output\n");
   printf("1. Answer only\n");
   printf("2. All intermeditate approximations\n");
   printf("Enter 1 or 2: ");
   scanf("%d", FLAG);
   fprintf(*OUP,"Newtons Method\n");
   if (*FLAG == 2) fprintf(*OUP, "  I                P             F(P)\n");
}   
     

/* Absolute Value Function */
static double absval(double val)
{
   if (val >= 0) return val;
   else return -val;
}