//=========================================================================
#define PROGRAMMER "SOLUTIONS, NoFrills"
#define PROG_CODE  "soln"
#define COURSE     "ECE-1021"
#define YEAR       (2003)
#define TERM       "Fall"
#define SECTION    (0)
#define ASSIGNMENT "HW #1B"
#define REVISION   (0)
#define TITLE      "Zeros of Functions"
#define SUBTITLE   "by Newton's Method"
#define EMAIL      "wbahn@eas.uccs.edu"
#define FILENAME   "01b0soln.c"
//=========================================================================

// PROBLEM:
//
// Find the zeroes of a function using Newton's Method.
//
// PSEUDOCODE:
//
// 1) TASK: Get data from the user
// 1.1) GET: x_guess (initial guess)
// 1.2) GET: n_max (maximum number of iterations to perform)
// 1.3) GET: h (width of derivative secant)
// 1.4) GET: tol (tolerance of function zero)
// 2) TASK: Compute Estimate of Function Zero
// 2.1) SET: n = 0
// 2.2) SET: x = x_guess
// 2.3) SET: f_x = FUNCTION
// 2.4) WHILE: ( (abs(f_x) > tol) AND (n < n_max) )
// 2.4.1) SET: x = x_guess - (h/2.0);
// 2.4.2) SET: f_xlower = FUNCTION;
// 2.4.3) SET: x = x_guess + (h/2.0);
// 2.4.4) SET: f_xupper =  FUNCTION;
// 2.4.5) SET: x_guess = x_guess - [ (h*f_x) / (f_xupper - f_xlower) ]
// 2.4.6) SET: x = x_guess;
// 2.4.7) SET: f_x =  FUNCTION;
// 2.4.8) SET: n = n+1
// 3) TASK: Report Results
// 3.1) PUT: "Iterations Performed: " n
// 3.2) PUT: "Last estimate of function zero = " x_guess
// 3.3) PUT: "Function evaluated at nominal zero = " f_x

//== INCLUDE FILES ========================================================
#include <stdio.h> // printf(), scanf()
#include <math.h>  // fabs()

//== #DEFINES =============================================================
#define FUNCTION ((x)*(x)*(x) - 3.0)

//== FUNCTION PROTOTYPES ==================================================
void PrintHeader(void);

//== MAIN FUNCTION ========================================================
int main(void)
{
	int n, n_max;
	double x_guess, h, tol;
	double x, f_x, f_xupper, f_xlower;

	PrintHeader();
	printf("\n"); // Print a blank line

	// 1) TASK: Get data from the user
	printf("Enter initial guess: ");
	scanf("%lf", &x_guess);
	printf("Enter maximum number of iterations: ");
	scanf("%i", &n_max);
	printf("Enter width of the derivative secant: ");
	scanf("%lf", &h);
	printf("Enter tolerance for function zero: ");
	scanf("%lf", &tol);

	// 2) TASK: Compute Estimate of Function Zero
	n = 0;
	x = x_guess;
	f_x = FUNCTION;

	while ( (fabs(f_x) > tol) && (n < n_max) )
	{
		x = x_guess - (h/2.0);
		f_xlower = FUNCTION;
		x = x_guess + (h/2.0);
		f_xupper =  FUNCTION;
		x_guess = x_guess - ( (h*f_x) / (f_xupper - f_xlower) );
		x = x_guess;
		f_x =  FUNCTION;
		n = n + 1;
	}

	// 3) TASK: Report Results
	printf("Iterations Performed: %i\n", n);
	printf("Last estimate of function zero = %f\n", x_guess);
	printf("Function evaluated at last nominal zero = %f\n", f_x);

	return(0);
}

//== SUPPORT FUNCTIONS ====================================================
void PrintHeader(void)
{
	printf("========================================"
			 "=======================================\n");
	printf("Course....... %s-%i (%s %i)\n", COURSE, SECTION, TERM, YEAR);
	printf("Programmer... %s (%s)\n", PROGRAMMER, PROG_CODE);
	printf("Assignment... %s (Rev %i) (Source Code in %s)\n",
		ASSIGNMENT, REVISION, FILENAME);
	printf("Description.. %s\n", TITLE);
	printf("              %s\n", SUBTITLE);
	printf("========================================"
			 "=======================================\n");

	return;
}