Thread: Find the first 3 roots of a function HELP! - bisection method

i'm trying to write a program that would find the root of a function using 2 the start and end inputs from a user and using the bisection method.However , it only gives me a root at 0 with f(x) = 50 which is wrong.

Now , the program is pretty lengthy so I only provided the parts needed however if u need the rest ask me.

Code:

/*----------------------------------------------------File: bisectionSearchSoln.c
Description: Applies bisection root finding method.
------------------------------------------------------*/
#include <stdio.h>
#include <math.h>
#include "gng1106plplot.h"
#define N 100  // number of points
#define TRUE 1
#define FALSE 0
#define EPSILON 1e-10
// Function Prototypes
void findInterval(double *, double *);
int findRoot(double, double, double *);
void plotFunc(double, double, int, double []);
double func(double);
void plot(int,  double[], double[], int, double[], double[]);
double getMin(double *, int );
double getMax(double *, int );
/*--------------------------------------------------------
Function: main()
---------------------------------------------------------*/
int main()
{
    double start, end;
    double root;
    int n;  // number of roots found
    // Get intervals from user
    findInterval(&start, &end);
    printf("Finding root for interval between %.4f and %.4f\n",
           start, end);
    if(findRoot(start, end, &root))
    {
        printf("Found root at: %.8f (f(x) = %.8f)\n",root, func(root));
        n = 1;
    }
    else
    {
         printf("Did not find root in interval.");
         n = 0;
    }
    plotFunc(start, end, n, &root);
    return 0;
}
/*----------------------------------------------------------
Function: findRoot
Parameters
    lower, upper:  lower and upper values of x for the interval
    root  - pointer to array for saving roots
Returns:  TRUE if a root was found (store in root), and FALSE
          if no root exists in interval.
Description: Find the root between the interval for the
             function using the bisection
             method.
---------------------------------------------------------------*/


int findRoot(double lower, double upper, double *root)
{
 double x0 , x1 ;


 x0=upper;
 x1= lower;
int retVal = FALSE;
if(func(x0)*func(x1) > 0)
{
    do
  {
    retVal = TRUE;


    *root = (x0+x1)/2;


    if(func(*root) > 0 )
     x1 = *root;
    else x0 = *root;




}while(fabs(*root)< EPSILON);


return(TRUE);
}
}
/*----------------------------------------------------------
Function: func
Parameters:
    x - x value function f(x)
Returns: value y of function f(x)
Description: Plots the value of the function:


f(x) = 50 - x^2 |cos(sqrt(x)| , x must be positive, if x
                         negative return 0.
-----------------------------------------------------------*/
double func(double x)
{
  double fx;


    if(x < 0)
      fx = 0;


  fx = 50 - x*x * fabs(cos(sqrt(x)));


  return fx;




}

> However , it only gives me a root at 0 with f(x) = 50 which is wrong
I suppose this is a lesson in testing as you go, rather than writing the whole thing and wondering why it doesn't work.

So put some print statements in - or use a debugger.

Code:

int findRoot(double lower, double upper, double *root)
{
 double x0 , x1 ;
 
 
 x0=upper;
 x1= lower;
int retVal = FALSE;
if(func(x0)*func(x1) > 0)
{
    do
  {
    retVal = TRUE;
 printf("Iteration: x0=%f, x1=%f\n", x0, x1 );
 
    *root = (x0+x1)/2;
 
 
    if(func(*root) > 0 )
     x1 = *root;
    else x0 = *root;
 
 
 
 
}while(fabs(*root)< EPSILON);
 
 
return(TRUE);
}
}

Oh, and fix your indentation.
Indentation style - Wikipedia

Originally Posted by jack jordan

[...] but you have a lot of comments. [...]

"Lots of" comments providing detailed descriptions of functions is generally good. The amount of commenting in the code provided by the author is suitable IMO (I'm not sure if the contents of the comments is good, but the size of the comments documenting the functions is quite normal)

Edit: Have a look at some source code that is documented using Doxygen at some point. The Amiga technical reference manuals were created, in part at least, in the same way using what they called AutoDoc. Detailed function documentation is a good thing.