secant_method.c File Reference

Secant Method implementation. More...

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

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Macros
#define	TOLERANCE   0.0001
	for assert
#define	NMAX   100

Functions
double	func (double x)
	Continuous function for which we want to find the root.
double	secant_method (double x0, double x1, double tolerance)
	Root-finding method for a continuous function given two points.
static void	test ()
	Self-test implementations.
int	main ()
	Main function.

Detailed Description

Secant Method implementation.

Find a continuous function's root by using a succession of roots of secant lines to approximate it, starting from the given points' secant line.

Author

Samuel Pires

Macro Definition Documentation

TOLERANCE

#define TOLERANCE   0.0001

for assert

for fabs for io operations

Function Documentation

func()

double func

(

double

x

)

Continuous function for which we want to find the root.

Parameters

x	Real input variable

Returns

The evaluation result of the function using the input value

{
    return x * x - 3.;  // x^2 = 3 - solution is sqrt(3)
}

main()

int main

(

void

)

Main function.

Returns

0 on exit

{
    test();  // run self-test implementations
    return 0;
}

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secant_method()

double secant_method	(	double	x0,
		double	x1,
		double	tolerance
	)

Root-finding method for a continuous function given two points.

Parameters

x0	One of the starting secant points
x1	One of the starting secant points
tolerance	Determines how accurate the returned value is. The returned value will be within tolerance of the actual root

Returns

root of the function if secant method succeed within the maximum number of iterations

-1 if secant method fails

{
    int n = 1;  // step counter
 
    while (n++ < NMAX)
    {
        // calculate secant line root
        double x2 = x1 - func(x1) * (x1 - x0) / (func(x1) - func(x0));
 
        // update values
        x0 = x1;
        x1 = x2;
 
        // return value if it meets tolerance
        if (fabs(x1 - x0) < tolerance)
            return x2;
    }
 
    return -1;  // method failed (maximum number of steps exceeded)
}

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test()

static void test ( void  )

static

Self-test implementations.

Returns

void

{
    // compares root values found by the secant method within the tolerance
    assert(secant_method(0.2, 0.5, TOLERANCE) - sqrt(3) < TOLERANCE);
    assert(fabs(secant_method(-2, -5, TOLERANCE)) - sqrt(3) < TOLERANCE);
    assert(secant_method(-3, 2, TOLERANCE) - sqrt(3) < TOLERANCE);
    assert(fabs(secant_method(1, -1.5, TOLERANCE)) - sqrt(3) < TOLERANCE);
 
    printf("All tests have successfully passed!\n");
}

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