/*----------------------------------------------------

File: bisectionSearchSoln.c

Description: Applies bisection root finding method.

------------------------------------------------------*/

#include

#include

#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 ",

start, end);

if(findRoot(start, end, &root))

{

printf("Found root at: %.8f (f(x) = %.8f) ",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

n - number of coefficients

coeffs - reference to array of coefficients

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)

{

// Complete this function

}

/*----------------------------------------------------------

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)

{

}

/*----------------------------------------------------------

Function: findInterval

Parameters:

begin, end: pointers to double variables for storing selected

begin and end values of x for the desired interval

Description: Repeatedly plot the graph of the function for the

intervals given by the user until the user

has made a selection of the interval for root

finding.

---------------------------------------------------------------*/

void findInterval(double *begin, double *end)

{

//Variables declarations

char answer; // sentinal

do

{

printf("Please give start and end values for plotting: ");

fflush(stdin);

scanf("%lf %lf",begin,end);

plotFunc(*begin, *end, 0, NULL);

printf("Are you happy with this interval: ");

fflush(stdin);

scanf("%c",&answer);

}

while(answer != 'y');

}

/*----------------------------------------------------------

Function: plotFunc

Parameters:

begin, end: beginning and end of interval (x values) to plot

flag - set to TRUE when root was found and needs to be plotted

root - value of root when flag is TRUE.

Description: Plot the function on the

interval between begin and end. Plots an x at the roots

if nRoots > 0.

---------------------------------------------------------------*/

void plotFunc(double begin, double end, int nRoots, double roots[])

{

double x[N];

double y[N];

double inc; // increment for incrementing x

double yRoots[nRoots];

int ix;

// Calculate function points

inc = (end - begin)/N;

x[0] = begin;

y[0] = func(x[0]); // Compute first point

for(ix = 1; ix

{

x[ix] = x[ix -1] + inc;

y[ix] = func(x[ix]);

}

// Calculate y points at the root

for(ix = 0; ix

{

yRoots[ix] = func(roots[ix]);

}

// Plot

plot(N, x, y, nRoots, roots, yRoots);

}

/*-------------------------------------------------

Function: plot()

Parameters:

n: number of points in the arrays

xPtr: pointer to x values (horizontal axis).

yPtr: pointer to y values (vertical axis).

Return value: none.

Description: Initialises the plot. The following values

in the referenced structure are used to setup

the plot:

x[0], x[n-1] - assume that x values are sequential

miny, maxy - vertical axis range (add 10% to min/max value)

Sets up white background and black forground

colors.

Then plots the curve accessed using xPtr and yPtr.

-------------------------------------------------*/

void plot(int n, double *xPtr, double *yPtr, int nRoots, double *xRoots, double *yRoots)

{

double miny, maxy;

double range; // range of vertical axix

// Setup plot configuration

plsdev("wingcc"); // Sets device to wingcc - CodeBlocks compiler

// Initialise the plot

plinit();

// Configure the axis and labels

plwidth(3); // select the width of the pen

// Find range for axis

miny = getMin(yPtr, n);

maxy = getMax(yPtr, n);

range = maxy - miny; // the width of the range

maxy = maxy + 0.1*range;

miny = miny - 0.1*range;

plenv0(xPtr[0], xPtr[n-1], miny, maxy,

0, 1);

plcol0(GREEN); // Select color for labels

pllab("x", "f(x)", "Function");

// Plot the velocity.

plcol0(BLUE); // Color for plotting curve

plline(n, xPtr, yPtr);

// Plot the points

if(nRoots > 0)

{

plcol0(RED);

plpoin(nRoots,xRoots, yRoots, 'x');

}

plend();

}

/*----------------------------------------------------------

Function: getMin

Parameters:

array - reference to an array with double values

n - number of elements in the array

Returns

min: the minimum value found in the array

Description: Traverses the array to find its minimum value.

----------------------------------------------------------------*/

double getMin(double *array, int n)

{

int ix;

double min = array[0];

for(ix = 1; ix

if(min > array[ix]) min = array[ix];

return(min);

}

/*----------------------------------------------------------

Function: getMax

Parameters:

array - reference to an array with double values

n - number of elements in the array

Returns

max: the maximum value found in the array

Description: Traverses the array to find its maximum value.

----------------------------------------------------------------*/

double getMax(double *array, int n)

{

int ix;

double max = array[0];

for(ix = 1; ix

if(max

return(max);

}

C. Exercise: Bisection root finding method. s the bisection rootfinding method to find the finst thre root fom Exercise B Guidelines Start with the project BisectionRootFinding (in file BisectionRootFinding.zip). Complete the following functions: * double findRoot (double lower, double upper, double root) double func (double x) The findRoot funetion must implement the bisection root finding method. Use the symbolie constant EPSILON (set to le-10) in developing the findRoot function. Consult the notes, in particular the bisection root finding algorithm. Take the time to design the functions first before coding, that is, ensure you understand the logic of each function. The function func shall return the value for f(x) for the given x according to Equation 2 (you have already created this function in Part B). Run the program to find the first three roots. Compare with the results from Part B. Show the TA your running program and the modifications to the code to get your marks. C. Exercise: Bisection root finding method. s the bisection rootfinding method to find the finst thre root fom Exercise B Guidelines Start with the project BisectionRootFinding (in file BisectionRootFinding.zip). Complete the following functions: * double findRoot (double lower, double upper, double root) double func (double x) The findRoot funetion must implement the bisection root finding method. Use the symbolie constant EPSILON (set to le-10) in developing the findRoot function. Consult the notes, in particular the bisection root finding algorithm. Take the time to design the functions first before coding, that is, ensure you understand the logic of each function. The function func shall return the value for f(x) for the given x according to Equation 2 (you have already created this function in Part B). Run the program to find the first three roots. Compare with the results from Part B. Show the TA your running program and the modifications to the code to get your marks