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

File: incremSearchFncSoln.c

Name: XXX

Student ID: XXX

This program plots function, asks the user to select

an interval for finding roots.

Function: f(x) = 50 - x^2 |cos(x^1/2)| An incremental search

root finding method is used.

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

#include

#include

#include "gng1106plplot.h"

#define N 100 // number of points

#define MAX_ROOTS 3 // Maximum number of roots

#define TRUE 1

#define FALSE 0

#define ALMOST_0 1e-5 // For testing zero values

#define SI_RESOLUTION 1000 // Subinterval resolution

// Function Prototypes

void findInterval(double *, double *);

int findAllRoots(double, 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()

Description: Call findInterval to allow the user to select

an interval for searching. Show the results

to the user.

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

int main()

{

double start, end;

double roots[MAX_ROOTS];

int n; // number of roots found

int ix;

// Get intervals from user

findInterval(&start, &end);

printf("Finding roots for intervals between %.4f and %.4f ",

start, end);

n = findAllRoots(start, end, roots);

printf("Found %d roots: ",n);

for(ix = 0; ix

printf(" %.8f (f(x) = %.8f) ",roots[ix], func(roots[ix]));

plotFunc(start, end, n, roots);

return 0;

}

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

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: findAllRoots

Parameters:

start, end: start and end of interval (x values) for seaching roots

roots - reference to array for storing roots

Returns:

The number of roots found (value of rootIx at the end of the loop)

Description: Find the roots between the interval for the

polynomial defined by coefficients.

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

int findAllRoots(double start, double end, double roots[])

{

/* Complete this function */

}

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

Function: findRoot

Parameters:

left, right: values of x at the edges of the subinterval

root - reference to save the value of the root found.

Description: Check if a root exists in the subinterval for the

polynomial defined by coefficients.

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

int findRoot(double left, double right, 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)

{

/* Complete this function */

}

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

Function: plotFunc

Parameters:

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

nRoots - number of roots in the root array.

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).

rRoots: number of roots

xRoots: x coordinate of roots

yRoots: y coordinate of roots.

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.

Plots x at the root points.

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

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);

}

B. Exercise: Finding Roots: Incremental Search Method Develop a program that will allow the user to select an interval over which a root can be found such that the following equation will hold. Equation 1 Equation 1 can be modified to give the following function f(x) (x)-50-x cos Vx Equation 2 Thus finding the root of f(x) from Equation 2 provides a solution for Equation 1. Note that x must be greater than zero. Find the first 3 roots Guidelines The project IncrementalSearchPoly (in zip file IncrementalSearchPoly) is a complete program that shows the functions studied in class to implement the incremental search method for finding roots. This project has been provided for your review. Do take the time to review the program before you come to the lab . o Compile and run the program to understand its operation. * The function in the sample code has roots at -3.2, 0.05, 7.18 * Run the software and experiment with selecting intervals. See how the selection of the interval affects the results. Try intervals that finds all three roots and intervals that finds 1 or 2 roots To complete this part, start with the provided program (project IncrementalSearchFnc in the zip file IncrementalSearchFnc.zip). The program is similar to the one found in the project IncrementalSearchPoly. Complete the following functions for finding roots: * * void findAllRoots (double start, double end, double roots]) double findRoot (double left, double right, double *root) double func (double x) Consult the notes, the sample program given to help with completing the above functions. 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 The plot of the function from 1 to 200 is shown to the right. Note the scale for the vertical axis (101) Start with the interval from 0 to 30 and find a proper interval to find the first three roots Show your running program and modifications to your TA for mark:s * (x10) Polynomiol 0 0 50 100 150