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Why am I getting garbage values? - Using arrays to calc polynomial roots

Shishykish (140)
Hello,

I am writing a program that will take coefficients of a polynomial, store them in an array and then using functions calculate the differntial of that polynomial and store it in another array.

Following this, I use the newton raphson formula to calculate a value after a set number of iterations and given a specific convergence factor.

I have got it to compile, but get garbage values when testing it with some quadratic equations.

For example, for the formula 2x^2 + 5x - 3 = 0, the roots would -3 and 0.5 respectively.

I can get the +ve root, but something mad with negative one. 

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#include <iostream> 
#include <cmath> 
#include <iomanip>

using namespace std;

const int polynomial_size = 100;
int highest_index = 0;
int highest_index_for_differentiated_polynomial = 0;

double polynomial[polynomial_size];
double diff_polynomial[polynomial_size];

void newton_raphson(double, double, int); // function prototype 
double f(double); // function prototype for f(x)
double f_prime(double); //function prototype for f'(x)
void make_polynomial(int); //make a coeff array for a polynomial, where the index = power, value = coeff.
void display_polynomial(double[], int);
void differentiate_polynomial(int);

int main() {
	int imax; // maximum number of iterations 
	double x_guess_negative; //declaration for initial guess of negative root
	double x_guess_positive;//declaration for the initial guess of the +ve root

	double epsilon; // convergence criterion
					// obtain the input data 
	int index;

	//Ask for max index of polynomial
	//Call make polynomial function
	//Call displayt polynomial function
	cout << "What is the highest index of your polynomial function?" << endl;
		cin >> highest_index;

	make_polynomial(highest_index);
	display_polynomial(polynomial, highest_index);
	differentiate_polynomial(highest_index);

	cout << endl;

	cout << "Enter the initial guess for the negative root" << endl;
	cin >> x_guess_negative;

	cout << "Enter the initial guess for the +ve root" << endl;
	cin >> x_guess_positive;

	cout << "Enter the convergence criteria: " << endl;
	cin >> epsilon;

	if (x_guess_negative > 0)
	{
		cout << "re-enter the initial guess for the negative root" << endl;
		cin >> x_guess_negative;
	}

	if (x_guess_positive < 0)
	{
		cout << "re-enter the initial guess for the +ve root" << endl;
		cin >> x_guess_positive;
	}


	cout << "Enter the maximum number of iterations allowed: ";
	cin >> imax;

	cout << endl;
	// find the -ve root
	newton_raphson(x_guess_negative, epsilon, imax);

	//find the +ve root
	newton_raphson(x_guess_positive, epsilon, imax);

	system("pause");

	return 0;
}

// This function implements the newton_raphson method for finding 
// a root of a function 
void newton_raphson(double x, double eps, int i_max)
{
	double x_i, x_i_plus_1, x0;

	int i = 0; // current iteration counte
			   // echo back the passed input data 
	cout << "\nThe original root is search interval is from " << x
		<< "\nThe convergence criterion is: interval  "
		<< eps << "\nThe maximum number of iterations allowed is " << i_max << endl;

	x0 = x;
	x_i = x;
	x_i_plus_1 = 0;

	//Headings for output as table
	cout << "Iteration" << setw(10) << "x(i)" << endl;

	for (i = 0; i < i_max; i++)
	{

		if (abs(x_i_plus_1 - x0) >= eps)
		{
			x_i_plus_1 = x_i - (f(x_i) / f_prime(x_i));

			x_i = x_i_plus_1;

			cout << setprecision(4) << i << setw(20) << x_i_plus_1 << endl;
		}
		else
		{
			return;
		}
	}
	/*do {

	if (abs(x_i_plus_1 - x0 >= eps))
	{
	x_i_plus_1 = x_i - (f(x_i) / f_prime(x_i));

	x_i = x_i_plus_1;

	i++;
	}
	else
	{
	return;
	}


	cout << i << "			" << x_i << "			" << x << endl;
	} while (i < i_max); */

	cout << "\nAfter " << i << " iterations, The root is " << x_i << endl;
}

// function to evaluate f(x) 
double f(double x)
{
	double sum = 0;
	for (int i = highest_index; i >= 0; i--)
	{
		sum = sum + (polynomial[i] * pow(x, i));
	}
	return sum;
}

//function to evaluate f'(x)
double f_prime(double x)
{
	double sum = 0;

	for (int i = highest_index_for_differentiated_polynomial; i >= 0; i--)
	{
		sum = sum + (diff_polynomial[i] * pow(x, i));
	}
	
	return sum;
}

void make_polynomial(int max_index)
{
	double coefficient;

	cout << "The highest index of your polynomial is" << "x^" << highest_index << endl;

	cout << "What are the coeffiencients for your polynomial when it is written in orders of ascending powers?" << endl;

	for (int i = highest_index; i >= 0; i--)
	{
		cin >> coefficient;

	polynomial[i] = coefficient;
	}
}

void display_polynomial(double p[], int h_index)
{
	int maxindex = sizeof(polynomial);

	cout << "Your polynomial is" << endl;

	for (int i = highest_index; i >= 0; i--)
	{
		cout << polynomial[i] << "x^" << i << " + ";
	}

	cout << "The array indexes to store the coeffs are" << endl;

	for (int i = highest_index; i >= 0; i--)
	{
		cout << "Array index " << i << " Coeff stored " << polynomial[i] << endl;
	}
}

void differentiate_polynomial(int h_index)
{
	highest_index_for_differentiated_polynomial = highest_index - 1;

	cout << "Differentiating each power by using the standard result of n * x ^(n-1)" << endl;

	for (int i = highest_index_for_differentiated_polynomial; i >= 0; i--)
	{
		diff_polynomial[i - 1] = polynomial[i];
	}

	cout << "Your differentiated polynomial is " << endl;

	for (int i = highest_index_for_differentiated_polynomial; i >= 0; i--)
	{
		cout << diff_polynomial[i] << "x^" << i << " + ";
	}
}



What is the highest index of your polynomial function?
2
The highest index of your polynomial isx^2
What are the coeffiencients for your polynomial when it is written in orders of ascending powers?
2
5
-3
Your polynomial is
2x^2 + 5x^1 + -3x^0 + The array indexes to store the coeffs are
Array index 2 Coeff stored 2
Array index 1 Coeff stored 5
Array index 0 Coeff stored -3
Differentiating each power by using the standard result of n * x ^(n-1)
Your differentiated polynomial is
0x^1 + 5x^0 +
Enter the initial guess for the negative root
-2.5
Enter the initial guess for the +ve root
0.1
Enter the convergence criteria:
0.1
Enter the maximum number of iterations allowed: 10


The original root is search interval is from -2.5
The convergence criterion is: interval  0.1
The maximum number of iterations allowed is 10
Iteration      x(i)
0                -1.9
1              -0.844
2              0.3151
3              0.5603
4              0.4744
5                0.51
6               0.496
7              0.5016
8              0.4994
9              0.5003

After 10 iterations, The root is 0.5003

The original root is search interval is from 0.1
The convergence criterion is: interval  0.1
The maximum number of iterations allowed is 10
Iteration      x(i)
0               0.596
1              0.4579
2              0.5161
3              0.4934
4              0.5026
5               0.499
6              0.5004
7              0.4998
8              0.5001
9                 0.5

After 10 iterations, The root is 0.5
Last edited on
Peter87 (11175)
diff_polynomial[i - 1] is out of bounds when i is 0.
Shishykish (140)
Finished it ! Thanks for your help!

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#include <iostream> 
#include <cmath> 
#include <iomanip>

using namespace std;

const int polynomial_size = 100;
int highest_index = 0;
int highest_index_for_differentiated_polynomial = 0;

double polynomial[polynomial_size];
double diff_polynomial[polynomial_size];

void newton_raphson(double, double, int); // function prototype 
double f(double); // function prototype for f(x)
double f_prime(double); //function prototype for f'(x)
void make_polynomial(int); //make a coeff array for a polynomial, where the index = power, value = coeff.
void display_polynomial(double[], int);
void differentiate_polynomial(int);

int main() {
	int imax; // maximum number of iterations 
	double x_guess_negative; //declaration for initial guess of negative root
	double x_guess_positive;//declaration for the initial guess of the +ve root

	double epsilon; // convergence criterion
					// obtain the input data 
	int index;

	//Ask for max index of polynomial
	//Call make polynomial function
	//Call displayt polynomial function
	cout << "What is the highest index of your polynomial function?" << endl;
		cin >> highest_index;

	make_polynomial(highest_index);
	display_polynomial(polynomial, highest_index);
	differentiate_polynomial(highest_index);

	cout << endl;

	cout << "Enter the initial guess for the negative root" << endl;
	cin >> x_guess_negative;

	cout << "Enter the initial guess for the +ve root" << endl;
	cin >> x_guess_positive;

	cout << "Enter the convergence criteria: " << endl;
	cin >> epsilon;

	if (x_guess_negative > 0)
	{
		cout << "re-enter the initial guess for the negative root" << endl;
		cin >> x_guess_negative;
	}

	if (x_guess_positive < 0)
	{
		cout << "re-enter the initial guess for the +ve root" << endl;
		cin >> x_guess_positive;
	}


	cout << "Enter the maximum number of iterations allowed: ";
	cin >> imax;

	cout << endl;
	// find the -ve root
	newton_raphson(x_guess_negative, epsilon, imax);

	//find the +ve root
	newton_raphson(x_guess_positive, epsilon, imax);

	system("pause");

	return 0;
}

// This function implements the newton_raphson method for finding 
// a root of a function 
void newton_raphson(double x, double eps, int i_max)
{
	double x_i, x_i_plus_1, x0;

	int i = 0; // current iteration counte
			   // echo back the passed input data 
	cout	<< "\nThe original root is search interval is from " << x
			<< "\nThe convergence criterion is: interval  "
			<< eps << "\nThe maximum number of iterations allowed is " << i_max << endl;

	x0 = x;
	x_i = x;
	x_i_plus_1 = 0;

	//Headings for output as table
	cout << "Iteration" << setw(15) << "x(i)" << setw(15) << "f(x)" << setw(15) << "f'(x)" <<endl;

	for (i = 0; i < i_max; i++)
	{

		if (abs(x_i_plus_1 - x0) >= eps)
		{
			x_i_plus_1 = x_i - (f(x_i) / f_prime(x_i));

			x_i = x_i_plus_1;

			cout << setprecision(4) << i << setw(20) << x_i_plus_1 << setw(20) << f(x)<< setw(20) << f_prime(x) <<endl;
		}
		else
		{
			return;
		}
	}
	cout << "\nAfter " << i << " iterations, The root is " << x_i << endl;
}

// function to evaluate f(x) 
double f(double x)
{
	double sum = 0;
	for (int i = highest_index; i >= 0; i--)
	{
		sum = sum + (polynomial[i] * pow(x, i));
	}
	return sum;
}

//function to evaluate f'(x)
double f_prime(double x)
{
	double sum = 0;

	for (int i = 0; i <=highest_index_for_differentiated_polynomial; i++)
	{
		sum = sum + (diff_polynomial[i] * pow(x, i));
	}
	
	return sum;
}

void make_polynomial(int max_index)
{
	double coefficient;

	cout << "The highest index of your polynomial is" << "x^" << highest_index << endl;

	cout << "What are the coeffiencients for your polynomial when it is written in orders of descending powers?" << endl;

	for (int i = highest_index; i >= 0; i--)
	{
		cin >> coefficient;
		polynomial[i] = coefficient;
	}
}

void display_polynomial(double p[], int h_index)
{
	int maxindex = sizeof(polynomial);

	cout << "Your polynomial is" << endl;

	for (int i = highest_index; i >= 0; i--)
	{
		cout << polynomial[i] << "x^" << i << " + ";
	}

	cout << "The array indexes to store the coeffs are" << endl;

	for (int i = highest_index; i >= 0; i--)
	{
		cout << "Array index " << i << " Coeff stored " << polynomial[i] << endl;
	}
}

void differentiate_polynomial(int h_index)
{
	h_index = highest_index;
	highest_index_for_differentiated_polynomial = h_index - 1;

	cout << "Differentiating each power by using the standard result of n * x ^(n-1)" << endl;

	for (int i = 1; i <= h_index; i++)
	{	
		diff_polynomial[i - 1] = polynomial[i] * i ;
	}
	cout << endl; 

	cout << "Your differentiated polynomial is " << endl;

	for (int i = 0; i <=highest_index_for_differentiated_polynomial; i++)
	{
		cout << diff_polynomial[i] << " * x^" << i << " + ";
	}
}
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