Power Method Using C++ with Output

Complete C++ program for finding largest or dominant Eigen value and corresponding Eigen vector using Power Method.

Program


#include<iostream>
#include<iomanip>
#include<stdio.h>
#include<math.h>

#define SIZE 10

using namespace std;

int main()
{
	 float a[SIZE][SIZE], x[SIZE],x_new[SIZE];
	 float temp, lambda_new, lambda_old, error;
	 int i,j,n, step=1;

     /* Setting precision and writing floating point values in fixed-point notation. */
     cout<< setprecision(3)<< fixed;

	 /* Inputs */
	 /* Reading order of square matrix */
	 cout<<"Enter Order of Matrix: ";
	 cin>>n;

     /* Reading tolerable error */
	 cout<<"Enter Tolerable Error: ";
	 cin>>error;

	 /* Reading Square Matrix of Order n */
	 cout<<"Enter Coefficient of Matrix: "<< endl;
	 for(i=1;i<=n;i++)
	 {
		  for(j=1;j<=n;j++)
		  {
			   cout<<"a["<< i<<"]"<< j<<"]= ";
               cin>>a[i][j];
		  }
	 }

	 /* Reading Intial Guess Vector */
	 cout<<"Enter Initial Guess Vector: "<< endl;
	 for(i=1;i<=n;i++)
	 {
		  cout<<"x["<< i<<"]= ";
		  cin>>x[i];
	 }

	 /* Initializing Lambda_Old */
	 lambda_old = 1;
	 /* Multiplication */

	 /* Setting label for repetition */
	 up:
	 for(i=1;i<=n;i++)
	 {
		  temp = 0.0;
		  for(j=1;j<=n;j++)
		  {
		   	temp = temp + a[i][j]*x[j];
		  }
		  x_new[i] = temp;
	 }

	 /* Replacing x by x_new */
	 for(i=1;i<=n;i++)
	 {
	  	x[i] = x_new[i];
	 }

	 /* Finding largest value from x*/
	 lambda_new = fabs(x[1]);
	 for(i=2;i<=n;i++)
	 {
		  if(fabs(x[i])>lambda_new)
		  {
		   	lambda_new = fabs(x[i]);
		  }
	 }

	 /* Normalization */
	 for(i=1;i<=n;i++)
	 {
	  	x[i] = x[i]/lambda_new;
	 }

	 /* Display */
	 cout<< endl<< endl<<"STEP-"<< step<< endl;
	 cout<<"Eigen Value = "<< lambda_new<< endl;
	 cout<<"Eigen Vector: "<< endl;
	 cout<<"[";
	 for(i=1;i<=n;i++)
	 {
	  	cout<< x[i]<<"\t";
	 }
     cout<<"\b\b\b]"; /* \b is for backspace */

	 /* Checking Accuracy */
	 if(fabs(lambda_new-lambda_old)>error)
	 {
		  lambda_old=lambda_new;
		  step++;
		  goto up;
	 }

	 return(0);
}

Output

Enter Order of Matrix: 2
Enter Tolerable Error: 0.00001
Enter Coefficient of Matrix:
a[1]1]= 5
a[1]2]= 4
a[2]1]= 1
a[2]2]= 2
Enter Initial Guess Vector:
x[1]= 1
x[2]= 1


STEP-1
Eigen Value = 9.000
Eigen Vector:
[1.000  0.333]

STEP-2
Eigen Value = 6.333
Eigen Vector:
[1.000  0.263]

STEP-3
Eigen Value = 6.053
Eigen Vector:
[1.000  0.252]

STEP-4
Eigen Value = 6.009
Eigen Vector:
[1.000  0.250]

STEP-5
Eigen Value = 6.001
Eigen Vector:
[1.000  0.250]

STEP-6
Eigen Value = 6.000
Eigen Vector:
[1.000  0.250]