Vector normalization - Unit vector

A vector can converted into unit vector by vector normalization in which each elements of the vector is divided by that vector's norm or length.

Vector X

Unit Vector X

Java code - vector normalization

The following code converts a vector into unit vector by vector normalization. A vector is defined in Java program by a integer array or a double array.

Example

Vector X = [5.0, 1.2, 2.0] , find unit vector of X by normalization.
1. find vector X norm || X || = sqrt ( 5.0^2 + 1.2^2 + 2.0 ^2 ) = sqrt ( 25.0 + 1.44 + 4.0 ) = sqrt ( 30.44) = 5.5172
2 Unit vector X = [ 5.0/5.5172 , 1.2/5.5172 , 2.0/5.5172] = [ 0.9062, 0.2175, 0.3625].

import java.util.Arrays;

public class Vector
 {
 
   public static double[] unit_vector(double vec[]) 
   {
     int nelement = vec.length; 
     double uvec[] = new double[nelement];
  
    double nrm =0.0;  
    for(int n=0;n<nelement;n++)
      nrm += (vec[n]*vec[n]);
    
    double enrm = Math.sqrt(nrm);
  
    for(int n=0;n<nelement;n++)
       uvec[n] = vec[n]/ enrm;
    return uvec;
   }
 
  public static double[] unit_vector(int vec[]) 
    {
    
     int nelement = vec.length; 
     double uvec[] = new double[nelement];
     double nrm =0.0;
  
     for(int n=0;n<nelement;n++)
       nrm += (vec[n]*vec[n]);
    
     double enrm = Math.sqrt(nrm);  
  
  
     for(int n=0;n<nelement;n++)
       uvec[n] = vec[n]/ enrm;
     return uvec;  
   }

 
 public static void main(String[] args) {
  
  System.out.println( "\n Find unit vector \n ");
  double U[]={5.0 ,1.2 , 2.0};  
    
  System.out.println( "\nVector U ");
  System.out.println( Arrays.toString(U));
  double uvec[] = Vector.unit_vector(U);
  System.out.println( "Unit Vector U  ");
  System.out.println( Arrays.toString(uvec)  );

  
  int V[] = {2, -1, 3};
  System.out.println( "\n Vector V ");
  System.out.println( Arrays.toString(V));
  double uvec2[] = Vector.unit_vector(V);
  System.out.println( "Unit Vector V  ");
  System.out.println( Arrays.toString(uvec2) );
   

 }

}

Output

Find unit vector of a vector

Vector U :[5.0, 1.2, 2.0]
Unit Vector U  :[0.9062, 0.21749, 0.36249]

Vector V :[2, -1, 3]
Unit Vector V :[0.53452, -0.26726, 0.80178]