Metric - Minkowski distance between two points

The java program finds distance between two points using minkowski distance equation.
when power is set P=1, minkowski metric results as same as manhattan distance equation and when set P=2, minkowski metric results as same as euclidean distance equation.

1-Dimensional distance
It measures the distance between two points. Each point lies on a line and has one element.

2-Dimensional distance
It measures the distance between two points. Each point lies on 2D cartesian plane and has 2 elements.

N-Dimensional distance
It measures the distance between two points and each point has N elements.

Example Calculation

This is an example calculation shown below explain how to find the distance between two vectors using Minkowski distance formula. A vector,array of elements declared and initialized in java using one dimensional array.

        int A[] = { 5 ,3 };    // 2D vector A 
 
 int B[] = { 2,1 };    // 2D vector B
 
 int P =3; 
 
 P th power sqrt cab be converted into exponential power 1/P 
 
    
 find  distance between two vectors A and B using 
            Minkowski distance equation. 

   
   ||A-B||     =  pow (  ((A[0]-B[0])^P  +  (A[1]-B[1])^P), 1/P )
   
               = pow ( ((5-2)^3  + (3-1)^3) ,0.333 );
      
        = pow ( ( 5^3  + 2^3 ),0.333 ); 
      
        = pow ( (125 + 8),0.333 ); 
      
        = pow ( 133,0.333 );
      
      ||A-B||  = 5.096      
      
 Minkowski Distance between vectors A=[5,3] and B=[2,1] is 5.096     

public class Minkowski 
{
 
 public static double distance(double x, double y,double p) {  
  return  Math.pow(Math.pow(x-y,p),1/p);  
 }
  
 public static double distance(int x, int y,double p) {  
  return   Math.pow(Math.pow(x-y,p),1/p);          
 }
 
 
public static double distance(double x[], double y[],double p) {
  
  double ds=0.0;
  for(int n=0;n<x.length;n++)
   ds += Math.pow(x[n]-y[n],p);
  
  ds = Math.pow(ds, 1/p);
  return  ds;  
 }
  
public static double distance(int x[], int y[],double p) 
{
  
  double ds=0.0;
  for(int n=0;n<x.length;n++)
   ds += Math.pow(x[n]-y[n],p);;
   
  ds = Math.pow(ds, 1/p); 
  return  ds;            
  }
 
 
public static double[] distance(int x[][], int y[],double p) {
  
    double ds[]=new double[x.length];
  for(int n=0;n<x.length;n++)
   ds[n]= distance(x[n],y,p);   
  return  ds;            
 }
 
public static double[] distance(double x[][], double y[],double p) {
  
  double ds[]=new double[x.length];
  for(int n=0;n<x.length;n++)
   ds[n] = distance(x[n],y,p);   
  return  ds;            
 }
 
}

import java.util.Arrays;
public class MinkowskiMain {

 public static void main(String[] args) 
   {    
       double p=3.0; 
           
       System.out.println("\n1D - Distance on integer" );
       System.out.println("Minkowski Distance between 
           scalar int x and y" );
 int ix=20; 
        int iy=30;          
        double dist=Minkowski.distance(ix, iy,p);
        System.out.println("x="+ix +",y="+iy);
 System.out.println("Distance :" + dist);
  
 System.out.println("\n1D - Distance on double " );
 System.out.println("Minkowski Distance between 
            scalar double x and y" );
 double dx=2.6; 
 double dy=3.2;          
 double ds2=Minkowski.distance(dx, dy,p);
 System.out.println("x="+dx +",y="+dy);
 System.out.println("Distance :" + ds2);
     
 System.out.println("2D - Distance on integer" );
 System.out.println("nMinkowski Distance between 
            int vector x and y " );
 int aix[]={2,3};
        int aiy[]={3,5};          
 double ds3=Minkowski.distance(ix, iy,p);     
 System.out.println("x="+Arrays.toString(aix) 
              +",y="+Arrays.toString(aiy));
 System.out.println("Distance :" + ds3);
     
 System.out.println("\n2 Dimensional - distance on double " );
        System.out.println("Minkowski Distance between 
              double vector x and y " );
 double adx[]={2.4,3.1};
 double ady[]={3.1,5.6};      
 System.out.println("x="+Arrays.toString(adx) 
            +",y="+Arrays.toString(ady));
 double ds4=Minkowski.distance(adx, ady,p);
 System.out.println("Distance :" + ds4);
     
 System.out.println("\nN Dimensional Distance on double" );
 System.out.println("Minkowski Distance between 
        set of int vectors x and int vector y " );
 int aix2[][]={ {2,3,5} ,{1,7,4}};
 int aiy2[]={3,5,7};            
 double ds5[]=Minkowski.distance(aix2, aiy2,p);     
 System.out.println("x="+Arrays.toString(aix2[0]) + "," 
  + Arrays.toString(aix2[1]) +",y="+Arrays.toString(aiy2));
 System.out.println( "Distance :" + Arrays.toString(ds5) );
     
               
 System.out.println("\nMinkowski Distance between 
  set of double vector x and a double vector y " );
 double adx2[][]={ {2.4,3.1,5.2},{1.2,7.2,4.5}};
 double ady2[]={3.1,5.6,7.8};          
 double ds6[]=Minkowski.distance(adx2, ady2,p);     
 System.out.println("x="+ Arrays.toString(adx2[0])+"," 
           +Arrays.toString(adx2[1])  +",y="+Arrays.toString(ady2));
 System.out.println( "Distance :" + Arrays.toString(ds6) );   
     
   }

}

Output

1D - Distance on integer
Minkowski Distance between scalar int x and y
x=20,y=30
Distance :10.0

1D - Distance on double
Minkowski Distance between scalar double x and y
x=2.6,y=3.2
Distance :0.6000000000000001
2D - Distance on integer

Minkowski Distance between int vector x and y 
x=[2, 3],y=[3, 5]
Distance :10.0

2 Dimensional - distance on double
Minkowski Distance between double vector x and y 
x=[2.4, 3.1],y=[3.1, 5.6]
Distance :2.5961509971494334

N Dimensional Distance on double
Minkowski Distance between set of int vectors x 
          and int vector y 
x=[2, 3, 5],[1, 7, 4],y=[3, 5, 7]
Distance :[3.0, 4.123105625617661]

Minkowski Distance between set of double vector x 
          and a double vector y 
x=[2.4, 3.1, 5.2],[1.2, 7.2, 4.5],y=[3.1, 5.6, 7.8]
Distance :[3.674234614174767, 4.1303752856126765]

Related Post
euclidean distance metric between two points
manhattan distance between two vectors
minkowski distance metric
Chebyshev distance metric