Java Program to Check Whether the Matrix is a Markov Matrix or Not

Java Program to Check Whether the Matrix is a Markov Matrix or Not

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In the previous article, we have discussed Java Program to Find Unique Elements in a Matrix

In this article we are going to see how we can check if a matrix is a markov matrix or not in JAVA language.

Java Program to Check Whether the Matrix is a Markov Matrix or Not

A 3*3 Matrix is having 3 rows and 3 columns where this 3*3 represents the dimension of the matrix. Means there are 3*3 i.e. total 9 elements in a 3*3 Matrix.

Let’s understand it in more simpler way.

                   | A00   A01   A02 |
Matrix A =  | A10   A11   A12 |
                   | A20   A21   A22 | 3*3
  • Matrix A represents a 3*3 matrix.
  • ‘A‘ represents the matrix element
  • ‘Aij‘ represents the matrix element at it’s matrix position/index.
  • ‘i‘ represents the row index
  • ‘j‘ represents the column index
  • Means A00=Aij  where i=0 and j=0,  A01=aij where i=0 and j=1 and like this.
  • Here we have started row value from 0 and column value from 0.

Let’s see different ways to check Markov Matrix.

Markov matrix is a matrix whose all rows add upto 1.

Example:

1 0 0
0 1 0
0 0 0

Method-1: Java Program to Check Markov Matrix By Static Initialization of Array Elements

Approach:

  • Initialize and declare one array of size 3×3 with elements.
  • Add each row elements and check if it is equal to 1.
  • If all the rows sum equals to 1, then it is a Markov matrix.

Program:

public class matrix
{
    public static void main(String args[])
    {
        // Initializing the 3X3 matrix i.e. 2D array
        double arr[][] = {{0.5,0,0.5},{0.5,0.5,0},{1,0,0}};
        int row, col;

        System.out.print("The matrix elements are : ");
        printMatrix(arr);

        if(checkMarkov(arr))
            System.out.println("\nIt is a Markov matrix");
        else
            System.out.println("\nIt is not a Markov matrix");
        
    }

    // Method to print the matrix
    static void printMatrix(double arr[][])
    {
        int row, col;
        // Loop to print the elements
        for(row=0;row<3;row++)
        {
            // Used for formatting
            System.out.print("\n");
            for(col=0;col<3;col++)
            {
                System.out.print(arr[row][col]+" ");
            }
        }
         System.out.print("\n");
    }

    // Checks whether the matrix is a Markov matrix or not
    static boolean checkMarkov(double arr[][])
    {
        int row, col;
        double sum;
        for(row =0;row<3;row++)
        {
            sum =0;
            for(col=0;col<3;col++)
                sum+=arr[row][col];
            if(sum!=1)
                return false;
        }
        return true;
    }

}


Output:

The matrix elements are : 
0.5 0.0 0.5 
0.5 0.5 0.0 
1.0 0.0 0.0

It is a Markov matrix

Method-2: Java Program to Check Markov Matrix By Dynamic Initialization of Array Elements

Approach:

  • Declare one array of size 3×3.
  • Use two for loops to input array elements.
  • Add each row elements and check if it is equal to 1.
  • If all the rows sum equals to 1, then it is a Markov matrix.

 Program:

import java.util.Scanner;
public class matrix{
    public static void main(String args[])
    {
        //Scanner class to take input
        Scanner scan = new Scanner(System.in);

        // Initializing the 3X3 matrix i.e. 2D array
        int arr[][] = new int[3][3];
        int row, col;

        // Taking matrix input
        System.out.println("\nEnter matrix elements : ");
        for(row=0;row<3;row++)
            for(col=0;col<3;col++)
                arr[row][col] = scan.nextInt();

        System.out.print("The matrix elements are:");
        printMatrix(arr);

        if(checkMarkov(arr))
            System.out.println("\nIt is a Markov matrix");
        else
            System.out.println("\nIt is not a Markov matrix");
        
    }

    // Method to print the matrix
    static void printMatrix(int arr[][])
    {
        int row, col;
        // Loop to print the elements
        for(row=0;row<3;row++)
        {
            // Used for formatting
            System.out.print("\n");
            for(col=0;col<3;col++)
            {
                System.out.print(arr[row][col]+" ");
            }
        }
         System.out.print("\n");
    }

    // Checks whether the matrix is a Markov matrix or not
    static boolean checkMarkov(int arr[][])
    {
        int row, col;
        double sum;
        for(row =0;row<3;row++)
        {
            sum =0;
            for(col=0;col<3;col++)
                sum+=arr[row][col];
            if(sum!=1)
                return false;
        }
        return true;
    }

}


Output:

Enter matrix elements : 1 0 0 0 0 1 0 1 0
The matrix elements are:
1 0 0 
0 0 1 
0 1 0

It is a Markov matrix

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