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

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.

By Static Initialization of Array Elements
By Dynamic Initialization of Array Elements

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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