Question

(Markov matrix)

An n by n matrix is called a positive Markov matrix if each element is positive and the sum of the elements in each column is 1. Write the following function to check whether a matrix is a Markov matrix:

def isMarkovMatrix(m):

Write a test program that prompts the user to enter a 3 by 3 matrix of numbers and tests whether it is a Markov matrix. Note that the matrix is entered by rows and the numbers in each row are separated by a space in one line.

Sample Run 1

Enter a 3-by-3 matrix row by row:

0.15 0.875 0.375

0.55 0.005 0.225

0.30 0.12 0.4

It is a Markov matrix

Sample Run 2

Enter a 3-by-3 matrix row by row:

0.95 -0.875 0.375

0.65 0.005 0.225

0.30 0.22 -0.4

It is not a Markov matrix

In Python.

Answer 1

Here is your code :-

Read comments to understand clearly.

import java.util.Scanner;

public class MarkovMatrix {

static Scanner sc=new Scanner(System.in);           //Scanner object to read values from the user

static String str[];

public static void main(String[] args) {

double mat[][]=new double[3][3];              //3X3 matrix of type double to store values

System.out.println("Enter a 3X3 matrix row by row");     //asking user to enter values into matrix row by row

for(int i=0;i<3;i++)

{

str=sc.nextLine().split(" ");//reading the whole row wntered by user and slitting into an string array by space as delimiter now the str array contains each value of that row column wise such as m[i][j]

for(int j=0;j<3;j++)

{

mat[i][j]=Double.parseDouble(str[j]);     //reading each value from str array and storing it in ith row

}

}

boolean flag=isMarkovMatrix(mat);   //calling function to test whether a matrix is positive markov matrix or not

if(flag)

System.out.println("This is a positive Markov Matrix"); //printing result based on the value returned by function if true yes

else

System.out.println("This is a not positive Markov Matrix"); //printing result based on the value returned by function if false no

}

private static boolean isMarkovMatrix(double[][] m) {

for(int i=0;i<3;i++)

{double count=0;

for(int j=0;j<3;j++)

{

count+=m[j][1];   //calculating column by column count

}

if(count!=1)   //checking column count if any of the rows count is not 1 then returning false

return false;

}

return true; //else returning true

}

}

Output :-