Question

Write a program that prompts the user to enter a 3 x 3 matrix of double values and tests whether it is a positive Markov matrix. There will be two methods which will be called from the main method: public static double [] [] createArray() 1. Creates a 3 by 3 two dimensional array of doubles 2. Prompts the user for values as shown in the sample run 3. Stores the numbers in the array in the order entered 4. Returns the array to the main method public boolean isMarkovMatrix(double [][] matrix) 1. Returns false if any value in the array is negative 2. Prints the sum of each column in the array 3. Returns false if any the sum of any of the columns is not equal to 1.0 4. Otherwise, it returns true. Sample Program running: Enter a 3 x 3 matrix by row 0.15 0.875 0.375 0.55 0.005 0.225 0.30 0.12 0.4 The sum of the columns 1.0 1.0 1.0 It is a Markov matrix Enter a 3 x 3 matrix by row -0.2 0.875 0.375 0.75 0.005 0.225 0.45 0.12 0.4 The sum of the columns 1.0 1.0 1.0 It is not a Markov matrix

Answer 1

Code:

import java.util.Scanner;
public class MarkovMatrix
{
public static double [] [] createArray()
   {
       Scanner input=new Scanner(System.in); //creating scanner class
       double[][] input_array=new double[3][3]; //input_array declaration
       for (int i=0;i<3;i++)
           {
           for (int j=0;j<3;j++)
               {
                   input_array[i][j]=input.nextDouble(); //taking input_values from user
               }
           }
       return input_array; //returning input_Array
   }
public static boolean isMarkovMatrix(double [][] matrix) //ismarkovmatrix function which accepts input matrix
   {
   int isNegative=0,isSumNegative=0,k=0; //isnegative and issumnegative variables to check any column or sum is negative
   double[] sum=new double[3]; //sum array to store the sum of colums
   for (int i=0;i<3;i++) //iterate the loop for every row
       {
       for (int j=0;j<3;j++) //iterate loop for every column
           {
               sum[k]=sum[k]+matrix[j][i]; //add each element in the column to sum value
               if ((matrix[j][i])<0.0) //check any element is negative then make isNegative=1
                   isNegative=1;
           }
       k++; //increment k value
       }
   System.out.println("The sum of column values are : "); //print the sum of colums
   for (int i=0;i<3;i++)
       {
       if (sum[i]<0.0) //check if the sum value is negative then make isSumNegative=1
           isSumNegative=1;
       System.out.print (sum[i] + " " );
       }
       if (isNegative==1 || isSumNegative==1) //if element is negative or sum is negative return fals
           return false;
       else //else return true
           return true;
   }
public static void main(String args[])
   {
   System.out.println("Enter the 3x3 Matrix:");
   double [][] input_Array=createArray(); //calling createArray function and storing array that was returned by function
   boolean result=isMarkovMatrix(input_Array)   ; .//calling isMarkovMatrix() function by passing input_array and storing result
   if (result==true) //if result true print markov matrix else print not markov matrix
       System.out.println("\nThe given matrix is Markov Matrix");
   else
       System.out.println("\nThe given matrix is Not Markov Matrix");
   }
}

Code and Output Screenshots:

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