Question

1. Define a two-dimensional int array which has 5 rows and 3 columns. The elements in array is randomly initialized (using Math.random()).

1. Write a method to find the maximum value in this two dimensional array;
2. Write a method to find the average value in the array;
3. Write a method to count how many elements are smaller than average;

2. Write a method to copy contents in a two-dimensional array to a one-dimensional array. The method will return this one-dimensional array. Method is declared as below:

public static double [] copyArray (float [][] m);

Test this method in main().

3. Write a method to define and return an identity matrix. The input argument to this method is an integer n, specifying the size of this matrix. So if you pass n to the method, the method will returnan n × n identify matrix. (An identity matrix of size n is an n × n square matrix with ‘1’s on the main diagonal and ‘0’s elsewhere). Method is declared as below:

public static double [][] generateIdentityMatrix (int n);

Test this method in main().

4. An n × n matrix can be saved in a two-dimensional array. Write a method to get the sum of the major diagonal of the matrix. The base type of this matrix is ‘float’. Test method from main().
5. Define a two-dimensional array with m rows and n columns. Write a method that will initialize

the array with numbers from 1 to m × n in the way as below: first row, initialize the elements from left to right; next row, initialize from right to left; then switch order. So if m=5; and n = 4; the array should be initialized to:

1 2 3 4

8 7 6 5

9 10 11 12

16 15 14 13

17 18 19 20

Display returned array in main().

6. Implement a method to perform matrices addition: the method is declared as below:

public static double [][] addMatrices(double [][] m1, double [][] m2);

m1 and m2 have the same size. Test method in main().

7. Implement a method to multiply matrix and a vector. The general formula for a matrix-vector product is:

A is a matrix, and x is vector. The method is declared as below:

public static double [] productOfMatrixAndVector (double [][] A, double [] x);

Test method in main().

Answer 1

// ArrayOperations.java

import java.util.Arrays;

public class ArrayOperations {

      

       // method to find the maximum value in this two dimensional array;

       public double maximum(double arr[][])

       {

             double max = arr[0][0];

             for(int i=0;i<arr.length;i++)

                    for(int j=0;j<arr[i].length;j++)

                           if(arr[i][j] > max)

                                 max = arr[i][j];

             return max;

       }

      

       // method to find the average value in the array;

       public double average(double arr[][])

       {

             double total = 0;

             for(int i=0;i<arr.length;i++)

                    for(int j=0;j<arr[i].length;j++)

                           total += arr[i][j];

             return(total/(arr.length*arr[0].length));

       }

      

       // method to count how many elements are smaller than average;

       public int smallerThanAverage(double arr[][])

       {

             double avg = average(arr);

            

             int count = 0;

      

             for(int i=0;i<arr.length;i++)

                    for(int j=0;j<arr[0].length;j++)

                           if(arr[i][j] < avg)

                                 count++;

             return count;

       }

      

       // method to copy contents in a two-dimensional array to a one-dimensional array.

       public static double [] copyArray (float [][] m)

       {

             double singM[] = new double[0];

            

             for(int i=0;i<m.length;i++)

                    for(int j=0;j<m[i].length;j++)

                    {

                           singM = Arrays.copyOf(singM, singM.length+1);

                           singM[singM.length-1] = m[i][j];

                    }

            

             return singM;

       }

      

       // method to generate an identity matrix of size n

       public static double [][] generateIdentityMatrix (int n)

       {

             double identity[][] = new double[n][n];

            

             for(int i=0;i<n;i++)

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

                           if(i==j)

                                 identity[i][j] = 1;

                           else

                                 identity[i][j] = 0;

             return identity;

       }

      

       // method to get the sum of the major diagonal of the matrix

       public double sumMajorDiagonal(float m[][])

       {

             double total = 0;

            

             for(int i=0;i<m.length;i++)

                    for(int j=0;j<m[0].length;j++)

                           if(i == j)

                                 total += m[i][j];

             return total;

       }

      

       // method to generate an array given its rows and columns

       public int[][] generateArray(int m, int n)

       {

             int arr[][] = new int[m][n];

             int count=1;

            

             for(int i=0;i<m;i++)

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

                    {

                           arr[i][j] = count;

                           count++;

                    }

            

             return arr;

       }

      

       // method to add 2 matrices and return its resultant array

       public static double [][] addMatrices(double [][] m1, double [][] m2)

       {

             if((m1.length == m2.length ) && (m1[0].length == m2[0].length))

             {

                    double result[][] = new double[m1.length][m1[0].length];

                   

                    for(int i=0;i<result.length;i++)

                    {

                           for(int j=0;j<result[i].length;j++)

                                 result[i][j] = m1[i][j] + m2[i][j];

                    }

                   

                    return result;

             }

            

             return null;

       }

      

       // method to multiply a matrix and a vector and return its resultant vector

       public static double [] productOfMatrixAndVector (double [][] A, double [] x)

       {

             if(A[0].length == x.length)

             {

                    double result[] = new double[A.length];

                   

                    for(int i=0;i<A.length;i++)

                    {

                           result[i] = 0;

                           for(int k=0;k<x.length;k++)

                                 result[i] += A[i][k]*x[k];

                          

                    }

                   

                    return result;

             }

            

            

             return null;

       }

      

}

//end of ArrayOperations.java