Matrix Multiplication in Java

Introduction

Matrix multiplication in Java is the process of multiplying two matrices together. As a result, a new matrix is created with the results. It involves three steps. First, it iterates through the rows and columns of the matrices. Second, it multiplies the corresponding elements. Finally, it gathers the results to generate the resulting matrix.

Overview

In this tutorial, we will deal with the various concepts related to matrix multiplication in Java, Java programs to multiply two matrices, multiplication using for loops, and Java programs to multiply two matrices of any size, among other concepts.

Matrix Multiplication in Java

Matrix multiplication is an arithmetic operation performed on matrices to obtain a new matrix by multiplying corresponding elements and summing the results. In Java, we can perform matrix multiplication with the help of nested loops to iterate over the elements of the matrices and apply the multiplication rule.

In the above example, matrix1 is a 2x3 matrix, and matrix2 is a 3x2 matrix. After performing the matrix multiplication, the resulting matrix will be a 2x2 matrix. The program prints the elements of the resulting matrix as the output.

Code:

public class upGradTutorials {
    public static void main(String[] args) {
        int[][] matrix1 = {{1, 2, 3}, {4, 5, 6}};  // 2x3 matrix
        int[][] matrix2 = {{7, 8}, {9, 10}, {11, 12}};  // 3x2 matrix
        int rowsMatrix1 = matrix1.length;
        int columnsMatrix1 = matrix1[0].length;
        int columnsMatrix2 = matrix2[0].length;
        // Create a new matrix to store the multiplication result
        int[][] resultMatrix = new int[rowsMatrix1][columnsMatrix2];
        // Perform matrix multiplication
        for (int i = 0; i < rowsMatrix1; i++) {
            for (int j = 0; j < columnsMatrix2; j++) {
                for (int k = 0; k < columnsMatrix1; k++) {
                    resultMatrix[i][j] += matrix1[i][k] * matrix2[k][j];
                }
            }
        }
        // Print the result matrix
        for (int i = 0; i < rowsMatrix1; i++) {
            for (int j = 0; j < columnsMatrix2; j++) {
                System.out.print(resultMatrix[i][j] + " ");
            }
            System.out.println();
        }
    }
}

We start by defining two matrices, matrix1, and matrix2, with their respective dimensions. We determine the number of rows and columns for each matrix using the length property of arrays. We create a new matrix, resultMatrix, with dimensions equal to the number of rows in matrix1 and the number of columns in matrix2.

We use nested loops to perform the matrix multiplication. The outer loops iterate over the rows of matrix1 and the columns of matrix2. The inner loop iterates over the columns of matrix1 (or the rows of matrix2). Inside the innermost loop, we multiply the corresponding elements of matrix1 and matrix2 and accumulate the result in the corresponding position of resultMatrix.

Finally, we print the elements of resultMatrix to display the resulting matrix.

Matrix Multiplication Syntax

Here is the syntax for performing matrix multiplication in Java:

Defining the matrices

int[][] matrix1 = {
    {element, element, element},
    {element, element, element},
    {element, element, element}
};
int[][] matrix2 = {
    {element, element, element},
    {element, element, element},
    {element, element, element}
};

Checking the compatibility of matrices for multiplication

if (matrix1[0].length != matrix2.length) {
    System.out.println("Matrix multiplication is not possible.");
    return;
}

Creating the result matrix

int[][] resultMatrix = new int[matrix1.length][matrix2[0].length];

Performing matrix multiplication

for (int i = 0; i < matrix1.length; i++) {
    for (int j = 0; j < matrix2[0].length; j++) {
        int sum = 0;
        for (int k = 0; k < matrix1[0].length; k++) {
            sum += matrix1[i][k] * matrix2[k][j];
        }
        resultMatrix[i][j] = sum;
    }
}

Java Program to Multiply Two Matrices

In this program, we have two 2x2 matrices, matrix1 and matrix2. Like the previous program, it checks if the matrices are compatible for multiplication. If they are not compatible, it displays a message and exits.

If the matrices are compatible, the program creates a new matrix resultMatrix to store the multiplication result. It uses nested loops to iterate over the rows and columns of the matrices. For each element of the resulting matrix, it calculates the sum of the products of corresponding elements from the input matrices.

The calculated sum is then assigned to the corresponding position in resultMatrix. Finally, it prints the elements of resultMatrix, representing the product of the two matrices. You can modify the values and dimensions of matrix1 and matrix2 to perform matrix multiplication for different matrices.

Code:

public class upGradTutorials {
    public static void main(String[] args) {
        int[][] matrix1 = {{1, 2}, {3, 4}}; // 2x2 matrix
        int[][] matrix2 = {{5, 6}, {7, 8}}; // 2x2 matrix
        int rowsMatrix1 = matrix1.length;
        int columnsMatrix1 = matrix1[0].length;
        int rowsMatrix2 = matrix2.length;
        int columnsMatrix2 = matrix2[0].length;
        if (columnsMatrix1 != rowsMatrix2) {
            System.out.println("Matrix multiplication is not possible.");
            return;
        }
        int[][] resultMatrix = new int[rowsMatrix1][columnsMatrix2];
        // Perform matrix multiplication
        for (int i = 0; i < rowsMatrix1; i++) {
            for (int j = 0; j < columnsMatrix2; j++) {
                int sum = 0;
                for (int k = 0; k < columnsMatrix1; k++) {
                    sum += matrix1[i][k] * matrix2[k][j];
                }
                resultMatrix[i][j] = sum;
            }
        }
        // Print the resulting matrix
        System.out.println("Resulting matrix:");
        for (int i = 0; i < rowsMatrix1; i++) {
            for (int j = 0; j < columnsMatrix2; j++) {
                System.out.print(resultMatrix[i][j] + " ");
            }
            System.out.println();
        }
    }
}

Example Program for Multiplication of Matrices in Java Using For Loop

In the above program, we have two matrices matrix1 and matrix2. We first check the compatibility of matrices for multiplication by comparing the number of columns in matrix1 with the number of rows in matrix2. If they are incompatible, it displays a message and exits the program.

If the matrices are compatible, we create a new matrix resultMatrix to store the multiplication result. We use three nested for loops to iterate over the rows and columns of the matrices.

For each element of the resulting matrix, we calculate the sum of the products of corresponding elements from matrix1 and matrix2. The calculated sum is then assigned to the corresponding position in resultMatrix. Finally, we print the elements of resultMatrix, which represents the product of the two matrices.

Code:

public class upGradTutorials {
    public static void main(String[] args) {
        int[][] matrix1 = {
            {1, 2, 3},
            {4, 5, 6}
        };
        int[][] matrix2 = {
            {7, 8},
            {9, 10},
            {11, 12}
        };
        int rowsMatrix1 = matrix1.length;
        int columnsMatrix1 = matrix1[0].length;
        int rowsMatrix2 = matrix2.length;
        int columnsMatrix2 = matrix2[0].length;
        if (columnsMatrix1 != rowsMatrix2) {
            System.out.println("Matrix multiplication is not possible.");
            return;
        }
        int[][] resultMatrix = new int[rowsMatrix1][columnsMatrix2];
        // Perform matrix multiplication
        for (int i = 0; i < rowsMatrix1; i++) {
            for (int j = 0; j < columnsMatrix2; j++) {
                int sum = 0;
                for (int k = 0; k < columnsMatrix1; k++) {
                    sum += matrix1[i][k] * matrix2[k][j];
                }
                resultMatrix[i][j] = sum;
            }
        }
        // Print the resulting matrix
        for (int i = 0; i < rowsMatrix1; i++) {
            for (int j = 0; j < columnsMatrix2; j++) {
                System.out.print(resultMatrix[i][j] + " ");
            }
            System.out.println();
        }
    }
}

Java Program to Multiply Two Matrices of Any Size

This program follows a similar structure as the previous one. However, instead of using a separate variable to store the sum of products, we directly accumulate the result in the resultMatrix. This avoids unnecessary assignments and improves the efficiency of the multiplication process.

The innermost loop iterates over the common dimension of the matrices (columnsMatrix1 in matrix1 and rowsMatrix2 in matrix2). The elements from matrix1 and matrix2 are multiplied, and the result is added to the corresponding position in resultMatrix.

Finally, the program prints the elements of resultMatrix, which represents the product of the two matrices

This approach is more efficient because it reduces the number of variable assignments and eliminates the need for an intermediate sum variable.

Code:

public class upGradTutorials {
    public static void main(String[] args) {
        int[][] matrix1 = {
            {1, 2, 3},
            {4, 5, 6},
            {7, 8, 9}
        };
        int[][] matrix2 = {
            {10, 11},
            {12, 13},
            {14, 15}
        };
        int rowsMatrix1 = matrix1.length;
        int columnsMatrix1 = matrix1[0].length;
        int rowsMatrix2 = matrix2.length;
        int columnsMatrix2 = matrix2[0].length;
        if (columnsMatrix1 != rowsMatrix2) {
            System.out.println("Matrix multiplication is not possible.");
            return;
        }
        int[][] resultMatrix = new int[rowsMatrix1][columnsMatrix2];
        // Perform matrix multiplication
        for (int i = 0; i < rowsMatrix1; i++) {
            for (int j = 0; j < columnsMatrix2; j++) {
                for (int k = 0; k < columnsMatrix1; k++) {
                    resultMatrix[i][j] += matrix1[i][k] * matrix2[k][j];
                }
            }
        }
        // Print the resulting matrix
        for (int i = 0; i < rowsMatrix1; i++) {
            for (int j = 0; j < columnsMatrix2; j++) {
                System.out.print(resultMatrix[i][j] + " ");
            }
            System.out.println();
        }
    }
}

Conclusion

Matrix multiplication is a fundamental operation in Java. It has many applications in maths and computer science. It serves as a handy tool for performing calculations. It also helps in transformations on multiple dimensions of data.

If you wish to learn more about matrix multiplication in Java, enroll in a credible course in computer science. Online learning platforms like upGrad provide the best-in-class courses for aspiring computer science experts. Visit upGrad to learn more.

FAQs

1. Can matrices of different sizes be multiplied?

No, matrices of different sizes cannot be multiplied. For it to multiply, the number of columns in the first matrix must be the same as the number of rows in the second matrix.

2. How can I handle exceptions during matrix multiplication?

You can handle exceptions in Java by using try-catch blocks. For example, if the matrices have incompatible sizes for multiplication, you can catch an exception and handle it appropriately, such as displaying an error message or taking alternative actions.

3. Are there any optimization techniques for matrix multiplication in Java?

Yes, there are various optimization techniques for matrix multiplication, such as Strassen's algorithm or parallelization using multi-threading. These techniques can improve the efficiency of matrix multiplication for large matrices.