Finding the Cholesky decomposition of a matrix

Here’s a Java program that finds the Cholesky decomposition of a given matrix:

   public class CholeskyDecomposition {

    public static double[][] choleskyDecomposition(double[][] matrix) {

        int n = matrix.length;

        double[][] lower = new double[n][n];

        for (int i = 0; i < n; i++) {

            for (int j = 0; j <= i; j++) {

                double sum = 0;

                if (j == i) {

                    for (int k = 0; k < j; k++) {

                        sum += Math.pow(lower[j][k], 2);

                    }

                    lower[j][j] = Math.sqrt(matrix[j][j] - sum);

                } else {

                    for (int k = 0; k < j; k++) {

                        sum += (lower[i][k] * lower[j][k]);

                    }

                    lower[i][j] = (matrix[i][j] - sum) / lower[j][j];

                }

            }

        }

        return lower;

    }

    public static void printMatrix(double[][] matrix) {

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

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

                System.out.print(matrix[i][j] + " ");

            }

            System.out.println();

        }

    }

    public static void main(String[] args) {

        double[][] matrix = {

            {25, 15, -5},

            {15, 18, 0},

            {-5, 0, 11}

        };

        double[][] lower = choleskyDecomposition(matrix);

        System.out.println("Lower triangular matrix (Cholesky decomposition):");

        printMatrix(lower);

    }

}

This program demonstrates the Cholesky decomposition for a 3×3 matrix. You can modify the `matrix` variable in the `main` method to use different matrices. The program calculates the lower triangular matrix, which represents the Cholesky decomposition of the input matrix. The `printMatrix` method is used to display the result.

Note that this implementation assumes that the input matrix is symmetric and positive definite, which are the requirements for Cholesky decomposition.