//  -----------------------------------------------------------
//  -------  Prüfung 4.9      Ib03             ----------------
//  -------                                    ----------------
//  -------  Cholesky-Zerlegung von Matrizen   ----------------
//  -------                                    ----------------
//  -------  21.04.2005    M. Vogel            ----------------
//  -----------------------------------------------------------

/**
 * Hinweis : Mit der Verwendung der Indices i-1 etc. in den Matrizen können
 *           sowohl Algorithmus wie auch Initialiserung der Matrix A
 *           direkt aus der Vorlesung resp. Aufgabenstellung übernommen werden !
 */
 
public class Cholesky {

	static int n = 10;
	static double[][] A = new double[n][n];
	static double[][] L = new double[n][n];

	public static void main(String[] args) {
		for (int i = 1; i <= n; i++) {
			for (int j = 1; j <= n; j++) A[i-1][j-1] = (i + j - 1) * 0.05;
 		}
        
		for (int i = 1; i <= n; i++) A[i-1][i-1] = 1.0 ;
		
        printMatrix(A);

 		double sum;

		L[0][0] = Math.sqrt(A[0][0]);
		for (int j = 2; j <= n; j++) L[j-1][0] = A[j-1][0] / L[0][0];
		
		for (int i = 2; i <= n - 1; i++) {
			sum = 0;
			for (int k = 1; k <= i - 1; k++) sum += L[i-1][k-1] * L[i-1][k-1];
			L[i-1][i-1] = Math.sqrt(A[i-1][i-1] - sum);
			
			for (int j = i + 1; j <= n; j++) {
				sum = 0;
				for (int k = 1; k <= i - 1; k++) sum += L[j-1][k-1] * L[i-1][k-1];
				L[j-1][i-1] = 1.0 / L[i-1][i-1] * (A[j-1][i-1] - sum);
			}
		}
		
		sum=0;
		for (int k=1; k<=n-1; k++)  sum += L[n-1][k-1] * L[n-1][k-1];
		L[n-1][n-1]=Math.sqrt(A[n-1][n-1]-sum);

        printMatrix(L);
	}
	
	static void printMatrix(double[][] matrix) {
		for (int i = 0; i < matrix.length; i++) {
			for (int j = 0; j < matrix.length; j++) {	
				InOut.print(matrix[i][j], 1, 3);
				System.out.print("  ");
			}
			System.out.print("\n");
		}
		System.out.print("\n");
		System.out.print("\n");
	}
}