import java.util.*;
public class question1partA {
    public static void main (String[] args){
        double[][] output = {
                  { 4, 12, -16},
                  { 12, 37, -43},
                  { -16, -43, 98}
        };
        double[] b = {100,200,150};

        //print matrix
        for (int i = 0; i < output.length; i++){
            for (int j = 0; j < output.length; j++){
                System.out.print(output[i][j] + " ");
            }
            System.out.println();
        }
        System.out.println();

        double[][] out = findL(output);
        //print L
        for (int i = 0; i < out.length; i++){
            for (int j = 0; j < out.length; j++){
                System.out.print(out[i][j] + " ");
            }
            System.out.println();
        }
        System.out.println();

        double[] yout = findY(out, b);
        //print y
        for (int i = 0; i < yout.length; i++){
            System.out.print(yout[i] + " ");
        }
    }
    //Choleski decomposition
    public static double[][] findL(double[][] array){
        double[][] L = new double[array.length][array.length];

        //populating L array with 0's first
        for (int i = 0; i < L.length ; i++){
            for (int j = 0; j < L.length; j++){
                L[i][j] = 0;
            }
        }
        for (int j = 0; j < array.length; j++){
            double f1 = 0;
            //computes for the sub of Ljj to Ljj-1
            for (int a = 0 ; a < j  ; a++){
                f1 = f1 + Math.pow((double) L[j][a], 2);
            }
            L[j][j] = Math.sqrt(array[j][j] - f1);

            for (int i = j+1; i < array.length; i++){
                double f2 = 0;
                for (int b = 0; b < j ; b++){
                    f2 = f2 + L[i][b] * L[j][b];
                }
                L[i][j] = (array[i][j] - f2) / L[j][j];
            }
        }
        return L;


    }
    //find Y
    public static double[] findY(double[][] larray, double[] barray){
        double[] y = new double[larray.length];

        for (int i = 0; i < y.length ; i++){
            y[i] = 0;
        }

        double f3 = 0;
        for (int i = 0; i < larray.length; i++) {
            for (int j = 0; j <= i - 1 ; j++){
                f3 = f3 + larray[i][j]*y[j];
            }
            y[i] = (barray[i] - f3)/larray[i][i];
        }
        return y;
    }


}