package com.company;

import java.text.NumberFormat;
import java.util.Arrays;

public class Main {
    public static double[][] matrixAT(double [][] a,int n,int m){
        double[][] b=new double[n][m];
        for (int i = 0;i < n; i++) {
            for (int j = 0; j < n; j++) {
                b[i][j]=a[j][i];
            }
        }
        return b;
    }
    public static void printMatrix(double [][] matrix)
    {
        for (int i = 0; i < matrix.length; i++)
        {
            for (int j = 0; j < matrix[0].length; j++)
            {

                System.out.printf("%.4f",matrix[i][j]);
                System.out.print("   ");

            }
            System.out.println();
        }
        System.out.println("-----------");
    }
    public static  void print(double[][] a,int n,int m){
        NumberFormat formatter = NumberFormat.getNumberInstance();
        formatter.setMaximumFractionDigits(4);
        for (int i = 0;i < n; i++) {
            for (int j = 0; j < m; j++) {
                System.out.print(formatter.format(a[i][j])+"\t\t");
            }
            System.out.println();
        }
        System.out.println();
    }

    public static  void printArray(double[] a,int n){
        NumberFormat formatter = NumberFormat.getNumberInstance();
        formatter.setMaximumFractionDigits(4);
        System.out.println();
        for (int i=0;i<n;i++){
            System.out.print(formatter.format(a[i])+" ");
        }
        System.out.println();
    }

    public static  void printArrayexp(double[] a,int n){
        System.out.println();
        for (int i=0;i<n;i++){
            System.out.printf("%e",a[i]);
            System.out.print("     ");
        }
        System.out.println();
    }

    public static void main(String[] args) {
        int n = 5;
        double epc=0.00001;
        double[][] A=
                {
                        {0.8918, 0.0000, -0.2330, 0.1638, 0.2730, 1.7545},
                        {-0.0546, 0.5824, 0.0000, -0.1110, 0.0364, 2.3278},
                        {0.0182, -0.1638, 1.0556, 0.0200, 0.0637, -3.2742},
                        {0.0546, 0.0000, -0.1329, 1.0556, 0.0000, -9.0472},
                        {0.0364, -0.0546, 0.2639, -0.0218, 0.7644, 3.9239},
                };
        double[][] A1 = {{1,2,3,4},{2,1,-1,-2},{3,-1,5,1}};
        double[][] B = new double[n][n + 1];
        double[][] H = new double[n][n];
        double[][] F = new double[n][n];
        double[] prewx=new double[n];
        double[] newx=new double[n];
        double[][] AT;
        AT=matrixAT(A,n,n);
        for (int i = 0; i<n; i++) {//AT*A
            for (int j = 0; j<n; j++) {
                for (int k = 0; k<n; k++)
                    B[i][j] += AT[i][k] * A[k][j];
            }
        }
        double[][] ATA=new double[n][n];
        for (int i = 0; i<n; i++) {//B=E-AT*A
            for (int j = 0; j < n; j++) {
                ATA[i][j] = B[i][j];
            }
        }
        for (int i = 0; i<n; i++) {//B=E-AT*A
            for (int j = 0; j<n; j++) {
                if (i == j){
                    B[i][j]=1-B[i][j];
                }
                else {
                    B[i][j]=-B[i][j];
                }
            }
        }
        double[] g=new double[n];
        for (int i = 0; i < n; i++) {//g=AT*b
            for (int j = 0; j < n ; j++) {
                g[i]+=AT[i][j]*A[j][n];
                B[i][n]+=AT[i][j]*A[j][n];
            }
        }
        System.out.println("Расширенная матрица B|g:");
        print(B,n,n+1);
        for (int i = 0; i < n; i++) {//g=AT*b
            for (int j = 0; j < n; j++) {
                if (i > j) {
                    H[i][j] = B[i][j];
                }
                else {
                    F[i][j]=B[i][j];
                }
            }
        }
        double sum=0,max=0;
        for (int i = 0; i < n; i++) {
            sum=0;
            for (int j = 0; j < n; j++) {
                sum += B[i][j];
            }
            if (sum>max){
                max=sum;
            }
        }
        if (Math.abs(max)<1){
            System.out.println("Проверка сходимости: сходится");
            System.out.println();
        }
        for (int i=0;i<n;i++){
            prewx[i]=g[i];
        }
        double norm;
        int count=0;
        do{
            count++;
            double sum1=0;
            for (int i = 0; i < n; i++) {
                sum1=0;
                for (int j=0;j<i;j++) {
                    sum1 += H[i][j] * newx[j];
                }
                for (int j = i; j < n ; j++) {
                    sum1+=F[i][j]*prewx[j];
                }
                newx[i]=sum1+g[i];
            }
            System.out.println(Arrays.toString(newx));
            norm=Math.abs(newx[0]-prewx[0]);
            for (int i=0;i<n;i++){
                if (Math.abs(newx[i]-prewx[i])>norm){
                    norm=Math.abs(newx[i]-prewx[i]);
                }
                prewx[i]=newx[i];
            }
            System.out.print("норма: "+norm+'\n');
        }
        while (norm>=epc);
        System.out.print("Решение системы:\n");
        System.out.println(Arrays.toString(newx));
        System.out.println();
        System.out.println("Количество итераций: "+count);
        double[] r1=new double[n];
        double[] r2=new double[n];
        double sum1=0;
        printMatrix(B);
        for (int i = 0; i < n; i++) {
            sum1=0;
            for (int j = 0; j < n ; j++) {
                sum1+=ATA[i][j]*newx[j];
            }
            r1[i]=sum1-B[i][n];
        }
        for (int i = 0; i < n; i++) {
            sum1=0;
            for (int j = 0; j < n ; j++) {
                sum1+=A[i][j]*newx[j];
            }
            r2[i]=sum1-A[i][n];
        }
        System.out.println();
        System.out.print("r=AX-b");
        System.out.println('\n'+Arrays.toString(r1));
        System.out.print("r=AT*AX-AT*b");
        System.out.println('\n'+Arrays.toString(r2));
    }
}