chunwailin's closet little girl

/*************************************************************************
  > File Name: a.cpp
  > datauthor: Samuel
  > Mail: enminghuang21119@gmail.com
  > Created Time: Sun Oct 18 10:15:00 2020
*************************************************************************/

#include <iostream>
#include <iomanip>
using namespace std;

struct Vector {
    long double data[2];
    Vector() {data[0] = data[1] = 0;}
    Vector(long double x[2]) {
        data[0] = x[0];
        data[1] = x[1];
    }
    void out() {
        for (int i = 0; i < 2; i++)
            cout << setw(10) << data[i] << '\n';
    }
};
struct Matrix {
    long double data[2][2];
    Matrix() {data[0][0] = data[0][1] = data[1][0] = data[1][1] = 0;}
    Matrix(long double x[2][2]) {
        data[0][0] = x[0][0];
        data[1][0] = x[1][0];
        data[0][1] = x[0][1];
        data[1][1] = x[1][1];
    }
    long double det() {
        return data[0][0] * data[1][1] - data[0][1] * data[1][0];
    }
    Matrix operator* (const Matrix &b) const {
        Matrix re;
        for (int i = 0; i < 2; i++)
            for (int k = 0; k < 2; k++)
                for (int j = 0; j < 2; j++)
                    re.data[i][k] += data[i][j] * b.data[j][k];
        return re;
    }
    Vector operator* (const Vector &b) const {
        Vector re;
        for (int i = 0; i < 2; i++)
            for (int j = 0; j < 2; j++)
                re.data[i] += data[i][j] * b.data[j];
        return re;
    }
    Matrix inv() {
        Matrix re;
        long double d = det();
        re.data[0][0] = data[1][1];
        re.data[1][1] = data[0][0];
        re.data[0][1] = -data[0][1];
        re.data[1][0] = -data[1][0];
        for (int i = 0; i < 2; i++)
            for (int j = 0; j < 2; j++)
                re.data[i][j] /= d;
        return re;
    }
    Matrix transpose() {
        Matrix re;
        re.data[0][0] = data[0][0];
        re.data[1][1] = data[1][1];
        re.data[0][1] = data[1][0];
        re.data[1][0] = data[0][1];
        return re;
    }
    void out() {
        for (int i = 0; i < 2; i++) {
            for (int j = 0; j < 2; j++)
                cout << setw(10) << data[i][j];
            cout << '\n';
        }
    }
};
Vector project(Matrix &A, Vector &b) {
    return A.transpose() * (A.transpose() * A).inv() * A * b;
}

long double in1[2], in2[2][2];
int main() {
    for (int i = 0; i < 2; i++)
        for (int j = 0; j < 2; j++)
            cin >> in2[i][j];
    cin >> in1[0] >> in1[1];
    Matrix A(in2);
    Vector b(in1);

    cout << "Transpose Matrix of A:\n";
    A.transpose().out();

    cout << "Inverse Matrix of A:\n";;
    A.inv().out();

    cout << "Project b on A:\n";
    project(A, b).out();

    return 0;
}