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#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <iomanip>
#include <cmath>
#include <algorithm>
#include <vector>
#define vd vector<double>
#define vvd vector<vector<double> >
#define ui unsigned int
using namespace std;
inline void print(vd g);
inline double sqr(const double& a) {
return a * a;
}
inline double dot(const vd& a, const vd& b) {
double ret = 0;
for (int i = 0; i < a.size(); ++i)
ret += a[i] * b[i];
return ret;
}
inline double norm(const vd& a) {
double ret = 0;
for (int i = 0; i < a.size(); ++i)
ret += sqr(a[i]);
return sqrt(ret);
}
vd operator +(const vd& a, const vd& b) {
vd ret = vd(a.size());
for (int i = 0; i < a.size(); ++i)
ret[i] = a[i] + b[i];
return ret;
}
vd operator -(const vd& a, const vd& b) {
vd ret = vd(a.size());
for (int i = 0; i < a.size(); ++i)
ret[i] = a[i] - b[i];
return ret;
}
vd operator *(const vd& a, double d) {
vd ret = vd(a.size());
for (int i = 0; i < a.size(); ++i)
ret[i] = a[i] * d;
return ret;
}
vd operator *(const vvd& a, const vd& b) {
vd ret = vd(a.size(), 0.0);
for (int i = 0; i < a.size(); ++i) {
ret[i] = dot(a[i], b);
}
return ret;
}
int n;
int k = 0;
vvd A;
vd B;
vvd p;
vvd q;
vvd x;
vvd e;
void solve();
int main(){
freopen("input.txt", "r", stdin);
//freopen("output.txt", "w", stdout);
n;
cin >> n;
A.resize(n, vd(n, 0.0));
B.resize(n);
p.resize(2, vd(n, 0.0));
q.resize(2, vd(n, 0.0));
x.resize(2, vd(n, 0.0));
e.resize(2, vd(n, 0.0));
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
cin >> A[i][j];
}
cin >> B[i];
}
/*
vd test = A * B;
print(test);
return 0;*/
e[k] = B - A * x[k];
p[k] = e[k];
solve();
cout << "solution:" << endl;
for (int i = 0; i < n; ++i)
cout << "x[" << i + 1 << "] " << setw(12) << fixed << setprecision(6) << x[k][i] << endl;
cout << endl;
}
void solve() {
/*for (int i = 0; i < n; ++i)
cout << "x[" << i + 1 << "] " << setw(12) << fixed << setprecision(6) << x[k][i] << endl;
cout << endl << endl;*/
q[k] = A * p[k];
double alpha = dot(e[k], p[k]) / dot(q[k], p[k]);
x[1 - k] = x[k] + p[k] * alpha;
e[1 - k] = e[k] - q[k] * alpha;
double norm_e = norm(e[1 - k]);
if (norm(e[1 - k]) < 1e-18)
return;
double beta = dot(e[1 - k], q[k]) / dot(p[k], q[k]);
p[1 - k] = e[1 - k] - p[k] * beta;
k = 1 - k;
solve();
}
inline void print(vd g) {
cout << "( ";
for (int j = 0; j < n; ++j)
cout << setw(12) << fixed << setprecision(6) << g[j];
cout << endl;
}