// DFT.cpp: определяет точку входа для консольного приложения.
//

#include "stdafx.h"
#include<cstdlib>
#include<cstdio>
#include<iostream>
#include<cmath>
#include"gnuplot_i.hpp"
#include<Windows.h>
#include<conio.h>

using namespace std;

#define pi 2*acos(0.0)
#define eps 0.01



double x[510];
double dft[510];
int n = 501;
double f1, f2;
vector<vector<double>> M;
vector<double> b;
vector<double> c;

void DFT()
{
	for (int i = 0; i < n; i++)
	{
		double r = 0.;
		double im = 0.;
		for (int j = 0; j < n; ++j) {

			double alpha = double((2 * pi* i * j) / n);

			r += x[j] * double(cos(alpha));
			im += x[j] * double(sin(alpha));

		}

		dft[i] = sqrt(r*r+im*im);
	}
}
void wait() {
	FlushConsoleInputBuffer(GetStdHandle(STD_INPUT_HANDLE));
#ifndef FOUT
	cout << endl << "Press any key to continue..." << endl;
#endif
	_getch();
}
void Plot()
{
	Gnuplot gnu("lines");
	string a = "set style line 1 lc rgb '#0060ad' lt 2 lw 2 pt 0 ps 1.5";
	string b = "C:/Users/Asus/Documents/Visual Studio 2015/Projects/DFT/DFT/temp.txt"; b = "plot '" + b; b += "' using ($1*1):($2)  with linespoints ls 1";

	gnu.plot_points(b, a);
	wait();
	system("pause");
}
pair<double,double> Find_extr()
{
	vector<double> a;
	for (int i = 1; i < n / 2; i++)
	{
		if (dft[i] - dft[i-1] > eps && dft[i] - dft[i + 1] > eps) a.push_back((i+1)*0.002);
	}
	if (a.size() > 2) cout << "ERROR" << endl; else
		if (a.size() == 2) return make_pair(a[0], a[1]); else
			return make_pair(a[0],0);
}
vector<vector<double>> Matrix()
{
	vector<vector<double>> A;
	vector<double> a1, a2, a3, a4, a5;
	double sum = 0;
	for (int i = 0; i < n; i++) sum += pow(i*0.01, 6.);
	a1.push_back(sum);

	sum = 0;
	for (int i = 0; i < n; i++) sum += pow(i*0.01, 5.);
	a1.push_back(sum);
	a2.push_back(sum);

	sum = 0;
	for (int i = 0; i < n; i++) sum += pow(i*0.01, 4.);
	a1.push_back(sum);
	a2.push_back(sum);
	a3.push_back(sum);

	sum = 0;
	for (int i = 0; i < n; i++) sum += pow(i*0.01, 3.)*sin(2*pi*f1*i*0.01);
	a1.push_back(sum);
	a4.push_back(sum);


	sum = 0;
	for (int i = 0; i < n; i++) sum += pow(i*0.01, 3.);
	a1.push_back(sum);
	a2.push_back(sum);
	a3.push_back(sum);
	a5.push_back(sum);

	sum = 0;
	for (int i = 0; i < n; i++) sum += pow(i*0.01, 2.)*sin(2 * pi*i*0.01*f1);
	a2.push_back(sum);
	a4.push_back(sum);

		sum = 0;
	for (int i = 0; i < n; i++) sum += pow(i*0.01, 2.);
	a2.push_back(sum);
	a3.push_back(sum);
	a5.push_back(sum);

	sum = 0;
	for (int i = 0; i < n; i++) sum += (i*0.01)*sin(2 * pi*i*0.01*f1);
	a3.push_back(sum);
	a4.push_back(sum);


	sum = 0;
	for (int i = 0; i < n; i++) sum += i*0.01;
	a3.push_back(sum);
	a5.push_back(sum);

	sum = 0;
	for (int i = 0; i < n; i++) sum += pow(sin(2 * pi*i*0.01*f1),2);
	a4.push_back(sum);


	sum = 0;
	for (int i = 0; i < n; i++) sum +=sin(2 * pi*i*0.01*f1);
	a4.push_back(sum);
	a5.push_back(sum);


	a5.push_back(500.);


	A.push_back(a1);
	A.push_back(a2);
	A.push_back(a3);
	A.push_back(a4);
	A.push_back(a5);

	for (int i = 0; i < 5; i++) cout << A[i].size() << endl;
	return A;

}
vector<double> BB()
{
	vector<double> B;
	double sum;

	sum = 0;
	for (int i = 0; i < n; i++) sum += pow(double(i)/100.,3)*x[i];
	B.push_back(sum);

	sum = 0;
	for (int i = 0; i < n; i++) sum += pow(i*0.01, 2)*x[i];
	B.push_back(sum);

	sum = 0;
	for (int i = 0; i < n; i++) sum += pow(i*0.01, 1)*x[i];
	B.push_back(sum);

	sum = 0;
	for (int i = 0; i < n; i++) sum += (sin(2 * pi*i*0.01*f1))*x[i];
	B.push_back(sum);

	sum = 0;
	for (int i = 0; i < n; i++) sum += x[i];
	B.push_back(sum);

	cout << B.size() << endl;
	return B;
}
vector<double> MKK()
{
	vector<double>res;
	double temp;
	double U[10][10] = {0};
	double y[10] = { 0 };
	double ans[10] = { 0 };
	for (int i = 0; i < 5; i++)
	{
		temp = 0;
		for (int k = 0; k < i; k++)
			temp = temp + U[k][i] * U[k][i];
		U[i][i] = sqrt(M[i][i] - temp);
		for (int j = i; j < 5; j++)
		{
			temp = 0;
			for (int k = 0; k < i; k++)
				temp = temp + U[k][i] * U[k][j];
			U[i][j] = (M[i][j] - temp) / U[i][i];
		}
	}
	for (int i = 0; i < 5; i++) {
		for (int j = 0; j < 5; j++) {
			cout << U[i][j] << " ";
		}
		cout << endl;
	}
	for (int i = 0; i < 5; i++)
	{
		temp = 0;
		for (int k = 0; k < i; k++)
			temp = temp + U[k][i] * y[k];
		y[i] = (b[i] - temp) / U[i][i];
	}
	for (int i = 4; i >= 0; i--)
	{
		temp = 0;
		for (int k = i + 1; k < 5; k++)
			temp = temp + U[i][k] * ans[k];
		ans[i] = (y[i] - temp) / U[i][i];
	}
	for (int i = 0; i < 5; i++)
	{
		res.push_back(ans[i]);
		cout << "x" << i << "= " << ans[i] << endl;
	}

	return res;
}
int main()
{
	freopen("f3.txt","r",stdin);
	freopen("temp.txt","w",stdout);
	for (int i = 0; i < n; i++) scanf("%lf",&x[i]);
	DFT();
	for (int i = 0; i < n; i++) printf("%.3lf %.3lf\n",double(i)/100.,dft[i]);
	fclose(stdout);
	freopen("CON","w",stdout);

//	Plot();
	pair<double,double> extr = Find_extr();
	cout << extr.first << " " << extr.second<< endl;
	f1 = extr.first; f2 = extr.second;
	M = Matrix();

	for (int i = 0; i < 5; i++)
	{
		for (int j = 0; j < 5; j++) cout << M[i][j] << " ";
		cout << endl;
	}


	b = BB();

	for (int i = 0; i < 5; i++) cout << b[i] << " ";
	cout << endl;

	c = MKK();
    return 0;
}