#include "pch.h"
#define _USE_MATH_DEFINES
#include <SDKDDKVer.h>
#include <cmath>
#include <stdlib.h>
#include <stdio.h>
#include <iostream>
#include <windows.h>

using namespace std;
const double step = 0.2;
int npoint = trunc(3.14 / step);
const int maxChebDat = 12;
double pi = 3.14;
double e = 2.72;

int chebdat[maxChebDat][maxChebDat / 2 + 1] =
{ { 1, 0, 0, 0, 0, 0, 0 },
{ 2, -1, 0, 0, 0, 0, 0 },
{ 4, -3, 0, 0, 0, 0, 0 },
{ 8, -8, 1, 0, 0, 0, 0 },
{ 16, -20, 5, 0, 0, 0, 0 },
{ 32, -48, 18, -1, 0, 0, 0 },
{ 64, -112, 56, -7, 0, 0, 0 },
{ 128, -256, 160, -32, 1, 0, 0 },
{ 256, -576, 432, -120, 9, 0, 0 },
{ 512, -1280, 1120, -400, 50, -1, 0 },
{ 1024, -2816, 2816, -1232, 220, -11, 0 },
{ 2048, -6144, 6912, -3584, 840, -72, 1 }
};

// Вычисление исходной функции
double F(double z) {
	//return 1 * pow(sin(1.3 * z), 2);
	//return  5 * z*pow(e, -z);
	return 2 * pow(sin(1.2 * z), 2);
}

//double F0(double z) {
//	return sqrt(z * sin(z));
//}

//Весовая функция
double F11(double z) {
	return sqrt(1 - pow(((2 * z - pi) / pi), 2));
}
// погрешность абсолютная (среднеквадратическая ошибка)
double delta(double* Q1, double* F1, int n) {
	double sum;
	for (int i = 0; i < n; i++) {
		sum = pow((Q1[i] - F1[i]), 2);
	}
	return sqrt(sum / n);
}
// погрешность относительная
double sigma(double delta, double F0max) {
	return delta / F0max * 100;
}
// Вычисление полинома Чебышева
double cheb(double x, int st) {
	double xst;
	int nst;
	double sum;
	int n;
	x = (2 * x - pi) / pi;
	if (st == 0) {
		return 1;
	}
	sum = 0;
	nst = st % 2;
	if (nst == 0) {
		xst = 1;
	}
	else {
		xst = x;
	}
	n = (st + 2) / 2;
	while (nst <= st) {
		sum = sum + chebdat[st - 1][n - 1] * xst;
		nst += 2;
		xst = xst * pow(x, 2);
		n--;
	}
	return sum;
}

int main(int argc, char *argv[]) {
	int j, n;
	double mnog, c, q, e, F0max = 0;
	double a[20];
	double* Q1 = (double *)malloc((npoint + npoint) * sizeof(double));
	double* F1 = (double *)malloc((npoint + npoint) * sizeof(double));
	printf("%d \n", npoint);
	printf("Enter n : ");
	scanf_s("%d", &n);
	//first part, вычисление А
	a[0] = 0;
	c = step;
	while (c <= 3) {
		a[0] = a[0] + F(c)*step * 2 / (F11(c) * pow(pi, 2));
		c = c + step;
	}
	for (int i = 1; i < n; i++) {
		a[i] = 0;
		c = 0;
		c = c + step;
		while (c <= pi) {
			mnog = cheb(c, i);
			a[i] = a[i] + F(c)*mnog*step * 4 / (F11(c) * pow(pi, 2));
			c = c + step;
		}
	}
	printf("\n");
	c = 0;
	//second part, вычисление аппроксимирующей функции по Чебышеву
	double delta = 0;
	while (c <= pi) {
		q = 0.0;
		for (int i = 0; i < n; i++) {
			mnog = cheb(c, i);
			q = q + a[i] * mnog;
		}
		printf("|Q = %5.3f", q);
		printf("|   c = %5.3f", c);
		printf("|   F = %5.3f", F(c));
		e = c / step;
		j = round(e);
		Q1[j] = q;
		F1[j] = F(c);
		printf("| q1 = %5.3f", Q1[j]);
		printf("| f1 = %5.3f|", F1[j]);
		printf("\n");
		c = c + step;
		delta = delta + pow((Q1[j] - F1[j]), 2);
	}
	Q1[j + 1] = q;
	double d = sqrt(delta / npoint);
	double sig = 100 * delta / 2.913;
	printf("\n");
	printf("delta = %5.3f\n", d);
	printf("sigma = %5.3f%%\n", sig);
	FILE *filex, *filey, *fileq;
	fopen_s(&filex, "C:\\x.txt", "w");
	fopen_s(&filey, "C:\\y.txt", "w");
	fopen_s(&fileq, "C:\\q.txt", "w");
	double x = 0.0, y = 0.0;
	fprintf(filex, "x = [");
	for (double i = 0; i < npoint; i++) {
		x = i / npoint;
		fprintf(filex, "%f", x);
		fprintf(filex, ", ");
	}
	fprintf(filex, "]");
	fclose(filex);
	x = 0.0, y = 0.0;
	fprintf(filey, "y = [");
	for (int i = 0; i < npoint; i++) {
		y = F1[i];
		fprintf(filey, "%f", y);
		fprintf(filey, ", ");
	}
	fprintf(filey, "]");
	fclose(filey);
	x = 0.0, y = 0.0;
	fprintf(fileq, "q = [");
	for (int i = 0; i < npoint; i++) {
		y = Q1[i];
		fprintf(fileq, "%f", y);
		fprintf(fileq, ", ");
	}
	fprintf(fileq, "]");
	fclose(fileq);
	system("pause");
	return 0;
}