#include <bits/stdc++.h>

using namespace std;

#define Train_Set_Size 20
#define PI 3.141592653589793238463
#define N 5
#define epsilon 0.05
#define epoch 50000

long double c[N];
long double W[N];
long double V[N];
long double b;

/*
Camada oculta e 5 neurônios
Função Sigmoid para a ativação de cada nó
*/
long double sigmoid(long double x){
	return (1.0/(1.0+abs(x)));
}

long double f_theta(long double x){
	long double result = b;
	for(int i = 0; i < N; i++){
		result += V[i] * sigmoid(c[i] + W[i] * x);
	}
	return result;
}

void train(long double x, long double y){
	for (int i = 0; i < N; i++) {
		W[i] = W[i] - epsilon * 2 * (f_theta(x) - y) * V[i] * x *
           (1 - sigmoid(c[i] + W[i] * x)) * sigmoid(c[i] + W[i] * x);
	}
	for (int i = 0; i < N; i++) {
		V[i] = V[i] - epsilon * 2 * (f_theta(x) - y) * sigmoid(c[i] + W[i] * x);
	}
	b = b - epsilon * 2 * (f_theta(x) - y);
	for (int i = 0; i < N; i++) {
		c[i] = c[i] - epsilon * 2 * (f_theta(x) - y) * V[i] *
           (1 - sigmoid(c[i] + W[i] * x)) * sigmoid(c[i] + W[i] * x);
	}
}

void initRandom(){
	for(int i=0;i<N;i++){
		W[i] = 2 * rand() / RAND_MAX - 1;
		V[i] = 2 * rand() / RAND_MAX - 1;
		c[i] = 2 * rand() / RAND_MAX - 1;
	}
}

int main(){

	initRandom();

	vector<pair<double, double>> trainSet;
	trainSet.resize(Train_Set_Size);

	for(int i=0;i<Train_Set_Size;i++){
		trainSet[i] = {i*2*PI/Train_Set_Size, sin(i*2*PI/Train_Set_Size)};
	}

	for(int j=0;j<epoch;j++){
		for(int i=0;i<Train_Set_Size;i++){
			train(trainSet[i].first, trainSet[i].second);
		}
		cout << "J : " << j << endl;
	}

	//Plot
	vector<float> x;
	vector<float> y1, y2;

	for (int i = 0; i < 1000; i++) {
		x.push_back(i * 2 * PI / 1000);
		y1.push_back(sin(i * 2 * PI / 1000));
		y2.push_back(f_theta(i * 2 * PI / 1000));
	}

	FILE * gp = fopen("gnuplot", "w");
	fprintf(gp, "set terminal wxt size 600,400 \n");
	fprintf(gp, "set grid \n");
	fprintf(gp, "set title '%s' \n", "f(x) = sin (x)");
	fprintf(gp, "set style line 1 lt 3 pt 7 ps 0.1 lc rgb 'green' lw 1 \n");
	fprintf(gp, "set style line 2 lt 3 pt 7 ps 0.1 lc rgb 'red' lw 1 \n");
	fprintf(gp, "plot '-' w p ls 1, '-' w p ls 2 \n");

	//Exact f(x) = sin(x) -> Green Graph
	for (int k = 0; k < x.size(); k++) {
		fprintf(gp, "%f %f \n", x[k], y1[k]);
	}
	fprintf(gp, "e\n");

	//Neural Network Approximate f(x) = sin(x) -> Red Graph
	for (int k = 0; k < x.size(); k++) {
		fprintf(gp, "%f %f \n", x[k], y2[k]);
	}
	fprintf(gp, "e\n");

	fflush(gp);


	system("pause");
	fclose(gp);

	return 0;
}