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#include <iostream>
#include <array>
#include <cmath>
template<typename T, typename U, size_t DATA_NUM>
using dataType = std::array<std::pair<T, U>, DATA_NUM>;
template<typename Array = std::array<double, 2>>
using Array = Array;
constexpr double operator*(Array<> a, Array<> b) {
double num = 0;
for(size_t i = 0; i < a.size(); ++i)
num += a[i]*b[i];
return num;
}
constexpr Array<> operator*(double a, Array<> b) {
return {b[0]*a, b[1]*a};
}
constexpr Array<> operator+(Array<> a, Array<> b) {
return {a[0]+b[0], a[1]+b[1]};
}
constexpr Array<> operator+(Array<> a, double b) {
return {a[0]+b, a[1]+b};
}
constexpr Array<> operator/(Array<> a, double b) {
return {a[0]/b, a[1]/b};
}
constexpr Array<> operator/(Array<> a, Array<> b) {
return {a[0]/b[0], a[1]/b[1]};
}
constexpr Array<> operator-(Array<> a, Array<> b) {
return {a[0]-b[0], a[1]-b[1]};
}
constexpr double pow(double num, int times){
if(times == 0) return 1;
return num*pow(num, times-1);
}
constexpr double constexpr_sqrt(double num){
double current = num;
double prev = 0;
while(current-prev != 0) {
prev = current;
current = (current+num/current)/2;
}
return current;
}
constexpr std::uint64_t fact(int num){
if(num == 0) return 1;
return num*fact(num-1);
}
constexpr double constexpr_exp(double num){
double result = 0;
for(int i = 0; i < 10; ++i){
result += (pow(num, i)/fact(i));
}
return result;
}
constexpr double sigmoid(Array<> _w, Array<> _ed) {
double num = _w*_ed;
return 1 / (1 + constexpr_exp(-num));
}
constexpr Array<> pow(Array<> a, int b) {
return {pow(a[0], 2), pow(a[1], 2)};
}
constexpr Array<> sqrt(Array<> a) {
return {constexpr_sqrt(a[0]), constexpr_sqrt(a[1])};
}
constexpr Array<> train() {
constexpr dataType<double, int, 12> data = {
std::make_pair(1.0, 0), std::make_pair(1.15, 0), std::make_pair(1.2, 0),
std::make_pair(1.25, 0), std::make_pair(1.3, 0), std::make_pair(1.35, 0),
std::make_pair(1.4, 0), std::make_pair(1.45, 1), std::make_pair(1.5, 1),
std::make_pair(1.55, 1), std::make_pair(1.6, 1), std::make_pair(1.65, 1),
};
Array<> w = {1.0, 0.0};
double alpha = 0.001;
double pred = 0.0;
for(size_t time = 1; time <= 3000; ++time) {
for(auto& d: data) {
Array<> extended_data = {d.first, 1};
pred = sigmoid(w, extended_data);
w = w-alpha*(pred-d.second)*pred*(1-pred)*extended_data;
}
}
return w;
}
int main(int argc, char const *argv[]) {
constexpr Array<> result = train();
std::cout << result[0] << " " << result[1] << std::endl;
return 0;
}
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