#include <iostream>
#include "forwardad.hpp"
#include "types/dual.hpp"

using namespace forwardad;

// 一阶测试函数
Dual f(Dual x) {
    return x + x*x + pow(x,3);
}

// 二阶测试函数
Dual g(Dual x, Dual y) {
    return exp(x) * log(y);
}

// 高阶测试函数
Dual h(Dual x, Dual y, Dual z) {
    return pow(x, 3) + pow(y, 2) + z + cos(x * y * z);
}

int main() {
    std::cout << "Testing f(x) = x^2 + sin(x) at x=2.0\n";
    auto r = diff(f, 2.0);
    std::cout << "value = " << r.value << "\n";
    std::cout << "grad  = " << r.gradient[0] << "\n";

    std::cout << "\nTesting g(x,y) = exp(x)*log(y) at (x,y)=(1.0, 2.0)\n";
    auto r2 = diff(g, 1.0, 2.0);
    std::cout << "value = " << r2.value << "\n";
    std::cout << "grad  = (" << r2.gradient[0] << ", " << r2.gradient[1] << ")\n";

    std::cout << "\nTesting h(x,y,z) = x^3 + y^2 + z + cos(x*y*z) at (x,y,z)=(1.0, 2.0, 3.0)\n";
    auto r3 = diff(h, 1.0, 2.0, 3.0);
    std::cout << "value = " << r3.value << "\n";
    std::cout << "grad  = (" << r3.gradient[0] << ", " << r3.gradient[1] << ", " << r3.gradient[2] << ")\n";


    return 0;
}