// NOTE: 使用自定义标量（复数）的单变量函数的导数

// C++ includes
#include <iostream>
#include <complex>
using namespace std;

// autodiff include
#include <autodiff/forward/dual.hpp>
using namespace autodiff;

// Specialize isArithmetic for complex to make it compatible with dual
namespace autodiff::detail {
    template<typename T>
    struct ArithmeticTraits<complex<T>>: ArithmeticTraits<T> {};
} // autodiff::detail

using cxdual = Dual<complex<double>, complex<double>>;

cxdual f(cxdual x){
    return 1+x+x*x+1/x+log(x);
}

int main(){
    cxdual x = 2.0; // the input variable x
    cxdual u = f(x); // the output variable u
    cxdual dudx = derivative(f, wrt(x), at(x)); // evaluate the derivative du/dx

    cout << "u = " << u << endl;
    cout << "du/dx = " << dudx << endl;
    return 0;
}