#include "../AutomaticDifferentiation.hpp"

#include <iostream>
#include <iomanip>
#include <Eigen/Dense>
using std::cout;
using std::endl;
using std::setw;
#define PRINT_VAR(x) std::cout << #x << "\t= " << std::setprecision(16) << (x) << std::endl
#define PRINT_DUAL(x) std::cout << #x << "\t= " << std::fixed << std::setprecision(4) << std::setw(10) << (x).a << ", " << std::setw(10) << (x).b << std::endl

template<typename T>
T f(const T & x)
{
    return 1 + x + x*x + 1/x + log(x);
}

template<typename T>
T df(const T & x)
{
    return 2*x + 1 + 1.0/x - 1/pow(x, 2);
}

template<typename T>
T ddf(const T & x)
{
    return 2 - 1/pow(x, 2) + 2/pow(x, 3);
}

CREATE_GRAD_FUNCTION_OBJECT(f, GradF);

int main()
{
    cout.precision(16);
    double xdbl = 1.5;

    {
        cout << "Analytical\n";
        cout << "f(x)       = " << f(xdbl) << endl;
        cout << "df(x)/dx   = " << df(xdbl) << endl;
        cout << "d²f(x)/dx² = " << ddf(xdbl) << endl;
    }

    // 1st derivative forward
    {
        using Fd = Dual<double>;
        Fd x = xdbl;
        x.diff(0);
        Fd y = f(x);
        cout << "\nForward\n";
        cout << "f(x)       = " << y.a << endl;
        cout << "df(x)/dx   = " << y.d(0) << endl;
    }

    // first derivative using the gradient functor
    {
        GradFunc gradf(f<Dual<double>>, xdbl);

        double fx, dfdx;
        gradf.get_f_grad(xdbl, fx, dfdx);

        cout << "\nForward using gradient function object\n";
        cout << "f(x)       = " << fx << endl;
        cout << "df(x)/dx   = " << dfdx << endl;
        cout << "df(x)/dx   = " << gradf(xdbl) << endl;
    }

    // using a vector type
    {
        // using vtype = std::valarray<double>;
        using vtype = Eigen::Array3d;
        GradF gradf;
        // vtype x(3, xdbl);
        vtype x(xdbl/2, xdbl, xdbl*2);
        vtype fx, dfx;
        gradf.get_f_grad(x, fx, dfx);

        // Dual<vtype> X(x);
        // X.diff(0,1);
        // Dual<vtype> Fx = f(X);
        // fx = Fx.x();
        // dfx = Fx.d(0);

        PRINT_VAR(x);
        PRINT_VAR(fx);
        PRINT_VAR(dfx);

        // also, using a single dual<vector_type> in a R^n -> R function to get the full gradient does not work : no operator[] in Dual, and adding it does not seem to work either...
    }

    return 0;
}