AutomaticDifferentiation/include/dual_ops.hpp

/*对偶数的声明部分*/
#pragma once
#include <cmath>
#include "types/dual.hpp"

// 前向自动微分的运算部分，两个deriv相乘为0
namespace forwardad{
    // 加减乘除
    inline Dual operator+(const Dual& a, const Dual& b) {
        return Dual(a.value + b.value, a.deriv + b.deriv);
    }

    inline Dual operator-(const Dual& a, const Dual& b) {
        return Dual(a.value - b.value, a.deriv - b.deriv);
    }

    inline Dual operator*(const Dual& a, const Dual& b) {
        return Dual(a.value * b.value, a.value * b.deriv + a.deriv * b.value);
    }

    inline Dual operator/(const Dual& a, const Dual& b) {
        return Dual(a.value / b.value, (a.deriv * b.value - a.value * b.deriv) / (b.value * b.value));
    }

    // 下面的函数需要用到链式法则(使用泰勒展开后保留一次项)
    // 三角函数
    inline Dual sin(const Dual& x) {
        return Dual(std::sin(x.value), std::cos(x.value) * x.deriv);
    }

    inline Dual cos(const Dual& x) {
        return Dual(std::cos(x.value), -std::sin(x.value) * x.deriv);
    }

    // 指数和对数
    inline Dual exp(const Dual& x) {
        double exp_val = std::exp(x.value);
        return Dual(exp_val, exp_val * x.deriv);
    }

    inline Dual log(const Dual& x) {
        return Dual(std::log(x.value), x.deriv / x.value);
    }

    // 幂函数
    inline Dual pow(const Dual& x, double n) {
        double pow_val = std::pow(x.value, n);
        return Dual(pow_val, n * std::pow(x.value, n - 1) * x.deriv);
    }

    // 反三角函数
    inline Dual asin(const Dual& x) {
        return Dual(std::asin(x.value), x.deriv / std::sqrt(1 - x.value * x.value));
    }

    inline Dual acos(const Dual& x) {
        return Dual(std::acos(x.value), -x.deriv / std::sqrt(1 - x.value * x.value));
    }

    inline Dual atan(const Dual& x) {
        return Dual(std::atan(x.value), x.deriv / (1 + x.value * x.value));
    }
}// namespace forwardad