AutomaticDifferentiation/include/dual.hpp

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

namespace backwardad {
    inline Node operator+(const Node& a, const Node& b) {
        Node out(a.value() + b.value());
        out.inputs() = {a, b};
        out.backward() = [out, a, b]() {
            a.add_gradient(out.gradient()); // da = dout * 1
            b.add_gradient(out.gradient()); // db = dout * 1
        };
        return out;
    }

    inline Node operator-(const Node& a, const Node& b) {
        Node out(a.value() - b.value());
        out.inputs() = {a, b};
        out.backward() = [out, a, b]() {
            a.add_gradient(out.gradient()); // da = dout * 1
            b.add_gradient(-out.gradient()); // db = dout * (-1)
        };
        return out;
    }

    inline Node operator*(const Node& a, const Node& b) {
        Node out(a.value() * b.value());
        out.inputs() = {a, b};
        out.backward() = [out, a, b]() {
            a.add_gradient(out.gradient() * b.value()); // da = dout * b
            b.add_gradient(out.gradient() * a.value()); // db = dout * a
        };
        return out;
    }

    inline Node operator/(const Node& a, const Node& b) {
        Node out(a.value() / b.value());
        out.inputs() = {a, b};
        out.backward() = [out, a, b]() {
            a.add_gradient(out.gradient() / b.value()); // da = dout * (1/b)
            b.add_gradient(-out.gradient() * a.value() / (b.value() * b.value())); // db = dout * (-a/b^2)
        };
        return out;
    }

    // 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 Node sin(const Node& x) {
        Node out(std::sin(x.value()));
        out.inputs() = {x};
        out.backward() = [out, x]() {
            x.add_gradient(out.gradient() * std::cos(x.value())); // dx = dout * cos(x)
        };
        return out;
    }

    inline Node cos(const Node& x) {
        Node out(std::cos(x.value()));
        out.inputs() = {x};
        out.backward() = [out, x]() {
            x.add_gradient(-out.gradient() * std::sin(x.value())); // dx = dout * (-sin(x))
        };
        return out;
    }

    // 指数和对数
    inline Node exp(const Node& x) {
        Node out(std::exp(x.value()));
        out.inputs() = {x};
        out.backward() = [out, x]() {
            x.add_gradient(out.gradient() * out.value()); // dx = dout * exp(x) = dout * out.value
        };
        return out;
    }

    inline Node log(const Node& x) {
        Node out(std::log(x.value()));
        out.inputs() = {x};
        out.backward() = [out, x]() {
            x.add_gradient(out.gradient() / x.value()); // dx = dout * (1/x)
        };
        return out;
    }

    inline Node pow(const Node& x, double n) {
        Node out(std::pow(x.value(), n));
        out.inputs() = {x};
        out.backward() = [out, x, n]() {
            x.add_gradient(out.gradient() * n * std::pow(x.value(), n - 1)); // dx = dout * (n * x^(n-1))
        };
        return out;
    }

    // 反三角函数
    inline Node asin(const Node& x) {
        Node out(std::asin(x.value()));
        out.inputs() = {x};
        out.backward() = [out, x]() {
            x.add_gradient(out.gradient() / std::sqrt(1 - x.value() * x.value())); // dx = dout * (1/sqrt(1-x^2))
        };
        return out;
    }

    inline Node acos(const Node& x) {
        Node out(std::acos(x.value()));
        out.inputs() = {x};
        out.backward() = [out, x]() {
            x.add_gradient(-out.gradient() / std::sqrt(1 - x.value() * x.value())); // dx = dout * (-1/sqrt(1-x^2))
        };
        return out;
    }

    inline Node atan(const Node& x) {
        Node out(std::atan(x.value()));
        out.inputs() = {x};
        out.backward() = [out, x]() {
            x.add_gradient(out.gradient() / (1 + x.value() * x.value())); // dx = dout * (1/(1+x^2))
        };
        return out;
    }

}