63 lines
1.9 KiB
C++
63 lines
1.9 KiB
C++
/*对偶数的声明部分*/
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#pragma once
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#include <cmath>
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#include "types/dual.hpp"
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// 前向自动微分的运算部分，两个deriv相乘为0
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namespace forwardad{
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// 加减乘除
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inline Dual operator+(const Dual& a, const Dual& b) {
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return Dual(a.value + b.value, a.deriv + b.deriv);
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}
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inline Dual operator-(const Dual& a, const Dual& b) {
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return Dual(a.value - b.value, a.deriv - b.deriv);
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}
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inline Dual operator*(const Dual& a, const Dual& b) {
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return Dual(a.value * b.value, a.value * b.deriv + a.deriv * b.value);
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}
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inline Dual operator/(const Dual& a, const Dual& b) {
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return Dual(a.value / b.value, (a.deriv * b.value - a.value * b.deriv) / (b.value * b.value));
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}
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// 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)
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// 三角函数
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inline Dual sin(const Dual& x) {
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return Dual(std::sin(x.value), std::cos(x.value) * x.deriv);
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}
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inline Dual cos(const Dual& x) {
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return Dual(std::cos(x.value), -std::sin(x.value) * x.deriv);
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}
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// 指数和对数
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inline Dual exp(const Dual& x) {
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double exp_val = std::exp(x.value);
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return Dual(exp_val, exp_val * x.deriv);
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}
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inline Dual log(const Dual& x) {
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return Dual(std::log(x.value), x.deriv / x.value);
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}
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// 幂函数
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inline Dual pow(const Dual& x, double n) {
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double pow_val = std::pow(x.value, n);
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return Dual(pow_val, n * std::pow(x.value, n - 1) * x.deriv);
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}
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// 反三角函数
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inline Dual asin(const Dual& x) {
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return Dual(std::asin(x.value), x.deriv / std::sqrt(1 - x.value * x.value));
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}
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inline Dual acos(const Dual& x) {
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return Dual(std::acos(x.value), -x.deriv / std::sqrt(1 - x.value * x.value));
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}
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inline Dual atan(const Dual& x) {
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return Dual(std::atan(x.value), x.deriv / (1 + x.value * x.value));
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}
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}// namespace forwardad
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