feat: 前向自动微分纯头文件库

tests/basic.cpp

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+#include <iostream>
+#include "forwardad.hpp"
+#include "types/dual.hpp"
+
+using namespace forwardad;
+
+// 一阶测试函数
+Dual f(Dual x) {
+    return x + x*x + pow(x,3);
+}
+
+// 二阶测试函数
+Dual g(Dual x, Dual y) {
+    return exp(x) * log(y);
+}
+
+// 高阶测试函数
+Dual h(Dual x, Dual y, Dual z) {
+    return pow(x, 3) + pow(y, 2) + z + cos(x * y * z);
+}
+
+int main() {
+    std::cout << "Testing f(x) = x^2 + sin(x) at x=2.0\n";
+    auto r = diff(f, 2.0);
+    std::cout << "value = " << r.value << "\n";
+    std::cout << "grad  = " << r.gradient[0] << "\n";
+
+    std::cout << "\nTesting g(x,y) = exp(x)*log(y) at (x,y)=(1.0, 2.0)\n";
+    auto r2 = diff(g, 1.0, 2.0);
+    std::cout << "value = " << r2.value << "\n";
+    std::cout << "grad  = (" << r2.gradient[0] << ", " << r2.gradient[1] << ")\n";
+
+    std::cout << "\nTesting h(x,y,z) = x^3 + y^2 + z + cos(x*y*z) at (x,y,z)=(1.0, 2.0, 3.0)\n";
+    auto r3 = diff(h, 1.0, 2.0, 3.0);
+    std::cout << "value = " << r3.value << "\n";
+    std::cout << "grad  = (" << r3.gradient[0] << ", " << r3.gradient[1] << ", " << r3.gradient[2] << ")\n";
+
+
+    return 0;
+}