chore: 添加散度

include/backwardad.hpp

@@ -51,6 +51,17 @@ ADResult diff(const Func f, Args... args) {
     for (auto& in : inputs)
         res.gradient.push_back(in.gradient());
 
+    // 散度
+    res.divergence = 0.0;
+    for (const auto& g : res.gradient)        res.divergence += g;
+
+    // 旋度
+    // 标量场的旋度始终为0
+    res.curl.resize(inputs.size());
+    for (size_t i = 0; i < inputs.size(); ++i) {
+        res.curl[i] = 0.0; // 标量场的旋度为0
+    }
+
     return res;
 }
 } // namespace backwardad

include/forwardad.hpp

@@ -18,6 +18,8 @@ ADResult diff(const Func& f, Args... args) {
 
     // 2. 对每个输入变量求偏导（seed 依次设为 1）
     double args_arr[] = { (double)args... };
+
+    // 梯度
     [&]<size_t... Is>(std::index_sequence<Is...>) {
         ([&]() {
             // 创建 Dual 输入，第 Is 个变量导数=1，其余=0
@@ -31,6 +33,22 @@ ADResult diff(const Func& f, Args... args) {
         }(), ...);
     }(std::make_index_sequence<N>{});
 
+    // 散度
+    res.divergence = 0.0;
+    [&]<size_t... Is>(std::index_sequence<Is...>) {
+        ([&]() {
+            res.divergence += [&]<size_t... Js>(std::index_sequence<Js...>) {
+                return res.gradient[Is]; // 这里直接用梯度值，因为散度是梯度的和
+            }(std::make_index_sequence<N>{});
+        }(), ...);
+    }(std::make_index_sequence<N>{});
+
+    // 旋度
+    // 标量场的旋度始终为0
+    res.curl.resize(N);
+    for (size_t i = 0; i < N; ++i) {
+        res.curl[i] = 0.0; // 标量场的旋度为0
+    }
     return res;
 }
 } // namespace forwardad

include/types/common.hpp

@@ -6,4 +6,6 @@
 struct ADResult{
     double value; // 函数值
     std::vector<double> gradient; // 梯度
+    std::vector<double> curl; // 旋度
+    double divergence; // 散度 
 };

tests/test_backward.cpp

@@ -21,16 +21,23 @@ int test_backward_ad() {
     auto r = backwardad::diff(f2, 2.0);
     std::cout << "value = " << r.value << "\n";
     std::cout << "grad  = " << r.gradient[0] << "\n";
+    std::cout << "div   = " << r.divergence << "\n";
+    std::cout << "curl  = " << r.curl[0] << "\n";
 
     std::cout << "\nTesting g(x,y) = exp(x)*log(y) at (x,y)=(1.0, 2.0)\n";
     auto r2 = backwardad::diff(g2, 1.0, 2.0);
     std::cout << "value = " << r2.value << "\n";
     std::cout << "grad  = (" << r2.gradient[0] << ", " << r2.gradient[1] << ")\n";
+    std::cout << "div   = " << r2.divergence << "\n";
+    std::cout << "curl  = (" << r2.curl[0] << ", " << r2.curl[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 = backwardad::diff(h2, 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";
+    std::cout << "div   = " << r3.divergence << "\n";
+    std::cout << "curl  = (" << r3.curl[0] << ", " << r3.curl[1] << ", " << r3.curl[2] << ")\n";
+
     return 0;
 }
 

tests/test_forward.cpp

@@ -21,16 +21,22 @@ int test_forward_ad() {
     auto r = forwardad::diff(f1, 2.0);
     std::cout << "value = " << r.value << "\n";
     std::cout << "grad  = " << r.gradient[0] << "\n";
+    std::cout << "div   = " << r.divergence << "\n";
+    std::cout << "curl  = " << r.curl[0] << "\n";
 
     std::cout << "\nTesting g(x,y) = exp(x)*log(y) at (x,y)=(1.0, 2.0)\n";
     auto r2 = forwardad::diff(g1, 1.0, 2.0);
     std::cout << "value = " << r2.value << "\n";
     std::cout << "grad  = (" << r2.gradient[0] << ", " << r2.gradient[1] << ")\n";
+    std::cout << "div   = " << r2.divergence << "\n";
+    std::cout << "curl  = (" << r2.curl[0] << ", " << r2.curl[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 = forwardad::diff(h1, 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";
+    std::cout << "div   = " << r3.divergence << "\n";
+    std::cout << "curl  = (" << r3.curl[0] << ", " << r3.curl[1] << ", " << r3.curl[2] << ")\n";
     return 0;
 }