feat: 后向自动微分

include/types/common.hpp

@@ -1,9 +1,9 @@
 /*返回数据结构体*/
+#pragma once
+#include <functional>
 #include <vector>
 
-namespace forwardad{
-    struct Result{
-        double value; // 函数值
-        std::vector<double> gradient; // 梯度
-    };
-}
+struct ADResult{
+    double value; // 函数值
+    std::vector<double> gradient; // 梯度
+};

include/types/dual.hpp

@@ -1,5 +1,9 @@
 /*对偶数的数据类型定义部分*/
 #pragma once
+#include <iostream>
+#include <functional>
+#include <memory>
+#include <vector>
 
 namespace forwardad {
 struct Dual {
@@ -9,4 +13,43 @@ struct Dual {
     Dual(double v = 0.0, double d = 0.0) : value(v), deriv(d) {}
 
 };
-} // namespace forwardad
+} // namespace forwardad
+
+namespace backwardad{
+    struct NodeData;
+
+    struct Node{
+        std::shared_ptr<NodeData> ptr;
+
+        Node() = default;
+        explicit Node(double v);
+
+        double value() const;
+        double gradient() const;
+        void add_gradient(double g) const;
+        void set_gradient(double g) const;
+        const std::vector<Node>& inputs() const;
+        std::vector<Node>& inputs();
+        std::function<void()>& backward();
+        const std::function<void()>& backward() const;
+    };
+
+    struct NodeData {
+        double value;
+        double gradient;
+        std::vector<Node> inputs;
+        std::function<void()> backward;
+
+        explicit NodeData(double v) : value(v), gradient(0.0) {}
+    };
+
+    inline Node::Node(double v) : ptr(std::make_shared<NodeData>(v)) {}
+    inline double Node::value() const { return ptr->value; }
+    inline double Node::gradient() const { return ptr->gradient; }
+    inline void Node::add_gradient(double g) const { ptr->gradient += g; }
+    inline void Node::set_gradient(double g) const { ptr->gradient = g; }
+    inline const std::vector<Node>& Node::inputs() const { return ptr->inputs; }
+    inline std::vector<Node>& Node::inputs() { return ptr->inputs; }
+    inline std::function<void()>& Node::backward() { return ptr->backward; }
+    inline const std::function<void()>& Node::backward() const { return ptr->backward; }
+} // namespace backwardad