From b6def1d51698bc2bde2b40052206e94479c866ce Mon Sep 17 00:00:00 2001
From: Precreator <1689487228@qq.com>
Date: Thu, 26 Jun 2025 16:16:24 +0800
Subject: [PATCH] =?UTF-8?q?=E8=A1=A5=E5=85=A8=E4=BA=86autodiff.h=E7=9A=84?=
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---
 cc/operators/autodiff.h | 24 ++++++++++++++----------
 1 file changed, 14 insertions(+), 10 deletions(-)

diff --git a/cc/operators/autodiff.h b/cc/operators/autodiff.h
index a485db5..f250267 100644
--- a/cc/operators/autodiff.h
+++ b/cc/operators/autodiff.h
@@ -7,9 +7,13 @@
 namespace autodiff {
 
 template<typename T, typename F>
-auto central_difference(std::vector<T>& vec, F func, std::size_t arg, float epsilon = 1e-6) {
-    // 补全函数，并修改return语句
-    return 0;
+auto central_difference(std::vector<T>& vec, F func, std::size_t arg, float epsilon = 1e-6) -> decltype(func(vec))
+{
+    std::vector<T> vec1=vec;
+    std::vector<T> vec2=vec;
+    vec1[arg]+=epsilon;
+    vec2[arg]-=epsilon;
+    return (func(vec1)-func(vec2))/(2.0*epsilon);
 }
 
 class ScalarFunction {
@@ -40,11 +44,11 @@ public:
     }
     float forward() {
         // 修改这里的return
-        return 0;
+        return a->data+b->data;
     }
     std::vector<float> backward(float d_input) {
         // 修改这里的return
-        return {0, 0};
+        return {d_input, d_input};
     }
 }; // class Add
 
@@ -58,7 +62,7 @@ public:
     }
     float forward() {
         // 补全这里的return语句
-        return 0.0f;
+        return logf(a->data);
     }
     std::vector<float> backward(float d_input) {
         // 算了，我来帮你写求导的部分吧
@@ -78,11 +82,11 @@ public:
     }
     float forward() {
         // 修改这里的return
-        return 0;
+        return 1.0f* (a->data)*(b->data);
     }
     std::vector<float> backward(float d_input) {
         // 修改这里的return
-        return {0, 0};
+        return {1.0f*b->data, 1.0f*a->data};
     }
 }; // class Mul
 
@@ -100,7 +104,7 @@ public:
     std::vector<float> backward(float d_input) {
         // 修改这里的return语句
         // 1/x求导是-1/x^2
-        return {0.0f};
+        return {1.0f*d_input/(a->data*a->data)};
     }
 }; // class Inv
 
@@ -123,7 +127,7 @@ public:
     std::vector<float> backward(float d_input) {
         // 你还是来求一下导吧，预防上大学以后变傻了
         // 补全这里的代码
-        return {0.0f};
+        return {1.0f*d_input*expf(-this->a->data)/((1-expf(-this->a->data))*(1-expf(-this->a->data)))};
     }
 }; // class Sigmoid