From 998a705b341a9483174a4418f5f7cd62e7e204ab Mon Sep 17 00:00:00 2001
From: Xcreate672 <3534270192@qq.com>
Date: Sat, 6 Jun 2026 15:51:33 +0800
Subject: [PATCH 1/3] =?UTF-8?q?=E6=94=B9=E6=88=90=E5=AF=B9=E8=B1=A1?=
 =?UTF-8?q?=E6=A0=BC=E5=BC=8F=20Update=20ignore=5Fusers.json?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
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改成对象格式
---
 ignore_users.json | 11 +++++++----
 1 file changed, 7 insertions(+), 4 deletions(-)

diff --git a/ignore_users.json b/ignore_users.json
index ed695fe839..584595373e 100644
--- a/ignore_users.json
+++ b/ignore_users.json
@@ -1,5 +1,8 @@
 [
-    "Haidong Wang",
-    "donghaiwang",
-    "whd@hutb.edu.cn"
-]
\ No newline at end of file
+    {
+        "name": "Haidong Wang",
+        "github": "donghaiwang",
+        "email": "whd@hutb.edu.cn",
+        "role": "author"
+    }
+]

From 97797c0c66da04312ff80b24a22c7732fdd6253e Mon Sep 17 00:00:00 2001
From: Xcreate672 <3534270192@qq.com>
Date: Tue, 9 Jun 2026 15:10:59 +0800
Subject: [PATCH 2/3] =?UTF-8?q?Update=20gaussian=5Fmixture.md=E8=A1=A5?=
 =?UTF-8?q?=E5=85=85=E9=AB=98=E6=96=AF=E6=B7=B7=E5=90=88=E6=A8=A1=E5=9E=8B?=
 =?UTF-8?q?=E5=85=AC=E5=BC=8F=E4=B8=8E=E4=BB=A3=E7=A0=81=E7=A4=BA=E4=BE=8B?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

补充高斯混合模型公式与代码示例
---
 docs/gaussian_mixture.md | 31 +++++++++++++++++++++++++++++++
 1 file changed, 31 insertions(+)

diff --git a/docs/gaussian_mixture.md b/docs/gaussian_mixture.md
index 4f2ea7cbce..5bc0e45fb0 100644
--- a/docs/gaussian_mixture.md
+++ b/docs/gaussian_mixture.md
@@ -44,3 +44,34 @@
 - 异常检测
 - 图像分割
 - 语音识别
+- 
+## 数学公式
+
+GMM 的概率密度函数为：
+
+`p(x) = Σ π_k * N(x | μ_k, Σ_k)`
+
+其中：
+- K 为高斯成分数量
+- π_k 为第 k 个成分的混合权重，满足 Σπ_k = 1
+- N(x | μ_k, Σ_k) 为第 k 个高斯分布
+
+## 代码示例
+
+使用 scikit-learn 拟合高斯混合模型：
+
+```python
+from sklearn.mixture import GaussianMixture
+import numpy as np
+
+# 生成示例数据
+X = np.random.randn(300, 2)
+
+# 创建并训练模型
+gmm = GaussianMixture(n_components=3, random_state=0)
+gmm.fit(X)
+
+# 预测类别
+labels = gmm.predict(X)
+print("各成分权重:", gmm.weights_)
+```

From 785fb2c1c2690ec0db1f8810415d8191fb4ff719 Mon Sep 17 00:00:00 2001
From: Xcreate672 <3534270192@qq.com>
Date: Wed, 10 Jun 2026 23:05:40 +0800
Subject: [PATCH 3/3] =?UTF-8?q?=E8=A1=A5=E5=85=85=E7=83=AD=E8=BA=AB?=
 =?UTF-8?q?=E7=A4=BA=E4=BE=8B=E9=A2=84=E6=9C=9F=E8=BE=93=E5=87=BA=E4=B8=8E?=
 =?UTF-8?q?=E5=B8=B8=E8=A7=81=E9=97=AE=E9=A2=98=20Update=20warmup.md?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

补充热身示例预期输出与常见问题
---
 docs/warmup.md | 24 ++++++++++++++++++++++++
 1 file changed, 24 insertions(+)

diff --git a/docs/warmup.md b/docs/warmup.md
index 95aa32aa8d..5c7803a2d4 100644
--- a/docs/warmup.md
+++ b/docs/warmup.md
@@ -33,3 +33,27 @@ python src/chap01_warmup/numpy_tutorial.py
 ## 完整代码
 
 [完整代码](https://github.com/OpenHUTB/nn/blob/main/src/chap01_warmup/numpy_tutorial.py)
+
+## 预期输出
+
+运行后终端会依次输出：
+数组形状: (5,)
+矩阵乘法结果: [[19 22] [43 50]]
+切片结果: [2 3 4]
+同时弹出 sin(x) 函数图像窗口。
+
+## 常见问题
+
+**Q：运行报错 `ModuleNotFoundError: No module named 'numpy'`**
+
+执行以下命令安装依赖：
+```bash
+pip install numpy matplotlib
+```
+
+**Q：图像窗口不弹出**
+
+在代码末尾将 `plt.show()` 改为：
+```python
+plt.savefig('output.png')
+```