From e1929eaac4b3a880781800bec7bfa0abc6e2f543 Mon Sep 17 00:00:00 2001
From: Zihan <32484940+wzh4464@users.noreply.github.com>
Date: Mon, 17 Jun 2024 17:11:40 +0800
Subject: [PATCH] math equations

---
 add_ctexart_comment.py      | 42 +++++++++++++++++++++++++++++++++++++
 cocluster_note/Cocluster.md |  8 +++----
 2 files changed, 45 insertions(+), 5 deletions(-)
 create mode 100644 add_ctexart_comment.py

diff --git a/add_ctexart_comment.py b/add_ctexart_comment.py
new file mode 100644
index 0000000..ed44451
--- /dev/null
+++ b/add_ctexart_comment.py
@@ -0,0 +1,42 @@
+import glob
+
+###
+ # File: /add_ctexart_comment.py
+ # Created Date: Monday, June 17th 2024
+ # Author: Zihan
+ # -----
+ # Last Modified: Monday, 17th June 2024 4:31:23 pm
+ # Modified By: the developer formerly known as Zihan at <wzh4464@gmail.com>
+ # -----
+ # HISTORY:
+ # Date      		By   	Comments
+ # ----------		------	---------------------------------------------------------
+###
+
+# Find all Markdown files recursively
+md_files = glob.glob('**/*.md', recursive=True)
+
+# Comment to be added
+comment = '''---
+toc: true
+documentclass: "ctexart"
+classoption: "UTF8"
+---
+'''
+
+# Add the comment to each file
+for file in md_files:
+  with open(file, 'r+') as f:
+    content = f.read()
+    f.seek(0, 0)
+    f.write(comment + content)
+
+# delete first blank lines
+# for file in md_files:
+#   with open(file, 'r+') as f:
+#     content = f.readlines()
+#     f.seek(0, 0)
+#     for line in content:
+#       if line.strip() != '':
+#         f.write(line)
+#     f.truncate()
\ No newline at end of file
diff --git a/cocluster_note/Cocluster.md b/cocluster_note/Cocluster.md
index ed8deec..4f92306 100644
--- a/cocluster_note/Cocluster.md
+++ b/cocluster_note/Cocluster.md
@@ -100,9 +100,7 @@ $$\min_{Z^\top D Z = I} \mathrm{Tr} (Z^\top L Z)$$
 优化目标成为
 
 $$
-\begin{equation}
 \max_{U^\top U + V^\top V = I} \mathrm{Tr} (O)
-\end{equation}
 $$
 
 ### Proof
@@ -137,7 +135,9 @@ $$
 $$Z^\top L Z = I - O - O^\top$$
 $$Z^\top D Z = U^\top U + V^\top V = I$$
 则直接计算有
-$$\begin{equation}\max_{U^\top U + V^\top V = I} \mathrm{Tr} (O)\end{equation}$$
+$$
+\max_{U^\top U + V^\top V = I} \mathrm{Tr} (O)
+$$
 
 ### Lemma 连续情况的优化
 
@@ -148,12 +148,10 @@ $$
 其中$M \in \mathbb{R}^{n_1 \times n_2}$,$X \in \mathbb{R}^{n_1 \times k}$,$Y \in \mathbb{R}^{n_2 \times k}$.
 那么其解为
 $$
-\begin{equation}
 \begin{cases}
 X = \frac{\sqrt{2}}{2} U_1 \\
 Y = \frac{\sqrt{2}}{2} V_1
 \end{cases}
-\end{equation}
 $$
 其中,$U_1$和$V_1$是$M$前$k$个最大的奇异值对应的左右奇异向量.
 > Proof: