From 89ad8d0f1f1a9a05df5e70db25bb323394847028 Mon Sep 17 00:00:00 2001
From: 123 <629825095@qq.com>
Date: Tue, 10 Jun 2025 14:27:18 +0800
Subject: [PATCH] 111

---
 1.py      |  0
 160-11.py |  1 +
 160-12.py |  1 +
 227-3.py  | 21 ++++++++++++---------
 227-4.py  | 11 ++++++-----
 227-7.py  | 22 +++++++++++-----------
 227-8.py  |  4 ++--
 228-12.py |  3 ++-
 228-13.py |  3 ++-
 228-15.py |  9 +++++----
 228-17.py |  3 ++-
 279-3.py  |  2 +-
 12 files changed, 45 insertions(+), 35 deletions(-)
 create mode 100644 1.py

diff --git a/1.py b/1.py
new file mode 100644
index 0000000..e69de29
diff --git a/160-11.py b/160-11.py
index 5a06fe6..9e8d44c 100644
--- a/160-11.py
+++ b/160-11.py
@@ -1,3 +1,4 @@
+#正割法计算方程
 def SecantSolve(fx, x0, x1, err=1e-10, N0=100):
     count = 0
     print(f"k={count}: x{count}={x0}, f(x{count})={fx(x0)}")
diff --git a/160-12.py b/160-12.py
index 06666a7..50335c5 100644
--- a/160-12.py
+++ b/160-12.py
@@ -1,3 +1,4 @@
+#抛物线法解方程（主）
 def MullerSolve(fx,x0,x1,x2,err1,err2,N):
     count = 0
     f0 = fx(x0)
diff --git a/227-3.py b/227-3.py
index 9f18459..c56f62c 100644
--- a/227-3.py
+++ b/227-3.py
@@ -1,10 +1,3 @@
-A = [
-    [0, 3, 4],
-    [1, -1, 1],
-    [2, 1, 2]
-]
-
-b = [1, 2, 3]
 
 # 列主元高斯消元法
 def SovleRowMain(A,b):
@@ -61,7 +54,7 @@ def SovleRowMain(A,b):
 
         P[i][p[i]] = 1
     return P,L,U,b
-
+#打印矩阵
 def prettyPrintMatrix(matrix):
     for row in matrix:
         print(row)
@@ -70,6 +63,15 @@ def prettyPrintMatrix(matrix):
 if __name__ == "__main__":
     # A = np.array(A, dtype=float)
     # b = np.array(b, dtype=float)
+      
+    A = [
+        [0, 3, 4],
+        [1, -1, 1],
+        [2, 1, 2]
+    ]
+
+    b = [1, 2, 3]
+
     P,L,U,x = SovleRowMain(A, b)
     print("P:")
     prettyPrintMatrix(P)
@@ -79,4 +81,5 @@ if __name__ == "__main__":
     prettyPrintMatrix(U)
     print("x:")
     print(x)
-    
\ No newline at end of file
+        
+ 
\ No newline at end of file
diff --git a/227-4.py b/227-4.py
index 94390e1..115fa58 100644
--- a/227-4.py
+++ b/227-4.py
@@ -1,8 +1,3 @@
-# 储存下三角矩阵 a11, a21, a22, a31, a32, a33 ...
-A = [4,2,2,-2,-3,14]
-
-
-b = [10,5,4]
 
 #列 行
 def getIndexFromDownMatrix(col, row):
@@ -41,5 +36,11 @@ def SqrtSolve(A,b):
 
 
 if __name__ == "__main__":
+    # 储存下三角矩阵 a11, a21, a22, a31, a32, a33 ...
+    A = [4,2,2,-2,-3,14]
+
+
+    b = [10,5,4]
+
     print("x:")
     print(SqrtSolve(A,b))
diff --git a/227-7.py b/227-7.py
index a28d919..05e1cd2 100644
--- a/227-7.py
+++ b/227-7.py
@@ -1,14 +1,3 @@
-# 储存追赶法A矩阵
-A = [
-    [0,4,-1],
-    [-1,4,-1],
-    [-1,4,-1],
-    [-1,4,-1],
-    [-1,4,0]
-]
-
-
-b = [100,200,200,200,100]
 
 # 追赶法求解
 def ZGsolve(A,b):
@@ -33,5 +22,16 @@ def ZGsolve(A,b):
 
 
 if __name__ == "__main__":
+    # 储存追赶法A矩阵
+    A = [
+        [0,4,-1],
+        [-1,4,-1],
+        [-1,4,-1],
+        [-1,4,-1],
+        [-1,4,0]
+    ]
+
+
+    b = [100,200,200,200,100]
     print("x:")
     print(ZGsolve(A,b))
\ No newline at end of file
diff --git a/227-8.py b/227-8.py
index f72283b..e31aa58 100644
--- a/227-8.py
+++ b/227-8.py
@@ -1,4 +1,4 @@
-
+#模 范数
 def Norm(x,v):
     if len(x[0]) == 1:
         if v == 1:
@@ -13,7 +13,7 @@ def Norm(x,v):
         elif v == float("inf"):
             return max([sum([abs(i) for i in x[j]]) for j in range(len(x))])
     return None
-
+# 计算矩阵的点积
 def Dot(A,B):
     if len(A[0]) != len(B):
         return None
diff --git a/228-12.py b/228-12.py
index d09e170..dde776c 100644
--- a/228-12.py
+++ b/228-12.py
@@ -1,3 +1,4 @@
+#抛物线法解方程
 def MullerSolve(fx,x0,x1,x2,err1,err2,N):
     count = 0
     f0 = fx(x0)
@@ -40,7 +41,7 @@ def MullerSolve(fx,x0,x1,x2,err1,err2,N):
         f1 = f2
         f2 = f3
         q = h1
-
+#计算矩阵的行列式
 def Det(A):
     if len(A) == 2:
         return A[0][0] * A[1][1] - A[0][1] * A[1][0]
diff --git a/228-13.py b/228-13.py
index 9e458b6..a6e2525 100644
--- a/228-13.py
+++ b/228-13.py
@@ -1,3 +1,4 @@
+#模 范数
 def Norm(x,v):
     if len(x[0]) == 1:
         if v == 1:
@@ -12,7 +13,7 @@ def Norm(x,v):
         elif v == float("inf"):
             return max([sum([abs(i) for i in x[j]]) for j in range(len(x))])
     return None
-
+#SOR方法 逐次超松弛迭代
 def SOR(A,b,x,w,err,N):
     count = 0
     n = len(A)
diff --git a/228-15.py b/228-15.py
index 1693e0a..2590a04 100644
--- a/228-15.py
+++ b/228-15.py
@@ -1,4 +1,5 @@
-def Norm(x,v):
+#模 范数
+def Norm(x,v):    
     if len(x[0]) == 1:
         if v == 1:
             return sum([abs(i[0]) for i in x])
@@ -13,7 +14,7 @@ def Norm(x,v):
             return max([sum([abs(i) for i in x[j]]) for j in range(len(x))])
     return None
 
-
+# 计算矩阵的行列式
 def Det(A):
     if len(A) == 2:
         return A[0][0] * A[1][1] - A[0][1] * A[1][0]
@@ -22,7 +23,7 @@ def Det(A):
         sub_matrix = [row[:c] + row[c+1:] for row in A[1:]]
         det += ((-1) ** c) * A[0][c] * Det(sub_matrix)
     return det
-
+# 计算矩阵的逆矩阵
 def Inverse(A):
     n = len(A)
     # 计算代数余子式矩阵
@@ -38,7 +39,7 @@ def Inverse(A):
         return None
     A_inv = [[B[i][j] / det for j in range(n)] for i in range(n)]
     return A_inv
-
+# 计算矩阵的条件数
 def Cond(A,v):
     inv_A = Inverse(A)
     print(inv_A,Norm(A, v), Norm(inv_A, v))
diff --git a/228-17.py b/228-17.py
index 9399933..9b80816 100644
--- a/228-17.py
+++ b/228-17.py
@@ -1,3 +1,4 @@
+#列主元高斯消元法
 def SovleRowMain(A,b,round_num=15):
     ks = 0.00000001
     n = len(A)
@@ -56,7 +57,7 @@ def SovleRowMain(A,b,round_num=15):
 
         P[i][p[i]] = 1
     return P,L,U,b
-
+#迭代改善法
 def IterativeMethod(A, b, err, N):
     b_c = [b[i] for i in range(len(b))]
     A_c = [[A[i][j] for j in range(len(A[0]))] for i in range(len(A))]
diff --git a/279-3.py b/279-3.py
index 20b49b1..9c81095 100644
--- a/279-3.py
+++ b/279-3.py
@@ -1,4 +1,4 @@
-#
+#经典R-K，龙格-库塔法
 def ClassicRK(x0,y0,h,xk,fxy):
     k1=k2=k3=k4=0
     result = [(x0,y0)]