all

227-3.py

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+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):
+    ks = 0.00000001
+    n = len(A)
+    if len(A[0]) != n:
+        raise ValueError("A要为方阵")
+    if len(b) != n:
+        raise ValueError("b与A的行数不匹配")
+    p = list(range(n))
+    for i in range(n):
+        row_max = abs(A[i][i])
+        row_max_index = i
+        for j in range(i + 1, n):
+            if abs(A[j][i]) > row_max:
+                row_max = abs(A[j][i])
+                row_max_index = j
+        A[i], A[row_max_index] = A[row_max_index], A[i]
+        b[i], b[row_max_index] = b[row_max_index], b[i]
+        p[i], p[row_max_index] = p[row_max_index], p[i]
+
+        if abs(A[i][i]) < ks:
+            raise ValueError("A矩阵奇异，无法进行高斯消元")
+        for j in range(i + 1, n):
+            m = A[j][i] / A[i][i]
+            A[j][i] = m
+            for k in range(i + 1, n):
+                A[j][k] -= m * A[i][k]
+            b[j] -= m * b[i]
+
+    if abs(A[n - 1][n - 1]) < ks:
+        raise ValueError("A矩阵奇异，无法进行高斯消元")
+    
+    # 回代求解
+    b[n - 1] /= A[n - 1][n - 1]
+    for i in range(n - 2, -1, -1):
+        for j in range(i + 1, n):
+            b[i] -= A[i][j] * b[j]
+        b[i] /= A[i][i]
+
+    # 得到L,U和P矩阵
+    L = [[0 for i in range(n)] for j in range(n)]
+    U = [[0 for i in range(n)] for j in range(n)]
+    P = [[0 for i in range(n)] for j in range(n)]
+    for i in range(n):
+        for j in range(n):
+            if i == j:
+                L[i][j] = 1
+                U[i][j] = A[i][j]
+            elif i < j:
+                U[i][j] = A[i][j]
+            else:
+                L[i][j] = A[i][j]
+
+        P[i][p[i]] = 1
+    return P,L,U,b
+
+def prettyPrintMatrix(matrix):
+    for row in matrix:
+        print(row)
+
+
+if __name__ == "__main__":
+    # A = np.array(A, dtype=float)
+    # b = np.array(b, dtype=float)
+    P,L,U,x = SovleRowMain(A, b)
+    print("P:")
+    prettyPrintMatrix(P)
+    print("L:")
+    prettyPrintMatrix(L)
+    print("U:")
+    prettyPrintMatrix(U)
+    print("x:")
+    print(x)
+