python单纯形法代码

你好，以下是一个使用Python实现单纯形法求解线性规划问题的示例代码：

import numpy as np

def simplex_method(c, A, b):
    m, n = A.shape
    c = np.concatenate([c, [0]])
    A = np.concatenate([A, np.eye(m)], axis=1)
    z = np.zeros(n + 1)
    B = np.arange(n, n + m)

    while True:
        cb = c[B]
        Ab = A[:, B]
        y = cb @ Ab
        cn = c - y @ A
        if np.all(cn >= 0):
            break
        j0 = np.argmin(cn)
        Aj0 = A[:, j0]
        if np.all(Aj0 <= 0):
            return np.inf, None
        xB = np.linalg.solve(Ab, b)
        q = xB / Aj0
        i0 = np.argmin(q)
        x0 = q[i0]
        B[i0] = j0

    xB = np.linalg.solve(A[:, B], b)
    x = np.zeros(n)
    x[B] = xB

    return c @ x, x

使用方法如下：

c = np.array([1, 2, 3])
A = np.array([[1, 2, 2],
              [2, 1, 2],
              [2, 2, 1]])
b = np.array([20, 20, 20])

z, x = simplex_method(c, A, b)
print(f"最优解: {x}")
print(f"最优值: {z}")

以上示例代码实现了求解如下线性规划问题：

   maximize   1*x1 + 2*x2 + 3*x3
   subject to x1 + 2*x2 + 2*x3 <= 20
              2*x1 + 1*x2 + 2*x3 <= 20
              2*x1 + 2*x2 + 1*x3 <= 20
              x1, x2, x3 >= 0