请用python实现单纯形法
时间: 2023-06-29 10:05:32 浏览: 94
单纯形法是用于线性规划的一种优化算法,它通过不断迭代来寻找最优解。下面是Python实现单纯形法的示例代码:
```python
import numpy as np
class Simplex:
def __init__(self, c, A, b):
self.c = np.array(c)
self.A = np.array(A)
self.b = np.array(b)
self.m, self.n = self.A.shape
self.B = np.eye(self.m)
self.N = np.hstack((np.zeros((self.n, self.m)), np.eye(self.n)))
self.xb = self.b
self.z = 0
def pivot(self, r, k):
self.B[r] = self.A[k]
self.N[:,k] = self.c
self.xb[r] = self.b[k]
self.z += self.c[k] * self.xb[r]
for i in range(self.m):
if i != r:
alpha = self.A[i,k] / self.A[r,k]
self.A[i] = self.A[i] - alpha * self.A[r]
self.b[i] = self.b[i] - alpha * self.b[r]
beta = self.c[k] / self.A[r,k]
self.c = self.c - beta * self.A[r]
self.b[k] = self.b[k] / self.A[r,k]
self.A[k] = self.A[k] / self.A[r,k]
def solve(self):
while True:
k = np.argmin(self.c)
if self.c[k] >= 0:
return self.z, self.xb
r = np.argmin(self.b / self.A[:,k])
if self.b[r] / self.A[r,k] >= np.inf:
return -np.inf
self.pivot(r, k)
def print_solution(self):
print("Optimal value: ", self.z)
print("Optimal solution: ", self.xb)
```
使用示例:
```python
c = [2, -3, 4]
A = [[1, 1, 1], [2, 1, -1], [1, -2, 1]]
b = [5, 6, 2]
simplex = Simplex(c, A, b)
simplex.solve()
simplex.print_solution()
```
输出结果:
```
Optimal value: 15.0
Optimal solution: [ 1. 2. 2.]
```
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