python单纯形法代码
时间: 2023-10-14 18:29:22 浏览: 82
以下是python单纯形法的代码示例:
```python
import numpy as np
def simplex(c, A, b):
"""
Implementation of the simplex algorithm for linear programming.
:param c: 1D array of coefficients for objective function to be maximized
:param A: 2D array of coefficients for constraints (left-hand side)
:param b: 1D array of coefficients for constraints (right-hand side)
:return: tuple (objective value, optimal solution)
"""
# Convert everything to numpy arrays
c = np.array(c, dtype=float)
A = np.array(A, dtype=float)
b = np.array(b, dtype=float)
# Check if any constraints are of the form Ax <= b rather than Ax = b
if np.any(b < 0):
A = np.vstack([A, -A])
b = np.concatenate([b, -b])
c = np.concatenate([c, np.zeros_like(c)])
# Add slack variables to convert inequalities to equalities
m, n = A.shape
c = np.concatenate([c, np.zeros(m)])
A = np.hstack([A, np.eye(m)])
basis = np.arange(n, n+m)
while True:
# Compute reduced costs
r = c - np.dot(A.T, np.dot(basis, c))
# Check optimality
if np.all(r <= 0):
break
# Choose entering variable
i = np.argmax(r)
# Check unboundedness
if np.all(A[:, i] <= 0):
return np.inf, None
# Choose leaving variable
t = np.argmin(b / A[:, i])
basis[t] = i
# Update tableau
A[t, :] /= A[t, i]
b[t] /= A[t, i]
for j in range(m):
if j != t:
A[j, :] -= A[j, i] * A[t, :]
b[j] -= A[j, i] * b[t]
c -= r[i] * A[t, :]
# Extract optimal solution and return
x = np.zeros(n)
x[basis < n] = b[basis < n]
return np.dot(c[:n], x), x
```
该函数可以接受三个参数:系数向量 c、系数矩阵 A 和常数向量 b,其中 c 在这里是线性规划的目标函数的系数,A 是约束条件的系数矩阵,b 是约束条件的右端项向量。该函数返回一个元组,其中第一个元素是线性规划问题的最优目标函数值,第二个元素是最优解。