python - 解释为什么会发生错误：ValueError: 输入数组的所有大小，除了连接轴，必须完全匹配

Question

我正在使用scipy.optimize.minimize在 Python 中优化一个函数。我按照文档中的示例编写了代码：

import numpy as np
from scipy.optimize import minimize
# I set bounds and constraints
bnds = ((10e-6, 2000), (10e-6, 16000), (10e-6, 120), (10e-6, 5000), (10e-6, 2000), (85, 93), (90, 95), (3, 12), (1.2, 4), (145, 162))

eq_cons = {'type': 'eq',
           'fun': lambda x: np.array([1.22 * x[3] - x[0] - x[4],
                                      (98000 * x[2]) / x[3] * x[8] + 1000 * x[2] - x[5],
                                      ((x[1] + x[4]) / x[0]) - x[7]]),
           'jac': lambda x: np.array([[1.22, -1, -1],
                                      [98000, 1, 1, 1000, -1],
                                      [1, 1, 1, -1]])
           }
ineq_cons = {'type': 'ineq',
            'fun': lambda x: np.array([x[0] * (1.12 + 0.13167 * x[7] - 0.0067 * x[7] ** 2) - 0.99 * x[3],
                                       -(x[0] * (1.12 + 0.13167 * x[7] - 0.0067 * x[7] ** 2) + (100 / 99) * x[3]),
                                       (86.35 + 1.098 * x[7] - 0.038 * x[7] ** 2 + 0.325 * (x[5] - 89)) - 0.99 * x[6],
                                       -(86.35 + 1.098 * x[7] - 0.038 * x[7] ** 2 + 0.325 * (x[5] - 89)) + (100 / 99) * x[6],
                                       (35.82 - 0.222 * x[9]) - 0.9 * x[8],
                                       -(35.82 - 0.222 * x[9]) + (10 / 9) * x[8],
                                       (-133 + 3 * x[6]) - 0.99 * x[9],
                                       -(-133 + 3 * x[6]) + (100 / 99) * x[9]]),
            'jac': lambda x: np.array([[1, 0, 0.13167, -0.0134 * x[7], -0.99],
                                       [-1, 0, -0.13167, 0.0134 * x[7], -(100 / 99)],
                                       [0, 1.098, -0.076 * x[7], 0.325, -0.99],
                                       [0, -1.098, 0.076 * x[7], -0.325, -(100 / 99)],
                                       [0, -0.222, -0.9],
                                       [0, 0.222, -(10 / 9)],
                                       [0, 3, -0.99],
                                       [0, -3, -(100 / 99)]])
            }
# I set the initial values of variables
x0 = np.array([1745, 12000, 110, 3048, 1974, 89.2, 92.8, 8, 3.6, 145])

def f(x):
    return 0.063 * x[3] * x[6] - 5.04 * x[0] - 0.035 * x[1] - 10 * x[2] - 3.36 * x[4]


res = minimize(f, x0, method='SLSQP', constraints=[ineq_cons, eq_cons], bounds=bnds, options={'ftol': 1e-9, 'disp': True})
print(res.x)

这是回溯：

Traceback (most recent call last):
  File "C:\Users\user\Desktop\Python\optimize.py", line 41, in <module>
    res = minimize(f, x0, method='SLSQP', constraints=[ineq_cons, eq_cons], bounds=bnds, options={'ftol': 1e-9, 'disp': True})
  File "C:\Anaconda3\lib\site-packages\scipy\optimize\_minimize.py", line 611, in minimize
    constraints, callback=callback, **options)
  File "C:\Anaconda3\lib\site-packages\scipy\optimize\slsqp.py", line 422, in _minimize_slsqp
    a = vstack((a_eq, a_ieq))
  File "C:\Anaconda3\lib\site-packages\numpy\core\shape_base.py", line 234, in vstack
    return _nx.concatenate([atleast_2d(_m) for _m in tup], 0)
ValueError: all the input array dimensions except for the concatenation axis must match exactly

当我不在 eq_cons 和 ineq_cons 中使用 jac 时，计算会进行，但不正确。我得到输出：

C:\Anaconda3\python.exe C:\Users\user\Desktop\Python\optimize.py
Positive directional derivative for linesearch    (Exit mode 8)
            Current function value: 0.00610273865507208
            Iterations: 82
            Function evaluations: 1050
            Gradient evaluations: 78
     fun: 0.00610273865507208
     jac: array([-5.04000000e+00, -3.49999999e-02, -1.00000000e+01,  5.98500000e+00,
       -3.36000000e+00,  0.00000000e+00,  4.70466912e-04,  0.00000000e+00,
        0.00000000e+00,  0.00000000e+00])
 message: 'Positive directional derivative for linesearch'
    nfev: 1050
     nit: 82
    njev: 78
  status: 8
 success: False
       x: array([3.91761754e-03, 3.69776009e-02, 1.00000000e-05, 7.46772900e-03,
       5.19422947e-03, 9.30000000e+01, 9.50000000e+01, 1.10436932e+01,
       1.56130612e+00, 1.53536361e+02])

维度有什么问题？我不明白哪些数组的维度不匹配以及如何修复它？

标签： pythonnumpyscipyvalueerror