python - ValueError : setting an array element with a sequence. 函数可以单独正常工作，但在另一个函数中使用时会导致错误

Question

def netwon(f, J, p0, tol):
    for i in range(1,51):
        p = p0 - J(p0)/f(p0)
        if la.norm(p - p0) < tol:
            break
        p0 = p
    return p

def JJ(x):
    J = np.identity(4)
    u = sum(x)
    for i in range(0,4):
        for j in range(0,4):
            J[i][j] = J[i][j] + ((np.e**(np.cos(u))) * (np.sin(u)))
    return J

调用 newton 时抛出此错误消息:

netwon(f, JJ, [2.5, 2, 1.4, 9], 1*10**-12)
-
ValueError                                Traceback (most recent call last)
<ipython-input-58-b80f7ad38c88> in <module>()
----> 1 netwon(f, JJ, [2.5, 2, 1.4, 9], 1*10**-12)

<ipython-input-44-ae7c3122a6cf> in netwon(f, J, p0, tol)
      1 def netwon(f, J, p0, tol):
      2     for i in range(1,51):
----> 3         p = p0 - (J(p0)/f(p0))
      4         if la.norm(p - p0) < tol:
      5             break

<ipython-input-53-17a5f32512be> in JJ(x)
      4     for i in range(0,4):
      5         for j in range(0,4):
----> 6             J[i][j] = J[i][j] + ((np.e**(np.cos(u))) * (np.sin(u)))
      7     return J

ValueError: setting an array element with a sequence.

我可以单独使用JJ:

JJ([2.5, 2, 1.4, 9])
array([[1.36222766, 0.36222766, 0.36222766, 0.36222766],
       [0.36222766, 1.36222766, 0.36222766, 0.36222766],
       [0.36222766, 0.36222766, 1.36222766, 0.36222766],
       [0.36222766, 0.36222766, 0.36222766, 1.36222766]])

有人可以发现我的错误吗，我不明白为什么 JJ 可以单独工作，但在另一个函数中使用时会导致错误。

谢谢

Answer 1

问题在于牛顿函数第一次和第二次迭代之间 p0 的形状。在第一次中，它是一个一维数组 (4,)，但它被重新分配给一个二维数组 (4,4)。当输入二维数组时，JJ 会失败，因为 sum 函数不会将二维数组折叠为单个值，而是将其折叠为一维数组。
附言。我使用虚拟 f 函数，因为未提供原始 f 函数，但我认为 f 函数不会导致结果 p0 的形状发生变化。

import numpy as np

def f(x):
    return 1

def netwon(f, J, p0, tol):
    for i in range(1,51):
        p = p0 - J(p0)/f(p0)

#        if la.norm(p - p0) < tol:
        if i ==1: #at first iteration, p0 which used to be a (4,) array will be replaced with a (4,4)
            global inspect
            inspect = p
            break
        p0 = p
    return p

def JJ(x):
    J = np.identity(4)
    u = sum(x)
    for i in range(0,4):
        for j in range(0,4):
            J[i][j] = J[i][j] + ((np.e**(np.cos(u))) * (np.sin(u)))
    return J

a = [2.5, 2, 1.4, 9]
netwon(f, JJ, a, 1*10**-12)
#fine till here
print(inspect) #no longer a (4,) array. It is now a (4,4)
print(sum(inspect)) #no longer a single value, but a (4,) array
u = sum(inspect)
((np.e**(np.cos(u))) * (np.sin(u))) #no longer a single value.

# J[i][j] = J[i][j] + ((np.e**(np.cos(u))) * (np.sin(u))) #1 location is now attempting to be assigned with an array
JJ(inspect) #will result in error.