当使用内部函数时，Python操作数不能与形状（42，）（21，）一起广播形状不应该改变，但它会改变

Question

我想计算内部函数的积分

def H(x, z):

位于外部功能内

def integral_P_Vm(z):

有虚部的。以下是完整的代码：

from scipy.integrate import quad
import numpy as np
from scipy import interpolate
import quadpy

input="-0.5 0.0 \
-0.3 0.9    \
0.0 0.8 \
0.3 0.4 \
0.5 0.02"

input_coordinates = np.genfromtxt(input.splitlines()).reshape(-1,2) # shape to 2 columns, any number of rows
x_coordinates = input_coordinates[:,0]
H_values = input_coordinates[:,1]
H_interpolation = interpolate.InterpolatedUnivariateSpline(x_coordinates, H_values)

def k_x(z, M_r):
    print("k_x(z, M_r)")
    return (2)/(M_r(z))

def H(x, z):
    print("H(x, z)")
    print("X shape:", x.shape, "Current X", x)
    print("Z shape", z.shape, "Current z:", z)
    return H_interpolation(x)*np.exp(1j*k_x(z, M_r))#*x)

def f_D(x, z):
    print("f_D")
    return 1*np.exp(1j*x)*z

def M_r(z):
    print("M_r")
    return np.sqrt(z*z)

def psi_D(z):
    print("psi_D")
    return quadpy.quad(H, -0.5, 0.5, limit=50, args=[z])[0]

def integral_P_Vm(z):
    print("Calling function")
    return M_r(z)**2*np.exp(1j*psi_D(z))

Quadpy_integral = quadpy.quad(integral_P_Vm, 0, 1, limit=100)

print("Quadpy",Quadpy_integral)

但在这方面：

return H_interpolation(x)*np.exp(1j*k_x(z, M_r))

此代码给出以下错误：

Exception has occurred: ValueError
operands could not be broadcast together with shapes (42,) (21,) 

这对我来说很奇怪，因为首先在x和z积分变量中有形状（21，）： 输出：

X shape: (21,) Current X [-4.97828582e-01 -4.86953264e-01 -4.65078746e-01 -4.32531683e-01
 -3.90408863e-01 -3.39704784e-01 -2.81378567e-01 -2.16697697e-01
 -1.47196431e-01 -7.44371695e-02  1.11022302e-16  7.44371695e-02
  1.47196431e-01  2.16697697e-01  2.81378567e-01  3.39704784e-01
  3.90408863e-01  4.32531683e-01  4.65078746e-01  4.86953264e-01
  4.97828582e-01]
Z shape (21,) Current z: [0.00217142 0.01304674 0.03492125 0.06746832 0.10959114 0.16029522
 0.21862143 0.2833023  0.35280357 0.42556283 0.5        0.57443717
 0.64719643 0.7166977  0.78137857 0.83970478 0.89040886 0.93253168
 0.96507875 0.98695326 0.99782858]

但稍后在代码执行期间，x变量中有更多参数（42）： 输出：

X shape: (42,) Current X [-0.49891429 -0.49347663 -0.48253937 -0.46626584 -0.44520443 -0.41985239
 -0.39068928 -0.35834885 -0.32359822 -0.28721858 -0.25       -0.21278142
 -0.17640178 -0.14165115 -0.10931072 -0.08014761 -0.05479557 -0.03373416
 -0.01746063 -0.00652337 -0.00108571  0.00108571  0.00652337  0.01746063
  0.03373416  0.05479557  0.08014761  0.10931072  0.14165115  0.17640178
  0.21278142  0.25        0.28721858  0.32359822  0.35834885  0.39068928
  0.41985239  0.44520443  0.46626584  0.48253937  0.49347663  0.49891429]
Z shape (21,) Current z: [0.00217142 0.01304674 0.03492125 0.06746832 0.10959114 0.16029522
 0.21862143 0.2833023  0.35280357 0.42556283 0.5        0.57443717
 0.64719643 0.7166977  0.78137857 0.83970478 0.89040886 0.93253168
 0.96507875 0.98695326 0.99782858]

我不知道为什么X变量中的参数数量从（21，）变为（42，）。谁能解释一下为什么x变量中的参数数量从21变为42

因此，代码应该计算正确的积分