尝试将表达式与 lambda 集成时出现问题

Question

我正在尝试集成一个表达式，该表达式具有定义为 lambda 表达式的实数和复数值。积分变量是 kx，积分的结果解将在 x 和 y 维度上进行评估，但在我积分并尝试评估积分后，我得到以下错误：

  File "/opt/tools/anaconda/2020.11/lib/python3.8/site-packages/scipy/integrate/quadpack.py", line 351, in quad
    retval = _quad(func, a, b, args, full_output, epsabs, epsrel, limit,

  File "/opt/tools/anaconda/2020.11/lib/python3.8/site-packages/scipy/integrate/quadpack.py", line 463, in _quad
    return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit)

TypeError: <lambda>() missing 2 required positional arguments: 'x' and 'y'

这是我使用的代码：

import numpy as np
from scipy import integrate
import matplotlib.pyplot as plt


"Constants and parameters"
f = 8500            # Source frequency [Hz]
rho = 1.225         # Density of air [kg/m^3]
c0 = 343            # Speed of sound [m/s]
omega = 2*np.pi*f   # Angular velocity [rad/s]
k = omega/c0        # Wave number [rad/m]
Z = -426            # Impedance

"Domain parameters"
Lx = 0.1                        # Total x-dimension [m]
Ly = 0.1                        # Total y-dimension [m]
nx = 50                         # Number of points to discretize the domain in x
ny = int(nx/2)                  # Number of points to discretize the domain in y


integrandReal = lambda kx, x, y: np.real(((2*np.sqrt(k**2 - kx**2)*Z)/(np.sqrt(k**2 - kx**2)*Z + omega*rho))*((np.exp(1j*(kx*x + np.sqrt(k**2 - kx**2)*y)))/(np.sqrt(k^2 - kx^2))))
integrandImag = lambda kx, x, y: np.imag(((2*np.sqrt(k**2 - kx**2)*Z)/(np.sqrt(k**2 - kx**2)*Z + omega*rho))*((np.exp(1j*(kx*x + np.sqrt(k**2 - kx**2)*y)))/(np.sqrt(k**2 - kx**2))))

integral = lambda x, y: integrate.quad(integrandReal, -100*k, 100*k) + 1j*integrate.quad(integrandImag-100*k, 100*k)

G = integral(1,1)

如果有人能帮助我，我将不胜感激。

Answer 1

几件事

你忘记了最后一个 lambda 中的逗号
你的 lambda 有三个参数，quad 对第一个参数进行积分，你必须用 args=(x,y) 传递其他参数。您示例中的积分限制是 -100*k 到 +100*k。
有一些 ^ 是预期的 **。
quad returns 一个有整数值和整数误差的元组，所以你对输出的第一个元素感兴趣，你可以用 [0]

integrandReal = lambda kx, x, y: np.real(((2*np.sqrt(k**2 - kx**2)*Z)/(np.sqrt(k**2 - kx**2)*Z + omega*rho))*((np.exp(1j*(kx*x + np.sqrt(k**2 - kx**2)*y)))/(np.sqrt(k**2 - kx**2))))
integrandImag = lambda kx, x, y: np.imag(((2*np.sqrt(k**2 - kx**2)*Z)/(np.sqrt(k**2 - kx**2)*Z + omega*rho))*((np.exp(1j*(kx*x + np.sqrt(k**2 - kx**2)*y)))/(np.sqrt(k**2 - kx**2))))

integral = lambda x, y: integrate.quad(integrandReal, -100*k, 100*k, args=(1,1))[0] + 1j*integrate.quad(integrandImag,-100*k, 100*k, args=(1,1))[0]

G = integral(1,1)

尝试将表达式与 lambda 集成时出现问题

Problem trying to integrate an expression with lambda

python

numpy

scipy

numerical-integration

quad