Problem trying to integrate an expression with lambda-CodePudding

I am trying to integrate an expression that has real and complex values defining it as a lambda expression. The integration variable is kx and the resulting solution of the integral will be evaluated in x and y dimensions, but after I integrate and try to evaluate the integral I get the following error:

  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'

This is the code I am using:

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)

I will be grateful if someone can help me.

CodePudding user response：

A few things

You forgot a comma in the last lambda
your lambda has three arguments, quad integrates over the first argument, you have to pass the other arguments with args=(x,y). The limits of integration in your example are -100*k to 100*k.
there were some ^ where ** was expected.
The quad returns a tupple with integral value and integral error, so you are interested in the first element of the output, you can get it with the [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)