Problem using lambda expression to be integrated using quad from mpmath

Question

I am trying to integrate an oscillatory expression with mpmath.quad. The integral only has one variable but I need to evaluate it in a 2D space. I need the resulting function from the integral along kx to be evaluated for a group of coordinated in x and y that defined a plane. That's why I evaluate integral(x,y) as a test in a single point of that 2D array.

This is the code I am using:

import numpy as np
from numpy.lib.scimath import sqrt
from mpmath import *
import matplotlib.pyplot as plt
mp.dps = 15

f = 8500
rho = 1.225 
c0 = 343 
Omega = 2*np.pi*f  
k = Omega/c0 
Z = -426   

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

integral = lambda x, y: quad(integrandReal, [-100*k, 100*k], maxdegree=10)[0]  + 1j*quad(integrandImag, [-100*k, 100*k], maxdegree=10)[0]
G = integral(0.1,0.1)

I am getting the following errors when I try to evaluate the integral in an arbitrary point:

Traceback (most recent call last):

  File "<ipython-input-87-901e6e5dc630>", line 1, in <module>
    integral(1,1)

  File "/d/dfg/Documents/ImpedanceModel/GreenImpedance.py", line 55, in <lambda>
    integral = lambda x, y: quad(integrandReal, [-100*k, 100*k], maxdegree=10)[0]  + 1j*quad(integrandImag, [-100*k, 100*k], maxdegree=10)[0]

  File "/opt/tools/anaconda/2020.11/lib/python3.8/site-packages/mpmath/calculus/quadrature.py", line 742, in quad
    v, err = rule.summation(f, points[0], prec, epsilon, m, verbose)

  File "/opt/tools/anaconda/2020.11/lib/python3.8/site-packages/mpmath/calculus/quadrature.py", line 232, in summation
    results.append(self.sum_next(f, nodes, degree, prec, results, verbose))

  File "/opt/tools/anaconda/2020.11/lib/python3.8/site-packages/mpmath/calculus/quadrature.py", line 304, in sum_next
    S += self.ctx.fdot((w,f(x)) for (x,w) in nodes)

  File "/opt/tools/anaconda/2020.11/lib/python3.8/site-packages/mpmath/ctx_mp_python.py", line 944, in fdot
    for a, b in A:

  File "/opt/tools/anaconda/2020.11/lib/python3.8/site-packages/mpmath/calculus/quadrature.py", line 304, in <genexpr>
    S += self.ctx.fdot((w,f(x)) for (x,w) in nodes)

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

I thought the error was because I wasn't defining the arguments in the integration as it has to be done with scipy.integrate.quad (as you can see in one of my last posts) but with mpmath I don't know what is generating this error.

Thanks in advance for any help!

Your lambdas (e.g. integrandReal) require 3 input arguments and you are passing only one in quad (you can see quad's syntax here) — nonDucor
– nonDucor, Commented Mar 3, 2022 at 13:03
Also, what do you mean with "The integral only has one variable but I need to evaluate it in a 2D space". If the integral has only one variable, it cannot be evaluated over a 2D space. — nonDucor
– nonDucor, Commented Mar 3, 2022 at 13:03
@nonDucor I will try to explain it better. I need the resulting integral to be evaluated for a group of coordinated in x and y that defined a plane. That's why I evaluate integral (x,y) as a test in a single point of that 2D array. — Monosgaitnas
– Monosgaitnas, Commented Mar 3, 2022 at 13:06
That's why I define first my whole function in terms of (kx, x, y), then I integrate in kx and then I evaluate the resulting function in (x,y). It's not a multivariable integral. — Monosgaitnas
– Monosgaitnas, Commented Mar 3, 2022 at 13:12
With scipy quad parameters like this are either global to the function, or passed in via the args tuple. If the mpmath doesn't provide args then you need to go the global route. — hpaulj
– hpaulj, Commented Mar 3, 2022 at 15:56

nonDucor · Accepted Answer · 2022-03-03 14:25:05Z

1

You need to pass x and y to your lambdas (integrandReal and integrandImag). Also, there is another issue with your example as you try to subscript the mpc object returned by quad. I removed it to get a result, it shows you how to pass x and y through the calls, but I cannot assure you the numerical result is correct:

integral = lambda x, y: quad(integrandReal, [-100*k, 100*k], [x], [y], maxdegree=10)  + 1j*quad(integrandImag, [-100*k, 100*k], [x], [y], maxdegree=10)
G = integral(0.1,0.1)
# Returns: mpc(real='0.0', imag='0.0')

answered Mar 3, 2022 at 14:25

nonDucor

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1 Comment

Monosgaitnas Over a year ago

Thanks! There are no errors when I run the code, nevertheless for any point I evaluate in integral(x,y) I get mpc(real='0.0', imag='0.0') :/

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