How can I integrate this function using the scipy.integrate library?

Question

so I have coded this formula

Which I get:

def sumAN(theta,CoefAN,n_cl):
    # this function give us the sumatory in the right side of the formula
    Sumatorio = np.array([])
    for count,i in enumerate(theta):
        sumatorio = 0
        for count2,j in enumerate(n_cl):
            sumatorio = sumatorio +CoefAN[count2]*sin(int(count2+1)*i)
        Sumatorio = np.append(Sumatorio,sumatorio)
    return Sumatorio

cl= 4*((np.radians(alpha)+A0)*tan(theta/2)+sumAN(theta,CoefAN,n_cl))

To explain a little bit this:
- Alpha: constant
- A0: constant
- AN : np.array([])(n values)
- theta: independent variable
After this, I need to calculate the next integral:

Here is where Im having the problems:

ch = integrate.quad(lambda theta:(4*((alpha_char+A0)*tan(theta/2)+sumAN(theta,CoefAN,n_charl)))*(cos(theta)-cos(xa))*sin(theta),0,xa)[0]

I have all the limits and everything. But I get the next error:

'float' object is not iterable

I dont know how to continue. So my question is: how can I integrate this function using the integrate.quad method? Maybe I shall change the way the sumatorie is made? How I can write the function in other way that this works? Thanks in advance

I have found an error in the ch= integrate.quad(lambda theta:(4*((alpha_char+A0)*tan(theta/2)+sumAN(theta,CoefAN,n_charl)))*(cos(theta)-cos(xa))*sin(theta),0,xa)[0], which should be : ch= integrate.quad(lambda theta:-(((alpha_char+A0)*tan(theta/2)+sumAN(theta,CoefAN,n_charl)))*(cos(theta)-cos(xa))*sin(theta),0,xa)[0] — jaimebw
– jaimebw, Commented Apr 15, 2020 at 16:32
There is a typo in your question I think it should be sin instead of sen in the first function. — MachineLearner
– MachineLearner, Commented Apr 15, 2020 at 16:45
Yeah, you are right. The first formula is a pic from my presentation and in Spain is quite common to call the sinus "sen" instead of "sin". Thanks anyways ;) ! — jaimebw
– jaimebw, Commented Apr 15, 2020 at 16:54

MachineLearner · Accepted Answer · 2020-04-15 16:43:35Z

1

This should work

import numpy as np
from scipy.integrate import quad

def integrand(theta, theta_a, alpha, A):
    sum = 0
    # get sum
    for index, value in enumerate(A):
        if index == 0:
            sum += (alpha + A[index]) * np.tan(0.5 * theta)
        else:
            sum += A[index] * np.sin(index * theta)
    # note that multiplication with 4 and multiplication with 1/4
    # result in one as prefactor
    return -sum * (np.cos(theta) - np.cos(theta_a))

# calculate integral 
theta_a = 0
alpha = 0 
array_coefficients = np.array([1, 2, 3, 4])
integral = quad(integrand, 0, 1, args=(theta_a , alpha, array_coefficients))

answered Apr 15, 2020 at 16:43

MachineLearner

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