Integral calculation using matlab

2020 8 4
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更新时间：2020 8 4
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Hello i wish to calculate the following integral
My difficulty stems from the absolute value which is "outside" of the integral with respect to θ

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Bruno Luong
Bruno Luong 2020-8-4
编辑：Bruno Luong 2020-8-4

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Feel free to change these hyper-parameters
n = 3
k = 2*pi*rand()
integral(@(phi) arrayfun(@(phi) abs(integral(@(theta) exp(1i*k*cos(theta-phi)).*cos(n*theta), 0, 2*pi)).^2, phi), 0, 2*pi)

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Thank you for your reply, i get this error message
Error using subsindex
Function 'subsindex' is not defined for values of class 'function_handle'.
Error in sym/subsref (line 771)
R_tilde = builtin('subsref',L_tilde,Idx);
Bruno Luong
Bruno Luong 2020-8-4
编辑：Bruno Luong 2020-8-4
I proposed numerical method, not symbolic. You enter n and k as double numbers then it will work fine.
Can't hep you if you want symbolic integration; someone else might help you because I don't own symbolic tbx.
Matt J
Matt J 2020-8-4
Looks like a square .^2 is missing from the absolute value.
Bruno Luong
Bruno Luong 2020-8-4
Oh heah, thank you for spotting the error Matt. I'll fix it.

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Matt J
Matt J 2020-8-4
编辑：Matt J 2020-8-4

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My difficulty stems from the absolute value which is "outside" of the integral
Why is this a difficulty? Because it prevents you from using integral2()? Just apply integral() twice instead.

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Can you please elaborate, i am ashamed to say that i don't see how i can do it without integral2()?
Tried everything, nothing!
Matt J
Matt J 2020-8-4
Use integral() to evaluate the inner integral (over theta). Then take the absolute value squared of that. Then apply integral() again to integrate the result fo the previous step over phi.
This is what i do and i get an error message
fun=@(x,y)exp(-1i*cos(x-y)).*cos(x)
fun = @(x,y)exp(-1i*cos(x-y)).*cos(x)
>> integral(@(x) f(x,y),0,2*pi)
Error using subsindex
Function 'subsindex' is not defined for values of class 'function_handle'.
Error in sym/subsref (line 771)
R_tilde = builtin('subsref',L_tilde,Idx);
Steven Lord
Steven Lord 2020-8-4
Write a function to compute the inner integral. This function should accept phi. One wrinkle here is that since the outer integral call is going to pass a vector of values into it as phi, your inner integral call will need to say that the function is ArrayValued.
Write a function that takes the absolute value of that inner integral function.
Write a function to compute the outer integral of the absolute value function.
If you try this and it doesn't work, show us the code you wrote and we may be able to offer some guidance.

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