Trying to integrate an problem with no analytic solution, can't figure out why my function file isn't working

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Russell
Russell on 28 Feb 2013
My limits of integration are a changing variable
This is my function file xint.m:
function fuxc = xint(T)
k = 1.38e-23;
e = 1.6e-19;
range = 50:0.01:y(T);
ex = exp(-e./(k.*range))
fuxc = trapz(range,ex);
end
function yrange = y(T)
yrange = T;
end
If i call xint for an arbitrary value of T it works i.e. xint(200) = 2.2224e-25
But if I want it to solve an array of T values i.e. T=200:1:300, xint(T):
I still get a single value of 2.2224e-25 instead of 101 different values...
I've been struggling with this all day and feeling like an idiot for not getting it to work, please help!

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Answers (1)

Walter Roberson
Walter Roberson on 28 Feb 2013
When T is a vector, your y(T) returns the vector, and then your
range = 50:0.01:y(T);
would be attempting to start at 50, step by 1/100, with an endpoint that is a vector. That is not going to generate some kind of odd matrix that has 50:0.01:T(1) in one row, 50:0.01:T(2) in another row, and so on. Instead it is going to warn you and it is going to be the same as 50:0.01:T(1) . Which would be the same as if you had only passed in a single value instead of a vector.
If you want to process a number of different values, you will need to loop over them, or else find some way of optimizing. Hint: cumtrapz and max(T)
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Walter Roberson
Walter Roberson on 28 Feb 2013
Why are you using a numeric approximation? Why not just integrate once with a symbolic upper bound, and then use the resulting formula?
a = 50;
b = T;
fucx = -exp(-e*(a+b)/(b*k*a))*(-e*(Ei(1, e/(a*k))-Ei(1, e/(b*k)))*exp(e*(a+b)/(b*k*a))+k*(exp(e/(b*k))*a-exp(e/(a*k))*b))/k;
You will need to convert the expression into vectorized form, and you will need to convert Ei to the appropriate MATLAB routine name. And for clarity I would recommend against mixing a variable named "e" in an expression that uses exp(), as it is too easy for humans to read "e" as meaning the base of the natural logs, exp(1)
Matt J
Matt J on 28 Feb 2013
Edited: Matt J on 28 Feb 2013
It gets really messy when I put a loop in my function file.
I don't see how. Since your function already works for scalar T, it should just be a matter of enclosing what you have already in a for-loop. In what way is the following "messy" than what you had originally, other than the few extra lines bracketing your original code?
function fuxc = xint(T)
k = 1.38e-23;
e = 1.6e-19;
N=length(T);
fuxc=zeros(1,N);
for i=1:N
range = 50:0.01:y(T(i));
ex = exp(-e./(k.*range))
fuxc(i) = trapz(range,ex);
end
end

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