calculating an integral of complex function substituting data from excel
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I have an excel data whose components are all numbers ranging from 2.9 to 3(ex) 2.90234 2.90343 ~ 2.98021).
I want to import these data as variable 'e'. Also, I have other parameters and substituting those values including 'e', I want to get a series of resulting values of 'I' and eventually plot them. However, when I run the code below, I get NaN for 'I' for every data. What should I do?
x = 3.01;
k = 8.62*10^-5;
T = 160;
a = 0.2;
fun = @(x,k,T,a,b,e) exp(-b.^2./(2.*a.^2)).*heaviside(x-b-e).*exp(-(x-b-e)./(k.*T));
I = integral(@(b) fun(x,k,T,a,b,e),0,Inf)
%plot(e,I)
1 个评论
dpb
2021-1-18
>> x = 3.01;
k = 8.62*10^-5;
T = 160;
a = 0.2;
fun = @(x,k,T,a,b,e) exp(-b.^2./(2.*a.^2)).*heaviside(x-b-e).*exp(-(x-b-e)./(k.*T));
e=2.903;fun(x,k,T,a,b,e)
Unrecognized function or variable 'b'.
>>
so you're missing more than just e
Use readmatrix or similar to read the spreadsheet.
Then, of course, check that your function actually produces what you expect it to for a range of cases first...
采纳的回答
Walter Roberson
2021-1-18
format long g
e = [2.90234, 2.90343, 2.98021];
x = 3.01;
k = 8.62*10^-5;
T = 160;
a = 0.2;
fun = @(x,k,T,a,b,e) exp(-b.^2./(2.*a.^2)).*heaviside(x-b-e).*exp(-(x-b-e)./(k.*T));
F = @(b) fun(x,k,T,a,b,e);
I = integral(F,0,Inf, 'arrayvalued', true);
fplot(F, [0 100])
F(9), F(10)
b = 10,[exp(-b.^2./(2.*a.^2)), heaviside(x-b-e), exp(-(x-b-e)./(k.*T))]
[(x-b-e), (k.*T)], (x-b-e)./(k.*T)
It appears that what is happening is that in some cases where heaviside() would be 0, that the corresponding exp() term is infinite because of the value inside the exp() becomes a large positive number. However, 0 times infinity is NaN.
I would suggest a piecewise() would be in order,
fun = @(x,k,T,a,b,e) piecewise(x-b-e > 0, exp(-b.^2./(2.*a.^2)).*exp(-(x-b-e)./(k.*T)), 0);
syms b
F = arrayfun(@(E) fun(x,k,T,a,b,E), e)
I = vpaintegral(F, b, 0, inf)
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