Integration Limits on Trapz
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MLPhysics
le 24 Fév 2021
Commenté : MLPhysics
le 24 Fév 2021
Hi Everyone!
I have a very simple question. I used MATLAB to solve a set of coupled ODEs from zero to Inf. And now I have the vectors containing the solution for these functions and their first derivatives in this semi-infinite interval.
My question is: How can I ask trapz to integrate a functional (depending on these solutions and their derivatives) from xmin=1e-5 to xmax=100, only? Is it enough to insert extra inputs into trapz?
Thank you,
MdL.
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Walter Roberson
le 24 Fév 2021
x = sort(rand(1,20));
y = exp(sin(2*pi*x));
yint = cumtrapz(x, y);
plot(x, y, 'k', x, yint, 'b')
syms X B
Y = exp(sin(2*pi*X));
Yint = int(Y, X, 0, X);
fplot([Y, Yint], [0 1])
This illustrates that you can use trapz() with irregular spacing, and that if the values are close enough, it will approximate the true integral.
If you only want to integrate over a particular range, then find the endpoints of the range in the data and only do that portion:
mask = pi/10 <= x & x <= 2*pi/10;
px = x(mask);
py = y(mask);
pyint = cumtrapz(px, py);
plot(px, py, 'k', px, pyint, 'b')
The reason this does not look the same is that you are not bringing in the accumulated value from 0 to pi/10, and definite integration always starts at 0.
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Walter Roberson
le 24 Fév 2021
Watch out for the places you had 1/s.sx1tau : s.sx1tau is a vector so 1/ it is matrix division . Notice I corrected them to 1./
The .* I put in are important too.
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