is possible use some function to find derivatives of a vector?
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by example:
NO2=( 1.1 2.4 3.3 4.7 5.9 6.0)' that corresponding to depth: Z=(4.5 6.2 8.4 10.3 12.5 14.8)'
I want find d(NO2)/dz and d^2(NO2)/dz^2
Exist some function that calculate this?
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Answers (3)
Azzi Abdelmalek
on 30 Nov 2012
Edited: Azzi Abdelmalek
on 2 Dec 2012
Edit
NO2=[1.1 2.4 3.3 4.7 5.9 6.0]
Z=[4.5 6.2 8.4 10.3 12.5 14.8]
d1=diff(NO2)./diff(Z)
d2=diff(NO2,2)./diff(Z(2:end)).^2
6 Comments
Jan
on 2 Dec 2012
Edited: Jan
on 2 Dec 2012
As far as I can see, your approximation is based on the assumption, that Z is equidistant. This is neither the general case, nor does it match the question. Therefore I think, that this approximation in unnecessarily rough, especially if the 2nd derivative is wanted.
Your method, cropped edges:
d2 = [-0.0826, 0.1385, -0.0413, -0.2079]
Suggest 2nd order method, one-sided differences at the edges:
d2 = [-0.0912, -0.0563, 0.0126, -0.0555, -0.1354, -0.1116]
Azzi Abdelmalek
on 2 Dec 2012
No, even Z is not equidistant, there is no reason that diff(Z) will change at each point, we are not looking for the variation of Z, it's No2. if the approximation is bad, it's because the distance between Z's value is big. To improve the result, maybe we can interpolate.
Jan
on 1 Dec 2012
Matlab's GRADIENT is accurate in the fist order only for not equidistant input. See FEX: DGradient and FEX: central_difference.
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