is possible use some function to find derivatives of a vector?

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jonathan valle 2012-11-30

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https://ww2.mathworks.cn/matlabcentral/answers/55311-is-possible-use-some-function-to-find-derivatives-of-a-vector

 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?

回答（3 个）

Azzi Abdelmalek 2012-11-30

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https://ww2.mathworks.cn/matlabcentral/answers/55311-is-possible-use-some-function-to-find-derivatives-of-a-vector#answer_67107

编辑：Azzi Abdelmalek 2012-12-2

在 MATLAB Online 中打开

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

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Jan 2012-12-2

编辑：Jan 2012-12-2

在 MATLAB Online 中打开

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 2012-12-2

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.

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