Differentiate and store results in matrix

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Benjamin 2018-11-5

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https://ww2.mathworks.cn/matlabcentral/answers/428136-differentiate-and-store-results-in-matrix

编辑： Star Strider 2018-11-5

I have two matrices. The first matrix is Density and it 311x1. The second matrix is Temperature and it is 311x21. The column in density matrix corresponds to each distinct column in temperature matrix.

So if I want to plot the first line I could just do:

plot(Density, Temperature(:,1))

and second line would just be:

plot(Density, Temperature(:,2))

How can I create a new matrix that takes the derivative of each temperature line (isotherm) with respect to density, and put this in a new matrix, such as diffTemperature?

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Star Strider 2018-11-5

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/428136-differentiate-and-store-results-in-matrix#answer_345330

在 MATLAB Online 中打开

Try this:

Density = (0:310)';                                         % Create Data
Temperature = sin((0:310)'*(0:20)*2*pi/20);                 % Create Data
dTdD = gradient(Temperature, mean(diff(Density)));          % Equal Spacing
dTdD = gradient(Temperature) ./ gradient(Density);          % Unequal Spacing
figure
plot(Density, Temperature(:,5))
hold on
plot(Density, dTdD(:,5))
hold off
grid
title('Example')
legend('Temperature', 'Derivative')
xlim([0 30])

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Benjamin 2018-11-5

编辑：Benjamin 2018-11-5

Wow, hey that works! What would it be to take 2nd derivative?

[~,ddPddD] = gradient(dPdD, mean(diff(density)));

Star Strider 2018-11-5

编辑：Star Strider 2018-11-5

Great!

Yes. That will work for equally-spaced data.

EDIT — An alternative could also be the del2 (link) function on ‘Temperature’ (or any other dependent variable), not the derivative, (although you may need to multiply the result by 4). The syntax is essentially the same.

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