Second Derivative using diff
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Claire
el 9 de Abr. de 2015
Comentada: Victor Quezada
el 19 de Mayo de 2020
I have a quick question concerning second derivatives using the diff function.
So, after I put in my x and y arrays I did
y1=diff(y)./diff(x)
I know that I have to change the length of y1 to take the second derivative. But I'm not sure in which order it should go. Should it be:
y1=[0 y1]
or
y1=[y1 0]
Then I would proceed to do
y2=diff(y1)./diff(x)
Any help is greatly appreciated! Thank you!
1 comentario
Victor Quezada
el 19 de Mayo de 2020
Hi,
I'm coming from the future (from the coronavirus-age, actually). Sorry for being late.
Try: (just a suggestion)
diff(diff(y)./diff(x))./diff(x(1:length(x)-1))
or
diff(diff(y)./diff(x))./diff(x(2:length(x)))
Ciao.
Respuesta aceptada
Star Strider
el 9 de Abr. de 2015
I wouldn’t use diff to calculate numerical derivatives. It has its uses, but I always use the gradient function for derivative calculations, since gradient produces a result the same size as its argument.
2 comentarios
Star Strider
el 9 de Abr. de 2015
Claire’s Answer moved here...
But if I had to use diff for a certain problem, how would I go about this? (The problem specifies to use diff)
Star Strider
el 9 de Abr. de 2015
I wouldn’t zero-pad it if you’re using it to calculate a numerical derivative, and for that matter you don’t have to since both ‘diff(y)’ and ‘diff(x)’ are going to be the same lengths. You have to live with the fact that the calculation using diff is going to be shorter than the original vectors. (You would have to zero-pad both at the same location. That would create a NaN value where both were zero. So you can pad with NaN values or use interp1 with the 'extrap' option if you wanted the derivative vectors to be the same lengths as the original vectors.)
For the second derivative, just go directly to it:
x = randi(10, 1, 10);
y = randi(10, 1, 10);
d2ydx2 = diff(y,2)./diff(x,2);
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