about gradient and diff

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Yuji Zhang
Yuji Zhang on 15 Jun 2013
The help of my matlab says: (in article "gradient -Gradient vector of scalar function")
-If x is a scalar, gradient(f,x) = diff(f, x).
This is wrong, right?
diff(f,2) should = diff( diff(f) ) % means 2nd order diff
while gradient (f, 2) means the grid increment is 2. which means, for a curve f-t, or f(t), t is a linear space and dt = t(2)-t(1) = 2
Let me know everybody~ Thanks~
Yuji Zhang
Yuji Zhang on 15 Jun 2013
Edited: Yuji Zhang on 15 Jun 2013
I think, if your input y is a symbolic function, like y = x^2, then gradient(y) is symbolic gradient.
If the y is a numerical curve, like y = [1 2 3 4 ....]; then gradient(y) is the numerical gradient.

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Accepted Answer

Walter Roberson
Walter Roberson on 15 Jun 2013
Symbolic gradient, http://www.mathworks.com/help/symbolic/gradient.html, is the gradient vector of a scalar function, but numeric gradient, http://www.mathworks.com/help/matlab/ref/gradient.html is just "Numerical gradient". It is numerical gradient for which the "2" would mean a point spacing of 2, and it is the symbolic gradient for which the "2" would mean double differentiation.
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Yuji Zhang
Yuji Zhang on 15 Jun 2013
Hi Walter~
Nice explanation! Thank you so much! I didn't know there were two different gradient functions. Yea, I see - makes sense. These two gradient functions are in different contexts.
Thanks again~

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