about gradient and diff

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~

[Matt J]

Which gradient() and diff() methods are you referring to? The ones in the Symbolic Toolbox?

[Image Analyst]

For base MATLAB, the help says this:

"Y = diff(X,n) applies diff recursively n times,resulting in the nth difference. Thus, diff(X,2) isthe same as diff(diff(X))."

[Yuji Zhang]

Hi folks,

Thanks for discussion.

There are actually two different gradient functions - see Walter's answer.

[Image Analyst]

How do you tell your code which one to use?

[Yuji Zhang]

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.

Answer 1

[Walter Roberson]

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.

[Yuji Zhang]

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~