There is no need to transpose the matrix. Just tell diff what dimension on which to operate. Look at the third input argument of diff.
Yes, you could compute that difference by a pair of transposes, but why bother? Or, what if you have a 3 dimensional array?
diff(magic(3),[],2)
ans =
-7 5
2 2
5 -7
HOWEVER! This is NOT a derivative. It IS only a difference.
There IS a difference between the two, and it may be important. If the stride between columns of the matrix (viewed in real world units) should be some other number than 1, then you would at least want to divide by that stride.
Next, remember that a derivative is approximated as delta_y/delta_x. This is still not a derivative though. It is only an approximation to one.
x = 0:.1:1
x =
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
y = x.^2
y =
0 0.01 0.04 0.09 0.16 0.25 0.36 0.49 0.64 0.81 1
Don't forget to divide by the stride between terms! If that stride is 1, then all is good of course, and diff(y) works just fine on its own.
diff(y)/0.1
ans =
0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9
The true derivative at those points is of course:
2*x
ans =
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
And finally, note that diff produces one less element in the result, because it really is just a successive difference. Think of that derivative estimate as being most accurate midway between teach pair of elements.
