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I have X as a 616 x 1 double. I calculated the differences between adjacent elements of X by using:

Y=diff(X);

and get Y as a 615 x 1 double, containing positive and negative numbers, including 0 (zero).

If I'm using

Y=diff>0;

I'll get the answer as 615 x 1 logical, which is not the answer I'm expecting.

My questions are

  • how can I extract only the element of X which the difference is 0?
  • how can I detect where the decrease and increase trends starts?
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If you are trying to find the entries with numerical difference being zero, you might end up with nothing because the differences may be non-zero for all entries because they are double, and assuming these 616 entries are approximation to something.

I suggest you might wanna try to set a tolerance Tol: for example

 X = sin(linspace(0,2*pi,616)'); 
 % this gives you an X being the grid approximation to sine
 Y = diff(X);
 Tol = 1e-2*2*pi/615;
 indY = find(abs(Y) < Tol);
 % the index of the difference vector that has absolute value < Tolerance

Then X(indY) and X(indY+1) will give you the entries of X that produces these less-than-tolerance differences. If the latter is bigger than the former, then X starts to increase (approximation), vice versa.

MATLAB gives:

  >> X(indY)
     ans =
         0.99997
               1
        -0.99992
              -1
  >> X(indY+1)
     ans =
               1
         0.99992
              -1
        -0.99997

The criteria for choosing Tol is more like an a priori guess. First you have the length of the interval I set being $2\pi$, there is $616$ grid points, which has a magnitude of 1e2. The true derivative of $\sin x$ is $\cos x$, which has absolute value less than $1$, so the all the numerical differences should be less than or equal to $h = 2\pi/615$. Now I already know sine, when near its extrema, increases or decreases like a linear function (imagine Taylor expansion, or small angle approximation), and it takes about 100 grids to make it the maximum (knowing a priori for sine). Therefore the absolute value of the difference being less than the magnitude of the 1e-2 times the grid size would suffice to say that, X almost remains the same. It is problem dependent.

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  • $\begingroup$ may i know how do decide the value of tolerance? $\endgroup$ – newbee Jul 26 '13 at 3:24
  • $\begingroup$ @newbee Please see my edits. $\endgroup$ – Shuhao Cao Jul 26 '13 at 3:38

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