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Differences in Differentiation Implementations in MATLAB

user2293 Published in July 17, 2018, 3:22 pm

I'm trying to find the (numerical) curvature at specific points. I have data stored in an array, and I essentially want to find the local curvature at every separate point. I've searched around, and found three different implementations for this in MATLAB: diff, gradient, and del2.

If my array's name is arr I have tried the following implementations:

curvature = diff(diff(arr));
curvature = diff(arr,2); 
curvature = gradient(gradient(arr)); 
curvature = del2(arr); 

The first two seem to output the same values. This makes sense, because they're essentially the same implementation. However, the gradient and del2 implementations give different values from each other and from diff.

I can't figure out from the documentation precisely how the implementations work. My guess is that some of them are some type of two-sided derivative, and some of them are not two-sided derivatives. Another thing that confuses me is that my current implementations use only the data from arr. arr is my y-axis data, the x-axis essentially being time. Do these functions default to a stepsize of 1 or something like that?

If it helps, I want an implementation that takes the curvature at the current point using only previous array elements. For context, my data is such that a curvature calculation based on data in the future of the current point wouldn't be useful for my purposes.

tl;dr I need a rigorous curvature at a point implementation that uses only data to the left of the point.

Edit: I kind of better understand what's going on based on this, thanks to the answers below. This is what I'm referring to:

gradient calculates the central difference for interior data points. For example, consider a matrix with unit-spaced data, A, that has horizontal gradient G = gradient(A). The interior gradient values, G(:,j), are

G(:,j) = 0.5*(A(:,j+1) - A(:,j-1)); The subscript j varies between 2 and N-1, with N = size(A,2).

Even so, I still want to know how to do a "lefthand" computation.

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