[FIXED] Second order gradient in numpy

Issue

I am trying to calculate the 2nd-order gradient numerically of an array in numpy.

a = np.sin(np.arange(0, 10, .01))
da = np.gradient(a)
dda = np.gradient(da)

This is what I come up. Is the the way it should be done?

I am asking this, because in numpy there isn't an option saying np.gradient(a, order=2). I am concerned about whether this usage is wrong, and that is why numpy does not have this implemented.

PS1: I do realize that there is np.diff(a, 2). But this is only single-sided estimation, so I was curious why np.gradient does not have a similar keyword.

PS2: The np.sin() is a toy data - the real data does not have an analytic form.

Thank you!

Solution

There's no universal right answer for numerical gradient calculation. Before you can calculate the gradient about sample data, you have to make some assumption about the underlying function that generated that data. You can technically use np.diff for gradient calculation. Using np.gradient is a reasonable approach. I don't see anything fundamentally wrong with what you are doing---it's one particular approximation of the 2nd derivative of a 1-D function.

Answered By - jrennie