If I have a 2D numpy array composed of points (x, y) that give some value z(x, y) at each point, can I find the standard deviation along the x-axis and along the y-axis? I know that np.std(data) will simply find the standard deviation of the entire dataset, but that's not want I want. Also, adding in axis=0 or axis=1 computes the standard deviations along each axis for as many rows or columns that you have. If I just want one standard deviation along the y-axis, and another along the x-axis, can I find these in a dataset like this? From my understanding, standard deviations along x and y normally make sense when you have points x with values y(x). But I need some sigma_x and sigma_y for a 2D Gaussian fit I'm trying to do. Is this possible?

Here is an oversimplified example, since my actual data is much larger.

import numpy as np
data = np.array([[1, 5, 0, 3], [3, 5, 1, 1], [41, 33, 9, 20], [11, 20, 4, 13]])

print(np.std(data)) #not what I want
>>> 11.78386 

print(np.std(data, axis=0)) #this gives me as many results as there are rows/columns so it's not what I want
>>> [16.03 11.69 3.5 7.69]

I'm not sure how the output corresponding to what I want would look like, since I'm not even sure if it's possible in a 2D array with shape > nx2. But I want to know if it's possible to compute a standard deviation along the x-axis, and one along the y-axis. I'm not even sure if this makes sense for a 2D array... But if it doesn't, I'm not sure what to input as my sigma_x and sigma_y for a 2D Gaussian fit.