human
Solve the following python programming problem given the following code:
# Here's my weight function class
# Remember, to use a class, you first create an "instance"
# of it, e.g.:  weight = GaussAp(sigma=2.6)
# and then you can call this instance like a function of dx,dy

class GaussAp:
    # A tophat weight function of radius sigma
    def __init__(self,sigma):
        self.sigma = sigma
        return
    def __call__(self,dx,dy):
        # Given equal-shaped arrays dx=x-x0, dy=y-y0,
        # returns an array of the same shape giving weight function.

        # Calculate distance of a pixel from the center
        rsq = np.square(dx) + np.square(dy)
    
        # Now return the weight
        return np.exp(-rsq/(2.*self.sigma*self.sigma))

# Your work here...
Given the above code, generate some markdown instructions for it.
assistant
#Here is Python program to calculate distance of a pixel from the center
.

(b) Write a function aperture_centroid(img,R) that will return the values of $(y0,x0)$ that satisfy 
$$ M_x = \sum_{xy} I_{xy} W(x-x0,y-y0) (x-x0)=0$$
(and the same for y0), where $W$ is a weight function. I provide for you below a class GaussAp which you can use to create a Gaussian-aperture weight function with some $\sigma_w$:
$$ W(x,y) = \exp{\left(-\frac{x^2+y^2}{2\sigma_w^2}\right)}$$
To do this, you'll need to start with an initial guess for $(y0,x0),$ and then calculate the values of $M_f, M_x$ and $M_y$.  Then move the aperture's $x_0,y_0$ by $(M_x/M_f, M_y/M_f)$ and try again.  Iterate until the centroid doesn't move any more (or until you have done 10 iterations and need to quit!).