Points within a circle - numpy

Question

I am trying to find the points within a circle by using numpy.where():
coord=[]
x=np.random.randint(1000, size=1000)
y=np.random.randint(1000, size=1000)
coord.append(x)
coord.append(y)
neighbouring_points= np.where(np.roots((coord[0]-coord[0][10])**2 + (coord[1]-coord[1][10])**2)<=0.01,)
#protein_coordinates[0],
#protein_coordinates[1],)
#np.delete(protein_coordinates[0],protein_coordinates[0][10]),
#np.delete(protein_coordinates[1],protein_coordinates[1][10]))
plt.scatter(coord[0],coord[1], color='blue')
The result is that all points are selected and not only those satisfying the condition, I have also tried to add x,y alongside the condition to satisfy:
coord=[]
x=np.random.randint(1000, size=1000)
y=np.random.randint(1000, size=1000)
coord.append(x) #easier to plot than "protein_coordinates.append([x,y])"
coord.append(y)
neighbouring_points= np.where(np.roots((coord[0]-coord[0][10])**2 + (coord[1]-coord[1][10])**2)<=0.01,
coord[0],
coord[1],)
In this last case I get the error:
ValueError: operands could not be broadcast together with shapes (999,) (1000,) (1000,)
I have fixed the error by removing the centre of the circle, but the code still does not work.
Any suggestion on how to fix it?

Answer 1

you are not using the correct formula for the circle. Use np.sqrt() instead of np.roots
you are not correctly plotting your points. Use
idx = neighbouring_points[0]
plt.scatter(coord[0][idx], coord[1][idx])
your radius is probably too small. So inside of np.where check for something like <= 400 instead. Otherwise you only get back your central point at coord[0][10], coord[1][10]
If your central point is too close to the board of your 1000x1000 square, you also wont get a full circle. You can fix that by choosing your central to be i.e. 500,500 in your circle equation
So in total:
import numpy as np
import matplotlib.pyplot as plt
coord=[]
x=np.random.randint(1000, size=1000)
y=np.random.randint(1000, size=1000)
coord.append(x)
coord.append(y)
neighbouring_points = np.where(np.sqrt((coord[0]-500)**2 + (coord[1]-500)**2)<=400,)
idx = neighbouring_points[0]
plt.scatter(coord[0][idx],coord[1][idx], color='blue')