I need to plot contour and quiver plots of scalar and vector fields defined on an uneven grid in (r,theta) coordinates.
As a minimal example of the problem I have, consider the contour plot of a Stream function for a magnetic dipole, contours of such a function are streamlines of the corresponeding vector field (in this case, the magnetic field).
The code below takes an uneven grid in (r,theta) coordinates, maps it to the cartesian plane and plots a contour plot of the stream function.
import numpy as np
import matplotlib.pyplot as plt
r = np.logspace(0,1,200)
theta = np.linspace(0,np.pi/2,100)
N_r = len(r)
N_theta = len(theta)
# Polar to cartesian coordinates
theta_matrix, r_matrix = np.meshgrid(theta, r)
x = r_matrix * np.cos(theta_matrix)
y = r_matrix * np.sin(theta_matrix)
m = 5
psi = np.zeros((N_r, N_theta))
# Stream function for a magnetic dipole
psi = m * np.sin(theta_matrix)**2 / r_matrix
contour_levels = m * np.sin(np.linspace(0, np.pi/2,40))**2.
fig, ax = plt.subplots()
# ax.plot(x,y,'b.') # plot grid points
ax.set_aspect('equal')
ax.contour(x, y, psi, 100, colors='black',levels=contour_levels)
plt.show()
For some reason though, the plot I get doesn't look right:
If I interchange x and y in the contour function call, I get the desired result:
Same thing happens when I try to make a quiver plot of a vector field defined on the same grid and mapped to the x-y plane, except that interchanging x and y in the function call no longer works.
It seems like I made a stupid mistake somewhere but I can't figure out what it is.