xytouv.py

import numpy as np

def uvtoxy(u, v, Bu=1.4, A=3., Bv=1.8):

	u = np.array(u, dtype=float)
	v = np.array(v, dtype=float)
	R = A * np.sqrt(np.exp(2*u/ Bu) - (2*np.exp(u/Bu)*np.cos(v/Bv)) + 1)
	phi = np.arctan2(
		(np.exp(u/Bu)*np.sin(v/Bv)),
		((np.exp(u/Bu)*np.cos(v/Bv))-1)
		)
	x = R*np.cos(phi)
	y = R*np.sin(phi)
	return x, y

def xytouv(x, y, Bu=1.4, A=3., Bv=1.8):

	x = np.array(x, dtype=float)
	y = np.array(y, dtype=float)
	R = np.sqrt(x**2 + y**2)
	phi = np.arctan2(y, x)
	u = Bu*np.log(
		np.sqrt(R**2 + A**2 + 2*A*R*np.cos(phi))) \
		 - Bu*np.log(A)
	v = Bv*np.arctan2(
		(R*np.sin(phi)),
		R*np.cos(phi)+A
		)
	return u, v

def unit_test():

	x1 = np.random.random(1000)*20-10
	y1 = np.random.random(1000)*20-10
	u, v = xytouv(x1, y1)
	x2, y2 = uvtoxy(u, v)
	assert(np.sum(np.abs(x1-x2)) < .0001)
	assert(np.sum(np.abs(y1-y2)) < .0001)

unit_test()