smathot · February 22, 2016 11:24 · Feb 22, 2016 · Feb 22, 2016
diff --git a/xytouv.py b/xytouv.py
@@ -22,17 +22,19 @@ def xytouv(x, y, Bu=1.4, A=3., Bv=1.8):
 	u = Bu*np.log(
 		np.sqrt(R**2 + A**2 + 2*A*R*np.cos(phi))) \
 		 - Bu*np.log(A)
-	v = Bv*np.arctan(
-		(R*np.sin(phi)) \
-		/ (R*np.cos(phi)+A)
+	v = Bv*np.arctan2(
+		(R*np.sin(phi)),
+		R*np.cos(phi)+A
 		)
 	return u, v
 
 def unit_test():
 
-	x1 = np.random.randint(0, 10, 1000)
-	y1 = np.random.randint(-10, 10, 1000)
+	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()
diff --git a/xytouv.py b/xytouv.py
@@ -0,0 +1,38 @@
+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.arctan(
+		(R*np.sin(phi)) \
+		/ (R*np.cos(phi)+A)
+		)
+	return u, v
+
+def unit_test():
+
+	x1 = np.random.randint(0, 10, 1000)
+	y1 = np.random.randint(-10, 10, 1000)
+	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)