def create_random_initial_conditions(N):
"""
Create an ensemble of `N` randomly chosen vortices and vortex strengths.
"""
phi = np.random.rand(N, 2) + 1j*np.random.rand(N, 2)
gamma = np.random.rand(N)
# Normalize
norms = np.sum(phi.conj()*phi, axis=1)**.5
phi = row_product(1./norms, phi)
return phi, gamma
def setUp(self):
# Random initial conditions
self.gamma = np.random.rand(self.N)
phi = np.random.rand(self.N, 2) + 1j*np.random.rand(self.N, 2)
# Normalize phi
norms = np.sum(phi.conj()*phi, axis=1)**.5
phi = row_product(1./norms, phi)
# Perturb away from the unit sphere somewhat
phi *= 1.01
self.phi = phi
# Compute projected point
self.x = hopf(phi)
