def gradient_S3_pullback(gamma, psi, sigma):
"""
Compute the gradient on S3 by first calculating the gradient on S2
and pulling back the result to S3.
"""
x = hopf(psi)
grad_S2 = gradient_S2_slow(gamma, x, sigma)
return np.einsum('ij, abj, ib -> ia', grad_S2, pauli, psi)
def test_compare_S2_optimized(self):
"""
Compare different implementations of gradient on S2.
"""
# Pre-allocate buffer
DH2a = np.zeros(self.x.shape)
gradient_S2(DH2a, self.gamma, self.x, self.sigma)
DH2b = gradient_S2_slow(self.gamma, self.x, self.sigma)
self.assertTrue( np.allclose(DH2a, DH2b, atol=1e-12) )