// the distance.
m = self.man
x = self.man.rand()
v = np.random.randn(self.m, self.n)
g = m.proj(x, v)
// Displace g a little
g_disp = g + 0.01 * m.randvec(x)
// Return to the ambient representation
g = m.tangent2ambient(x, g)
g_disp = m.tangent2ambient(x, g_disp)
g = g[0].dot(g[1]).dot(g[2].T)
g_disp = g_disp[0].dot(g_disp[1]).dot(g_disp[2].T)
assert np.linalg.norm(g - v) > np.linalg.norm(g_disp - v)