0d8e1953722d6b89b4508572cdcf0a6259f3d6e1,geomstats/connection.py,LeviCivitaConnection,christoffel_symbols,#LeviCivitaConnection#Any#,67

Before Change

        Christoffel symbols associated with the connection.
        
        // TODO(nina): implement with automatic differentiation.
        raise NotImplementedError(
                "The Christoffel symbols are not implemented.")

    def torsion(self, base_point):
        
        Torsion tensor associated with the Levi-Civita connection is zero.

After Change

        term_2 = gs.einsum("nim,nmlk->nilk",
                           self.cometric_matrix(base_point),
                           self.metric_derivative(base_point))
        term_3 = - gs.einsum("nim,nklm->nikl",
                             self.cometric_matrix(base_point),
                             self.metric_derivative(base_point))

        christoffel_symbols = 0.5 * (term_1 + term_2 + term_3)
        return christoffel_symbols

    def torsion(self, base_point):
        
        Torsion tensor associated with the Levi-Civita connection is zero.

Instances