def inverse_differential_gram(tangent_vec, base_point):
"""Compute inverse differential of gram map.
Parameters
----------
tangent_vec : array_like, shape=[..., n, n]
tanget vector at gram(base_point)
Symmetric Matrix.
base_point : array_like, shape=[..., n, n]
Base point.
Returns
-------
inverse_differential_gram : array-like, shape=[..., n, n]
Inverse differential of gram.
Lower triangular matrix.
"""
inv_base_point = gs.linalg.inv(base_point)
inv_transpose_base_point = Matrices.transpose(inv_base_point)
aux = Matrices.to_lower_triangular_diagonal_scaled(
Matrices.mul(inv_base_point, tangent_vec, inv_transpose_base_point)
)
inverse_differential_gram = Matrices.mul(base_point, aux)
return inverse_differential_gram
