def test_horizontal_projection(self):
mat = self.bundle.total_space.random_uniform()
vec = self.bundle.total_space.random_uniform()
horizontal_vec = self.bundle.horizontal_projection(vec, mat)
product = GeneralLinear.mul(horizontal_vec, GeneralLinear.inverse(mat))
is_horizontal = GeneralLinear.is_symmetric(product)
self.assertTrue(is_horizontal)
def belongs(mat, atol=TOLERANCE):
"""Check if a matrix is symmetric and invertible."""
is_symmetric = GeneralLinear.is_symmetric(mat)
eigvalues, _ = gs.linalg.eigh(mat)
is_positive = gs.all(eigvalues > 0, axis=-1)
belongs = gs.logical_and(is_symmetric, is_positive)
return belongs