basis_quality_evaluation

compute_basis_quality_characteristics(basis, reduced)

Computes key quality metrics for a lattice basis. This function evaluates the shortest vector norm, Hermite factor, and orthogonality defect for a given lattice basis. If the basis is not reduced, column norms are sorted to provide a more meaningful comparison.

Parameters:

Name	Type	Description	Default
basis	ndarray	A 2D NumPy array of shape (n, n) representing the lattice basis.	required
reduced	bool	Indicates whether the basis is already reduced. If False, column norms are sorted before computing metrics.	required

Returns:

Type	Description
list	A list containing Shortest column norm (float), Hermite factor (float), Orthogonality defect (float).

Source code in bkz/BasisQualityEvaluation/basis_quality_evaluation.py

def compute_basis_quality_characteristics(basis, reduced):
	"""Computes key quality metrics for a lattice basis.
	This function evaluates the shortest vector norm, Hermite factor, and
	orthogonality defect for a given lattice basis. If the basis is not reduced,
	column norms are sorted to provide a more meaningful comparison.

	Args:
	    basis (np.ndarray):
	        A 2D NumPy array of shape (n, n) representing the lattice basis.

	    reduced (bool):
	        Indicates whether the basis is already reduced. If False, column norms
	        are sorted before computing metrics.

	Returns:
	    (list): A list containing Shortest column norm (float), Hermite factor (float), Orthogonality defect (float).
	"""
	lattice_dim = basis.shape[1]
	log_lattice_volume = compute_lattice_volume_log(basis)
	col_norms = compute_column_norms(basis)
	if not reduced:
		col_norms = np.sort(col_norms)
	root_hermite_factor = compute_root_hermite_factor(col_norms[0], log_lattice_volume, lattice_dim)
	orthogonality_defect = compute_orthogonality_defect(col_norms, log_lattice_volume, lattice_dim)

	return [col_norms[0], root_hermite_factor, orthogonality_defect]