\(\newcommand{\AA}{\text{Å}}\)

lmodea_k.NormalModes

class NormalModes(H: NDArray[floating], masses: NDArray[floating], wavevector: NDArray[floating] | None = None, coords_frac: NDArray[floating] | None = None, convert_phase: bool = False, asr: bool = False, rot_axis: str | None = None, generalized: bool = True, ignore_negative: bool = False, matrix_type: str = 'dynamical', eigval_min: float | None = None)

Solve normal modes from a dynamical matrix or Hessian.

By default this class reproduces the generalized eigenproblem workflow used by the command-line entry point:

• convert a dynamical matrix to a Cartesian Hessian when required;

• optionally apply the acoustic sum rule at the Gamma point;

• solve H L = M L K using eigh(H, M);

• apply phase conversion to eigenvectors for non-Gamma wavevectors;

• optionally raise on negative eigenvalues away from Gamma.

The legacy mass-weighted diagonalisation path is still available through the generalized=False option.

__init__(H: NDArray[floating], masses: NDArray[floating], wavevector: NDArray[floating] | None = None, coords_frac: NDArray[floating] | None = None, convert_phase: bool = False, asr: bool = False, rot_axis: str | None = None, generalized: bool = True, ignore_negative: bool = False, matrix_type: str = 'dynamical', eigval_min: float | None = None)

Parameters:

• H ((3N, 3N) array) – Input matrix. If matrix_type='dynamical' this is treated as a dynamical matrix and converted to a Cartesian Hessian before solving. If matrix_type='hessian' it is used directly as the Hessian.

• masses ((N,) array) – Atomic masses (amu).

• wavevector ((3,) array, optional) – Reduced wavevector for phase conversion.

• coords_frac ((N, 3) array, optional) – Fractional coordinates for phase conversion.

• convert_phase (bool, default False) – Whether to phase-shift eigenvectors for non-Γ wavevectors.

• asr (bool, default False) – Apply the acoustic sum rule before diagonalisation at Gamma.

• rot_axis ({"x","y","z",None}, optional) – Rotation axis for ASR rotational mode removal.

• generalized (bool, default True) – If True, solve the generalized eigenproblem H L = M L K. If False, diagonalise the dynamical matrix (mass-weighted Hessian).

• ignore_negative (bool, default False) – If True, permit negative eigenvalues at non-Gamma wavevectors. Otherwise raise a ValueError.

• matrix_type ({"dynamical", "hessian"}, default "dynamical") – Whether the input matrix is a dynamical matrix or a Hessian.

• eigval_min (float, optional) – Minimum eigenvalue threshold used to prevent singularities in downstream analyses. When provided, eigenvalues are clamped to this minimum value and methods like get_hessian() and eigenvalues_clamped() return modified results.

Methods

__init__(H, masses[, wavevector, ...])	param H: Input matrix. If matrix_type='dynamical' this is treated as a
get_hessian([eigval_min])	Get the Cartesian Hessian, optionally with eigenvalue clamping applied.
summary([n])	Print the first n frequencies for inspection.

Attributes

dynmat_eigenvalues	Eigenvalues from the dynamical-matrix diagonalisation, shape (3N,).
dynmat_eigenvectors	Eigenvectors from the dynamical-matrix diagonalisation, shape (3N, 3N).
eigenvalues	Eigenvalues from the generalized eigenproblem H L = M L K, shape (3N,).
eigenvalues_clamped	Eigenvalues with eigval_min applied if set, shape (3N,).
eigenvectors	Eigenvectors from the generalized eigenproblem H L = M L K, shape (3N, 3N).
frequencies	Frequencies in cm⁻¹ (negative for imaginary modes), shape (3N,).
hessian	Cartesian Hessian used in the solve, shape (3N, 3N).