PAOFLOW.projection.do_ortho#

Functions#

do_ortho(Hks, Sks)

Apply the orthogonalising similarity transformation to the Hamiltonian.

do_orthogonalize(data_controller)

Orthogonalise the PAO Hamiltonian and transform back to real space.

Module Contents#

PAOFLOW.projection.do_ortho.do_ortho(Hks, Sks)[source]#

Apply the orthogonalising similarity transformation to the Hamiltonian.

Parameters:

  • Hks (np.ndarray, shape (nawf, nawf, nkpnts, nspin), complex) – Non-orthogonal PAO Hamiltonian in k-space.

  • Sks (np.ndarray, shape (nawf, nawf, nkpnts), complex) – Overlap matrix \(S(\mathbf{k})\) in k-space.

Returns:

Orthogonalised Hamiltonian \(\tilde{H} = S^{-1/2} H S^{-1/2}\).

Return type:

np.ndarray, shape (nawf, nawf, nkpnts, nspin), complex

Notes

The transformation is applied k-point by k-point:

\[\tilde{H}(\mathbf{k}) = S^{-1/2}(\mathbf{k})\, H(\mathbf{k})\, S^{-1/2}(\mathbf{k})\]

where \(S^{-1/2}\) is the matrix inverse of the matrix square root of \(S\), computed via scipy.linalg.sqrtm.

PAOFLOW.projection.do_ortho.do_orthogonalize(data_controller)[source]#

Orthogonalise the PAO Hamiltonian and transform back to real space.

Parameters:

data_controller (DataController) – Object providing data_arrays and data_attributes. Required arrays: HRs (shape (nawf, nawf, nk1, nk2, nk3, nspin)), SRs (shape (nawf, nawf, nk1, nk2, nk3)). Required attributes: nkpnts, nawf, nk1, nk2, nk3, nspin, use_cuda.

Returns:

Modifies data_controller.data_arrays and data_controller.data_attributes in place:

  • HRs : np.ndarray — replaced with the orthogonalised real-space Hamiltonian, broadcast to all MPI ranks.

  • Hks : np.ndarray, shape (nawf, nawf, nk1, nk2, nk3, nspin) — orthogonalised k-space Hamiltonian (intermediate; may be removed by subsequent steps).

  • Sks : np.ndarray, shape (nawf, nawf, nk1, nk2, nk3) — overlap matrix in k-space (intermediate).

Deletes SRs. Sets attribute acbn0 = False.

Return type:

None

Notes

The workflow is: HRs, SRs → FFT → Hks, Sks → do_ortho() → orthogonal Hks → inverse FFT → HRs. When CUDA is available the FFTs are delegated to cuda_fftn() and cuda_ifftn().