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Optimized slightly orthogonalization routine

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At one step of the orthogonaliztion procedure two matrix multiplications
have been replaced with one matrix multiplication and a element-wise
multiplication of a vector and a matrix.
This commit is contained in:
Oleg E. Peil 2015-11-21 14:23:30 +01:00
parent b2b25a9fd0
commit 7db721c8d1
1 changed files with 4 additions and 2 deletions
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python/vasp/proj_group.py
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@ -240,14 +240,16 @@ class ProjectorGroup:
Orthogonalized projector matrix, initial overlap matrix and its eigenvalues. Orthogonalized projector matrix, initial overlap matrix and its eigenvalues.
""" """
# TODO: check the precision of the calculations below,
# it seems to be inferior to that of Fortran implementation
# Overlap matrix O_{m m'} = \sum_{v} P_{m v} P^{*}_{v m'} # Overlap matrix O_{m m'} = \sum_{v} P_{m v} P^{*}_{v m'}
overlap = np.dot(p_matrix, p_matrix.conj().T) overlap = np.dot(p_matrix, p_matrix.conj().T)
# Calculate [O^{-1/2}]_{m m'} # Calculate [O^{-1/2}]_{m m'}
eig, eigv = np.linalg.eigh(overlap) eig, eigv = np.linalg.eigh(overlap)
assert np.all(eig > 0.0), ("Negative eigenvalues of the overlap matrix:" assert np.all(eig > 0.0), ("Negative eigenvalues of the overlap matrix:"
"projectors are ill-defined") "projectors are ill-defined")
sqrt_eig = np.diag(1.0 / np.sqrt(eig)) sqrt_eig = 1.0 / np.sqrt(eig)
shalf = np.dot(eigv, np.dot(sqrt_eig, eigv.conj().T)) shalf = np.dot(eigv * sqrt_eig, eigv.conj().T)
# Apply \tilde{P}_{m v} = \sum_{m'} [O^{-1/2}]_{m m'} P_{m' v} # Apply \tilde{P}_{m v} = \sum_{m'} [O^{-1/2}]_{m m'} P_{m' v}
p_ortho = np.dot(shalf, p_matrix) p_ortho = np.dot(shalf, p_matrix)