def get_mlwf_initial_guess(self):
"""calculate initial guess for maximally localized
wannier functions. Does not work for the infinite band limit.
cu_nl: rotation coefficents of unoccupied states
U_ii: rotation matrix of eigenstates and edf.
"""
Vu_ni = self.Vu_ni[self.M:self.N]
cu_nl = np.dot(Vu_ni, self.b_il)
U_ii = np.vstack((self.Uo_ni, self.Uu_li))
lowdin(U_ii)
return U_ii, cu_nl
def __init__(self, V_nM, No, ortho=False):
Nw = V_nM.shape[1]
assert No <= Nw
V_oM, V_uM = V_nM[:No], V_nM[No:]
F_MM = np.dot(V_uM.T.conj(), V_uM)
U_ow, U_lw, U_Ml = get_rot(F_MM, V_oM, Nw - No)
self.U_nw = np.vstack((U_ow, dots(V_uM, U_Ml, U_lw)))
# stop here ?? XXX
self.S_ww = self.rotate_matrix(np.ones(1))
if ortho:
lowdin(self.U_nw, self.S_ww)
self.S_ww = np.identity(Nw)
self.norms_n = np.dot(self.U_nw, np.linalg.solve(
self.S_ww, self.U_nw.T.conj())).diagonal()
def get_locfun_rotation(projections_nj, M=None, T=0, ortho=False):
"""Mikkel Strange's localized functions.
projections_nj = <psi_n|p_j>
psi_n: eigenstates
p_j: localized function
Nw = number of localized functions
M = Number of fixed states
T = Number of virtual states to exclude (from above)
"""
Nbands, Nw = projections_nj.shape
if M is None:
M = Nw
L = Nw - M # Extra degrees of freedom
V = Nbands - M - T # Virtual states
a0_nj = projections_nj[:M, :]
a0_vj = projections_nj[M:M + V, :]
if V == 0:
D_jj = np.dot(dagger(projections_nj), projections_nj)
U_nj = 1.0 / np.sqrt(D_jj.diagonal()) * projections_nj
S_jj = np.dot(dagger(U_nj), U_nj)
assert np.diagonal(np.linalg.cholesky(S_jj)).min() > .01, \
'Close to linear dependence.'
if ortho:
lowdin(U_nj, S_jj)
S_jj = np.identity(len(S_jj))
return U_nj, S_jj
#b_v, b_vv = np.linalg.eigh(np.dot(a0_vj, dagger(a0_vj)))
#T_vp = b_vv[:, np.argsort(-b_v)[:L]]
b_j, b_jj = np.linalg.eigh(np.dot(dagger(a0_vj), a0_vj))
T_vp = np.dot(a0_vj, b_jj[:, np.argsort(-b_j.real)[:L]])
R_vv = np.dot(T_vp, dagger(T_vp))
D_jj = np.dot(dagger(a0_nj), a0_nj) + np.dot(dagger(a0_vj),
np.dot(R_vv, a0_vj))
D2_j = 1.0 / np.sqrt(D_jj.diagonal())
ap_nj = D2_j * a0_nj
ap_vj = D2_j * np.dot(R_vv, a0_vj)
S_jj = np.dot(dagger(ap_nj), ap_nj) + np.dot(dagger(ap_vj), ap_vj)
# Check for linear dependencies
Scd = np.diagonal(np.linalg.cholesky(S_jj)).min()
if Scd < 0.01:
print(('Warning: possibly near linear dependence.\n'
'Minimum eigenvalue of cholesky decomposition is %s' % Scd))
if ortho:
lowdin(ap_nj, S_jj)
lowdin(ap_vj, S_jj)
S_jj = np.identity(len(S_jj))
U_nj = np.concatenate([ap_nj.flat, ap_vj.flat]).reshape(M + V, Nw)
return U_nj, S_jj
