def diagonalize(self, H_sS):
if self.coupling: # Non-Hermitian matrix can only use linalg.eig
self.printtxt('Use numpy.linalg.eig')
H_SS = np.zeros((self.nS, self.nS), dtype=complex)
if self.nS % world.size == 0:
world.all_gather(H_sS, H_SS)
else:
H_SS = gatherv(H_sS)
self.w_S, self.v_SS = np.linalg.eig(H_SS)
self.par_save('v_SS', 'v_SS', self.v_SS[self.nS_start:self.nS_end, :].copy())
else:
if world.size == 1:
self.printtxt('Use lapack.')
from gpaw.utilities.lapack import diagonalize
self.w_S = np.zeros(self.nS)
H_SS = H_sS
diagonalize(H_SS, self.w_S)
self.v_SS = H_SS.conj() # eigenvectors in the rows, transposed later
else:
self.printtxt('Use scalapack')
self.w_S, self.v_sS = self.scalapack_diagonalize(H_sS)
self.v_SS = self.v_sS # just use the same name
self.par_save('v_SS', 'v_SS', self.v_SS)
return
def diagonalize(self, H_sS):
if self.coupling: # Non-Hermitian matrix can only use linalg.eig
self.printtxt('Use numpy.linalg.eig')
H_SS = np.zeros((self.nS, self.nS), dtype=complex)
if self.nS % world.size == 0:
world.all_gather(H_sS, H_SS)
else:
H_SS = gatherv(H_sS)
self.w_S, self.v_SS = np.linalg.eig(H_SS)
self.par_save('v_SS', 'v_SS',
self.v_SS[self.nS_start:self.nS_end, :].copy())
else:
if world.size == 1:
self.printtxt('Use lapack.')
from gpaw.utilities.lapack import diagonalize
self.w_S = np.zeros(self.nS)
H_SS = H_sS
diagonalize(H_SS, self.w_S)
self.v_SS = H_SS.conj(
) # eigenvectors in the rows, transposed later
else:
self.printtxt('Use scalapack')
self.w_S, self.v_sS = self.scalapack_diagonalize(H_sS)
self.v_SS = self.v_sS # just use the same name
self.par_save('v_SS', 'v_SS', self.v_SS)
return
def get_dielectric_function(self, filename='df.dat', readfile=None):
if self.epsilon_w is None:
self.initialize()
if readfile is None:
H_sS = self.calculate()
self.printtxt('Diagonalizing %s matrix.' % self.mode)
self.diagonalize(H_sS)
self.printtxt('Calculating dielectric function.')
elif readfile == 'H_SS':
H_sS = self.par_load('H_SS', 'H_SS')
self.printtxt('Finished reading H_SS.gpw')
self.diagonalize(H_sS)
self.printtxt('Finished diagonalizing BSE matrix')
elif readfile == 'v_SS':
self.v_SS = self.par_load('v_SS', 'v_SS')
self.printtxt('Finished reading v_SS.gpw')
else:
XX
w_S = self.w_S
if not self.coupling:
v_SS = self.v_SS.T # v_SS[:,lamda]
else:
v_SS = self.v_SS
rhoG0_S = self.rhoG0_S
focc_S = self.focc_S
# get overlap matrix
if self.coupling:
tmp = np.dot(v_SS.conj().T, v_SS )
overlap_SS = np.linalg.inv(tmp)
# get chi
epsilon_w = np.zeros(self.Nw, dtype=complex)
t0 = time()
A_S = np.dot(rhoG0_S, v_SS)
B_S = np.dot(rhoG0_S*focc_S, v_SS)
if self.coupling:
C_S = np.dot(B_S.conj(), overlap_SS.T) * A_S
else:
if world.size == 1:
C_S = B_S.conj() * A_S
else:
tmp = B_S.conj() * A_S
C_S = gatherv(tmp, self.nS)
for iw in range(self.Nw):
tmp_S = 1. / (iw*self.dw - w_S + 1j*self.eta)
epsilon_w[iw] += np.dot(tmp_S, C_S)
epsilon_w *= - 4 * pi / np.inner(self.qq_v, self.qq_v) / self.vol
epsilon_w += 1
self.epsilon_w = epsilon_w
if rank == 0:
f = open(filename,'w')
#g = open('excitons.dat', 'w')
for iw in range(self.Nw):
energy = iw * self.dw * Hartree
print >> f, energy, np.real(epsilon_w[iw]), np.imag(epsilon_w[iw])
#print >> g, energy, np.real(C_S[iw])/max(abs(C_S))
f.close()
#g.close()
# Wait for I/O to finish
world.barrier()
"""Check f-sum rule."""
N1 = 0
for iw in range(self.Nw):
w = iw * self.dw
N1 += np.imag(epsilon_w[iw]) * w
N1 *= self.dw * self.vol / (2 * pi**2)
self.printtxt('')
self.printtxt('Sum rule:')
nv = self.nvalence
self.printtxt('N1 = %f, %f %% error' %(N1, (N1 - nv) / nv * 100) )
return epsilon_w
def get_dielectric_function(self, filename='df.dat', readfile=None):
if self.epsilon_w is None:
self.initialize()
if readfile is None:
H_sS = self.calculate()
self.printtxt('Diagonalizing %s matrix.' % self.mode)
self.diagonalize(H_sS)
self.printtxt('Calculating dielectric function.')
elif readfile == 'H_SS':
H_sS = self.par_load('H_SS', 'H_SS')
self.printtxt('Finished reading H_SS.gpw')
self.diagonalize(H_sS)
self.printtxt('Finished diagonalizing BSE matrix')
elif readfile == 'v_SS':
self.v_SS = self.par_load('v_SS', 'v_SS')
self.printtxt('Finished reading v_SS.gpw')
else:
1 / 0
w_S = self.w_S
if not self.coupling:
v_SS = self.v_SS.T # v_SS[:,lamda]
else:
v_SS = self.v_SS
rhoG0_S = self.rhoG0_S
focc_S = self.focc_S
# get overlap matrix
if self.coupling:
tmp = np.dot(v_SS.conj().T, v_SS)
overlap_SS = np.linalg.inv(tmp)
# get chi
epsilon_w = np.zeros(self.Nw, dtype=complex)
A_S = np.dot(rhoG0_S, v_SS)
B_S = np.dot(rhoG0_S * focc_S, v_SS)
if self.coupling:
C_S = np.dot(B_S.conj(), overlap_SS.T) * A_S
else:
if world.size == 1:
C_S = B_S.conj() * A_S
else:
tmp = B_S.conj() * A_S
C_S = gatherv(tmp, self.nS)
for iw in range(self.Nw):
tmp_S = 1. / (iw * self.dw - w_S + 1j * self.eta)
epsilon_w[iw] += np.dot(tmp_S, C_S)
epsilon_w *= -4 * pi / np.inner(self.qq_v, self.qq_v) / self.vol
epsilon_w += 1
self.epsilon_w = epsilon_w
if rank == 0:
f = open(filename, 'w')
for iw in range(self.Nw):
energy = iw * self.dw * Hartree
print(energy,
np.real(epsilon_w[iw]),
np.imag(epsilon_w[iw]),
file=f)
f.close()
#g.close()
# Wait for I/O to finish
world.barrier()
"""Check f-sum rule."""
N1 = 0
for iw in range(self.Nw):
w = iw * self.dw
N1 += np.imag(epsilon_w[iw]) * w
N1 *= self.dw * self.vol / (2 * pi**2)
self.printtxt('')
self.printtxt('Sum rule:')
nv = self.nvalence
self.printtxt('N1 = %f, %f %% error' % (N1, (N1 - nv) / nv * 100))
return epsilon_w
