def _calculate_fxc(self, gd, n_sG):
if self.functional == 'ALDA_x':
n_G = np.sum(n_sG, axis=0)
fx_G = -1. / 3. * (3. / np.pi)**(1. / 3.) * n_G**(-2. / 3.)
return fx_G
else:
fxc_sG = np.zeros_like(n_sG)
xc = XC(self.functional[1:])
xc.calculate_fxc(gd, n_sG, fxc_sG)
return fxc_sG[0]
def calculate_Kxc(gd,
nt_sG,
npw,
Gvec_Gc,
nG,
vol,
bcell_cv,
R_av,
setups,
D_asp,
functional='ALDA',
density_cut=None):
"""ALDA kernel"""
# The soft part
#assert np.abs(nt_sG[0].shape - nG).sum() == 0
if functional == 'ALDA_X':
x_only = True
A_x = -3. / 4. * (3. / np.pi)**(1. / 3.)
nspins = len(nt_sG)
assert nspins in [1, 2]
fxc_sg = nspins**(1. / 3.) * 4. / 9. * A_x * nt_sG**(-2. / 3.)
else:
assert len(nt_sG) == 1
x_only = False
fxc_sg = np.zeros_like(nt_sG)
xc = XC(functional[1:])
xc.calculate_fxc(gd, nt_sG, fxc_sg)
if density_cut is not None:
fxc_sg[np.where(nt_sG * len(nt_sG) < density_cut)] = 0.0
# FFT fxc(r)
nG0 = nG[0] * nG[1] * nG[2]
tmp_sg = [np.fft.fftn(fxc_sg[s]) * vol / nG0 for s in range(len(nt_sG))]
r_vg = gd.get_grid_point_coordinates()
Kxc_sGG = np.zeros((len(fxc_sg), npw, npw), dtype=complex)
for s in range(len(fxc_sg)):
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
if (nG / 2 - np.abs(dG_c) > 0).all():
index = (dG_c + nG) % nG
Kxc_sGG[s, iG, jG] = tmp_sg[s][index[0],
index[1],
index[2]]
else: # not in the fft index
dG_v = np.dot(dG_c, bcell_cv)
dGr_g = gemmdot(dG_v, r_vg, beta=0.0)
Kxc_sGG[s, iG, jG] = gd.integrate(np.exp(-1j * dGr_g)
* fxc_sg[s])
# The PAW part
KxcPAW_sGG = np.zeros_like(Kxc_sGG)
dG_GGv = np.zeros((npw, npw, 3))
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
dG_GGv[iG, jG] = np.dot(dG_c, bcell_cv)
for a, setup in enumerate(setups):
if rank == a % size:
rgd = setup.xc_correction.rgd
n_qg = setup.xc_correction.n_qg
nt_qg = setup.xc_correction.nt_qg
nc_g = setup.xc_correction.nc_g
nct_g = setup.xc_correction.nct_g
Y_nL = setup.xc_correction.Y_nL
dv_g = rgd.dv_g
D_sp = D_asp[a]
B_pqL = setup.xc_correction.B_pqL
D_sLq = np.inner(D_sp, B_pqL.T)
nspins = len(D_sp)
f_sg = rgd.empty(nspins)
ft_sg = rgd.empty(nspins)
n_sLg = np.dot(D_sLq, n_qg)
nt_sLg = np.dot(D_sLq, nt_qg)
# Add core density
n_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nc_g
nt_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nct_g
coefatoms_GG = np.exp(-1j * np.inner(dG_GGv, R_av[a]))
for n, Y_L in enumerate(Y_nL):
w = weight_n[n]
f_sg[:] = 0.0
n_sg = np.dot(Y_L, n_sLg)
if x_only:
f_sg = nspins * (4 / 9.) * A_x * (nspins * n_sg)**(-2 / 3.)
else:
xc.calculate_fxc(rgd, n_sg, f_sg)
ft_sg[:] = 0.0
nt_sg = np.dot(Y_L, nt_sLg)
if x_only:
ft_sg = nspins * (4 / 9.) * (A_x
* (nspins * nt_sg)**(-2 / 3.))
else:
xc.calculate_fxc(rgd, nt_sg, ft_sg)
for i in range(len(rgd.r_g)):
coef_GG = np.exp(-1j * np.inner(dG_GGv, R_nv[n])
* rgd.r_g[i])
for s in range(len(f_sg)):
KxcPAW_sGG[s] += w * np.dot(coef_GG,
(f_sg[s, i] -
ft_sg[s, i])
* dv_g[i]) * coefatoms_GG
world.sum(KxcPAW_sGG)
Kxc_sGG += KxcPAW_sGG
return Kxc_sGG / vol
def calculate_Kxc(pd, nt_sG, R_av, setups, D_asp, functional='ALDA',
density_cut=None):
"""ALDA kernel"""
gd = pd.gd
npw = pd.ngmax
nG = pd.gd.N_c
vol = pd.gd.volume
bcell_cv = np.linalg.inv(pd.gd.cell_cv)
G_Gv = pd.get_reciprocal_vectors()
# The soft part
#assert np.abs(nt_sG[0].shape - nG).sum() == 0
if functional == 'ALDA_X':
x_only = True
A_x = -3. / 4. * (3. / np.pi)**(1. / 3.)
nspins = len(nt_sG)
assert nspins in [1, 2]
fxc_sg = nspins**(1. / 3.) * 4. / 9. * A_x * nt_sG**(-2. / 3.)
else:
assert len(nt_sG) == 1
x_only = False
fxc_sg = np.zeros_like(nt_sG)
xc = XC(functional[1:])
xc.calculate_fxc(gd, nt_sG, fxc_sg)
if density_cut is not None:
fxc_sg[np.where(nt_sG * len(nt_sG) < density_cut)] = 0.0
# FFT fxc(r)
nG0 = nG[0] * nG[1] * nG[2]
tmp_sg = [np.fft.fftn(fxc_sg[s]) * vol / nG0 for s in range(len(nt_sG))]
r_vg = gd.get_grid_point_coordinates()
Kxc_sGG = np.zeros((len(fxc_sg), npw, npw), dtype=complex)
for s in range(len(fxc_sg)):
for iG, iQ in enumerate(pd.Q_qG[0]):
iQ_c = (np.unravel_index(iQ, nG) + nG // 2) % nG - nG // 2
for jG, jQ in enumerate(pd.Q_qG[0]):
jQ_c = (np.unravel_index(jQ, nG) + nG // 2) % nG - nG // 2
ijQ_c = (iQ_c - jQ_c)
if (abs(ijQ_c) < nG // 2).all():
Kxc_sGG[s, iG, jG] = tmp_sg[s][tuple(ijQ_c)]
# The PAW part
KxcPAW_sGG = np.zeros_like(Kxc_sGG)
dG_GGv = np.zeros((npw, npw, 3))
for v in range(3):
dG_GGv[:, :, v] = np.subtract.outer(G_Gv[:, v], G_Gv[:, v])
for a, setup in enumerate(setups):
if rank == a % size:
rgd = setup.xc_correction.rgd
n_qg = setup.xc_correction.n_qg
nt_qg = setup.xc_correction.nt_qg
nc_g = setup.xc_correction.nc_g
nct_g = setup.xc_correction.nct_g
Y_nL = setup.xc_correction.Y_nL
dv_g = rgd.dv_g
D_sp = D_asp[a]
B_pqL = setup.xc_correction.B_pqL
D_sLq = np.inner(D_sp, B_pqL.T)
nspins = len(D_sp)
f_sg = rgd.empty(nspins)
ft_sg = rgd.empty(nspins)
n_sLg = np.dot(D_sLq, n_qg)
nt_sLg = np.dot(D_sLq, nt_qg)
# Add core density
n_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nc_g
nt_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nct_g
coefatoms_GG = np.exp(-1j * np.inner(dG_GGv, R_av[a]))
for n, Y_L in enumerate(Y_nL):
w = weight_n[n]
f_sg[:] = 0.0
n_sg = np.dot(Y_L, n_sLg)
if x_only:
f_sg = nspins * (4 / 9.) * A_x * (nspins * n_sg)**(-2 / 3.)
else:
xc.calculate_fxc(rgd, n_sg, f_sg)
ft_sg[:] = 0.0
nt_sg = np.dot(Y_L, nt_sLg)
if x_only:
ft_sg = nspins * (4 / 9.) * (A_x
* (nspins * nt_sg)**(-2 / 3.))
else:
xc.calculate_fxc(rgd, nt_sg, ft_sg)
for i in range(len(rgd.r_g)):
coef_GG = np.exp(-1j * np.inner(dG_GGv, R_nv[n])
* rgd.r_g[i])
for s in range(len(f_sg)):
KxcPAW_sGG[s] += w * np.dot(coef_GG,
(f_sg[s, i] -
ft_sg[s, i])
* dv_g[i]) * coefatoms_GG
world.sum(KxcPAW_sGG)
Kxc_sGG += KxcPAW_sGG
return Kxc_sGG / vol
def calculate_Kxc(pd, calc, functional='ALDA', density_cut=None):
"""ALDA kernel"""
gd = pd.gd
npw = pd.ngmax
nG = pd.gd.N_c
vol = pd.gd.volume
G_Gv = pd.get_reciprocal_vectors()
nt_sG = calc.density.nt_sG
R_av = calc.atoms.positions / Bohr
setups = calc.wfs.setups
D_asp = calc.density.D_asp
# The soft part
# assert np.abs(nt_sG[0].shape - nG).sum() == 0
if functional == 'ALDA_X':
x_only = True
A_x = -3. / 4. * (3. / np.pi)**(1. / 3.)
nspins = len(nt_sG)
assert nspins in [1, 2]
fxc_sg = nspins**(1. / 3.) * 4. / 9. * A_x * nt_sG**(-2. / 3.)
else:
assert len(nt_sG) == 1
x_only = False
fxc_sg = np.zeros_like(nt_sG)
xc = XC(functional[1:])
xc.calculate_fxc(gd, nt_sG, fxc_sg)
if density_cut is not None:
fxc_sg[np.where(nt_sG * len(nt_sG) < density_cut)] = 0.0
# FFT fxc(r)
nG0 = nG[0] * nG[1] * nG[2]
tmp_sg = [np.fft.fftn(fxc_sg[s]) * vol / nG0 for s in range(len(nt_sG))]
Kxc_sGG = np.zeros((len(fxc_sg), npw, npw), dtype=complex)
for s in range(len(fxc_sg)):
for iG, iQ in enumerate(pd.Q_qG[0]):
iQ_c = (np.unravel_index(iQ, nG) + nG // 2) % nG - nG // 2
for jG, jQ in enumerate(pd.Q_qG[0]):
jQ_c = (np.unravel_index(jQ, nG) + nG // 2) % nG - nG // 2
ijQ_c = (iQ_c - jQ_c)
if (abs(ijQ_c) < nG // 2).all():
Kxc_sGG[s, iG, jG] = tmp_sg[s][tuple(ijQ_c)]
# The PAW part
KxcPAW_sGG = np.zeros_like(Kxc_sGG)
dG_GGv = np.zeros((npw, npw, 3))
for v in range(3):
dG_GGv[:, :, v] = np.subtract.outer(G_Gv[:, v], G_Gv[:, v])
for a, setup in enumerate(setups):
if rank == a % size:
rgd = setup.xc_correction.rgd
n_qg = setup.xc_correction.n_qg
nt_qg = setup.xc_correction.nt_qg
nc_g = setup.xc_correction.nc_g
nct_g = setup.xc_correction.nct_g
Y_nL = setup.xc_correction.Y_nL
dv_g = rgd.dv_g
D_sp = D_asp[a]
B_pqL = setup.xc_correction.B_pqL
D_sLq = np.inner(D_sp, B_pqL.T)
nspins = len(D_sp)
f_sg = rgd.empty(nspins)
ft_sg = rgd.empty(nspins)
n_sLg = np.dot(D_sLq, n_qg)
nt_sLg = np.dot(D_sLq, nt_qg)
# Add core density
n_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nc_g
nt_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nct_g
coefatoms_GG = np.exp(-1j * np.inner(dG_GGv, R_av[a]))
for n, Y_L in enumerate(Y_nL):
w = weight_n[n]
f_sg[:] = 0.0
n_sg = np.dot(Y_L, n_sLg)
if x_only:
f_sg = nspins * (4 / 9.) * A_x * (nspins * n_sg)**(-2 / 3.)
else:
xc.calculate_fxc(rgd, n_sg, f_sg)
ft_sg[:] = 0.0
nt_sg = np.dot(Y_L, nt_sLg)
if x_only:
ft_sg = nspins * (4 / 9.) * (A_x *
(nspins * nt_sg)**(-2 / 3.))
else:
xc.calculate_fxc(rgd, nt_sg, ft_sg)
for i in range(len(rgd.r_g)):
coef_GG = np.exp(-1j * np.inner(dG_GGv, R_nv[n]) *
rgd.r_g[i])
for s in range(len(f_sg)):
KxcPAW_sGG[s] += w * np.dot(coef_GG,
(f_sg[s, i] - ft_sg[s, i])
* dv_g[i]) * coefatoms_GG
world.sum(KxcPAW_sGG)
Kxc_sGG += KxcPAW_sGG
if pd.kd.gamma:
Kxc_sGG[:, 0, :] = 0.0
Kxc_sGG[:, :, 0] = 0.0
return Kxc_sGG / vol
def calculate_Kxc(gd, nt_sG, npw, Gvec_Gc, nG, vol, bcell_cv, R_av, setups,
D_asp):
"""LDA kernel"""
# The soft part
assert np.abs(nt_sG[0].shape - nG).sum() == 0
xc = XC('LDA')
fxc_sg = np.zeros_like(nt_sG)
xc.calculate_fxc(gd, nt_sG, fxc_sg)
fxc_g = fxc_sg[0]
# FFT fxc(r)
nG0 = nG[0] * nG[1] * nG[2]
tmp_g = np.fft.fftn(fxc_g) * vol / nG0
r_vg = gd.get_grid_point_coordinates()
Kxc_GG = np.zeros((npw, npw), dtype=complex)
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
if (nG / 2 - np.abs(dG_c) > 0).all():
index = (dG_c + nG) % nG
Kxc_GG[iG, jG] = tmp_g[index[0], index[1], index[2]]
else: # not in the fft index
dG_v = np.dot(dG_c, bcell_cv)
dGr_g = gemmdot(dG_v, r_vg, beta=0.0)
Kxc_GG[iG, jG] = gd.integrate(np.exp(-1j * dGr_g) * fxc_g)
KxcPAW_GG = np.zeros_like(Kxc_GG)
# The PAW part
dG_GGv = np.zeros((npw, npw, 3))
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
dG_GGv[iG, jG] = np.dot(dG_c, bcell_cv)
for a, setup in enumerate(setups):
if rank == a % size:
rgd = setup.xc_correction.rgd
n_qg = setup.xc_correction.n_qg
nt_qg = setup.xc_correction.nt_qg
nc_g = setup.xc_correction.nc_g
nct_g = setup.xc_correction.nct_g
Y_nL = setup.xc_correction.Y_nL
dv_g = rgd.dv_g
D_sp = D_asp[a]
B_pqL = setup.xc_correction.B_pqL
D_sLq = np.inner(D_sp, B_pqL.T)
nspins = len(D_sp)
assert nspins == 1
f_sg = rgd.empty(nspins)
ft_sg = rgd.empty(nspins)
n_sLg = np.dot(D_sLq, n_qg)
nt_sLg = np.dot(D_sLq, nt_qg)
# Add core density
n_sLg[:, 0] += sqrt(4 * pi) / nspins * nc_g
nt_sLg[:, 0] += sqrt(4 * pi) / nspins * nct_g
coefatoms_GG = np.exp(-1j * np.inner(dG_GGv, R_av[a]))
for n, Y_L in enumerate(Y_nL):
w = weight_n[n]
f_sg[:] = 0.0
n_sg = np.dot(Y_L, n_sLg)
xc.calculate_fxc(rgd, n_sg, f_sg)
ft_sg[:] = 0.0
nt_sg = np.dot(Y_L, nt_sLg)
xc.calculate_fxc(rgd, nt_sg, ft_sg)
coef_GGg = np.exp(
-1j *
np.outer(np.inner(dG_GGv, R_nv[n]), rgd.r_g)).reshape(
npw, npw, rgd.ng)
KxcPAW_GG += w * np.dot(
coef_GGg, (f_sg[0] - ft_sg[0]) * dv_g) * coefatoms_GG
world.sum(KxcPAW_GG)
Kxc_GG += KxcPAW_GG
return Kxc_GG / vol
class OmegaMatrix:
"""
Omega matrix in Casidas linear response formalism
Parameters
- calculator: the calculator object the ground state calculation
- kss: the Kohn-Sham singles object
- xc: the exchange correlation approx. to use
- derivativeLevel: which level i of d^i Exc/dn^i to use
- numscale: numeric epsilon for derivativeLevel=0,1
- filehandle: the oject can be read from a filehandle
- txt: output stream or file name
- finegrid: level of fine grid to use. 0: nothing, 1 for poisson only,
2 everything on the fine grid
"""
def __init__(self,
calculator=None,
kss=None,
xc=None,
derivativeLevel=None,
numscale=0.001,
filehandle=None,
txt=None,
finegrid=2,
eh_comm=None,
):
if not txt and calculator:
txt = calculator.txt
self.txt = get_txt(txt, mpi.rank)
if eh_comm is None:
eh_comm = mpi.serial_comm
self.eh_comm = eh_comm
if filehandle is not None:
self.kss = kss
self.read(fh=filehandle)
return None
self.fullkss = kss
self.finegrid = finegrid
if calculator is None:
return
self.paw = calculator
wfs = self.paw.wfs
# handle different grid possibilities
self.restrict = None
# self.poisson = PoissonSolver(nn=self.paw.hamiltonian.poisson.nn)
self.poisson = calculator.hamiltonian.poisson
if finegrid:
self.poisson.set_grid_descriptor(self.paw.density.finegd)
self.poisson.initialize()
self.gd = self.paw.density.finegd
if finegrid == 1:
self.gd = wfs.gd
else:
self.poisson.set_grid_descriptor(wfs.gd)
self.poisson.initialize()
self.gd = wfs.gd
self.restrict = Transformer(self.paw.density.finegd, wfs.gd,
self.paw.input_parameters.stencils[1]
).apply
if xc == 'RPA':
xc = None # enable RPA as keyword
if xc is not None:
self.xc = XC(xc)
self.xc.initialize(self.paw.density, self.paw.hamiltonian,
wfs, self.paw.occupations)
# check derivativeLevel
if derivativeLevel is None:
derivativeLevel = \
self.xc.get_functional().get_max_derivative_level()
self.derivativeLevel = derivativeLevel
# change the setup xc functional if needed
# the ground state calculation may have used another xc
if kss.npspins > kss.nvspins:
spin_increased = True
else:
spin_increased = False
else:
self.xc = None
self.numscale = numscale
self.singletsinglet = False
if kss.nvspins < 2 and kss.npspins < 2:
# this will be a singlet to singlet calculation only
self.singletsinglet = True
nij = len(kss)
self.Om = np.zeros((nij, nij))
self.get_full()
def get_full(self):
self.paw.timer.start('Omega RPA')
self.get_rpa()
self.paw.timer.stop()
if self.xc is not None:
self.paw.timer.start('Omega XC')
self.get_xc()
self.paw.timer.stop()
self.eh_comm.sum(self.Om)
self.full = self.Om
def get_xc(self):
"""Add xc part of the coupling matrix"""
# shorthands
paw = self.paw
wfs = paw.wfs
gd = paw.density.finegd
comm = gd.comm
eh_comm = self.eh_comm
fg = self.finegrid is 2
kss = self.fullkss
nij = len(kss)
Om_xc = self.Om
# initialize densities
# nt_sg is the smooth density on the fine grid with spin index
if kss.nvspins == 2:
# spin polarised ground state calc.
nt_sg = paw.density.nt_sg
else:
# spin unpolarised ground state calc.
if kss.npspins == 2:
# construct spin polarised densities
nt_sg = np.array([.5 * paw.density.nt_sg[0],
.5 * paw.density.nt_sg[0]])
else:
nt_sg = paw.density.nt_sg
# check if D_sp have been changed before
D_asp = self.paw.density.D_asp
for a, D_sp in D_asp.items():
if len(D_sp) != kss.npspins:
if len(D_sp) == 1:
D_asp[a] = np.array([0.5 * D_sp[0], 0.5 * D_sp[0]])
else:
D_asp[a] = np.array([D_sp[0] + D_sp[1]])
# restrict the density if needed
if fg:
nt_s = nt_sg
else:
nt_s = self.gd.zeros(nt_sg.shape[0])
for s in range(nt_sg.shape[0]):
self.restrict(nt_sg[s], nt_s[s])
gd = paw.density.gd
# initialize vxc or fxc
if self.derivativeLevel == 0:
raise NotImplementedError
if kss.npspins == 2:
v_g = nt_sg[0].copy()
else:
v_g = nt_sg.copy()
elif self.derivativeLevel == 1:
pass
elif self.derivativeLevel == 2:
fxc_sg = np.zeros(nt_sg.shape)
self.xc.calculate_fxc(gd, nt_sg, fxc_sg)
else:
raise ValueError('derivativeLevel can only be 0,1,2')
# self.paw.my_nuclei = []
ns = self.numscale
xc = self.xc
print('XC', nij, 'transitions', file=self.txt)
for ij in range(eh_comm.rank, nij, eh_comm.size):
print('XC kss[' + '%d' % ij + ']', file=self.txt)
timer = Timer()
timer.start('init')
timer2 = Timer()
if self.derivativeLevel >= 1:
# vxc is available
# We use the numerical two point formula for calculating
# the integral over fxc*n_ij. The results are
# vvt_s smooth integral
# nucleus.I_sp atom based correction matrices (pack2)
# stored on each nucleus
timer2.start('init v grids')
vp_s = np.zeros(nt_s.shape, nt_s.dtype.char)
vm_s = np.zeros(nt_s.shape, nt_s.dtype.char)
if kss.npspins == 2: # spin polarised
nv_s = nt_s.copy()
nv_s[kss[ij].pspin] += ns * kss[ij].get(fg)
xc.calculate(gd, nv_s, vp_s)
nv_s = nt_s.copy()
nv_s[kss[ij].pspin] -= ns * kss[ij].get(fg)
xc.calculate(gd, nv_s, vm_s)
else: # spin unpolarised
nv = nt_s + ns * kss[ij].get(fg)
xc.calculate(gd, nv, vp_s)
nv = nt_s - ns * kss[ij].get(fg)
xc.calculate(gd, nv, vm_s)
vvt_s = (0.5 / ns) * (vp_s - vm_s)
timer2.stop()
# initialize the correction matrices
timer2.start('init v corrections')
I_asp = {}
for a, P_ni in wfs.kpt_u[kss[ij].spin].P_ani.items():
# create the modified density matrix
Pi_i = P_ni[kss[ij].i]
Pj_i = P_ni[kss[ij].j]
P_ii = np.outer(Pi_i, Pj_i)
# we need the symmetric form, hence we can pack
P_p = pack(P_ii)
D_sp = self.paw.density.D_asp[a].copy()
D_sp[kss[ij].pspin] -= ns * P_p
setup = wfs.setups[a]
I_sp = np.zeros_like(D_sp)
self.xc.calculate_paw_correction(setup, D_sp, I_sp)
I_sp *= -1.0
D_sp = self.paw.density.D_asp[a].copy()
D_sp[kss[ij].pspin] += ns * P_p
self.xc.calculate_paw_correction(setup, D_sp, I_sp)
I_sp /= 2.0 * ns
I_asp[a] = I_sp
timer2.stop()
timer.stop()
t0 = timer.get_time('init')
timer.start(ij)
for kq in range(ij, nij):
weight = self.weight_Kijkq(ij, kq)
if self.derivativeLevel == 0:
# only Exc is available
if kss.npspins == 2: # spin polarised
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] += kss[ij].get(fg)
nv_g[kss[kq].pspin] += kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(
nv_g[0], v_g, nv_g[1], v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] += kss[ij].get(fg)
nv_g[kss[kq].pspin] -= kss[kq].get(fg)
Excpm = xc.get_energy_and_potential(
nv_g[0], v_g, nv_g[1], v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] -=\
kss[ij].get(fg)
nv_g[kss[kq].pspin] +=\
kss[kq].get(fg)
Excmp = xc.get_energy_and_potential(
nv_g[0], v_g, nv_g[1], v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] -= \
kss[ij].get(fg)
nv_g[kss[kq].pspin] -=\
kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(
nv_g[0], v_g, nv_g[1], v_g)
else: # spin unpolarised
nv_g = nt_sg + ns * kss[ij].get(fg)\
+ ns * kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(nv_g, v_g)
nv_g = nt_sg + ns * kss[ij].get(fg)\
- ns * kss[kq].get(fg)
Excpm = xc.get_energy_and_potential(nv_g, v_g)
nv_g = nt_sg - ns * kss[ij].get(fg)\
+ ns * kss[kq].get(fg)
Excmp = xc.get_energy_and_potential(nv_g, v_g)
nv_g = nt_sg - ns * kss[ij].get(fg)\
- ns * kss[kq].get(fg)
Excmm = xc.get_energy_and_potential(nv_g, v_g)
Om_xc[ij, kq] += weight *\
0.25 * \
(Excpp - Excmp - Excpm + Excmm) / (ns * ns)
elif self.derivativeLevel == 1:
# vxc is available
timer2.start('integrate')
Om_xc[ij, kq] += weight *\
self.gd.integrate(kss[kq].get(fg) *
vvt_s[kss[kq].pspin])
timer2.stop()
timer2.start('integrate corrections')
Exc = 0.
for a, P_ni in wfs.kpt_u[kss[kq].spin].P_ani.items():
# create the modified density matrix
Pk_i = P_ni[kss[kq].i]
Pq_i = P_ni[kss[kq].j]
P_ii = np.outer(Pk_i, Pq_i)
# we need the symmetric form, hence we can pack
# use pack as I_sp used pack2
P_p = pack(P_ii)
Exc += np.dot(I_asp[a][kss[kq].pspin], P_p)
Om_xc[ij, kq] += weight * self.gd.comm.sum(Exc)
timer2.stop()
elif self.derivativeLevel == 2:
# fxc is available
if kss.npspins == 2: # spin polarised
Om_xc[ij, kq] += weight *\
gd.integrate(kss[ij].get(fg) *
kss[kq].get(fg) *
fxc_sg[kss[ij].pspin, kss[kq].pspin])
else: # spin unpolarised
Om_xc[ij, kq] += weight *\
gd.integrate(kss[ij].get(fg) *
kss[kq].get(fg) *
fxc_sg)
# XXX still numeric derivatives for local terms
timer2.start('integrate corrections')
Exc = 0.
for a, P_ni in wfs.kpt_u[kss[kq].spin].P_ani.items():
# create the modified density matrix
Pk_i = P_ni[kss[kq].i]
Pq_i = P_ni[kss[kq].j]
P_ii = np.outer(Pk_i, Pq_i)
# we need the symmetric form, hence we can pack
# use pack as I_sp used pack2
P_p = pack(P_ii)
Exc += np.dot(I_asp[a][kss[kq].pspin], P_p)
Om_xc[ij, kq] += weight * self.gd.comm.sum(Exc)
timer2.stop()
if ij != kq:
Om_xc[kq, ij] = Om_xc[ij, kq]
timer.stop()
# timer2.write()
if ij < (nij - 1):
print('XC estimated time left',
self.time_left(timer, t0, ij, nij), file=self.txt)
def Coulomb_integral_kss(self, kss_ij, kss_kq, phit, rhot,
timer=None):
# smooth part
if timer:
timer.start('integrate')
I = self.gd.integrate(rhot * phit)
if timer:
timer.stop()
timer.start('integrate corrections 2')
wfs = self.paw.wfs
Pij_ani = wfs.kpt_u[kss_ij.spin].P_ani
Pkq_ani = wfs.kpt_u[kss_kq.spin].P_ani
# Add atomic corrections
Ia = 0.0
for a, Pij_ni in Pij_ani.items():
Pi_i = Pij_ni[kss_ij.i]
Pj_i = Pij_ni[kss_ij.j]
Dij_ii = np.outer(Pi_i, Pj_i)
Dij_p = pack(Dij_ii)
Pk_i = Pkq_ani[a][kss_kq.i]
Pq_i = Pkq_ani[a][kss_kq.j]
Dkq_ii = np.outer(Pk_i, Pq_i)
Dkq_p = pack(Dkq_ii)
C_pp = wfs.setups[a].M_pp
# ----
# 2 > P P C P P
# ---- ip jr prst ks qt
# prst
Ia += 2.0 * np.dot(Dkq_p, np.dot(C_pp, Dij_p))
I += self.gd.comm.sum(Ia)
if timer:
timer.stop()
return I
def get_rpa(self):
"""calculate RPA part of the omega matrix"""
# shorthands
kss = self.fullkss
finegrid = self.finegrid
wfs = self.paw.wfs
eh_comm = self.eh_comm
# calculate omega matrix
nij = len(kss)
print('RPA', nij, 'transitions', file=self.txt)
Om = self.Om
for ij in range(eh_comm.rank, nij, eh_comm.size):
print('RPA kss[' + '%d' % ij + ']=', kss[ij], file=self.txt)
timer = Timer()
timer.start('init')
timer2 = Timer()
# smooth density including compensation charges
timer2.start('with_compensation_charges 0')
rhot_p = kss[ij].with_compensation_charges(
finegrid is not 0)
timer2.stop()
# integrate with 1/|r_1-r_2|
timer2.start('poisson')
phit_p = np.zeros(rhot_p.shape, rhot_p.dtype.char)
self.poisson.solve(phit_p, rhot_p, charge=None)
timer2.stop()
timer.stop()
t0 = timer.get_time('init')
timer.start(ij)
if finegrid == 1:
rhot = kss[ij].with_compensation_charges()
phit = self.gd.zeros()
# print "shapes 0=",phit.shape,rhot.shape
self.restrict(phit_p, phit)
else:
phit = phit_p
rhot = rhot_p
for kq in range(ij, nij):
if kq != ij:
# smooth density including compensation charges
timer2.start('kq with_compensation_charges')
rhot = kss[kq].with_compensation_charges(
finegrid is 2)
timer2.stop()
pre = 2 * sqrt(kss[ij].get_energy() * kss[kq].get_energy() *
kss[ij].get_weight() * kss[kq].get_weight())
I = self.Coulomb_integral_kss(kss[ij], kss[kq],
rhot, phit, timer2)
Om[ij, kq] = pre * I
if ij == kq:
Om[ij, kq] += kss[ij].get_energy() ** 2
else:
Om[kq, ij] = Om[ij, kq]
timer.stop()
# timer2.write()
if ij < (nij - 1):
t = timer.get_time(ij) # time for nij-ij calculations
t = .5 * t * \
(nij - ij) # estimated time for n*(n+1)/2, n=nij-(ij+1)
print('RPA estimated time left',
self.timestring(t0 * (nij - ij - 1) + t), file=self.txt)
def singlets_triplets(self):
"""Split yourself into singlet and triplet transitions"""
assert(self.fullkss.npspins == 2)
assert(self.fullkss.nvspins == 1)
# strip kss from down spins
skss = KSSingles()
tkss = KSSingles()
map = []
for ij, ks in enumerate(self.fullkss):
if ks.pspin == ks.spin:
skss.append((ks + ks) / sqrt(2))
tkss.append((ks - ks) / sqrt(2))
map.append(ij)
nkss = len(skss)
# define the singlet and the triplet omega-matrixes
sOm = OmegaMatrix(kss=skss)
sOm.full = np.empty((nkss, nkss))
tOm = OmegaMatrix(kss=tkss)
tOm.full = np.empty((nkss, nkss))
for ij in range(nkss):
for kl in range(nkss):
sOm.full[ij, kl] = (self.full[map[ij], map[kl]] +
self.full[map[ij], nkss + map[kl]])
tOm.full[ij, kl] = (self.full[map[ij], map[kl]] -
self.full[map[ij], nkss + map[kl]])
return sOm, tOm
def timestring(self, t):
ti = int(t + 0.5)
td = ti // 86400
st = ''
if td > 0:
st += '%d' % td + 'd'
ti -= td * 86400
th = ti // 3600
if th > 0:
st += '%d' % th + 'h'
ti -= th * 3600
tm = ti // 60
if tm > 0:
st += '%d' % tm + 'm'
ti -= tm * 60
st += '%d' % ti + 's'
return st
def time_left(self, timer, t0, ij, nij):
t = timer.get_time(ij) # time for nij-ij calculations
t = .5 * t * (nij - ij) # estimated time for n*(n+1)/2, n=nij-(ij+1)
return self.timestring(t0 * (nij - ij - 1) + t)
def get_map(self, istart=None, jend=None, energy_range=None):
"""Return the reduction map for the given requirements"""
self.istart = istart
self.jend = jend
if istart is None and jend is None and energy_range is None:
return None, self.fullkss
# reduce the matrix
print('# diagonalize: %d transitions original'
% len(self.fullkss), file=self.txt)
if energy_range is None:
if istart is None:
istart = self.kss.istart
if self.fullkss.istart > istart:
raise RuntimeError('istart=%d has to be >= %d' %
(istart, self.kss.istart))
if jend is None:
jend = self.kss.jend
if self.fullkss.jend < jend:
raise RuntimeError('jend=%d has to be <= %d' %
(jend, self.kss.jend))
else:
try:
emin, emax = energy_range
except:
emax = energy_range
emin = 0.
emin /= Hartree
emax /= Hartree
map = []
kss = KSSingles()
for ij, k in zip(range(len(self.fullkss)), self.fullkss):
if energy_range is None:
if k.i >= istart and k.j <= jend:
kss.append(k)
map.append(ij)
else:
if k.energy >= emin and k.energy < emax:
kss.append(k)
map.append(ij)
kss.update()
print('# diagonalize: %d transitions now' % len(kss), file=self.txt)
return map, kss
def diagonalize(self, istart=None, jend=None, energy_range=None,
TDA=False):
"""Evaluate Eigenvectors and Eigenvalues:"""
if TDA:
raise NotImplementedError
map, kss = self.get_map(istart, jend, energy_range)
nij = len(kss)
if map is None:
evec = self.full.copy()
else:
evec = np.zeros((nij, nij))
for ij in range(nij):
for kq in range(nij):
evec[ij, kq] = self.full[map[ij], map[kq]]
assert(len(evec) > 0)
self.eigenvectors = evec
self.eigenvalues = np.zeros((len(kss)))
self.kss = kss
diagonalize(self.eigenvectors, self.eigenvalues)
def Kss(self, kss=None):
"""Set and get own Kohn-Sham singles"""
if kss is not None:
self.fullkss = kss
if(hasattr(self, 'fullkss')):
return self.fullkss
else:
return None
def read(self, filename=None, fh=None):
"""Read myself from a file"""
if fh is None:
f = open(filename, 'r')
else:
f = fh
f.readline()
nij = int(f.readline())
full = np.zeros((nij, nij))
for ij in range(nij):
l = f.readline().split()
for kq in range(ij, nij):
full[ij, kq] = float(l[kq - ij])
full[kq, ij] = full[ij, kq]
self.full = full
if fh is None:
f.close()
def write(self, filename=None, fh=None):
"""Write current state to a file."""
if mpi.rank == mpi.MASTER:
if fh is None:
f = open(filename, 'w')
else:
f = fh
f.write('# OmegaMatrix\n')
nij = len(self.fullkss)
f.write('%d\n' % nij)
for ij in range(nij):
for kq in range(ij, nij):
f.write(' %g' % self.full[ij, kq])
f.write('\n')
if fh is None:
f.close()
def weight_Kijkq(self, ij, kq):
"""weight for the coupling matrix terms"""
kss = self.fullkss
return 2. * sqrt(kss[ij].get_energy() * kss[kq].get_energy() *
kss[ij].get_weight() * kss[kq].get_weight())
def __str__(self):
str = '<OmegaMatrix> '
if hasattr(self, 'eigenvalues'):
str += 'dimension ' + ('%d' % len(self.eigenvalues))
str += '\neigenvalues: '
for ev in self.eigenvalues:
str += ' ' + ('%f' % (sqrt(ev) * Hartree))
return str
class OmegaMatrix:
"""
Omega matrix in Casidas linear response formalism
Parameters
- calculator: the calculator object the ground state calculation
- kss: the Kohn-Sham singles object
- xc: the exchange correlation approx. to use
- derivativeLevel: which level i of d^i Exc/dn^i to use
- numscale: numeric epsilon for derivativeLevel=0,1
- filehandle: the oject can be read from a filehandle
- txt: output stream or file name
- finegrid: level of fine grid to use. 0: nothing, 1 for poisson only,
2 everything on the fine grid
"""
def __init__(self,
calculator=None,
kss=None,
xc=None,
derivativeLevel=None,
numscale=0.001,
filehandle=None,
txt=None,
finegrid=2,
eh_comm=None,
):
if not txt and calculator:
txt = calculator.txt
self.txt, firsttime = initialize_text_stream(txt, mpi.rank)
if eh_comm == None:
eh_comm = mpi.serial_comm
self.eh_comm = eh_comm
if filehandle is not None:
self.kss = kss
self.read(fh=filehandle)
return None
self.fullkss = kss
self.finegrid = finegrid
if calculator is None:
return
self.paw = calculator
wfs = self.paw.wfs
# handle different grid possibilities
self.restrict = None
self.poisson = PoissonSolver(nn=self.paw.hamiltonian.poisson.nn)
if finegrid:
self.poisson.set_grid_descriptor(self.paw.density.finegd)
self.poisson.initialize()
self.gd = self.paw.density.finegd
if finegrid == 1:
self.gd = wfs.gd
else:
self.poisson.set_grid_descriptor(wfs.gd)
self.poisson.initialize()
self.gd = wfs.gd
self.restrict = Transformer(self.paw.density.finegd, wfs.gd,
self.paw.input_parameters.stencils[1]
).apply
if xc == 'RPA':
xc = None # enable RPA as keyword
if xc is not None:
self.xc = XC(xc)
self.xc.initialize(self.paw.density, self.paw.hamiltonian,
wfs, self.paw.occupations)
# check derivativeLevel
if derivativeLevel is None:
derivativeLevel= \
self.xc.get_functional().get_max_derivative_level()
self.derivativeLevel = derivativeLevel
# change the setup xc functional if needed
# the ground state calculation may have used another xc
if kss.npspins > kss.nvspins:
spin_increased = True
else:
spin_increased = False
else:
self.xc = None
self.numscale = numscale
self.singletsinglet = False
if kss.nvspins<2 and kss.npspins<2:
# this will be a singlet to singlet calculation only
self.singletsinglet=True
nij = len(kss)
self.Om = np.zeros((nij,nij))
self.get_full()
def get_full(self):
self.paw.timer.start('Omega RPA')
self.get_rpa()
self.paw.timer.stop()
if self.xc is not None:
self.paw.timer.start('Omega XC')
self.get_xc()
self.paw.timer.stop()
self.eh_comm.sum(self.Om)
self.full = self.Om
def get_xc(self):
"""Add xc part of the coupling matrix"""
# shorthands
paw = self.paw
wfs = paw.wfs
gd = paw.density.finegd
comm = gd.comm
eh_comm = self.eh_comm
fg = self.finegrid is 2
kss = self.fullkss
nij = len(kss)
Om_xc = self.Om
# initialize densities
# nt_sg is the smooth density on the fine grid with spin index
if kss.nvspins==2:
# spin polarised ground state calc.
nt_sg = paw.density.nt_sg
else:
# spin unpolarised ground state calc.
if kss.npspins==2:
# construct spin polarised densities
nt_sg = np.array([.5*paw.density.nt_sg[0],
.5*paw.density.nt_sg[0]])
else:
nt_sg = paw.density.nt_sg
# check if D_sp have been changed before
D_asp = self.paw.density.D_asp
for a, D_sp in D_asp.items():
if len(D_sp) != kss.npspins:
if len(D_sp) == 1:
D_asp[a] = np.array([0.5 * D_sp[0], 0.5 * D_sp[0]])
else:
D_asp[a] = np.array([D_sp[0] + D_sp[1]])
# restrict the density if needed
if fg:
nt_s = nt_sg
else:
nt_s = self.gd.zeros(nt_sg.shape[0])
for s in range(nt_sg.shape[0]):
self.restrict(nt_sg[s], nt_s[s])
gd = paw.density.gd
# initialize vxc or fxc
if self.derivativeLevel==0:
raise NotImplementedError
if kss.npspins==2:
v_g=nt_sg[0].copy()
else:
v_g=nt_sg.copy()
elif self.derivativeLevel==1:
pass
elif self.derivativeLevel==2:
fxc_sg = np.zeros(nt_sg.shape)
self.xc.calculate_fxc(gd, nt_sg, fxc_sg)
else:
raise ValueError('derivativeLevel can only be 0,1,2')
## self.paw.my_nuclei = []
ns=self.numscale
xc=self.xc
print >> self.txt, 'XC',nij,'transitions'
for ij in range(eh_comm.rank, nij, eh_comm.size):
print >> self.txt,'XC kss['+'%d'%ij+']'
timer = Timer()
timer.start('init')
timer2 = Timer()
if self.derivativeLevel >= 1:
# vxc is available
# We use the numerical two point formula for calculating
# the integral over fxc*n_ij. The results are
# vvt_s smooth integral
# nucleus.I_sp atom based correction matrices (pack2)
# stored on each nucleus
timer2.start('init v grids')
vp_s=np.zeros(nt_s.shape,nt_s.dtype.char)
vm_s=np.zeros(nt_s.shape,nt_s.dtype.char)
if kss.npspins == 2: # spin polarised
nv_s = nt_s.copy()
nv_s[kss[ij].pspin] += ns * kss[ij].get(fg)
xc.calculate(gd, nv_s, vp_s)
nv_s = nt_s.copy()
nv_s[kss[ij].pspin] -= ns * kss[ij].get(fg)
xc.calculate(gd, nv_s, vm_s)
else: # spin unpolarised
nv = nt_s + ns * kss[ij].get(fg)
xc.calculate(gd, nv, vp_s)
nv = nt_s - ns * kss[ij].get(fg)
xc.calculate(gd, nv, vm_s)
vvt_s = (0.5 / ns) * (vp_s - vm_s)
timer2.stop()
# initialize the correction matrices
timer2.start('init v corrections')
I_asp = {}
for a, P_ni in wfs.kpt_u[kss[ij].spin].P_ani.items():
# create the modified density matrix
Pi_i = P_ni[kss[ij].i]
Pj_i = P_ni[kss[ij].j]
P_ii = np.outer(Pi_i, Pj_i)
# we need the symmetric form, hence we can pack
P_p = pack(P_ii)
D_sp = self.paw.density.D_asp[a].copy()
D_sp[kss[ij].pspin] -= ns * P_p
setup = wfs.setups[a]
I_sp = np.zeros_like(D_sp)
self.xc.calculate_paw_correction(setup, D_sp, I_sp)
I_sp *= -1.0
D_sp = self.paw.density.D_asp[a].copy()
D_sp[kss[ij].pspin] += ns * P_p
self.xc.calculate_paw_correction(setup, D_sp, I_sp)
I_sp /= 2.0 * ns
I_asp[a] = I_sp
timer2.stop()
timer.stop()
t0 = timer.get_time('init')
timer.start(ij)
for kq in range(ij,nij):
weight = self.weight_Kijkq(ij, kq)
if self.derivativeLevel == 0:
# only Exc is available
if kss.npspins==2: # spin polarised
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] += kss[ij].get(fg)
nv_g[kss[kq].pspin] += kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(
nv_g[0], v_g, nv_g[1], v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] += kss[ij].get(fg)
nv_g[kss[kq].pspin] -= kss[kq].get(fg)
Excpm = xc.get_energy_and_potential(\
nv_g[0],v_g,nv_g[1],v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] -=\
kss[ij].get(fg)
nv_g[kss[kq].pspin] +=\
kss[kq].get(fg)
Excmp = xc.get_energy_and_potential(\
nv_g[0],v_g,nv_g[1],v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] -= \
kss[ij].get(fg)
nv_g[kss[kq].pspin] -=\
kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(\
nv_g[0],v_g,nv_g[1],v_g)
else: # spin unpolarised
nv_g=nt_sg + ns*kss[ij].get(fg)\
+ ns*kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(nv_g,v_g)
nv_g=nt_sg + ns*kss[ij].get(fg)\
- ns*kss[kq].get(fg)
Excpm = xc.get_energy_and_potential(nv_g,v_g)
nv_g=nt_sg - ns*kss[ij].get(fg)\
+ ns*kss[kq].get(fg)
Excmp = xc.get_energy_and_potential(nv_g,v_g)
nv_g=nt_sg - ns*kss[ij].get(fg)\
- ns*kss[kq].get(fg)
Excmm = xc.get_energy_and_potential(nv_g,v_g)
Om_xc[ij,kq] += weight *\
0.25*(Excpp-Excmp-Excpm+Excmm)/(ns*ns)
elif self.derivativeLevel == 1:
# vxc is available
timer2.start('integrate')
Om_xc[ij,kq] += weight*\
self.gd.integrate(kss[kq].get(fg)*
vvt_s[kss[kq].pspin])
timer2.stop()
timer2.start('integrate corrections')
Exc = 0.
for a, P_ni in wfs.kpt_u[kss[kq].spin].P_ani.items():
# create the modified density matrix
Pk_i = P_ni[kss[kq].i]
Pq_i = P_ni[kss[kq].j]
P_ii = np.outer(Pk_i, Pq_i)
# we need the symmetric form, hence we can pack
# use pack as I_sp used pack2
P_p = pack(P_ii)
Exc += np.dot(I_asp[a][kss[kq].pspin], P_p)
Om_xc[ij, kq] += weight * self.gd.comm.sum(Exc)
timer2.stop()
elif self.derivativeLevel == 2:
# fxc is available
if kss.npspins==2: # spin polarised
Om_xc[ij,kq] += weight *\
gd.integrate(kss[ij].get(fg) *
kss[kq].get(fg) *
fxc_sg[kss[ij].pspin, kss[kq].pspin])
else: # spin unpolarised
Om_xc[ij,kq] += weight *\
gd.integrate(kss[ij].get(fg) *
kss[kq].get(fg) *
fxc_sg)
# XXX still numeric derivatives for local terms
timer2.start('integrate corrections')
Exc = 0.
for a, P_ni in wfs.kpt_u[kss[kq].spin].P_ani.items():
# create the modified density matrix
Pk_i = P_ni[kss[kq].i]
Pq_i = P_ni[kss[kq].j]
P_ii = np.outer(Pk_i, Pq_i)
# we need the symmetric form, hence we can pack
# use pack as I_sp used pack2
P_p = pack(P_ii)
Exc += np.dot(I_asp[a][kss[kq].pspin], P_p)
Om_xc[ij, kq] += weight * self.gd.comm.sum(Exc)
timer2.stop()
if ij != kq:
Om_xc[kq,ij] = Om_xc[ij,kq]
timer.stop()
## timer2.write()
if ij < (nij-1):
print >> self.txt,'XC estimated time left',\
self.time_left(timer, t0, ij, nij)
def Coulomb_integral_kss(self, kss_ij, kss_kq, phit, rhot,
timer=None):
# smooth part
if timer:
timer.start('integrate')
I = self.gd.integrate(rhot * phit)
if timer:
timer.stop()
timer.start('integrate corrections 2')
wfs = self.paw.wfs
Pij_ani = wfs.kpt_u[kss_ij.spin].P_ani
Pkq_ani = wfs.kpt_u[kss_kq.spin].P_ani
# Add atomic corrections
Ia = 0.0
for a, Pij_ni in Pij_ani.items():
Pi_i = Pij_ni[kss_ij.i]
Pj_i = Pij_ni[kss_ij.j]
Dij_ii = np.outer(Pi_i, Pj_i)
Dij_p = pack(Dij_ii)
Pk_i = Pkq_ani[a][kss_kq.i]
Pq_i = Pkq_ani[a][kss_kq.j]
Dkq_ii = np.outer(Pk_i, Pq_i)
Dkq_p = pack(Dkq_ii)
C_pp = wfs.setups[a].M_pp
# ----
# 2 > P P C P P
# ---- ip jr prst ks qt
# prst
Ia += 2.0*np.dot(Dkq_p, np.dot(C_pp, Dij_p))
I += self.gd.comm.sum(Ia)
if timer:
timer.stop()
return I
def get_rpa(self):
"""calculate RPA part of the omega matrix"""
# shorthands
kss=self.fullkss
finegrid=self.finegrid
wfs = self.paw.wfs
eh_comm = self.eh_comm
# calculate omega matrix
nij = len(kss)
print >> self.txt,'RPA',nij,'transitions'
Om = self.Om
for ij in range(eh_comm.rank, nij, eh_comm.size):
print >> self.txt,'RPA kss['+'%d'%ij+']=', kss[ij]
timer = Timer()
timer.start('init')
timer2 = Timer()
# smooth density including compensation charges
timer2.start('with_compensation_charges 0')
rhot_p = kss[ij].with_compensation_charges(
finegrid is not 0)
timer2.stop()
# integrate with 1/|r_1-r_2|
timer2.start('poisson')
phit_p = np.zeros(rhot_p.shape, rhot_p.dtype.char)
self.poisson.solve(phit_p, rhot_p, charge=None)
timer2.stop()
timer.stop()
t0 = timer.get_time('init')
timer.start(ij)
if finegrid == 1:
rhot = kss[ij].with_compensation_charges()
phit = self.gd.zeros()
## print "shapes 0=",phit.shape,rhot.shape
self.restrict(phit_p,phit)
else:
phit = phit_p
rhot = rhot_p
for kq in range(ij,nij):
if kq != ij:
# smooth density including compensation charges
timer2.start('kq with_compensation_charges')
rhot = kss[kq].with_compensation_charges(
finegrid is 2)
timer2.stop()
pre = 2 * sqrt(kss[ij].get_energy() * kss[kq].get_energy() *
kss[ij].get_weight() * kss[kq].get_weight() )
I = self.Coulomb_integral_kss(kss[ij], kss[kq],
rhot, phit, timer2)
Om[ij,kq] = pre * I
if ij == kq:
Om[ij,kq] += kss[ij].get_energy()**2
else:
Om[kq,ij]=Om[ij,kq]
timer.stop()
## timer2.write()
if ij < (nij-1):
t = timer.get_time(ij) # time for nij-ij calculations
t = .5*t*(nij-ij) # estimated time for n*(n+1)/2, n=nij-(ij+1)
print >> self.txt,'RPA estimated time left',\
self.timestring(t0*(nij-ij-1)+t)
def singlets_triplets(self):
"""Split yourself into singlet and triplet transitions"""
assert(self.fullkss.npspins == 2)
assert(self.fullkss.nvspins == 1)
# strip kss from down spins
skss = KSSingles()
tkss = KSSingles()
map = []
for ij, ks in enumerate(self.fullkss):
if ks.pspin == ks.spin:
skss.append((ks + ks) / sqrt(2))
tkss.append((ks - ks) / sqrt(2))
map.append(ij)
nkss = len(skss)
# define the singlet and the triplet omega-matrixes
sOm = OmegaMatrix(kss=skss)
sOm.full = np.empty((nkss, nkss))
tOm = OmegaMatrix(kss=tkss)
tOm.full = np.empty((nkss, nkss))
for ij in range(nkss):
for kl in range(nkss):
sOm.full[ij, kl] = (self.full[map[ij], map[kl]] +
self.full[map[ij], nkss + map[kl]])
tOm.full[ij, kl] = (self.full[map[ij], map[kl]] -
self.full[map[ij], nkss + map[kl]])
return sOm, tOm
def timestring(self, t):
ti = int(t + 0.5)
td = ti // 86400
st = ''
if td > 0:
st += '%d' % td + 'd'
ti -= td * 86400
th = ti // 3600
if th > 0:
st += '%d' % th + 'h'
ti -= th * 3600
tm = ti // 60
if tm > 0:
st += '%d' % tm + 'm'
ti -= tm * 60
st += '%d' % ti + 's'
return st
def time_left(self, timer, t0, ij, nij):
t = timer.get_time(ij) # time for nij-ij calculations
t = .5 * t * (nij - ij) # estimated time for n*(n+1)/2, n=nij-(ij+1)
return self.timestring(t0 * (nij - ij - 1) + t)
def get_map(self, istart=None, jend=None, energy_range=None):
"""Return the reduction map for the given requirements"""
self.istart = istart
self.jend = jend
if istart is None and jend is None and energy_range is None:
return None, self.fullkss
# reduce the matrix
print >> self.txt,'# diagonalize: %d transitions original'\
% len(self.fullkss)
if energy_range is None:
if istart is None: istart = self.kss.istart
if self.fullkss.istart > istart:
raise RuntimeError('istart=%d has to be >= %d' %
(istart, self.kss.istart))
if jend is None: jend = self.kss.jend
if self.fullkss.jend < jend:
raise RuntimeError('jend=%d has to be <= %d' %
(jend, self.kss.jend))
else:
try:
emin, emax = energy_range
except:
emax = energy_range
emin = 0.
emin /= Hartree
emax /= Hartree
map= []
kss = KSSingles()
for ij, k in zip(range(len(self.fullkss)), self.fullkss):
if energy_range is None:
if k.i >= istart and k.j <= jend:
kss.append(k)
map.append(ij)
else:
if k.energy >= emin and k.energy < emax:
kss.append(k)
map.append(ij)
kss.update()
print >> self.txt, '# diagonalize: %d transitions now' % len(kss)
return map, kss
def diagonalize(self, istart=None, jend=None, energy_range=None,
TDA=False):
"""Evaluate Eigenvectors and Eigenvalues:"""
if TDA:
raise NotImplementedError
map, kss = self.get_map(istart, jend, energy_range)
nij = len(kss)
if map is None:
evec = self.full.copy()
else:
evec = np.zeros((nij,nij))
for ij in range(nij):
for kq in range(nij):
evec[ij,kq] = self.full[map[ij],map[kq]]
assert(len(evec) > 0)
self.eigenvectors = evec
self.eigenvalues = np.zeros((len(kss)))
self.kss = kss
diagonalize(self.eigenvectors, self.eigenvalues)
def Kss(self, kss=None):
"""Set and get own Kohn-Sham singles"""
if kss is not None:
self.fullkss = kss
if(hasattr(self,'fullkss')):
return self.fullkss
else:
return None
def read(self, filename=None, fh=None):
"""Read myself from a file"""
if fh is None:
f = open(filename, 'r')
else:
f = fh
f.readline()
nij = int(f.readline())
full = np.zeros((nij,nij))
for ij in range(nij):
l = f.readline().split()
for kq in range(ij,nij):
full[ij,kq] = float(l[kq-ij])
full[kq,ij] = full[ij,kq]
self.full = full
if fh is None:
f.close()
def write(self, filename=None, fh=None):
"""Write current state to a file."""
if mpi.rank == mpi.MASTER:
if fh is None:
f = open(filename, 'w')
else:
f = fh
f.write('# OmegaMatrix\n')
nij = len(self.fullkss)
f.write('%d\n' % nij)
for ij in range(nij):
for kq in range(ij,nij):
f.write(' %g' % self.full[ij,kq])
f.write('\n')
if fh is None:
f.close()
def weight_Kijkq(self, ij, kq):
"""weight for the coupling matrix terms"""
kss = self.fullkss
return 2.*sqrt( kss[ij].get_energy() * kss[kq].get_energy() *
kss[ij].get_weight() * kss[kq].get_weight() )
def __str__(self):
str='<OmegaMatrix> '
if hasattr(self,'eigenvalues'):
str += 'dimension '+ ('%d'%len(self.eigenvalues))
str += "\neigenvalues: "
for ev in self.eigenvalues:
str += ' ' + ('%f'%(sqrt(ev) * Hartree))
return str
def calculate_Kxc(gd,
nt_sG,
npw,
Gvec_Gc,
nG,
vol,
bcell_cv,
R_av,
setups,
D_asp,
functional='ALDA',
density_cut=None):
"""ALDA kernel"""
# The soft part
#assert np.abs(nt_sG[0].shape - nG).sum() == 0
if functional == 'ALDA_X':
x_only = True
A_x = -3. / 4. * (3. / np.pi)**(1. / 3.)
nspins = len(nt_sG)
assert nspins in [1, 2]
fxc_sg = nspins**(1. / 3.) * 4. / 9. * A_x * nt_sG**(-2. / 3.)
else:
assert len(nt_sG) == 1
x_only = False
fxc_sg = np.zeros_like(nt_sG)
xc = XC(functional[1:])
xc.calculate_fxc(gd, nt_sG, fxc_sg)
if density_cut is not None:
fxc_sg[np.where(nt_sG * len(nt_sG) < density_cut)] = 0.0
# FFT fxc(r)
nG0 = nG[0] * nG[1] * nG[2]
tmp_sg = [np.fft.fftn(fxc_sg[s]) * vol / nG0 for s in range(len(nt_sG))]
r_vg = gd.get_grid_point_coordinates()
Kxc_sGG = np.zeros((len(fxc_sg), npw, npw), dtype=complex)
for s in range(len(fxc_sg)):
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
if (nG / 2 - np.abs(dG_c) > 0).all():
index = (dG_c + nG) % nG
Kxc_sGG[s, iG, jG] = tmp_sg[s][index[0], index[1],
index[2]]
else: # not in the fft index
dG_v = np.dot(dG_c, bcell_cv)
dGr_g = gemmdot(dG_v, r_vg, beta=0.0)
Kxc_sGG[s, iG, jG] = gd.integrate(
np.exp(-1j * dGr_g) * fxc_sg[s])
# The PAW part
KxcPAW_sGG = np.zeros_like(Kxc_sGG)
dG_GGv = np.zeros((npw, npw, 3))
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
dG_GGv[iG, jG] = np.dot(dG_c, bcell_cv)
for a, setup in enumerate(setups):
if rank == a % size:
rgd = setup.xc_correction.rgd
n_qg = setup.xc_correction.n_qg
nt_qg = setup.xc_correction.nt_qg
nc_g = setup.xc_correction.nc_g
nct_g = setup.xc_correction.nct_g
Y_nL = setup.xc_correction.Y_nL
dv_g = rgd.dv_g
D_sp = D_asp[a]
B_pqL = setup.xc_correction.B_pqL
D_sLq = np.inner(D_sp, B_pqL.T)
nspins = len(D_sp)
f_sg = rgd.empty(nspins)
ft_sg = rgd.empty(nspins)
n_sLg = np.dot(D_sLq, n_qg)
nt_sLg = np.dot(D_sLq, nt_qg)
# Add core density
n_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nc_g
nt_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nct_g
coefatoms_GG = np.exp(-1j * np.inner(dG_GGv, R_av[a]))
for n, Y_L in enumerate(Y_nL):
w = weight_n[n]
f_sg[:] = 0.0
n_sg = np.dot(Y_L, n_sLg)
if x_only:
f_sg = nspins * (4 / 9.) * A_x * (nspins * n_sg)**(-2 / 3.)
else:
xc.calculate_fxc(rgd, n_sg, f_sg)
ft_sg[:] = 0.0
nt_sg = np.dot(Y_L, nt_sLg)
if x_only:
ft_sg = nspins * (4 / 9.) * (A_x *
(nspins * nt_sg)**(-2 / 3.))
else:
xc.calculate_fxc(rgd, nt_sg, ft_sg)
for i in range(len(rgd.r_g)):
coef_GG = np.exp(-1j * np.inner(dG_GGv, R_nv[n]) *
rgd.r_g[i])
for s in range(len(f_sg)):
KxcPAW_sGG[s] += w * np.dot(coef_GG,
(f_sg[s, i] - ft_sg[s, i])
* dv_g[i]) * coefatoms_GG
world.sum(KxcPAW_sGG)
Kxc_sGG += KxcPAW_sGG
return Kxc_sGG / vol
def calculate_Kxc(gd, nt_sG, npw, Gvec_Gc, nG, vol,
bcell_cv, R_av, setups, D_asp):
"""LDA kernel"""
# The soft part
assert np.abs(nt_sG[0].shape - nG).sum() == 0
xc = XC('LDA')
fxc_sg = np.zeros_like(nt_sG)
xc.calculate_fxc(gd, nt_sG, fxc_sg)
fxc_g = fxc_sg[0]
# FFT fxc(r)
nG0 = nG[0] * nG[1] * nG[2]
tmp_g = np.fft.fftn(fxc_g) * vol / nG0
r_vg = gd.get_grid_point_coordinates()
Kxc_GG = np.zeros((npw, npw), dtype=complex)
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
if (nG / 2 - np.abs(dG_c) > 0).all():
index = (dG_c + nG) % nG
Kxc_GG[iG, jG] = tmp_g[index[0], index[1], index[2]]
else: # not in the fft index
dG_v = np.dot(dG_c, bcell_cv)
dGr_g = gemmdot(dG_v, r_vg, beta=0.0)
Kxc_GG[iG, jG] = gd.integrate(np.exp(-1j*dGr_g)*fxc_g)
KxcPAW_GG = np.zeros_like(Kxc_GG)
# The PAW part
dG_GGv = np.zeros((npw, npw, 3))
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
dG_GGv[iG, jG] = np.dot(dG_c, bcell_cv)
for a, setup in enumerate(setups):
if rank == a % size:
rgd = setup.xc_correction.rgd
n_qg = setup.xc_correction.n_qg
nt_qg = setup.xc_correction.nt_qg
nc_g = setup.xc_correction.nc_g
nct_g = setup.xc_correction.nct_g
Y_nL = setup.xc_correction.Y_nL
dv_g = rgd.dv_g
D_sp = D_asp[a]
B_pqL = setup.xc_correction.B_pqL
D_sLq = np.inner(D_sp, B_pqL.T)
nspins = len(D_sp)
assert nspins == 1
f_sg = rgd.empty(nspins)
ft_sg = rgd.empty(nspins)
n_sLg = np.dot(D_sLq, n_qg)
nt_sLg = np.dot(D_sLq, nt_qg)
# Add core density
n_sLg[:, 0] += sqrt(4 * pi) / nspins * nc_g
nt_sLg[:, 0] += sqrt(4 * pi) / nspins * nct_g
coefatoms_GG = np.exp(-1j * np.inner(dG_GGv, R_av[a]))
for n, Y_L in enumerate(Y_nL):
w = weight_n[n]
f_sg[:] = 0.0
n_sg = np.dot(Y_L, n_sLg)
xc.calculate_fxc(rgd, n_sg, f_sg)
ft_sg[:] = 0.0
nt_sg = np.dot(Y_L, nt_sLg)
xc.calculate_fxc(rgd, nt_sg, ft_sg)
coef_GGg = np.exp(-1j * np.outer(np.inner(dG_GGv, R_nv[n]),
rgd.r_g)).reshape(npw,npw,rgd.ng)
KxcPAW_GG += w * np.dot(coef_GGg, (f_sg[0]-ft_sg[0]) * dv_g) * coefatoms_GG
world.sum(KxcPAW_GG)
Kxc_GG += KxcPAW_GG
return Kxc_GG / vol
