def Coulomb_integral_kss(self, kss_ij, kss_kq, phit, rhot):
# smooth part
I = self.gd.integrate(rhot * phit)
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)
return I
def calculate_paw_fHXC_corrections(self, kss_ip, kss_jq, I_asp):
i = kss_ip.occ_ind
p = kss_ip.unocc_ind
j = kss_jq.occ_ind
q = kss_jq.unocc_ind
Ia = 0.0
for a, P_ni in self.calc.wfs.kpt_u[kss_jq.spin_ind].P_ani.items():
Pip_ni = self.calc.wfs.kpt_u[kss_ip.spin_ind].P_ani[a]
Dip_ii = np.outer(Pip_ni[i], Pip_ni[p])
Dip_p = pack(Dip_ii)
Pjq_ni = self.calc.wfs.kpt_u[kss_jq.spin_ind].P_ani[a]
Djq_ii = np.outer(Pjq_ni[j], Pjq_ni[q])
Djq_p = pack(Djq_ii)
# Hartree part
C_pp = self.calc.wfs.setups[a].M_pp
# why factor of two here?
# see appendix A of J. Chem. Phys. 128, 244101 (2008)
#
# 2 sum_prst P P C P P
# ip jr prst ks qt
Ia += self.fH_pre * 2.0 * np.dot(Djq_p, np.dot(C_pp, Dip_p))
# XC part, CHECK THIS JQ EVERWHERE!!!
Ia += self.fxc_pre * np.dot(I_asp[a][kss_jq.spin_ind], Djq_p)
return Ia
def symmetrize_atomic_density_matrices(self, D_asp):
if len(self.kd.symmetry.op_scc) == 0:
return
if hasattr(D_asp, 'redistribute'):
a_sa = self.kd.symmetry.a_sa
D_asp.redistribute(self.atom_partition.as_serial())
for s in range(self.nspins):
D_aii = [unpack2(D_asp[a][s])
for a in range(len(D_asp))]
for a, D_ii in enumerate(D_aii):
setup = self.setups[a]
D_asp[a][s] = pack(setup.symmetrize(a, D_aii, a_sa))
D_asp.redistribute(self.atom_partition)
else:
all_D_asp = []
for a, setup in enumerate(self.setups):
D_sp = D_asp.get(a)
if D_sp is None:
ni = setup.ni
D_sp = np.empty((self.nspins, ni * (ni + 1) // 2))
self.gd.comm.broadcast(D_sp, self.atom_partition.rank_a[a])
all_D_asp.append(D_sp)
for s in range(self.nspins):
D_aii = [unpack2(D_sp[s]) for D_sp in all_D_asp]
for a, D_sp in D_asp.items():
setup = self.setups[a]
D_sp[s] = pack(setup.symmetrize(a, D_aii,
self.kd.symmetry.a_sa))
def write(self, writer):
"""Writes response specific data to disc.
During the writing process, the DeltaXC is calculated
(if not yet calculated).
"""
if self.Dxc_vt_sG is None:
self.calculate_delta_xc()
wfs = self.wfs
kpt_comm = wfs.kd.comm
gd = wfs.gd
nadm = 0
for setup in wfs.setups:
ni = setup.ni
nadm += ni * (ni + 1) // 2
# Not yet tested for parallerization
# assert world.size == 1
shape = (wfs.nspins,) + tuple(gd.get_size_of_global_array())
# Write the pseudodensity on the coarse grid:
writer.add_array('gllb_pseudo_response_potential', shape)
if kpt_comm.rank == 0:
for vt_G in self.vt_sG:
writer.fill(gd.collect(vt_G) * Hartree)
writer.add_array('gllb_dxc_pseudo_response_potential', shape)
if kpt_comm.rank == 0:
for Dxc_vt_G in self.Dxc_vt_sG:
writer.fill(gd.collect(Dxc_vt_G) * (Hartree / Bohr))
def pack(X0_asp):
X_asp = self.wfs.setups.empty_atomic_matrix(
self.wfs.nspins, self.wfs.atom_partition)
# XXX some of the provided X0_asp contain strangely duplicated
# elements. Take only the minimal set:
for a in X_asp:
X_asp[a][:] = X0_asp[a]
return pack_atomic_matrices(X_asp)
writer.write(gllb_atomic_density_matrices=pack(self.D_asp))
writer.write(gllb_atomic_response_matrices=pack(self.Dresp_asp))
writer.write(gllb_dxc_atomic_density_matrices=pack(self.Dxc_D_asp))
writer.write(
gllb_dxc_atomic_response_matrices=pack(self.Dxc_Dresp_asp))
def add_compensation_charges(self, nt_G, rhot_g):
"""Add compensation charges to input pair density, which
is interpolated to the fine grid if needed."""
if self.finegrid:
# interpolate the pair density to the fine grid
self.density.interpolator.apply(nt_G, rhot_g)
else:
# copy values
rhot_g[:] = nt_G
# Determine the compensation charges for each nucleus
Q_aL = {}
for a, P_ni in self.P_ani.items():
assert P_ni.dtype == float
# Generate density matrix
P1_i = P_ni[self.n1]
P2_i = P_ni[self.n2]
D_ii = np.outer(P1_i.conj(), P2_i)
# allowed to pack as used in the scalar product with
# the symmetric array Delta_pL
D_p = pack(D_ii, tolerance=1e30)
# Determine compensation charge coefficients:
Q_aL[a] = np.dot(D_p, self.density.setups[a].Delta_pL)
# Add compensation charges
if self.finegrid:
self.density.ghat.add(rhot_g, Q_aL)
else:
self.density.Ghat.add(rhot_g, Q_aL)
def calculate_pair_density(self, n1, n2, kpt1, kpt2, ik1, ik2, bzq_index):
psit1_G = self.kd.transform_wave_function(kpt1.psit_nG[n1], ik1)
psit2_G = self.kd.transform_wave_function(kpt2.psit_nG[n2], ik2)
nt_G = psit1_G.conj() * psit2_G
s1 = self.kd.sym_k[ik1]
s2 = self.kd.sym_k[ik2]
t1 = self.kd.time_reversal_k[ik1]
t2 = self.kd.time_reversal_k[ik2]
k1_c = self.kd.ibzk_kc[kpt1.k]
k2_c = self.kd.ibzk_kc[kpt2.k]
Q_aL = {}
for a in kpt1.P_ani.keys():
b1 = self.kd.symmetry.a_sa[s1, a]
b2 = self.kd.symmetry.a_sa[s2, a]
S1_c = np.dot(self.spos_ac[a], self.kd.symmetry.op_scc[s1]) - self.spos_ac[b1]
S2_c = np.dot(self.spos_ac[a], self.kd.symmetry.op_scc[s2]) - self.spos_ac[b2]
assert abs(S1_c.round() - S1_c).max() < 1e-13
assert abs(S2_c.round() - S2_c).max() < 1e-13
x1 = np.exp(2j * pi * np.dot(k1_c, S1_c))
x2 = np.exp(2j * pi * np.dot(k2_c, S2_c))
P1_i = np.dot(self.setups[a].R_sii[s1], kpt1.P_ani[b1][n1]) * x1
P2_i = np.dot(self.setups[a].R_sii[s2], kpt2.P_ani[b2][n2]) * x2
if t1:
P1_i = P1_i.conj()
if t2:
P2_i = P2_i.conj()
D_ii = np.outer(P1_i.conj(), P2_i)
D_p = pack(D_ii)
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
self.ghat.add(nt_G, Q_aL, bzq_index)
return nt_G
def raw_wignerseitz_LDOS(paw, a, spin):
"""Return a list of eigenvalues, and their weight on the specified atom"""
wfs = paw.wfs
assert wfs.dtype == float
gd = wfs.gd
atom_index = wignerseitz(gd, paw.atoms)
w_k = wfs.weight_k
nk = len(w_k)
nb = wfs.bd.nbands
energies = np.empty(nb * nk)
weights = np.empty(nb * nk)
x = 0
for k, w in enumerate(w_k):
u = spin * nk + k
energies[x:x + nb] = wfs.collect_eigenvalues(k=k, s=spin)
for n, psit_G in enumerate(wfs.kpt_u[u].psit_nG):
P_i = wfs.kpt_u[u].P_ani[a][n]
P_p = pack(np.outer(P_i, P_i))
Delta_p = sqrt(4 * pi) * wfs.setups[a].Delta_pL[:, 0]
weights[x + n] = w * (gd.integrate(abs(
np.where(atom_index == a, psit_G, 0.0))**2)
+ np.dot(Delta_p, P_p))
x += nb
return energies, weights
def raw_wignerseitz_LDOS(paw, a, spin):
"""Return a list of eigenvalues, and their weight on the specified atom"""
wfs = paw.wfs
assert wfs.dtype == float
gd = wfs.gd
atom_index = wignerseitz(gd, paw.atoms)
w_k = wfs.kd.weight_k
nk = len(w_k)
nb = wfs.bd.nbands
energies = np.empty(nb * nk)
weights = np.empty(nb * nk)
x = 0
for k, w in enumerate(w_k):
u = spin * nk + k
energies[x:x + nb] = wfs.collect_eigenvalues(k=k, s=spin)
for n, psit_G in enumerate(wfs.kpt_u[u].psit_nG):
P_i = wfs.kpt_u[u].P_ani[a][n]
P_p = pack(np.outer(P_i, P_i))
Delta_p = sqrt(4 * pi) * wfs.setups[a].Delta_pL[:, 0]
weights[x + n] = w * (
gd.integrate(abs(np.where(atom_index == a, psit_G, 0.0))**2) +
np.dot(Delta_p, P_p))
x += nb
return energies, weights
def with_compensation_charges(self, finegrid=False):
"""Get pair densisty including the compensation charges"""
rhot = self.get(finegrid)
# Determine the compensation charges for each nucleus
Q_aL = {}
for a, P_ni in self.P_ani.items():
# Generate density matrix
Pi_i = P_ni[self.i]
Pj_i = P_ni[self.j]
D_ii = np.outer(Pi_i, Pj_i)
# allowed to pack as used in the scalar product with
# the symmetric array Delta_pL
D_p = pack(D_ii)
# Determine compensation charge coefficients:
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
# Add compensation charges
if finegrid:
self.density.ghat.add(rhot, Q_aL)
else:
if not hasattr(self.density, 'Ghat'):
self.density.Ghat = LFC(self.density.gd,
[setup.ghat_l
for setup in self.setups],
integral=sqrt(4 * pi))
self.density.Ghat.set_positions(self.spos_ac)
self.density.Ghat.add(rhot, Q_aL)
return rhot
def add_compensation_charges(self, nt_G, rhot_g):
"""Add compensation charges to input pair density, which
is interpolated to the fine grid if needed."""
if self.finegrid:
# interpolate the pair density to the fine grid
self.density.interpolator.apply(nt_G, rhot_g)
else:
# copy values
rhot_g[:] = nt_G
# Determine the compensation charges for each nucleus
Q_aL = {}
for a, P_ni in self.P_ani.items():
assert P_ni.dtype == float
# Generate density matrix
P1_i = P_ni[self.n1]
P2_i = P_ni[self.n2]
D_ii = np.outer(P1_i.conj(), P2_i)
# allowed to pack as used in the scalar product with
# the symmetric array Delta_pL
D_p = pack(D_ii, tolerance=1e30)
# Determine compensation charge coefficients:
Q_aL[a] = np.dot(D_p, self.density.setups[a].Delta_pL)
# Add compensation charges
if self.finegrid:
self.density.ghat.add(rhot_g, Q_aL)
else:
self.density.Ghat.add(rhot_g, Q_aL)
def with_compensation_charges(self, finegrid=False):
"""Get pair densisty including the compensation charges"""
rhot = self.get(finegrid)
# Determine the compensation charges for each nucleus
Q_aL = {}
for a, P_ni in self.P_ani.items():
# Generate density matrix
Pi_i = P_ni[self.i]
Pj_i = P_ni[self.j]
D_ii = np.outer(Pi_i, Pj_i)
# allowed to pack as used in the scalar product with
# the symmetric array Delta_pL
D_p = pack(D_ii)
# Determine compensation charge coefficients:
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
# Add compensation charges
if finegrid:
self.density.ghat.add(rhot, Q_aL)
else:
if not hasattr(self.density, 'Ghat'):
self.density.Ghat = LFC(
self.density.gd, [setup.ghat_l for setup in self.setups],
integral=sqrt(4 * pi))
self.density.Ghat.set_positions(self.spos_ac)
self.density.Ghat.add(rhot, Q_aL)
return rhot
def initialize_density_matrix(self, f_si):
nspins, nao = f_si.shape
ni = self.ni
D_sii = np.zeros((nspins, ni, ni))
D_sp = np.zeros((nspins, ni * (ni + 1) // 2))
nj = len(self.n_j)
j = 0
i = 0
ib = 0
for phit in self.phit_j:
l = phit.get_angular_momentum_number()
# Skip projector functions not in basis set:
while j < nj and self.l_j[j] != l:
i += 2 * self.l_j[j] + 1
j += 1
if j == nj:
break
for m in range(2 * l + 1):
D_sii[:, i + m, i + m] = f_si[:, ib + m]
j += 1
i += 2 * l + 1
ib += 2 * l + 1
for s in range(nspins):
D_sp[s] = pack(D_sii[s])
return D_sp
def initialize_density_matrix(self, f_si):
nspins, nao = f_si.shape
ni = self.ni
D_sii = np.zeros((nspins, ni, ni))
D_sp = np.zeros((nspins, ni * (ni + 1) // 2))
nj = len(self.l_j)
j = 0
i = 0
ib = 0
for phit in self.phit_j:
l = phit.get_angular_momentum_number()
# Skip functions not in basis set:
while j < nj and self.l_j[j] != l:
i += 2 * self.l_j[j] + 1
j += 1
if j == nj:
break
for m in range(2 * l + 1):
D_sii[:, i + m, i + m] = f_si[:, ib + m]
j += 1
i += 2 * l + 1
ib += 2 * l + 1
for s in range(nspins):
D_sp[s] = pack(D_sii[s])
return D_sp
def get_orbital_density_matrix(self, a, kpt, n):
"""Add the nth band density from kpt to density matrix D_sp"""
ni = self.setups[a].ni
D_sii = np.zeros((self.nspins, ni, ni))
P_i = kpt.P_ani[a][n]
D_sii[kpt.s] += np.outer(P_i.conj(), P_i).real
D_sp = [pack(D_ii) for D_ii in D_sii]
return D_sp
def get_orbital_density_matrix(self, a, kpt, n):
"""Add the nth band density from kpt to density matrix D_sp"""
ni = self.setups[a].ni
D_sii = np.zeros((self.nspins, ni, ni))
P_i = kpt.P_ani[a][n]
D_sii[kpt.s] += np.outer(P_i.conj(), P_i).real
D_sp = [pack(D_ii) for D_ii in D_sii]
return D_sp
def calculate_delta_xc_perturbation(self):
h**o, lumo = self.occupations.get_homo_lumo(self.wfs)
Ksgap = lumo - h**o
# Calculate average of lumo reference response potential
method1_dxc = np.average(self.Dxc_vt_sG[0])
#print self.Dxc_vt_sG[0][0][0]
nt_G = self.gd.empty()
ne = self.nvalence # Number of electrons
assert self.nspins == 1
lumo_n = ne // 2
eps_u = []
eps_un = np.zeros((len(self.kpt_u), len(self.kpt_u[0].psit_nG)))
for u, kpt in enumerate(self.kpt_u):
#print "K-Point index: ",u
for n in range(len(kpt.psit_nG)):
nt_G[:] = 0.0
self.wfs.add_orbital_density(nt_G, kpt, n)
E = 0.0
for a in self.density.D_asp:
D_sp = self.Dxc_D_asp[a]
Dresp_sp = self.Dxc_Dresp_asp[a]
P_ni = kpt.P_ani[a]
Dwf_p = pack(np.outer(P_ni[n].T.conj(), P_ni[n]).real)
E += self.integrate_sphere(a, Dresp_sp, D_sp, Dwf_p)
#print "Atom corrections", E*27.21
E = self.grid_comm.sum(E)
E += self.gd.integrate(nt_G * self.Dxc_vt_sG[0])
E += kpt.eps_n[lumo_n]
#print "Old eigenvalue", kpt.eps_n[lumo_n]*27.21, " New eigenvalue ", E*27.21, " DXC", E*27.21-kpt.eps_n[lumo_n]*27.21
eps_un[u][n] = E
method2_lumo = min([eps_n[lumo_n] for eps_n in eps_un])
method2_lumo = -self.kpt_comm.max(-method2_lumo)
method2_dxc = method2_lumo - lumo
Ha = 27.2116
Ksgap *= Ha
method1_dxc *= Ha
method2_dxc *= Ha
if world.rank is not 0:
return (Ksgap, method2_dxc)
print
print "\Delta XC calulation"
print "-----------------------------------------------"
print "| Method | KS-Gap | \Delta XC | QP-Gap |"
print "-----------------------------------------------"
print "| Averaging | %7.2f | %9.2f | %7.2f |" % (Ksgap, method1_dxc,
Ksgap + method1_dxc)
print "| Lumo pert. | %7.2f | %9.2f | %7.2f |" % (Ksgap, method2_dxc,
Ksgap + method2_dxc)
print "-----------------------------------------------"
print
return (Ksgap, method2_dxc)
def calculate_delta_xc_perturbation_spin(self, s=0):
h**o, lumo = self.occupations.get_homo_lumo_by_spin(self.wfs, s)
Ksgap = lumo - h**o
# Calculate average of lumo reference response potential
method1_dxc = np.average(self.Dxc_vt_sG[s])
nt_G = self.gd.empty()
# Find the lumo-orbital of this spin
sign = 1 - s * 2
lumo_n = (self.occupations.nvalence +
sign * self.occupations.magmom) // 2
gaps = [1000.0]
for u, kpt in enumerate(self.kpt_u):
if kpt.s == s:
nt_G[:] = 0.0
self.wfs.add_orbital_density(nt_G, kpt, lumo_n)
E = 0.0
for a in self.density.D_asp:
D_sp = self.Dxc_D_asp[a]
Dresp_sp = self.Dxc_Dresp_asp[a]
P_ni = kpt.P_ani[a]
Dwf_p = pack(
np.outer(P_ni[lumo_n].T.conj(), P_ni[lumo_n]).real)
print(
"self.integrate_sphere DOES NOT SUPPORT SPIN POLARIZED? atc_response.py"
)
E += self.integrate_sphere(a, Dresp_sp, D_sp, Dwf_p)
E = self.grid_comm.sum(E)
E += self.gd.integrate(nt_G * self.Dxc_vt_sG[s])
E += kpt.eps_n[lumo_n]
gaps.append(E - lumo)
#print "Old eigenvalue", kpt.eps_n[lumo_n]*27.21, " New eigenvalue ", E*27.21, " DXC", E*27.21-kpt.eps_n[lumo_n]*27.21
#eps_un[u][n] = E
method2_dxc = -self.kpt_comm.max(-min(gaps))
Ha = 27.2116
Ksgap *= Ha
method1_dxc *= Ha
method2_dxc *= Ha
if world.rank is not 0:
return (Ksgap, method2_dxc)
print()
print("\Delta XC calulation")
print("-----------------------------------------------")
print("| Method | KS-Gap | \Delta XC | QP-Gap |")
print("-----------------------------------------------")
print("| Averaging | %7.2f | %9.2f | %7.2f |" %
(Ksgap, method1_dxc, Ksgap + method1_dxc))
print("| Lumo pert. | %7.2f | %9.2f | %7.2f |" %
(Ksgap, method2_dxc, Ksgap + method2_dxc))
print("-----------------------------------------------")
print()
return (Ksgap, method2_dxc)
def calculate_delta_xc_perturbation(self):
h**o, lumo = self.occupations.get_homo_lumo(self.wfs)
Ksgap = lumo - h**o
# Calculate average of lumo reference response potential
method1_dxc = np.average(self.Dxc_vt_sG[0])
#print self.Dxc_vt_sG[0][0][0]
nt_G = self.gd.empty()
ne = self.nvalence # Number of electrons
assert self.nspins == 1
lumo_n = ne // 2
eps_u =[]
eps_un = np.zeros((len(self.kpt_u),len(self.kpt_u[0].psit_nG)))
for u, kpt in enumerate(self.kpt_u):
#print "K-Point index: ",u
for n in range(len(kpt.psit_nG)):
nt_G[:] = 0.0
self.wfs.add_orbital_density(nt_G, kpt, n)
E = 0.0
for a in self.density.D_asp:
D_sp = self.Dxc_D_asp[a]
Dresp_sp = self.Dxc_Dresp_asp[a]
P_ni = kpt.P_ani[a]
Dwf_p = pack(np.outer(P_ni[n].T.conj(), P_ni[n]).real)
E += self.integrate_sphere(a, Dresp_sp, D_sp, Dwf_p)
#print "Atom corrections", E*27.21
E = self.grid_comm.sum(E)
E += self.gd.integrate(nt_G*self.Dxc_vt_sG[0])
E += kpt.eps_n[lumo_n]
#print "Old eigenvalue", kpt.eps_n[lumo_n]*27.21, " New eigenvalue ", E*27.21, " DXC", E*27.21-kpt.eps_n[lumo_n]*27.21
eps_un[u][n] = E
method2_lumo = min([ eps_n[lumo_n] for eps_n in eps_un])
method2_lumo = -self.kpt_comm.max(-method2_lumo)
method2_dxc = method2_lumo-lumo
Ha = 27.2116
Ksgap *= Ha
method1_dxc *= Ha
method2_dxc *= Ha
if world.rank is not 0:
return (Ksgap, method2_dxc)
print
print "\Delta XC calulation"
print "-----------------------------------------------"
print "| Method | KS-Gap | \Delta XC | QP-Gap |"
print "-----------------------------------------------"
print "| Averaging | %7.2f | %9.2f | %7.2f |" % (Ksgap, method1_dxc, Ksgap+method1_dxc)
print "| Lumo pert. | %7.2f | %9.2f | %7.2f |" % (Ksgap, method2_dxc, Ksgap+method2_dxc)
print "-----------------------------------------------"
print
return (Ksgap, method2_dxc)
def calculate_delta_xc_perturbation_spin(self, s=0):
h**o, lumo = self.wfs.get_homo_lumo(s)
Ksgap = lumo - h**o
# Calculate average of lumo reference response potential
method1_dxc = np.average(self.Dxc_vt_sG[s])
nt_G = self.gd.empty()
# Find the lumo-orbital of this spin
sign = 1 - s * 2
lumo_n = int((self.wfs.nvalence + sign * self.occupations.magmom) // 2)
gaps = [1000.0]
for u, kpt in enumerate(self.kpt_u):
if kpt.s == s:
nt_G[:] = 0.0
self.wfs.add_orbital_density(nt_G, kpt, lumo_n)
E = 0.0
for a in self.density.D_asp:
D_sp = self.Dxc_D_asp[a]
Dresp_sp = self.Dxc_Dresp_asp[a]
P_ni = kpt.P_ani[a]
Dwf_p = pack(
np.outer(P_ni[lumo_n].T.conj(), P_ni[lumo_n]).real)
E += self.integrate_sphere(a,
Dresp_sp,
D_sp,
Dwf_p,
spin=s)
E = self.grid_comm.sum(E)
E += self.gd.integrate(nt_G * self.Dxc_vt_sG[s])
E += kpt.eps_n[lumo_n]
gaps.append(E - lumo)
method2_dxc = -self.kpt_comm.max(-min(gaps))
Ha = 27.2116
Ksgap *= Ha
method1_dxc *= Ha
method2_dxc *= Ha
if world.rank is not 0:
return (Ksgap, method2_dxc)
if 0: # TODO print properly, not to stdout!
print()
print('\Delta XC calulation')
print('-----------------------------------------------')
print('| Method | KS-Gap | \Delta XC | QP-Gap |')
print('-----------------------------------------------')
print('| Averaging | %7.2f | %9.2f | %7.2f |' %
(Ksgap, method1_dxc, Ksgap + method1_dxc))
print('| Lumo pert. | %7.2f | %9.2f | %7.2f |' %
(Ksgap, method2_dxc, Ksgap + method2_dxc))
print('-----------------------------------------------')
print()
return (Ksgap, method2_dxc)
def symmetrize_atomic_density_matrices(self, D_asp):
if len(self.kd.symmetry.op_scc) == 0:
return
a_sa = self.kd.symmetry.a_sa
D_asp.redistribute(self.atom_partition.as_serial())
for s in range(self.nspins):
D_aii = [unpack2(D_asp[a][s]) for a in range(len(D_asp))]
for a, D_ii in enumerate(D_aii):
setup = self.setups[a]
D_asp[a][s] = pack(setup.symmetrize(a, D_aii, a_sa))
D_asp.redistribute(self.atom_partition)
def calculate_delta_xc_perturbation_spin(self, s=0):
h**o, lumo = self.occupations.get_homo_lumo_by_spin(self.wfs, s)
Ksgap = lumo - h**o
# Calculate average of lumo reference response potential
method1_dxc = np.average(self.Dxc_vt_sG[s])
nt_G = self.gd.empty()
# Find the lumo-orbital of this spin
sign = 1 - s * 2
lumo_n = (self.occupations.nvalence + sign * self.occupations.magmom) // 2
gaps = [ 1000.0 ]
for u, kpt in enumerate(self.kpt_u):
if kpt.s == s:
nt_G[:] = 0.0
self.wfs.add_orbital_density(nt_G, kpt, lumo_n)
E = 0.0
for a in self.density.D_asp:
D_sp = self.Dxc_D_asp[a]
Dresp_sp = self.Dxc_Dresp_asp[a]
P_ni = kpt.P_ani[a]
Dwf_p = pack(np.outer(P_ni[lumo_n].T.conj(), P_ni[lumo_n]).real)
print("self.integrate_sphere DOES NOT SUPPORT SPIN POLARIZED? atc_response.py")
E += self.integrate_sphere(a, Dresp_sp, D_sp, Dwf_p)
E = self.grid_comm.sum(E)
E += self.gd.integrate(nt_G*self.Dxc_vt_sG[s])
E += kpt.eps_n[lumo_n]
gaps.append(E-lumo)
#print "Old eigenvalue", kpt.eps_n[lumo_n]*27.21, " New eigenvalue ", E*27.21, " DXC", E*27.21-kpt.eps_n[lumo_n]*27.21
#eps_un[u][n] = E
method2_dxc = -self.kpt_comm.max(-min(gaps))
Ha = 27.2116
Ksgap *= Ha
method1_dxc *= Ha
method2_dxc *= Ha
if world.rank is not 0:
return (Ksgap, method2_dxc)
print()
print("\Delta XC calulation")
print("-----------------------------------------------")
print("| Method | KS-Gap | \Delta XC | QP-Gap |")
print("-----------------------------------------------")
print("| Averaging | %7.2f | %9.2f | %7.2f |" % (Ksgap, method1_dxc, Ksgap+method1_dxc))
print("| Lumo pert. | %7.2f | %9.2f | %7.2f |" % (Ksgap, method2_dxc, Ksgap+method2_dxc))
print("-----------------------------------------------")
print()
return (Ksgap, method2_dxc)
def calculate_atomic_density_matrices_with_occupation(self, D_asp, f_un):
"""Calculate atomic density matrices from projections with
custom occupation f_un."""
# Varying f_n used in calculation of response part of GLLB-potential
for a, D_sp in D_asp.items():
ni = self.setups[a].ni
D_sii = np.zeros((self.nspins, ni, ni))
for f_n, kpt in zip(f_un, self.kpt_u):
self.calculate_atomic_density_matrices_k_point(D_sii, kpt, a,
f_n)
D_sp[:] = [pack(D_ii) for D_ii in D_sii]
self.band_comm.sum(D_sp)
self.kpt_comm.sum(D_sp)
self.symmetrize_atomic_density_matrices(D_asp)
def calculate_atomic_density_matrices_with_occupation(self, D_asp, f_un):
"""Calculate atomic density matrices from projections with
custom occupation f_un."""
# Varying f_n used in calculation of response part of GLLB-potential
for a, D_sp in D_asp.items():
ni = self.setups[a].ni
D_sii = np.zeros((len(D_sp), ni, ni))
for f_n, kpt in zip(f_un, self.kpt_u):
self.calculate_atomic_density_matrices_k_point(D_sii, kpt, a,
f_n)
D_sp[:] = [pack(D_ii) for D_ii in D_sii]
self.band_comm.sum(D_sp)
self.kpt_comm.sum(D_sp)
self.symmetrize_atomic_density_matrices(D_asp)
def make_optimized(qstart, qend):
g_qG = np.zeros((qend - qstart,) + w_wG.shape[1:], float)
P_aqp = {}
for a, P_wi in P_awi.items():
ni = P_wi.shape[1]
nii = ni * (ni + 1) // 2
P_aqp[a] = np.zeros((qend - qstart, nii), float)
for w1, w1_G in enumerate(w_wG):
U = Uisq_iqj[w1, qstart: qend].copy()
gemm(1., w1_G * w_wG, U, 1.0, g_qG)
for a, P_wi in P_awi.items():
P_wp = np.array([pack(np.outer(P_wi[w1], P_wi[w2]))
for w2 in range(Ni)])
gemm(1., P_wp, U, 1.0, P_aqp[a])
return g_qG, P_aqp
def make_optimized(qstart, qend):
g_qG = np.zeros((qend - qstart,) + w_wG.shape[1:], float)
P_aqp = {}
for a, P_wi in P_awi.items():
ni = P_wi.shape[1]
nii = ni * (ni + 1) // 2
P_aqp[a] = np.zeros((qend - qstart, nii), float)
for w1, w1_G in enumerate(w_wG):
U = Uisq_iqj[w1, qstart: qend].copy()
gemm(1., w1_G * w_wG, U, 1.0, g_qG)
for a, P_wi in P_awi.items():
P_wp = np.array([pack(np.outer(P_wi[w1], P_wi[w2]))
for w2 in range(Ni)])
gemm(1., P_wp, U, 1.0, P_aqp[a])
return g_qG, P_aqp
def symmetrize_atomic_density_matrices(self, D_asp):
if len(self.kd.symmetry.op_scc) > 1:
all_D_asp = []
for a, setup in enumerate(self.setups):
D_sp = D_asp.get(a)
if D_sp is None:
ni = setup.ni
D_sp = np.empty((self.ns, ni * (ni + 1) // 2))
self.gd.comm.broadcast(D_sp, self.rank_a[a])
all_D_asp.append(D_sp)
for s in range(self.nspins):
D_aii = [unpack2(D_sp[s]) for D_sp in all_D_asp]
for a, D_sp in D_asp.items():
setup = self.setups[a]
D_sp[s] = pack(setup.symmetrize(a, D_aii, self.kd.symmetry.a_sa))
def calculate_atomic_density_matrices_with_occupation(self, D_asp, f_un):
"""Calculate atomic density matrices from projections with
custom occupation f_un."""
# Parameter check (if user accidentally passes f_n instead of f_un)
if f_un[0] is not None: # special case for transport calculations...
assert isinstance(f_un[0], np.ndarray)
# Varying f_n used in calculation of response part of GLLB-potential
for a, D_sp in D_asp.items():
ni = self.setups[a].ni
D_sii = np.zeros((len(D_sp), ni, ni))
for f_n, kpt in zip(f_un, self.kpt_u):
self.calculate_atomic_density_matrices_k_point(D_sii, kpt, a, f_n)
D_sp[:] = [pack(D_ii) for D_ii in D_sii]
self.kptband_comm.sum(D_sp)
self.symmetrize_atomic_density_matrices(D_asp)
def expand_wave_function(self, psit_G, u, n):
"""Get the weights of wave function in Wigner-Seitz cells
around the atoms. The spin-k-point index u and band number n
are needed for the augmentation sphere corrections."""
assert psit_G.dtype == float
# smooth part
weigths = self.expand(psit_G**2)
# add augmentation sphere corrections
for a, nucleus in enumerate(self.atoms):
P_i = nucleus.P_uni[u, n]
P_p = pack(np.outer(P_i, P_i))
Delta_p = sqrt(4 * pi) * nucleus.setup.Delta_pL[:, 0]
weigths[a] += np.dot(Delta_p, P_p)
return weigths
def symmetrize_atomic_density_matrices(self, D_asp):
if len(self.kd.symmetry.op_scc) > 1:
all_D_asp = []
for a, setup in enumerate(self.setups):
D_sp = D_asp.get(a)
if D_sp is None:
ni = setup.ni
D_sp = np.empty((self.ns, ni * (ni + 1) // 2))
self.gd.comm.broadcast(D_sp, self.rank_a[a])
all_D_asp.append(D_sp)
for s in range(self.nspins):
D_aii = [unpack2(D_sp[s]) for D_sp in all_D_asp]
for a, D_sp in D_asp.items():
setup = self.setups[a]
D_sp[s] = pack(
setup.symmetrize(a, D_aii, self.kd.symmetry.a_sa))
def expand_wave_function(self, psit_G, u, n):
"""Get the weights of wave function in Wigner-Seitz cells
around the atoms. The spin-k-point index u and band number n
are needed for the augmentation sphere corrections."""
assert psit_G.dtype == float
# smooth part
weigths = self.expand(psit_G**2)
# add augmentation sphere corrections
for a, nucleus in enumerate(self.atoms):
P_i = nucleus.P_uni[u, n]
P_p = pack(np.outer(P_i, P_i))
Delta_p = sqrt(4 * pi) * nucleus.setup.Delta_pL[:, 0]
weigths[a] += np.dot(Delta_p, P_p)
return weigths
def calculate_atomic_density_matrices_with_occupation(self, D_asp, f_un):
"""Calculate atomic density matrices from projections with
custom occupation f_un."""
# Parameter check (if user accidentally passes f_n instead of f_un)
if f_un[0] is not None: # special case for transport calculations...
assert isinstance(f_un[0], np.ndarray)
# Varying f_n used in calculation of response part of GLLB-potential
for a, D_sp in D_asp.items():
ni = self.setups[a].ni
D_sii = np.zeros((len(D_sp), ni, ni))
for f_n, kpt in zip(f_un, self.kpt_u):
self.calculate_atomic_density_matrices_k_point(
D_sii, kpt, a, f_n)
D_sp[:] = [pack(D_ii) for D_ii in D_sii]
self.kptband_comm.sum(D_sp)
self.symmetrize_atomic_density_matrices(D_asp)
def calculate_delta_xc_perturbation_spin(self, s=0):
h**o, lumo = self.occupations.get_homo_lumo_by_spin(self.wfs, s)
Ksgap = lumo - h**o
# Calculate average of lumo reference response potential
method1_dxc = np.average(self.Dxc_vt_sG[s])
nt_G = self.gd.empty()
epsilon = 1e-2
gaps = [ 1000.0 ]
for u, kpt in enumerate(self.kpt_u):
if kpt.s == s:
lumo_n = np.flatnonzero(kpt.f_n/kpt.weight <= epsilon)[0]
nt_G[:] = 0.0
self.wfs.add_orbital_density(nt_G, kpt, lumo_n)
E = 0.0
for a in self.density.D_asp:
D_sp = self.Dxc_D_asp[a]
Dresp_sp = self.Dxc_Dresp_asp[a]
P_ni = kpt.P_ani[a]
Dwf_p = pack(np.outer(P_ni[lumo_n].T.conj(), P_ni[lumo_n]).real)
E += self.integrate_sphere(a, Dresp_sp, D_sp, Dwf_p)
E = self.grid_comm.sum(E)
E += self.gd.integrate(nt_G*self.Dxc_vt_sG[s])
E += kpt.eps_n[lumo_n]
gaps.append(E-lumo)
method2_dxc = self.kpt_comm.min(min(gaps))
Ksgap *= Hartree
method1_dxc *= Hartree
method2_dxc *= Hartree
if world.rank is not 0:
return (Ksgap, method2_dxc)
print
print "\Delta XC calulation"
print "-----------------------------------------------"
print "| Method | KS-Gap | \Delta XC | QP-Gap |"
print "-----------------------------------------------"
print "| Averaging | %7.2f | %9.2f | %7.2f |" % (Ksgap, method1_dxc, Ksgap+method1_dxc)
print "| Lumo pert. | %7.2f | %9.2f | %7.2f |" % (Ksgap, method2_dxc, Ksgap+method2_dxc)
print "-----------------------------------------------"
print
return (Ksgap, method2_dxc)
def calculate_pair_density(self, n1, n2, kpt1, kpt2, q, invert):
if invert:
nt_G = kpt1.psit_nG[n1].conj() * kpt2.psit_nG[n2].conj()
else:
nt_G = kpt1.psit_nG[n1].conj() * kpt2.psit_nG[n2]
Q_aL = {}
for a, P1_ni in kpt1.P_ani.items():
P1_i = P1_ni[n1]
P2_i = kpt2.P_ani[a][n2]
if invert:
D_ii = np.outer(P1_i.conj(), P2_i.conj())
else:
D_ii = np.outer(P1_i.conj(), P2_i)
D_p = pack(D_ii)
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
self.ghat.add(nt_G, Q_aL, q)
return nt_G
def calculate_pair_density(self, n1, n2, kpt1, kpt2, q, invert):
if invert:
nt_G = kpt1.psit_nG[n1].conj() * kpt2.psit_nG[n2].conj()
else:
nt_G = kpt1.psit_nG[n1].conj() * kpt2.psit_nG[n2]
Q_aL = {}
for a, P1_ni in kpt1.P_ani.items():
P1_i = P1_ni[n1]
P2_i = kpt2.P_ani[a][n2]
if invert:
D_ii = np.outer(P1_i.conj(), P2_i.conj())
else:
D_ii = np.outer(P1_i.conj(), P2_i)
D_p = pack(D_ii)
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
self.ghat.add(nt_G, Q_aL, q)
return nt_G
def calculate_pair_density(self, n1, n2, kpt1, kpt2, q, k, eik1r_R,
eik2r_R, eiqr_R, ibz2):
if isinstance(self.wfs, PWWaveFunctions):
psit1_R = self.wfs.pd.ifft(kpt1.psit_nG[n1]) * eik1r_R
psit2_R = self.wfs.pd.ifft(kpt2.psit_nG[n2]) * eik2r_R
else:
psit1_R = kpt1.psit_nG[n1]
psit2_R = kpt2.psit_nG[n2]
if ibz2:
psit2_R = psit2_R
else:
psit2_R = np.asarray(self.kd.transform_wave_function(psit2_R, k),
complex)
nt_R = psit1_R.conj() * psit2_R
s = self.kd.sym_k[k]
time_reversal = self.kd.time_reversal_k[k]
k2_c = self.kd.ibzk_kc[kpt2.k]
Q_aL = {}
for a, P1_ni in kpt1.P_ani.items():
P1_i = P1_ni[n1]
b = self.kd.symmetry.a_sa[s, a]
S_c = (np.dot(self.spos_ac[a], self.kd.symmetry.op_scc[s]) -
self.spos_ac[b])
assert abs(S_c.round() - S_c).max() < 1e-13
x = np.exp(2j * pi * np.dot(k2_c, S_c))
P2_i = np.dot(self.setups[a].R_sii[s], kpt2.P_ani[b][n2]) * x
if time_reversal:
P2_i = P2_i.conj()
if ibz2:
P2_i = kpt2.P_ani[a][n2]
D_ii = np.outer(P1_i.conj(), P2_i)
D_p = pack(D_ii)
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
self.ghat.add(nt_R, Q_aL, q)
return nt_R / eiqr_R
def calculate_pair_density(self, n1, n2, psit_nG, P_ani):
Q_aL = {}
for a, P_ni in P_ani.items():
P1_i = P_ni[n1]
P2_i = P_ni[n2]
D_ii = np.outer(P1_i, P2_i.conj()).real
D_p = pack(D_ii)
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
nt_G = psit_nG[n1] * psit_nG[n2]
if self.finegd is self.gd:
nt_g = nt_G
else:
nt_g = self.finegd.empty()
self.interpolator.apply(nt_G, nt_g)
rhot_g = nt_g.copy()
self.ghat.add(rhot_g, Q_aL)
return nt_G, rhot_g
def calculate_pair_density(self, n1, n2, psit_nG, P_ani):
Q_aL = {}
for a, P_ni in P_ani.items():
P1_i = P_ni[n1]
P2_i = P_ni[n2]
D_ii = np.outer(P1_i, P2_i.conj()).real
D_p = pack(D_ii)
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
nt_G = psit_nG[n1] * psit_nG[n2]
if self.finegd is self.gd:
nt_g = nt_G
else:
nt_g = self.finegd.empty()
self.interpolator.apply(nt_G, nt_g)
rhot_g = nt_g.copy()
self.ghat.add(rhot_g, Q_aL)
return nt_G, rhot_g
def apply_oper(self, obj, sym, cart_rot, atom_deperm):
from gpaw.utilities import pack, unpack2
a_a = self.symmetry.a_sa[sym]
assert (
a_a == atom_deperm).all(), "mismatched oper order or something?"
# permute the 'a' axis (atoms in the dict)
obj = super().apply_oper(obj, sym, cart_rot, atom_deperm)
# and now the 'p' axis
dH_asp = obj
for a in range(len(dH_asp)):
R_ii = self.symmetry.R_asii[a][sym]
for s in range(self.nspins):
dH_p = dH_asp[a][s]
dH_ii = unpack2(dH_p)
tmp_ii = R_ii @ dH_ii @ R_ii.T
tmp_p = pack(tmp_ii)
dH_asp[a][s][...] = tmp_p
return dH_asp
def calculate_density(self, m):
# pseudo density
nt_G = self.phit_mG[m]**2
if self.finegd is self.gd:
nt_g = nt_G
else:
nt_g = self.finegd.empty()
self.interpolator.apply(nt_G, nt_g)
# normalize single-particle density
nt_g *= self.gd.integrate(nt_G) / self.finegd.integrate(nt_g)
# PAW corrections
Q_aL = {}
D_ap = {}
for a, P_mi in self.P_ami.items():
P_i = P_mi[m]
D_ii = np.outer(P_i, P_i.conj()).real
D_ap[a] = D_p = pack(D_ii)
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
return nt_g, Q_aL, D_ap
def calculate_density(self, m):
#
# pseudo density
nt_G = self.phit_mG[m]**2
if self.finegd is self.gd:
nt_g = nt_G
else:
nt_g = self.finegd.empty()
self.interpolator.apply(nt_G, nt_g)
# normalize single-particle density
nt_g *= self.gd.integrate(nt_G) / self.finegd.integrate(nt_g)
# PAW corrections
Q_aL = {}
D_ap = {}
for a, P_mi in self.P_ami.items():
P_i = P_mi[m]
D_ii = np.outer(P_i, P_i.conj()).real
D_ap[a] = D_p = pack(D_ii)
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
return nt_g, Q_aL, D_ap
def get_density(rho_MM, wfs, density, density_type='comp', u=0):
rho_G = density.gd.zeros()
kpt = wfs.kpt_u[u]
assert kpt.q == 0
rho_MM = rho_MM.astype(wfs.dtype)
wfs.basis_functions.construct_density(rho_MM, rho_G, kpt.q)
# Uncomment this if you want to add the static part
# rho_G += density.nct_G
if density_type == 'pseudocoarse':
return rho_G
rho_g = density.finegd.zeros()
density.distribute_and_interpolate(rho_G, rho_g)
rho_G = None
if density_type == 'pseudo':
return rho_g
if density_type == 'comp':
D_asp = density.atom_partition.arraydict(density.D_asp.shapes_a)
Q_aL = {}
for a, D_sp in D_asp.items():
P_Mi = wfs.P_aqMi[a][kpt.q]
assert np.max(np.absolute(P_Mi.imag)) == 0
P_Mi = P_Mi.real
assert P_Mi.dtype == float
D_ii = np.dot(np.dot(P_Mi.T.conj(), rho_MM), P_Mi)
D_sp[:] = pack(D_ii)[np.newaxis, :]
Q_aL[a] = np.dot(D_sp.sum(axis=0), wfs.setups[a].Delta_pL)
tmp_g = density.finegd.zeros()
density.ghat.add(tmp_g, Q_aL)
rho_g += tmp_g
return rho_g
raise RuntimeError('Unknown density type: %s' % density_type)
def calculate_pair_density(self, n1, n2, kpt1, kpt2, ik1, ik2, bzq_index):
psit1_G = self.kd.transform_wave_function(kpt1.psit_nG[n1], ik1)
psit2_G = self.kd.transform_wave_function(kpt2.psit_nG[n2], ik2)
nt_G = psit1_G.conj() * psit2_G
s1 = self.kd.sym_k[ik1]
s2 = self.kd.sym_k[ik2]
t1 = self.kd.time_reversal_k[ik1]
t2 = self.kd.time_reversal_k[ik2]
k1_c = self.kd.ibzk_kc[kpt1.k]
k2_c = self.kd.ibzk_kc[kpt2.k]
Q_aL = {}
for a in kpt1.P_ani.keys():
b1 = self.kd.symmetry.a_sa[s1, a]
b2 = self.kd.symmetry.a_sa[s2, a]
S1_c = (np.dot(self.spos_ac[a], self.kd.symmetry.op_scc[s1]) -
self.spos_ac[b1])
S2_c = (np.dot(self.spos_ac[a], self.kd.symmetry.op_scc[s2]) -
self.spos_ac[b2])
assert abs(S1_c.round() - S1_c).max() < 1e-13
assert abs(S2_c.round() - S2_c).max() < 1e-13
x1 = np.exp(2j * pi * np.dot(k1_c, S1_c))
x2 = np.exp(2j * pi * np.dot(k2_c, S2_c))
P1_i = np.dot(self.setups[a].R_sii[s1], kpt1.P_ani[b1][n1]) * x1
P2_i = np.dot(self.setups[a].R_sii[s2], kpt2.P_ani[b2][n2]) * x2
if t1:
P1_i = P1_i.conj()
if t2:
P2_i = P2_i.conj()
D_ii = np.outer(P1_i.conj(), P2_i)
D_p = pack(D_ii)
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
self.ghat.add(nt_G, Q_aL, bzq_index)
return nt_G
def get(self, nt_G, nt_g, rhot_g):
"""Get pair densities.
nt_G
Pair density without compensation charges on the coarse grid
nt_g
Pair density without compensation charges on the fine grid
rhot_g
Pair density with compensation charges on the fine grid
"""
# Coarse grid product
np.multiply(self.psit1_G.conj(), self.psit2_G, nt_G)
# Interpolate to fine grid
self.density.interpolator.apply(nt_G, nt_g)
# Determine the compensation charges for each nucleus
Q_aL = {}
for a, P_ni in self.P_ani.items():
assert P_ni.dtype == float
# Generate density matrix
P1_i = P_ni[self.n1]
P2_i = P_ni[self.n2]
D_ii = np.outer(P1_i.conj(), P2_i)
# allowed to pack as used in the scalar product with
# the symmetric array Delta_pL
D_p = pack(D_ii)
#FIXME: CHECK THIS D_p = pack(D_ii, tolerance=1e30)
# Determine compensation charge coefficients:
Q_aL[a] = np.dot(D_p, self.density.setups[a].Delta_pL)
# Add compensation charges
rhot_g[:] = nt_g[:]
self.density.ghat.add(rhot_g, Q_aL)
def calculate_paw_xc_pair_potentials(self, kss_ip):
# XC corrections
I_asp = {}
i = kss_ip.occ_ind
p = kss_ip.unocc_ind
# s = kss_ip.spin_ind
# FIXME, only spin unpolarized works
#self.timer.start('Atomic XC')
for a, P_ni in self.calc.wfs.kpt_u[kss_ip.kpt_ind].P_ani.items():
I_sp = np.zeros_like(self.calc.density.D_asp[a])
I_sp_2 = np.zeros_like(self.calc.density.D_asp[a])
Pip_ni = self.calc.wfs.kpt_u[kss_ip.spin_ind].P_ani[a]
Dip_ii = np.outer(Pip_ni[i], Pip_ni[p])
Dip_p = pack(Dip_ii)
# finite difference plus
D_sp = self.calc.density.D_asp[a].copy()
D_sp[kss_ip.spin_ind] += self.deriv_scale * Dip_p
self.xc.calculate_paw_correction(self.calc.wfs.setups[a], D_sp,
I_sp)
# finite difference minus
D_sp_2 = self.calc.density.D_asp[a].copy()
D_sp_2[kss_ip.spin_ind] -= self.deriv_scale * Dip_p
self.xc.calculate_paw_correction(self.calc.wfs.setups[a], D_sp_2,
I_sp_2)
# finite difference
I_asp[a] = (I_sp - I_sp_2) / (2. * self.deriv_scale)
#self.timer.stop('Atomic XC')
return I_asp
def calculate_interaction(self, n1_n, n2, kpt1, kpt2, q, k,
eik20r_R, eik2r_R, is_ibz2):
"""Calculate Coulomb interactions.
For all n1 in the n1_n list, calculate interaction with n2."""
# number of plane waves:
ng1 = self.wfs.ng_k[kpt1.k]
ng2 = self.wfs.ng_k[kpt2.k]
# Transform to real space and apply symmetry operation:
self.timer.start('IFFT1')
if is_ibz2:
u2_R = self.pd.ifft(kpt2.psit_nG[n2, :ng2], kpt2.k)
else:
psit2_R = self.pd.ifft(kpt2.psit_nG[n2, :ng2], kpt2.k) * eik20r_R
self.timer.start('Symmetry transform')
u2_R = self.kd.transform_wave_function(psit2_R, k) / eik2r_R
self.timer.stop()
self.timer.stop()
# Calculate pair densities:
nt_nG = self.pd2.zeros(len(n1_n), q=q)
for n1, nt_G in zip(n1_n, nt_nG):
self.timer.start('IFFT2')
u1_R = self.pd.ifft(kpt1.psit_nG[n1, :ng1], kpt1.k)
self.timer.stop()
nt_R = u1_R.conj() * u2_R
self.timer.start('FFT')
nt_G[:] = self.pd2.fft(nt_R, q)
self.timer.stop()
s = self.kd.sym_k[k]
time_reversal = self.kd.time_reversal_k[k]
k2_c = self.kd.ibzk_kc[kpt2.k]
self.timer.start('Compensation charges')
Q_anL = {} # coefficients for shape functions
for a, P1_ni in kpt1.P_ani.items():
P1_ni = P1_ni[n1_n]
if is_ibz2:
P2_i = kpt2.P_ani[a][n2]
else:
b = self.kd.symmetry.a_sa[s, a]
S_c = (np.dot(self.spos_ac[a], self.kd.symmetry.op_scc[s]) -
self.spos_ac[b])
assert abs(S_c.round() - S_c).max() < 1e-5
if self.ghat.dtype == complex:
x = np.exp(2j * pi * np.dot(k2_c, S_c))
else:
x = 1.0
P2_i = np.dot(self.wfs.setups[a].R_sii[s],
kpt2.P_ani[b][n2]) * x
if time_reversal:
P2_i = P2_i.conj()
D_np = []
for P1_i in P1_ni:
D_ii = np.outer(P1_i.conj(), P2_i)
D_np.append(pack(D_ii))
Q_anL[a] = np.dot(D_np, self.wfs.setups[a].Delta_pL)
self.timer.start('Expand')
if q != self.qlatest:
self.f_IG = self.ghat.expand(q)
self.qlatest = q
self.timer.stop('Expand')
# Add compensation charges:
self.ghat.add(nt_nG, Q_anL, q, self.f_IG)
self.timer.stop('Compensation charges')
if self.molecule and n2 in n1_n:
nn = (n1_n == n2).nonzero()[0][0]
nt_nG[nn] -= self.ngauss_G
else:
nn = None
iG2_G = self.iG2_qG[q]
# Calculate energies:
e_n = np.empty(len(n1_n))
for n, nt_G in enumerate(nt_nG):
e_n[n] = -4 * pi * np.real(self.pd2.integrate(nt_G, nt_G * iG2_G))
self.npairs += 1
if nn is not None:
e_n[nn] -= 2 * (self.pd2.integrate(nt_nG[nn], self.vgauss_G) +
(self.beta / 2 / pi)**0.5)
if self.write_timing_information:
t = (time() - self.t0) / len(n1_n)
self.log('Time for first pair-density: %10.3f seconds' % t)
self.log('Estimated total time: %10.3f seconds' %
(t * self.npairs0 / self.world.size))
self.write_timing_information = False
return e_n
def with_ae_corrections(self, finegrid=False):
"""Get pair density including the AE corrections"""
nij_g = self.get(finegrid)
# Generate the density matrix
D_ap = {}
# D_aii = {}
for a, P_ni in self.P_ani.items():
Pi_i = P_ni[self.i]
Pj_i = P_ni[self.j]
D_ii = np.outer(Pi_i.conj(), Pj_i)
# Note: D_ii is not symmetric but the products of partial waves are
# so that we can pack
D_ap[a] = pack(D_ii)
# D_aii[a] = D_ii
# Load partial waves if needed
if ((finegrid and (not hasattr(self, 'phi'))) or
((not finegrid) and (not hasattr(self, 'Phi')))):
# Splines
splines = {}
phi_aj = []
phit_aj = []
for a, id in enumerate(self.setups.id_a):
if id in splines:
phi_j, phit_j = splines[id]
else:
# Load splines:
phi_j, phit_j = self.setups[a].get_partial_waves()[:2]
splines[id] = (phi_j, phit_j)
phi_aj.append(phi_j)
phit_aj.append(phit_j)
# Store partial waves as class variables
if finegrid:
gd = self.density.finegd
self.__class__.phi = BasisFunctions(gd, phi_aj)
self.__class__.phit = BasisFunctions(gd, phit_aj)
self.__class__.phi.set_positions(self.spos_ac)
self.__class__.phit.set_positions(self.spos_ac)
else:
gd = self.density.gd
self.__class__.Phi = BasisFunctions(gd, phi_aj)
self.__class__.Phit = BasisFunctions(gd, phit_aj)
self.__class__.Phi.set_positions(self.spos_ac)
self.__class__.Phit.set_positions(self.spos_ac)
# Add AE corrections
if finegrid:
phi = self.phi
phit = self.phit
gd = self.density.finegd
else:
phi = self.Phi
phit = self.Phit
gd = self.density.gd
rho_MM = np.zeros((phi.Mmax, phi.Mmax))
M1 = 0
for a, setup in enumerate(self.setups):
ni = setup.ni
D_p = D_ap.get(a)
if D_p is None:
D_p = np.empty((ni * (ni + 1) // 2))
if gd.comm.size > 1:
gd.comm.broadcast(D_p, self.wfs.rank_a[a])
D_ii = unpack2(D_p)
# D_ii = D_aii.get(a)
# if D_ii is None:
# D_ii = np.empty((ni, ni))
# if gd.comm.size > 1:
# gd.comm.broadcast(D_ii, self.wfs.rank_a[a])
M2 = M1 + ni
rho_MM[M1:M2, M1:M2] = D_ii
M1 = M2
# construct_density assumes symmetric rho_MM and
# takes only the upper half of it
phi.construct_density(rho_MM, nij_g, q=-1)
phit.construct_density(-rho_MM, nij_g, q=-1)
# TODO: use ae_valence_density_correction
# phi.lfc.ae_valence_density_correction(
# rho_MM, nij_g, np.zeros(len(phi.M_W), np.intc), np.zeros(self.na))
# phit.lfc.ae_valence_density_correction(
# -rho_MM, nij_g, np.zeros(len(phit.M_W), np.intc), np.zeros(self.na))
return nij_g
import numpy.random as ra
from gpaw.setup import create_setup
from gpaw.xc.noncollinear import NonCollinearFunctional
from gpaw.xc import XC
from gpaw.test import equal
from gpaw.utilities import pack
x = 0.0000001
ra.seed(8)
for xc in ['LDA']:#, 'PBE']:
print(xc)
xc = XC(xc)
s = create_setup('N', xc)
ni = s.ni
D_sp = np.array([pack(np.outer(P_i, P_i))
for P_i in 0.2 * ra.random((2, ni)) - 0.1])
D_sp[1] += D_sp[0]
nii = ni * (ni + 1) // 2
E = xc.calculate_paw_correction(s, D_sp)
xc = NonCollinearFunctional(xc)
Dnc_sp = np.zeros((4, nii))
Dnc_sp[0] = D_sp.sum(0)
Dnc_sp[3] = D_sp[0] - D_sp[1]
Enc = xc.calculate_paw_correction(s, Dnc_sp)
print(E, E-Enc)
assert abs(E - Enc) < 1e-11
psit_ig = np.zeros((niAO, n, n, n))
pr.add(psit_ig, coefs)
nii = ni * (ni + 1) // 2
D_p = np.zeros(nii)
H_p = np.zeros(nii)
e_g = np.zeros((n, n, n))
n_g = np.zeros((1, n, n, n))
v_g = np.zeros((1, n, n, n))
P_ni = 0.2 * ra.random((20, ni))
P_ni[:, niAO:] = 0.0
D_ii = np.dot(np.transpose(P_ni), P_ni)
D_p = pack(D_ii)
p = 0
for i1 in range(niAO):
for i2 in range(i1, niAO):
n_g += D_p[p] * psit_ig[i1] * psit_ig[i2]
p += 1
p += ni - niAO
p = create_localized_functions([s.nct], gd, (0.5, 0.5, 0.5))
p.add(n_g[0], np.ones(1))
e_g = gd.zeros()
xc.calculate(gd, n_g, v_g, e_g)
r2_g = np.sum((np.indices((n, n, n)) - n / 2)**2, axis=0)
dv_g = gd.dv * np.less(r2_g, (rcut / a * n)**2)
import numpy.random as ra
from gpaw.setup import create_setup
from gpaw.xc.noncollinear import NonCollinearFunctional
from gpaw.xc import XC
from gpaw.test import equal
from gpaw.utilities import pack
x = 0.0000001
ra.seed(8)
for xc in ["LDA"]: # , 'PBE']:
print xc
xc = XC(xc)
s = create_setup("N", xc)
ni = s.ni
D_sp = np.array([pack(np.outer(P_i, P_i)) for P_i in 0.2 * ra.random((2, ni)) - 0.1])
D_sp[1] += D_sp[0]
nii = ni * (ni + 1) // 2
E = xc.calculate_paw_correction(s, D_sp)
xc = NonCollinearFunctional(xc)
Dnc_sp = np.zeros((4, nii))
Dnc_sp[0] = D_sp.sum(0)
Dnc_sp[3] = D_sp[0] - D_sp[1]
Enc = xc.calculate_paw_correction(s, Dnc_sp)
print E, E - Enc
assert abs(E - Enc) < 1e-11
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 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 makeU(gpwfile='grid.gpw', orbitalfile='w_wG__P_awi.pckl',
rotationfile='eps_q__U_pq.pckl', tolerance=1e-5,
writeoptimizedpairs=False, dppname='D_pp.pckl', S_w=None):
# S_w: None or diagonal of overlap matrix. In the latter case
# the optimized and truncated pair orbitals are obtained from
# normalized (to 1) orbitals.
#
# Tolerance is used for truncation of optimized pairorbitals
#calc = GPAW(gpwfile, txt=None)
from gpaw import GPAW
from gpaw.utilities import pack, unpack
from gpaw.utilities.blas import rk, gemm
from gpaw.mpi import world, MASTER
calc = GPAW(gpwfile, txt='pairorb.txt') # XXX
gd = calc.wfs.gd
setups = calc.wfs.setups
myatoms = calc.density.D_asp.keys()
del calc
# Load orbitals on master and distribute to slaves
if world.rank == MASTER:
wglobal_wG, P_awi = pickle.load(open(orbitalfile))
Nw = len(wglobal_wG)
print('Estimated total (serial) mem usage: %0.3f GB' % (
np.prod(gd.N_c) * Nw**2 * 8 / 1024.**3))
else:
wglobal_wG = None
Nw = 0
Nw = gd.comm.sum(Nw) #distribute Nw to all nodes
w_wG = gd.empty(n=Nw)
gd.distribute(wglobal_wG, w_wG)
del wglobal_wG
# Make pairorbitals
f_pG = gd.zeros(n=Nw**2)
Np = len(f_pG)
for p, (w1, w2) in enumerate(np.ndindex(Nw, Nw)):
np.multiply(w_wG[w1], w_wG[w2], f_pG[p])
del w_wG
assert f_pG.flags.contiguous
# Make pairorbital overlap (lower triangle only)
D_pp = np.zeros((Nw**2, Nw**2))
rk(gd.dv, f_pG, 0., D_pp)
# Add atomic corrections to pairorbital overlap
for a in myatoms:
if setups[a].type != 'ghost':
P_pp = np.array([pack(np.outer(P_awi[a][w1], P_awi[a][w2]))
for w1, w2 in np.ndindex(Nw, Nw)])
I4_pp = setups[a].four_phi_integrals()
A = np.zeros((len(I4_pp), len(P_pp)))
gemm(1.0, P_pp, I4_pp, 0.0, A, 't')
gemm(1.0, A, P_pp, 1.0, D_pp)
#D_pp += np.dot(P_pp, np.dot(I4_pp, P_pp.T))
# Summ all contributions to master
gd.comm.sum(D_pp, MASTER)
if world.rank == MASTER:
if S_w is not None:
print('renormalizing pairorb overlap matrix (D_pp)')
S2 = np.sqrt(S_w)
for pa, (wa1, wa2) in enumerate(np.ndindex(Nw, Nw)):
for pb, (wb1, wb2) in enumerate(np.ndindex(Nw, Nw)):
D_pp[pa, pb] /= S2[wa1] * S2[wa2] * S2[wb1] * S2[wb2]
D_pp.dump(dppname) # XXX if the diagonalization below (on MASTER only)
# fails, then one can always restart the stuff
# below using only the stored D_pp matrix
# Determine eigenvalues and vectors on master only
eps_q, U_pq = np.linalg.eigh(D_pp, UPLO='L')
del D_pp
indices = np.argsort(-eps_q.real)
eps_q = np.ascontiguousarray(eps_q.real[indices])
U_pq = np.ascontiguousarray(U_pq[:, indices])
# Truncate
indices = eps_q > tolerance
U_pq = np.ascontiguousarray(U_pq[:, indices])
eps_q = np.ascontiguousarray(eps_q[indices])
# Dump to file
pickle.dump((eps_q, U_pq), open(rotationfile, 'wb'), 2)
if writeoptimizedpairs is not False:
assert world.size == 1 # works in parallel if U and eps are broadcast
Uisq_qp = (U_pq / np.sqrt(eps_q)).T.copy()
g_qG = gd.zeros(n=len(eps_q))
gemm(1.0, f_pG, Uisq_qp, 0.0, g_qG)
g_qG = gd.collect(g_qG)
if world.rank == MASTER:
P_app = dict([(a, np.array([pack(np.outer(P_wi[w1], P_wi[w2]),
tolerance=1e3)
for w1, w2 in np.ndindex(Nw, Nw)]))
for a, P_wi in P_awi.items()])
P_aqp = dict([(a, np.dot(Uisq_qp, P_pp))
for a, P_pp in P_app.items()])
pickle.dump((g_qG, P_aqp), open(writeoptimizedpairs, 'wb'), 2)
def makeU(gpwfile='grid.gpw', orbitalfile='w_wG__P_awi.pckl',
rotationfile='eps_q__U_pq.pckl', tolerance=1e-5,
writeoptimizedpairs=False, dppname='D_pp.pckl', S_w=None):
# S_w: None or diagonal of overlap matrix. In the latter case
# the optimized and truncated pair orbitals are obtained from
# normalized (to 1) orbitals.
#
# Tolerance is used for truncation of optimized pairorbitals
#calc = GPAW(gpwfile, txt=None)
from gpaw import GPAW
from gpaw.utilities import pack, unpack
from gpaw.utilities.blas import rk, gemm
from gpaw.mpi import world, MASTER, serial_comm
calc = GPAW(gpwfile, txt='pairorb.txt') # XXX
gd = calc.wfs.gd
setups = calc.wfs.setups
myatoms = calc.density.D_asp.keys()
del calc
# Load orbitals on master and distribute to slaves
if world.rank == MASTER:
wglobal_wG, P_awi = pickle.load(open(orbitalfile))
Nw = len(wglobal_wG)
print 'Estimated total (serial) mem usage: %0.3f GB' % (
np.prod(gd.N_c) * Nw**2 * 8 / 1024.**3)
else:
wglobal_wG = None
Nw = 0
Nw = gd.comm.sum(Nw) #distribute Nw to all nodes
w_wG = gd.empty(n=Nw)
gd.distribute(wglobal_wG, w_wG)
del wglobal_wG
# Make pairorbitals
f_pG = gd.zeros(n=Nw**2)
Np = len(f_pG)
for p, (w1, w2) in enumerate(np.ndindex(Nw, Nw)):
np.multiply(w_wG[w1], w_wG[w2], f_pG[p])
del w_wG
assert f_pG.flags.contiguous
# Make pairorbital overlap (lower triangle only)
D_pp = np.zeros((Nw**2, Nw**2))
rk(gd.dv, f_pG, 0., D_pp)
# Add atomic corrections to pairorbital overlap
for a in myatoms:
if setups[a].type != 'ghost':
P_pp = np.array([pack(np.outer(P_awi[a][w1], P_awi[a][w2]))
for w1, w2 in np.ndindex(Nw, Nw)])
I4_pp = setups[a].four_phi_integrals()
A = np.zeros((len(I4_pp), len(P_pp)))
gemm(1.0, P_pp, I4_pp, 0.0, A, 't')
gemm(1.0, A, P_pp, 1.0, D_pp)
#D_pp += np.dot(P_pp, np.dot(I4_pp, P_pp.T))
# Summ all contributions to master
gd.comm.sum(D_pp, MASTER)
if world.rank == MASTER:
if S_w != None:
print 'renormalizing pairorb overlap matrix (D_pp)'
S2 = np.sqrt(S_w)
for pa, (wa1, wa2) in enumerate(np.ndindex(Nw, Nw)):
for pb, (wb1, wb2) in enumerate(np.ndindex(Nw, Nw)):
D_pp[pa, pb] /= S2[wa1] * S2[wa2] * S2[wb1] * S2[wb2]
D_pp.dump(dppname) # XXX if the diagonalization below (on MASTER only)
# fails, then one can always restart the stuff
# below using only the stored D_pp matrix
# Determine eigenvalues and vectors on master only
eps_q, U_pq = np.linalg.eigh(D_pp, UPLO='L')
del D_pp
indices = np.argsort(-eps_q.real)
eps_q = np.ascontiguousarray(eps_q.real[indices])
U_pq = np.ascontiguousarray(U_pq[:, indices])
# Truncate
indices = eps_q > tolerance
U_pq = np.ascontiguousarray(U_pq[:, indices])
eps_q = np.ascontiguousarray(eps_q[indices])
# Dump to file
pickle.dump((eps_q, U_pq), open(rotationfile, 'wb'), 2)
if writeoptimizedpairs is not False:
assert world.size == 1 # works in parallel if U and eps are broadcast
Uisq_qp = (U_pq / np.sqrt(eps_q)).T.copy()
g_qG = gd.zeros(n=len(eps_q))
gemm(1.0, f_pG, Uisq_qp, 0.0, g_qG)
g_qG = gd.collect(g_qG)
if world.rank == MASTER:
P_app = dict([(a, np.array([pack(np.outer(P_wi[w1], P_wi[w2]),
tolerance=1e3)
for w1, w2 in np.ndindex(Nw, Nw)]))
for a, P_wi in P_awi.items()])
P_aqp = dict([(a, np.dot(Uisq_qp, P_pp))
for a, P_pp in P_app.items()])
pickle.dump((g_qG, P_aqp), open(writeoptimizedpairs, 'wb'), 2)
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()
timer2.start('integrate')
pre = 2.*sqrt(kss[ij].get_energy()*kss[kq].get_energy()*
kss[ij].get_weight()*kss[kq].get_weight())
Om[ij,kq]= pre * self.gd.integrate(rhot*phit)
## print "int=",Om[ij,kq]
timer2.stop()
# Add atomic corrections
timer2.start('integrate corrections 2')
Ia = 0.
for a, P_ni in wfs.kpt_u[kss[ij].spin].P_ani.items():
Pi_i = P_ni[kss[ij].i]
Pj_i = P_ni[kss[ij].j]
Dij_ii = np.outer(Pi_i, Pj_i)
Dij_p = pack(Dij_ii)
Pkq_ni = wfs.kpt_u[kss[kq].spin].P_ani[a]
Pk_i = Pkq_ni[kss[kq].i]
Pq_i = Pkq_ni[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))
timer2.stop()
Om[ij,kq] += pre * self.gd.comm.sum(Ia)
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)
coefs = np.identity(nao, float)
psit_ig = np.zeros((nao, n, n, n))
pr.add(psit_ig, coefs)
nii = ni * (ni + 1) // 2
D_p = np.zeros(nii)
H_p = np.zeros(nii)
e_g = np.zeros((n, n, n))
n_g = np.zeros((1, n, n, n))
v_g = np.zeros((1, n, n, n))
P_ni = 0.2 * ra.random((20, ni))
P_ni[:, nao:] = 0.0
D_ii = np.dot(np.transpose(P_ni), P_ni)
D_p = pack(D_ii)
p = 0
for i1 in range(nao):
for i2 in range(i1, nao):
n_g += D_p[p] * psit_ig[i1] * psit_ig[i2]
p += 1
p += ni - nao
p = create_localized_functions([s.nct], gd, (0.5, 0.5, 0.5))
p.add(n_g[0], np.ones(1))
e_g = gd.zeros()
xc.calculate(gd, n_g, v_g, e_g)
r2_g = np.sum((np.indices((n, n, n)) - n / 2)**2, axis=0)
dv_g = gd.dv * np.less(r2_g, (rcut / a * n)**2)