def calculate_residuals(self,
kpt,
wfs,
hamiltonian,
psit_xG,
P_axi,
eps_x,
R_xG,
n_x=None,
calculate_change=False):
"""Calculate residual.
From R=Ht*psit calculate R=H*psit-eps*S*psit."""
for R_G, eps, psit_G in zip(R_xG, eps_x, psit_xG):
axpy(-eps, psit_G, R_G)
c_axi = {}
for a, P_xi in P_axi.items():
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
dO_ii = hamiltonian.setups[a].dO_ii
c_xi = (np.dot(P_xi, dH_ii) -
np.dot(P_xi * eps_x[:, np.newaxis], dO_ii))
c_axi[a] = c_xi
hamiltonian.xc.add_correction(kpt, psit_xG, R_xG, P_axi, c_axi, n_x,
calculate_change)
wfs.pt.add(R_xG, c_axi, kpt.q)
def calculate_residuals(self,
kpt,
wfs,
ham,
psit,
P,
eps_n,
R,
C,
n_x=None,
calculate_change=False):
"""Calculate residual.
From R=Ht*psit calculate R=H*psit-eps*S*psit."""
for R_G, eps, psit_G in zip(R.array, eps_n, psit.array):
axpy(-eps, psit_G, R_G)
ham.dH(P, out=C)
for a, I1, I2 in P.indices:
dS_ii = ham.setups[a].dO_ii
C.array[..., I1:I2] -= np.dot((P.array[..., I1:I2].T * eps_n).T,
dS_ii)
ham.xc.add_correction(kpt, psit.array, R.array,
{a: P_ni
for a, P_ni in P.items()},
{a: C_ni
for a, C_ni in C.items()}, n_x,
calculate_change)
wfs.pt.add(R.array, {a: C_ni for a, C_ni in C.items()}, kpt.q)
def __call__(self, residuals, kpt, ekin=None):
nb = len(residuals) # number of bands
phases = kpt.phase_cd
step = self.step
d0, q0 = self.scratch0[:,:nb]
r1, d1, q1 = self.scratch1[:, :nb]
r2, d2, q2 = self.scratch2[:, :nb]
self.restrictor0(-residuals, r1, phases)
d1[:] = 4 * step * r1
self.kin1.apply(d1, q1, phases)
q1 -= r1
self.restrictor1(q1, r2, phases)
d2 = 16 * step * r2
self.kin2.apply(d2, q2, phases)
q2 -= r2
d2 -= 16 * step * q2
self.interpolator2(d2, q1, phases)
d1 -= q1
self.kin1.apply(d1, q1, phases)
q1 -= r1
d1 -= 4 * step * q1
self.interpolator1(-d1, d0, phases)
self.kin0.apply(d0, q0, phases)
q0 -= residuals
axpy(-step, q0, d0) # d0 -= step * q0
d0 *= -1.0
return d0
def multi_zaxpy(self, a, x, y, nvec):
if isinstance(a, (float, complex)):
for i in range(nvec):
axpy(a * (1 + 0J), x[i], y[i])
else:
for i in range(nvec):
axpy(a[i] * (1.0 + 0.0J), x[i], y[i])
def multi_zaxpy(self, a,x,y, nvec):
if isinstance(a, (float, complex)):
for i in range(nvec):
axpy(a*(1+0J), x[i], y[i])
else:
for i in range(nvec):
axpy(a[i]*(1.0+0.0J), x[i], y[i])
def calculate_gga(self, e_g, nt_sg, v_sg, sigma_xg, dedsigma_xg):
try:
taut_sG = self.wfs.calculate_kinetic_energy_density()
except RuntimeError:
nspins = self.wfs.nspins
# Initialize with von Weizsaecker kinetic energy density
taut_sG = self.wfs.gd.empty((nspins))
gradn_g = self.gd.empty()
for s in range(nspins):
taut_g = self.gd.zeros()
for v in range(3):
self.grad_v[v](nt_sg[s], gradn_g)
axpy(0.125, gradn_g**2, taut_g)
ntinv_g = 0. * taut_g
nt_ok = np.where(nt_sg[s] > 1e-7)
ntinv_g[nt_ok] = 1.0 / nt_sg[s][nt_ok]
taut_g *= ntinv_g
self.restrict(taut_g, taut_sG[s])
taut_sg = np.empty_like(nt_sg)
for taut_G, taut_g in zip(taut_sG, taut_sg):
taut_G += 1.0 / self.wfs.nspins * self.tauct_G
self.interpolate(taut_G, taut_g)
dedtaut_sg = np.empty_like(nt_sg)
self.kernel.calculate(e_g, nt_sg, v_sg, sigma_xg, dedsigma_xg, taut_sg,
dedtaut_sg)
self.dedtaut_sG = self.wfs.gd.empty(self.wfs.nspins)
self.ekin = 0.0
for s in range(self.wfs.nspins):
self.restrict(dedtaut_sg[s], self.dedtaut_sG[s])
self.ekin -= self.wfs.gd.integrate(
self.dedtaut_sG[s] *
(taut_sG[s] - self.tauct_G / self.wfs.nspins))
def apply_orbital_dependent_hamiltonian(self, kpt, psit_xG, Htpsit_xG, dH_asp):
a_G = self.wfs.gd.empty(dtype=psit_xG.dtype)
for psit_G, Htpsit_G in zip(psit_xG, Htpsit_xG):
for v in range(3):
self.taugrad_v[v](psit_G, a_G, kpt.phase_cd)
self.taugrad_v[v](self.dedtaut_sG[kpt.s] * a_G, a_G, kpt.phase_cd)
axpy(-0.5, a_G, Htpsit_G)
def calculate_kinetic_energy_density(self):
if self.taugrad_v is None:
self.taugrad_v = [
Gradient(self.gd, v, n=3, dtype=self.dtype).apply
for v in range(3)
]
assert not hasattr(self.kpt_u[0], 'c_on')
if self.kpt_u[0].psit_nG is None:
raise RuntimeError('No wavefunctions yet')
if isinstance(self.kpt_u[0].psit_nG, FileReference):
# XXX initialize
raise RuntimeError('Wavefunctions have not been initialized.')
taut_sG = self.gd.zeros(self.nspins)
dpsit_G = self.gd.empty(dtype=self.dtype)
for kpt in self.kpt_u:
for f, psit_G in zip(kpt.f_n, kpt.psit_nG):
for v in range(3):
self.taugrad_v[v](psit_G, dpsit_G, kpt.phase_cd)
axpy(0.5 * f, abs(dpsit_G)**2, taut_sG[kpt.s])
self.kd.comm.sum(taut_sG)
self.band_comm.sum(taut_sG)
return taut_sG
def calculate_gga(self, e_g, nt_sg, v_sg, sigma_xg, dedsigma_xg):
try:
taut_sG = self.wfs.calculate_kinetic_energy_density()
except RuntimeError:
nspins = self.wfs.nspins
# Initialize with von Weizsaecker kinetic energy density
taut_sG = self.wfs.gd.empty((nspins))
gradn_g = self.gd.empty()
for s in range(nspins):
taut_g = self.gd.zeros()
for v in range(3):
self.grad_v[v](nt_sg[s], gradn_g)
axpy(0.125, gradn_g**2, taut_g)
ntinv_g = 0. * taut_g
nt_ok = np.where(nt_sg[s] > 1e-7)
ntinv_g[nt_ok] = 1.0 / nt_sg[s][nt_ok]
taut_g *= ntinv_g
self.restrict(taut_g, taut_sG[s])
taut_sg = np.empty_like(nt_sg)
for taut_G, taut_g in zip(taut_sG, taut_sg):
taut_G += 1.0 / self.wfs.nspins * self.tauct_G
self.interpolate(taut_G, taut_g)
dedtaut_sg = np.empty_like(nt_sg)
self.kernel.calculate(e_g, nt_sg, v_sg, sigma_xg, dedsigma_xg,
taut_sg, dedtaut_sg)
self.dedtaut_sG = self.wfs.gd.empty(self.wfs.nspins)
self.ekin = 0.0
for s in range(self.wfs.nspins):
self.restrict(dedtaut_sg[s], self.dedtaut_sG[s])
self.ekin -= self.wfs.gd.integrate(
self.dedtaut_sG[s] * (taut_sG[s] -
self.tauct_G / self.wfs.nspins))
def __call__(self, residuals, kpt, ekin=None):
nb = len(residuals) # number of bands
phases = kpt.phase_cd
step = self.step
d0, q0 = self.scratch0[:, :nb]
r1, d1, q1 = self.scratch1[:, :nb]
r2, d2, q2 = self.scratch2[:, :nb]
self.restrictor0(-residuals, r1, phases)
d1[:] = 4 * step * r1
self.kin1.apply(d1, q1, phases)
q1 -= r1
self.restrictor1(q1, r2, phases)
d2 = 16 * step * r2
self.kin2.apply(d2, q2, phases)
q2 -= r2
d2 -= 16 * step * q2
self.interpolator2(d2, q1, phases)
d1 -= q1
self.kin1.apply(d1, q1, phases)
q1 -= r1
d1 -= 4 * step * q1
self.interpolator1(-d1, d0, phases)
self.kin0.apply(d0, q0, phases)
q0 -= residuals
axpy(-step, q0, d0) # d0 -= step * q0
d0 *= -1.0
return d0
def calculate_sigma(gd, grad_v, n_sg):
"""Calculate sigma(r) and grad n(r).
_ __ _ 2 __ _
Returns sigma(r) = |\/ n(r)| and \/ n (r).
With multiple spins, sigma has the three elements
_ __ _ 2
sigma (r) = |\/ n (r)| ,
0 up
_ __ _ __ _
sigma (r) = \/ n (r) . \/ n (r) ,
1 up dn
_ __ _ 2
sigma (r) = |\/ n (r)| .
2 dn
"""
nspins = len(n_sg)
gradn_svg = gd.empty((nspins, 3))
sigma_xg = gd.zeros(nspins * 2 - 1)
for v in range(3):
for s in range(nspins):
grad_v[v](n_sg[s], gradn_svg[s, v])
axpy(1.0, gradn_svg[s, v]**2, sigma_xg[2 * s])
if nspins == 2:
axpy(1.0, gradn_svg[0, v] * gradn_svg[1, v], sigma_xg[1])
return sigma_xg, gradn_svg
def apply_mgga_orbital_dependent_hamiltonian(self, kpt, psit_xG, Htpsit_xG,
dH_asp, dedtaut_G):
a_G = self.gd.empty(dtype=psit_xG.dtype)
for psit_G, Htpsit_G in zip(psit_xG, Htpsit_xG):
for v in range(3):
self.taugrad_v[v](psit_G, a_G, kpt.phase_cd)
self.taugrad_v[v](dedtaut_G * a_G, a_G, kpt.phase_cd)
axpy(-0.5, a_G, Htpsit_G)
def apply_mgga_orbital_dependent_hamiltonian(self, kpt, psit_xG,
Htpsit_xG, dH_asp,
dedtaut_R):
G_Gv = self.pd.G_Qv[self.pd.Q_qG[kpt.q]] + self.pd.K_qv[kpt.q]
for psit_G, Htpsit_G in zip(psit_xG, Htpsit_xG):
for v in range(3):
a_R = self.pd.ifft(1j * G_Gv[:, v] * psit_G, kpt.q)
axpy(-0.5, 1j * G_Gv[:, v] *
self.pd.fft(dedtaut_R * a_R, kpt.q),
Htpsit_G)
def apply_mgga_orbital_dependent_hamiltonian(self, kpt, psit_xG,
Htpsit_xG, dH_asp,
dedtaut_R):
G_Gv = self.pd.get_reciprocal_vectors(q=kpt.q)
for psit_G, Htpsit_G in zip(psit_xG, Htpsit_xG):
for v in range(3):
a_R = self.pd.ifft(1j * G_Gv[:, v] * psit_G, kpt.q)
axpy(-0.5, 1j * G_Gv[:, v] *
self.pd.fft(dedtaut_R * a_R, kpt.q),
Htpsit_G)
def get_pbe_g(self, n_g, index=None):
if index is None:
gradn_vg = self.gradn_vg
else:
gradn_vg = self.calc.density.gd.empty(3)
for v in range(3):
gradn_vg[v] = (self.gradn_vg[v] +
self.gradn_vg[v].flatten()[index]) / 2
kf_g = (3. * np.pi**2 * n_g)**(1 / 3.)
s2_g = np.zeros_like(n_g)
for v in range(3):
axpy(1.0, gradn_vg[v]**2, s2_g)
s2_g /= 4 * kf_g**2 * n_g**2
e_g = self.A_x * n_g**(4 / 3.)
v_g = (4 / 3.) * e_g / n_g
f_g = (1 / 3.) * v_g / n_g
kappa = 0.804
mu = 0.2195149727645171
denom_g = (1 + mu * s2_g / kappa)
F_g = 1. + kappa - kappa / denom_g
Fn_g = -mu / denom_g**2 * 8 * s2_g / (3 * n_g)
Fnn_g = -11 * Fn_g / (3 * n_g) - 2 * Fn_g**2 / kappa
fxc_g = f_g * F_g
fxc_g += 2 * v_g * Fn_g
fxc_g += e_g * Fnn_g
# Contributions from varying the gradient
#Fgrad_vg = np.zeros_like(gradn_vg)
#Fngrad_vg = np.zeros_like(gradn_vg)
#for v in range(3):
# axpy(1.0, mu / den_g**2 * gradn_vg[v] / (2 * kf_g**2 * n_g**2),
# Fgrad_vg[v])
# axpy(-8.0, Fgrad_vg[v] / (3 * n_g), Fngrad_vg[v])
# axpy(-2.0, Fgrad_vg[v] * Fn_g / kappa, Fngrad_vg[v])
#tmp = np.zeros_like(fxc_g)
#tmp1 = np.zeros_like(fxc_g)
#for v in range(3):
#self.grad_v[v](Fgrad_vg[v], tmp)
#axpy(-2.0, tmp * v_g, fxc_g)
#for u in range(3):
#self.grad_v[u](Fgrad_vg[u] * tmp, tmp1)
#axpy(-4.0/kappa, tmp1 * e_g, fxc_g)
#self.grad_v[v](Fngrad_vg[v], tmp)
#axpy(-2.0, tmp * e_g, fxc_g)
#self.laplace(mu / den_g**2 / (2 * kf_g**2 * n_g**2), tmp)
#axpy(1.0, tmp * e_g, fxc_g)
return fxc_g
def get_pbe_g(self, n_g, index=None):
if index is None:
gradn_vg = self.gradn_vg
else:
gradn_vg = self.calc.density.gd.empty(3)
for v in range(3):
gradn_vg[v] = (self.gradn_vg[v] +
self.gradn_vg[v].flatten()[index]) / 2
kf_g = (3. * np.pi**2 * n_g)**(1 / 3.)
s2_g = np.zeros_like(n_g)
for v in range(3):
axpy(1.0, gradn_vg[v]**2, s2_g)
s2_g /= 4 * kf_g**2 * n_g**2
e_g = self.A_x * n_g**(4 / 3.)
v_g = (4 / 3.) * e_g / n_g
f_g = (1 / 3.) * v_g / n_g
kappa = 0.804
mu = 0.2195149727645171
denom_g = (1 + mu * s2_g / kappa)
F_g = 1. + kappa - kappa / denom_g
Fn_g = -mu / denom_g**2 * 8 * s2_g / (3 * n_g)
Fnn_g = -11 * Fn_g / (3 * n_g) - 2 * Fn_g**2 / kappa
fxc_g = f_g * F_g
fxc_g += 2 * v_g * Fn_g
fxc_g += e_g * Fnn_g
# Contributions from varying the gradient
#Fgrad_vg = np.zeros_like(gradn_vg)
#Fngrad_vg = np.zeros_like(gradn_vg)
#for v in range(3):
# axpy(1.0, mu / den_g**2 * gradn_vg[v] / (2 * kf_g**2 * n_g**2),
# Fgrad_vg[v])
# axpy(-8.0, Fgrad_vg[v] / (3 * n_g), Fngrad_vg[v])
# axpy(-2.0, Fgrad_vg[v] * Fn_g / kappa, Fngrad_vg[v])
#tmp = np.zeros_like(fxc_g)
#tmp1 = np.zeros_like(fxc_g)
#for v in range(3):
#self.grad_v[v](Fgrad_vg[v], tmp)
#axpy(-2.0, tmp * v_g, fxc_g)
#for u in range(3):
#self.grad_v[u](Fgrad_vg[u] * tmp, tmp1)
#axpy(-4.0/kappa, tmp1 * e_g, fxc_g)
#self.grad_v[v](Fngrad_vg[v], tmp)
#axpy(-2.0, tmp * e_g, fxc_g)
#self.laplace(mu / den_g**2 / (2 * kf_g**2 * n_g**2), tmp)
#axpy(1.0, tmp * e_g, fxc_g)
return fxc_g
def calculate_sigma(self, n_sg):
nspins = len(n_sg)
gradn_svg = self.gd.empty((nspins, 3))
sigma_xg = self.gd.zeros(nspins * 2 - 1)
for v in range(3):
for s in range(nspins):
self.grad_v[v](n_sg[s], gradn_svg[s, v])
axpy(1.0, gradn_svg[s, v] ** 2, sigma_xg[2 * s])
if nspins == 2:
axpy(1.0, gradn_svg[0, v] * gradn_svg[1, v], sigma_xg[1])
return sigma_xg, gradn_svg
def calculate_sigma(self, n_sg):
nspins = len(n_sg)
gradn_svg = self.gd.empty((nspins, 3))
sigma_xg = self.gd.zeros(nspins * 2 - 1)
for v in range(3):
for s in range(nspins):
self.grad_v[v](n_sg[s], gradn_svg[s, v])
axpy(1.0, gradn_svg[s, v]**2, sigma_xg[2 * s])
if nspins == 2:
axpy(1.0, gradn_svg[0, v] * gradn_svg[1, v], sigma_xg[1])
return sigma_xg, gradn_svg
def calculate_lda(self, e_g, n_sg, v_sg):
nspins = len(n_sg)
sigma_xg, gradn_svg = self.calculate_sigma(n_sg)
dedsigma_xg = self.gd.empty(nspins * 2 - 1)
self.calculate_gga(e_g, n_sg, v_sg, sigma_xg, dedsigma_xg)
vv_g = sigma_xg[0]
for v in range(3):
for s in range(nspins):
self.grad_v[v](dedsigma_xg[2 * s] * gradn_svg[s, v], vv_g)
axpy(-2.0, vv_g, v_sg[s])
if nspins == 2:
self.grad_v[v](dedsigma_xg[1] * gradn_svg[s, v], vv_g)
axpy(-1.0, vv_g, v_sg[1 - s])
def calculate_lda(self, e_g, n_sg, v_sg):
nspins = len(n_sg)
sigma_xg, gradn_svg = self.calculate_sigma(n_sg)
dedsigma_xg = self.gd.empty(nspins * 2 - 1)
self.calculate_gga(e_g, n_sg, v_sg, sigma_xg, dedsigma_xg)
vv_g = sigma_xg[0]
for v in range(3):
for s in range(nspins):
self.grad_v[v](dedsigma_xg[2 * s] * gradn_svg[s, v], vv_g)
axpy(-2.0, vv_g, v_sg[s])
if nspins == 2:
self.grad_v[v](dedsigma_xg[1] * gradn_svg[s, v], vv_g)
axpy(-1.0, vv_g, v_sg[1 - s])
def calculate_kinetic_energy_density(self, tauct, grad_v):
assert not hasattr(self.kpt_u[0], 'c_on')
if isinstance(self.kpt_u[0].psit_nG, TarFileReference):
raise RuntimeError('Wavefunctions have not been initialized.')
taut_sG = self.gd.zeros(self.nspins)
dpsit_G = self.gd.empty(dtype=self.dtype)
for kpt in self.kpt_u:
for f, psit_G in zip(kpt.f_n, kpt.psit_nG):
for v in range(3):
grad_v[v](psit_G, dpsit_G, kpt.phase_cd)
axpy(0.5 * f, abs(dpsit_G)**2, taut_sG[kpt.s])
self.kpt_comm.sum(taut_sG)
self.band_comm.sum(taut_sG)
return taut_sG
def calculate_kinetic_energy_density(self, tauct, grad_v):
assert not hasattr(self.kpt_u[0], 'c_on')
if isinstance(self.kpt_u[0].psit_nG, TarFileReference):
raise RuntimeError('Wavefunctions have not been initialized.')
taut_sG = self.gd.zeros(self.nspins)
dpsit_G = self.gd.empty(dtype=self.dtype)
for kpt in self.kpt_u:
for f, psit_G in zip(kpt.f_n, kpt.psit_nG):
for v in range(3):
grad_v[v](psit_G, dpsit_G, kpt.phase_cd)
axpy(0.5 * f, abs(dpsit_G)**2, taut_sG[kpt.s])
self.kpt_comm.sum(taut_sG)
self.band_comm.sum(taut_sG)
return taut_sG
def calculate_pseudo_density(self, wfs):
"""Calculate nt_sG from scratch.
nt_sG will be equal to nct_G plus the contribution from
wfs.add_to_density().
"""
nvspins = wfs.kd.nspins
npspins = self.nspins
self.nt_sG = self.gd.zeros(npspins)
for s in range(npspins):
for kpt in wfs.kpt_u:
if s == kpt.s or npspins > nvspins:
f_n = kpt.f_n / (1. + int(npspins > nvspins))
for f, psit_G in zip((f_n - self.wocc_sn[s] +
self.wunocc_sn[s]),
kpt.psit_nG):
axpy(f, psit_G**2, self.nt_sG[s])
self.nt_sG[:self.nspins] += self.nct_G
def calculate_residuals(self, kpt, wfs, hamiltonian, psit_xG, P_axi, eps_x,
R_xG, n_x=None, calculate_change=False):
"""Calculate residual.
From R=Ht*psit calculate R=H*psit-eps*S*psit."""
for R_G, eps, psit_G in zip(R_xG, eps_x, psit_xG):
axpy(-eps, psit_G, R_G)
c_axi = {}
for a, P_xi in P_axi.items():
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
dO_ii = hamiltonian.setups[a].dO_ii
c_xi = (np.dot(P_xi, dH_ii) -
np.dot(P_xi * eps_x[:, np.newaxis], dO_ii))
c_axi[a] = c_xi
hamiltonian.xc.add_correction(kpt, psit_xG, R_xG, P_axi, c_axi, n_x,
calculate_change)
wfs.pt.add(R_xG, c_axi, kpt.q)
def calculate_pseudo_density(self, wfs):
"""Calculate nt_sG from scratch.
nt_sG will be equal to nct_G plus the contribution from
wfs.add_to_density().
"""
nvspins = wfs.kd.nspins
npspins = self.nspins
self.nt_sG = self.gd.zeros(npspins)
for s in range(npspins):
for kpt in wfs.kpt_u:
if s == kpt.s or npspins > nvspins:
f_n = kpt.f_n / (1. + int(npspins > nvspins))
for f, psit_G in zip((f_n - self.wocc_sn[s] +
self.wunocc_sn[s]),
kpt.psit_nG):
axpy(f, psit_G ** 2, self.nt_sG[s])
self.nt_sG += self.nct_G
def calculate_kinetic_energy_density(self):
if self.taugrad_v is None:
self.taugrad_v = [
Gradient(self.gd, v, n=3, dtype=self.dtype).apply
for v in range(3)
]
assert not hasattr(self.kpt_u[0], 'c_on')
if not isinstance(self.kpt_u[0].psit_nG, np.ndarray):
return None
taut_sG = self.gd.zeros(self.nspins)
dpsit_G = self.gd.empty(dtype=self.dtype)
for kpt in self.kpt_u:
for f, psit_G in zip(kpt.f_n, kpt.psit_nG):
for v in range(3):
self.taugrad_v[v](psit_G, dpsit_G, kpt.phase_cd)
axpy(0.5 * f, abs(dpsit_G)**2, taut_sG[kpt.s])
self.kptband_comm.sum(taut_sG)
return taut_sG
def add_realspace_orbital_to_density(self, nt_G, psit_G):
if psit_G.dtype == float:
axpy(1.0, psit_G**2, nt_G)
else:
assert psit_G.dtype == complex
axpy(1.0, psit_G.real**2, nt_G)
axpy(1.0, psit_G.imag**2, nt_G)
def add_gradient_correction(grad_v, gradn_svg, sigma_xg, dedsigma_xg, v_sg):
"""Add gradient correction to potential.
::
__ / de(r) __ \
v (r) += -2 \/ . | --------- \/ n(r) |
xc \ dsigma(r) /
Adds arbitrary data to sigma_xg. Be sure to pass a copy if you need
sigma_xg after calling this function.
"""
nspins = len(v_sg)
# vv_g is a calculation buffer. Its contents will be corrupted.
vv_g = sigma_xg[0]
for v in range(3):
for s in range(nspins):
grad_v[v](dedsigma_xg[2 * s] * gradn_svg[s, v], vv_g)
axpy(-2.0, vv_g, v_sg[s])
if nspins == 2:
grad_v[v](dedsigma_xg[1] * gradn_svg[s, v], vv_g)
axpy(-1.0, vv_g, v_sg[1 - s])
def calculate_kinetic_energy_density(self):
if self.taugrad_v is None:
self.taugrad_v = [
Gradient(self.gd, v, n=3, dtype=self.dtype).apply
for v in range(3)]
assert not hasattr(self.kpt_u[0], 'c_on')
if self.kpt_u[0].psit_nG is None:
raise RuntimeError('No wavefunctions yet')
if isinstance(self.kpt_u[0].psit_nG, FileReference):
# XXX initialize
raise RuntimeError('Wavefunctions have not been initialized.')
taut_sG = self.gd.zeros(self.nspins)
dpsit_G = self.gd.empty(dtype=self.dtype)
for kpt in self.kpt_u:
for f, psit_G in zip(kpt.f_n, kpt.psit_nG):
for v in range(3):
self.taugrad_v[v](psit_G, dpsit_G, kpt.phase_cd)
axpy(0.5 * f, abs(dpsit_G)**2, taut_sG[kpt.s])
self.kpt_comm.sum(taut_sG)
self.band_comm.sum(taut_sG)
return taut_sG
def __call__(self, residuals, kpt, ekin=None, out=None):
if residuals.ndim == 3:
if out is None:
return self.__call__(residuals[np.newaxis], kpt)[0]
return self.__call__(residuals[np.newaxis], kpt,
out=out[np.newaxis])[0]
nb = len(residuals) # number of bands
phases = kpt.phase_cd
step = self.step
if out is None:
d0, q0 = self.scratch0[:, :nb]
else:
d0 = out
q0 = self.scratch0[0, :nb]
r1, d1, q1 = self.scratch1[:, :nb]
r2, d2, q2 = self.scratch2[:, :nb]
self.restrictor0(-residuals, r1, phases)
d1[:] = 4 * step * r1
self.kin1.apply(d1, q1, phases)
q1 -= r1
self.restrictor1(q1, r2, phases)
d2 = 16 * step * r2
self.kin2.apply(d2, q2, phases)
q2 -= r2
d2 -= 16 * step * q2
self.interpolator2(d2, q1, phases)
d1 -= q1
self.kin1.apply(d1, q1, phases)
q1 -= r1
d1 -= 4 * step * q1
self.interpolator1(-d1, d0, phases)
self.kin0.apply(d0, q0, phases)
q0 -= residuals
axpy(-step, q0, d0) # d0 -= step * q0
d0 *= -1.0
return d0
def calculate_lda(self, e_g, n_sg, v_sg):
nspins = len(n_sg)
gradn_svg = self.gd.empty((nspins, 3))
sigma_xg = self.gd.zeros(nspins * 2 - 1)
dedsigma_xg = self.gd.empty(nspins * 2 - 1)
for v in range(3):
for s in range(nspins):
self.grad_v[v](n_sg[s], gradn_svg[s, v])
axpy(1.0, gradn_svg[s, v]**2, sigma_xg[2 * s])
if nspins == 2:
axpy(1.0, gradn_svg[0, v] * gradn_svg[1, v], sigma_xg[1])
self.calculate_gga(e_g, n_sg, v_sg, sigma_xg, dedsigma_xg)
vv_g = sigma_xg[0]
for v in range(3):
for s in range(nspins):
self.grad_v[v](dedsigma_xg[2 * s] * gradn_svg[s, v], vv_g)
axpy(-2.0, vv_g, v_sg[s])
if nspins == 2:
self.grad_v[v](dedsigma_xg[1] * gradn_svg[s, v], vv_g)
axpy(-1.0, vv_g, v_sg[1 - s])
def add_to_density_from_k_point_with_occupation(self, nt_sG, kpt, f_n):
# Used in calculation of response part of GLLB-potential
nt_G = nt_sG[kpt.s]
if self.dtype == float:
for f, psit_G in zip(f_n, kpt.psit_nG):
axpy(f, psit_G**2, nt_G)
else:
for f, psit_G in zip(f_n, kpt.psit_nG):
axpy(f, psit_G.real**2, nt_G)
axpy(f, psit_G.imag**2, nt_G)
# Hack used in delta-scf calculations:
if hasattr(kpt, 'c_on'):
assert self.bd.comm.size == 1
d_nn = np.zeros((self.bd.mynbands, self.bd.mynbands),
dtype=complex)
for ne, c_n in zip(kpt.ne_o, kpt.c_on):
d_nn += ne * np.outer(c_n.conj(), c_n)
for d_n, psi0_G in zip(d_nn, kpt.psit_nG):
for d, psi_G in zip(d_n, kpt.psit_nG):
if abs(d) > 1.e-12:
nt_G += (psi0_G.conj() * d * psi_G).real
def add_to_density_from_k_point_with_occupation(self, nt_sG, kpt, f_n):
# Used in calculation of response part of GLLB-potential
nt_G = nt_sG[kpt.s]
if self.dtype == float:
for f, psit_G in zip(f_n, kpt.psit_nG):
axpy(f, psit_G**2, nt_G)
else:
for f, psit_G in zip(f_n, kpt.psit_nG):
axpy(f, psit_G.real**2, nt_G)
axpy(f, psit_G.imag**2, nt_G)
# Hack used in delta-scf calculations:
if hasattr(kpt, 'c_on'):
assert self.bd.comm.size == 1
d_nn = np.zeros((self.bd.mynbands, self.bd.mynbands),
dtype=complex)
for ne, c_n in zip(kpt.ne_o, kpt.c_on):
d_nn += ne * np.outer(c_n.conj(), c_n)
for d_n, psi0_G in zip(d_nn, kpt.psit_nG):
for d, psi_G in zip(d_n, kpt.psit_nG):
if abs(d) > 1.e-12:
nt_G += (psi0_G.conj() * d * psi_G).real
def iterate_one_k_point(self, hamiltonian, wfs, kpt):
"""Do a conjugate gradient iterations for the kpoint"""
niter = self.niter
phi_G = self.phi_G
phi_old_G = self.phi_old_G
self.subspace_diagonalize(hamiltonian, wfs, kpt)
R_nG = wfs.matrixoperator.suggest_temporary_buffer()
Htphi_G = R_nG[0]
R_nG[:] = self.Htpsit_nG
self.timer.start('Residuals')
self.calculate_residuals(kpt, wfs, hamiltonian, kpt.psit_nG,
kpt.P_ani, kpt.eps_n, R_nG)
self.timer.stop('Residuals')
self.timer.start('CG')
vt_G = hamiltonian.vt_sG[kpt.s]
total_error = 0.0
for n in range(self.nbands):
R_G = R_nG[n]
Htpsit_G = self.Htpsit_nG[n]
gamma_old = 1.0
phi_old_G[:] = 0.0
error = self.gd.comm.sum(np.vdot(R_G, R_G).real)
for nit in range(niter):
if error < self.tolerance / self.nbands:
# print >> self.f, "cg:iters", n, nit
break
pR_G = self.preconditioner(R_G, kpt)
# New search direction
gamma = self.gd.comm.sum(np.vdot(pR_G, R_G).real)
phi_G[:] = -pR_G - gamma/gamma_old * phi_old_G
gamma_old = gamma
phi_old_G[:] = phi_G[:]
# Calculate projections
P2_ai = wfs.pt.dict()
wfs.pt.integrate(phi_G, P2_ai, kpt.q)
# Orthonormalize phi_G to all bands
self.timer.start('CG: orthonormalize')
for nn in range(self.nbands):
overlap = np.vdot(kpt.psit_nG[nn], phi_G) * self.gd.dv
for a, P2_i in P2_ai.items():
P_i = kpt.P_ani[a][nn]
dO_ii = wfs.setups[a].dO_ii
overlap += np.vdot(P_i, np.inner(dO_ii, P2_i))
overlap = self.gd.comm.sum(overlap)
# phi_G -= overlap * kpt.psit_nG[nn]
axpy(-overlap, kpt.psit_nG[nn], phi_G)
for a, P2_i in P2_ai.items():
P_i = kpt.P_ani[a][nn]
P2_i -= P_i * overlap
norm = np.vdot(phi_G, phi_G) * self.gd.dv
for a, P2_i in P2_ai.items():
dO_ii = wfs.setups[a].dO_ii
norm += np.vdot(P2_i, np.inner(dO_ii, P2_i))
norm = self.gd.comm.sum(norm.real)
phi_G /= sqrt(norm)
for P2_i in P2_ai.values():
P2_i /= sqrt(norm)
self.timer.stop('CG: orthonormalize')
#find optimum linear combination of psit_G and phi_G
an = kpt.eps_n[n]
wfs.kin.apply(phi_G, Htphi_G, kpt.phase_cd)
Htphi_G += phi_G * vt_G
b = np.vdot(phi_G, Htpsit_G) * self.gd.dv
c = np.vdot(phi_G, Htphi_G) * self.gd.dv
for a, P2_i in P2_ai.items():
P_i = kpt.P_ani[a][n]
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
b += dot(P2_i, dot(dH_ii, P_i.conj()))
c += dot(P2_i, dot(dH_ii, P2_i.conj()))
b = self.gd.comm.sum(b.real)
c = self.gd.comm.sum(c.real)
theta = 0.5 * atan2(2 * b, an - c)
enew = (an * cos(theta)**2 +
c * sin(theta)**2 +
b * sin(2.0 * theta))
# theta can correspond either minimum or maximum
if ( enew - kpt.eps_n[n] ) > 0.0: #we were at maximum
theta += pi / 2.0
enew = (an * cos(theta)**2 +
c * sin(theta)**2 +
b * sin(2.0 * theta))
kpt.eps_n[n] = enew
kpt.psit_nG[n] *= cos(theta)
# kpt.psit_nG[n] += sin(theta) * phi_G
axpy(sin(theta), phi_G, kpt.psit_nG[n])
for a, P2_i in P2_ai.items():
P_i = kpt.P_ani[a][n]
P_i *= cos(theta)
P_i += sin(theta) * P2_i
if nit < niter - 1:
Htpsit_G *= cos(theta)
# Htpsit_G += sin(theta) * Htphi_G
axpy(sin(theta), Htphi_G, Htpsit_G)
#adjust residuals
R_G[:] = Htpsit_G - kpt.eps_n[n] * kpt.psit_nG[n]
coef_ai = wfs.pt.dict()
for a, coef_i in coef_ai.items():
P_i = kpt.P_ani[a][n]
dO_ii = wfs.setups[a].dO_ii
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
coef_i[:] = (dot(P_i, dH_ii) -
dot(P_i * kpt.eps_n[n], dO_ii))
wfs.pt.add(R_G, coef_ai, kpt.q)
error_new = self.gd.comm.sum(np.vdot(R_G, R_G).real)
if error_new / error < 0.30:
# print >> self.f, "cg:iters", n, nit+1
break
if (self.nbands_converge == 'occupied' and
kpt.f_n is not None and kpt.f_n[n] == 0.0):
# print >> self.f, "cg:iters", n, nit+1
break
error = error_new
if kpt.f_n is None:
weight = 1.0
else:
weight = kpt.f_n[n]
if self.nbands_converge != 'occupied':
weight = kpt.weight * float(n < self.nbands_converge)
total_error += weight * error
# if nit == 3:
# print >> self.f, "cg:iters", n, nit+1
self.timer.stop('CG')
return total_error
def calculate(self, seperate_spin=None):
"""Calculate the non-interacting density response function. """
calc = self.calc
kd = self.kd
gd = self.gd
sdisp_cd = gd.sdisp_cd
ibzk_kc = kd.ibzk_kc
bzk_kc = kd.bzk_kc
kq_k = self.kq_k
f_skn = self.f_skn
e_skn = self.e_skn
# Matrix init
chi0_wGG = np.zeros((self.Nw_local, self.npw, self.npw), dtype=complex)
if self.hilbert_trans:
specfunc_wGG = np.zeros((self.NwS_local, self.npw, self.npw), dtype = complex)
# Prepare for the derivative of pseudo-wavefunction
if self.optical_limit:
d_c = [Gradient(gd, i, n=4, dtype=complex).apply for i in range(3)]
dpsit_g = gd.empty(dtype=complex)
tmp = np.zeros((3), dtype=complex)
rhoG0_v = np.zeros(3, dtype=complex)
self.chi0G0_wGv = np.zeros((self.Nw_local, self.npw, 3), dtype=complex)
self.chi00G_wGv = np.zeros((self.Nw_local, self.npw, 3), dtype=complex)
specfuncG0_wGv = np.zeros((self.NwS_local, self.npw, 3), dtype=complex)
specfunc0G_wGv = np.zeros((self.NwS_local, self.npw, 3), dtype=complex)
use_zher = False
if self.eta < 1e-5:
use_zher = True
rho_G = np.zeros(self.npw, dtype=complex)
t0 = time()
if seperate_spin is None:
spinlist = np.arange(self.nspins)
else:
spinlist = [seperate_spin]
for spin in spinlist:
if not (f_skn[spin] > self.ftol).any():
self.chi0_wGG = chi0_wGG
continue
for k in range(self.kstart, self.kend):
k_pad = False
if k >= self.kd.nbzkpts:
k = 0
k_pad = True
# Find corresponding kpoint in IBZ
ibzkpt1 = kd.bz2ibz_k[k]
if self.optical_limit:
ibzkpt2 = ibzkpt1
else:
ibzkpt2 = kd.bz2ibz_k[kq_k[k]]
if self.pwmode:
N_c = self.gd.N_c
k_c = self.kd.ibzk_kc[ibzkpt1]
eikr1_R = np.exp(2j * pi * np.dot(np.indices(N_c).T, k_c / N_c).T)
k_c = self.kd.ibzk_kc[ibzkpt2]
eikr2_R = np.exp(2j * pi * np.dot(np.indices(N_c).T, k_c / N_c).T)
index1_g, phase1_g = kd.get_transform_wavefunction_index(self.gd.N_c - (self.pbc == False), k)
index2_g, phase2_g = kd.get_transform_wavefunction_index(self.gd.N_c - (self.pbc == False), kq_k[k])
for n in range(self.nvalbands):
if self.calc.wfs.world.size == 1:
if (self.f_skn[spin][ibzkpt1, n] - self.ftol < 0):
continue
t1 = time()
if self.pwmode:
u = self.kd.get_rank_and_index(spin, ibzkpt1)[1]
psitold_g = calc.wfs._get_wave_function_array(u, n, realspace=True, phase=eikr1_R)
else:
u = None
psitold_g = self.get_wavefunction(ibzkpt1, n, True, spin=spin)
psit1new_g = kd.transform_wave_function(psitold_g,k,index1_g,phase1_g)
P1_ai = self.pawstuff(psit1new_g, k, n, spin, u, ibzkpt1)
psit1_g = psit1new_g.conj() * self.expqr_g
for m in self.mlist:
if self.nbands > 1000 and m % 200 == 0:
print(' ', k, n, m, time() - t0, file=self.txt)
check_focc = (f_skn[spin][ibzkpt1, n] - f_skn[spin][ibzkpt2, m]) > self.ftol
if not self.pwmode:
psitold_g = self.get_wavefunction(ibzkpt2, m, check_focc, spin=spin)
if check_focc:
if self.pwmode:
u = self.kd.get_rank_and_index(spin, ibzkpt2)[1]
psitold_g = calc.wfs._get_wave_function_array(u, m, realspace=True, phase=eikr2_R)
psit2_g = kd.transform_wave_function(psitold_g, kq_k[k], index2_g, phase2_g)
# zero padding is included through the FFT
rho_g = np.fft.fftn(psit2_g * psit1_g, s=self.nGrpad) * self.vol / self.nG0rpad
# Here, planewave cutoff is applied
rho_G = rho_g.ravel()[self.Gindex_G]
if self.optical_limit:
phase_cd = np.exp(2j * pi * sdisp_cd * kd.bzk_kc[kq_k[k], :, np.newaxis])
for ix in range(3):
d_c[ix](psit2_g, dpsit_g, phase_cd)
tmp[ix] = gd.integrate(psit1_g * dpsit_g)
rho_G[0] = -1j * np.dot(self.qq_v, tmp)
for ix in range(3):
q2_c = np.diag((1,1,1))[ix] * self.qopt
qq2_v = np.dot(q2_c, self.bcell_cv) # summation over c
rhoG0_v[ix] = -1j * np.dot(qq2_v, tmp)
P2_ai = self.pawstuff(psit2_g, kq_k[k], m, spin, u, ibzkpt2)
for a, id in enumerate(calc.wfs.setups.id_a):
P_p = np.outer(P1_ai[a].conj(), P2_ai[a]).ravel()
gemv(1.0, self.phi_aGp[a], P_p, 1.0, rho_G)
if self.optical_limit:
gemv(1.0, self.phiG0_avp[a], P_p, 1.0, rhoG0_v)
if self.optical_limit:
if np.abs(self.enoshift_skn[spin][ibzkpt2, m] -
self.enoshift_skn[spin][ibzkpt1, n]) > 0.1/Hartree:
rho_G[0] /= self.enoshift_skn[spin][ibzkpt2, m] \
- self.enoshift_skn[spin][ibzkpt1, n]
rhoG0_v /= self.enoshift_skn[spin][ibzkpt2, m] \
- self.enoshift_skn[spin][ibzkpt1, n]
else:
rho_G[0] = 0.
rhoG0_v[:] = 0.
if k_pad:
rho_G[:] = 0.
if self.optical_limit:
rho0G_Gv = np.outer(rho_G.conj(), rhoG0_v)
rhoG0_Gv = np.outer(rho_G, rhoG0_v.conj())
rho0G_Gv[0,:] = rhoG0_v * rhoG0_v.conj()
rhoG0_Gv[0,:] = rhoG0_v * rhoG0_v.conj()
if not self.hilbert_trans:
if not use_zher:
rho_GG = np.outer(rho_G, rho_G.conj())
for iw in range(self.Nw_local):
w = self.w_w[iw + self.wstart] / Hartree
coef = ( 1. / (w + e_skn[spin][ibzkpt1, n] - e_skn[spin][ibzkpt2, m]
+ 1j * self.eta)
- 1. / (w - e_skn[spin][ibzkpt1, n] + e_skn[spin][ibzkpt2, m]
+ 1j * self.eta) )
C = (f_skn[spin][ibzkpt1, n] - f_skn[spin][ibzkpt2, m]) * coef
if use_zher:
czher(C.real, rho_G.conj(), chi0_wGG[iw])
else:
axpy(C, rho_GG, chi0_wGG[iw])
if self.optical_limit:
axpy(C, rho0G_Gv, self.chi00G_wGv[iw])
axpy(C, rhoG0_Gv, self.chi0G0_wGv[iw])
else:
rho_GG = np.outer(rho_G, rho_G.conj())
focc = f_skn[spin][ibzkpt1,n] - f_skn[spin][ibzkpt2,m]
w0 = e_skn[spin][ibzkpt2,m] - e_skn[spin][ibzkpt1,n]
scal(focc, rho_GG)
if self.optical_limit:
scal(focc, rhoG0_Gv)
scal(focc, rho0G_Gv)
# calculate delta function
w0_id = int(w0 / self.dw)
if w0_id + 1 < self.NwS:
# rely on the self.NwS_local is equal in each node!
if self.wScomm.rank == w0_id // self.NwS_local:
alpha = (w0_id + 1 - w0/self.dw) / self.dw
axpy(alpha, rho_GG, specfunc_wGG[w0_id % self.NwS_local] )
if self.optical_limit:
axpy(alpha, rho0G_Gv, specfunc0G_wGv[w0_id % self.NwS_local] )
axpy(alpha, rhoG0_Gv, specfuncG0_wGv[w0_id % self.NwS_local] )
if self.wScomm.rank == (w0_id+1) // self.NwS_local:
alpha = (w0 / self.dw - w0_id) / self.dw
axpy(alpha, rho_GG, specfunc_wGG[(w0_id+1) % self.NwS_local] )
if self.optical_limit:
axpy(alpha, rho0G_Gv, specfunc0G_wGv[(w0_id+1) % self.NwS_local] )
axpy(alpha, rhoG0_Gv, specfuncG0_wGv[(w0_id+1) % self.NwS_local] )
# deltaw = delta_function(w0, self.dw, self.NwS, self.sigma)
# for wi in range(self.NwS_local):
# if deltaw[wi + self.wS1] > 1e-8:
# specfunc_wGG[wi] += tmp_GG * deltaw[wi + self.wS1]
if self.kd.nbzkpts == 1:
if n == 0:
dt = time() - t0
totaltime = dt * self.nvalbands * self.nspins
self.printtxt('Finished n 0 in %d seconds, estimate %d seconds left.' %(dt, totaltime) )
if rank == 0 and self.nvalbands // 5 > 0:
if n > 0 and n % (self.nvalbands // 5) == 0:
dt = time() - t0
self.printtxt('Finished n %d in %d seconds, estimate %d seconds left.'%(n, dt, totaltime-dt))
if calc.wfs.world.size != 1:
self.kcomm.barrier()
if k == 0:
dt = time() - t0
totaltime = dt * self.nkpt_local * self.nspins
self.printtxt('Finished k 0 in %d seconds, estimate %d seconds left.' %(dt, totaltime))
if rank == 0 and self.nkpt_local // 5 > 0:
if k > 0 and k % (self.nkpt_local // 5) == 0:
dt = time() - t0
self.printtxt('Finished k %d in %d seconds, estimate %d seconds left. '%(k, dt, totaltime - dt) )
self.printtxt('Finished summation over k')
self.kcomm.barrier()
# Hilbert Transform
if not self.hilbert_trans:
for iw in range(self.Nw_local):
self.kcomm.sum(chi0_wGG[iw])
if self.optical_limit:
self.kcomm.sum(self.chi0G0_wGv[iw])
self.kcomm.sum(self.chi00G_wGv[iw])
if use_zher:
assert (np.abs(chi0_wGG[0,1:,0]) < 1e-10).all()
for iw in range(self.Nw_local):
chi0_wGG[iw] += chi0_wGG[iw].conj().T
for iG in range(self.npw):
chi0_wGG[iw, iG, iG] /= 2.
assert np.abs(np.imag(chi0_wGG[iw, iG, iG])) < 1e-10
else:
for iw in range(self.NwS_local):
self.kcomm.sum(specfunc_wGG[iw])
if self.optical_limit:
self.kcomm.sum(specfuncG0_wGv[iw])
self.kcomm.sum(specfunc0G_wGv[iw])
if self.wScomm.size == 1:
chi0_wGG = hilbert_transform(specfunc_wGG, self.w_w, self.Nw, self.dw, self.eta,
self.full_hilbert_trans)[self.wstart:self.wend]
self.printtxt('Finished hilbert transform !')
del specfunc_wGG
else:
# redistribute specfunc_wGG to all nodes
size = self.comm.size
assert self.NwS % size == 0
NwStmp1 = (rank % self.kcomm.size) * self.NwS // size
NwStmp2 = (rank % self.kcomm.size + 1) * self.NwS // size
specfuncnew_wGG = specfunc_wGG[NwStmp1:NwStmp2]
del specfunc_wGG
coords = np.zeros(self.wcomm.size, dtype=int)
nG_local = self.npw**2 // self.wcomm.size
if self.wcomm.rank == self.wcomm.size - 1:
nG_local = self.npw**2 - (self.wcomm.size - 1) * nG_local
self.wcomm.all_gather(np.array([nG_local]), coords)
specfunc_Wg = SliceAlongFrequency(specfuncnew_wGG, coords, self.wcomm)
self.printtxt('Finished Slice Along Frequency !')
chi0_Wg = hilbert_transform(specfunc_Wg, self.w_w, self.Nw, self.dw, self.eta,
self.full_hilbert_trans)[:self.Nw]
self.printtxt('Finished hilbert transform !')
self.comm.barrier()
del specfunc_Wg
chi0_wGG = SliceAlongOrbitals(chi0_Wg, coords, self.wcomm)
self.printtxt('Finished Slice along orbitals !')
self.comm.barrier()
del chi0_Wg
if self.optical_limit:
specfuncG0_WGv = np.zeros((self.NwS, self.npw, 3), dtype=complex)
specfunc0G_WGv = np.zeros((self.NwS, self.npw, 3), dtype=complex)
self.wScomm.all_gather(specfunc0G_wGv, specfunc0G_WGv)
self.wScomm.all_gather(specfuncG0_wGv, specfuncG0_WGv)
specfunc0G_wGv = specfunc0G_WGv
specfuncG0_wGv = specfuncG0_WGv
if self.optical_limit:
self.chi00G_wGv = hilbert_transform(specfunc0G_wGv, self.w_w, self.Nw, self.dw, self.eta,
self.full_hilbert_trans)[self.wstart:self.wend]
self.chi0G0_wGv = hilbert_transform(specfuncG0_wGv, self.w_w, self.Nw, self.dw, self.eta,
self.full_hilbert_trans)[self.wstart:self.wend]
if self.optical_limit:
self.chi00G_wGv /= self.vol
self.chi0G0_wGv /= self.vol
self.chi0_wGG = chi0_wGG
self.chi0_wGG /= self.vol
self.printtxt('')
self.printtxt('Finished chi0 !')
nt_G = calc.density.gd.zeros()
bfs = wfs.basis_functions
nao = wfs.setups.nao
f_n = kpt.f_n
rho_MM = np.zeros((nao, nao))
wfs.calculate_density_matrix(kpt.f_n, kpt.C_nM, rho_MM)
bfs.construct_density(rho_MM, nt_G, -1)
nbands = wfs.bd.nbands
psit_nG = wfs.gd.zeros(nbands)
bfs.lcao_to_grid(kpt.C_nM, psit_nG, -1)
nt2_G = calc.density.gd.zeros()
for f, psit_G in zip(f_n, psit_nG):
axpy(f, psit_G**2, nt2_G)
identity_MM = np.identity(nao)
Phit_MG = calc.wfs.gd.zeros(nao)
bfs.lcao_to_grid(identity_MM, Phit_MG, -1)
nt3_G = calc.density.gd.zeros()
for M1, Phit1_G in enumerate(Phit_MG):
for M2, Phit2_G in enumerate(Phit_MG):
nt3_G += rho_MM[M1, M2] * Phit1_G * Phit2_G
err1_G = nt2_G - nt_G
err2_G = nt3_G - nt_G
maxerr1 = np.abs(err1_G).max()
maxerr2 = np.abs(err2_G).max()
def iterate_one_k_point(self, hamiltonian, wfs, kpt):
"""Do a single RMM-DIIS iteration for the kpoint"""
psit_nG, R_nG = self.subspace_diagonalize(hamiltonian, wfs, kpt)
self.timer.start('RMM-DIIS')
self.timer.start('Calculate residuals')
if self.keep_htpsit:
self.calculate_residuals(kpt, wfs, hamiltonian, psit_nG,
kpt.P_ani, kpt.eps_n, R_nG)
self.timer.stop('Calculate residuals')
def integrate(a_G, b_G):
return np.real(wfs.integrate(a_G, b_G, global_integral=False))
comm = wfs.gd.comm
B = self.blocksize
dR_xG = wfs.empty(B, q=kpt.q)
P_axi = wfs.pt.dict(B)
errors_x = np.zeros(B)
state_done = np.zeros(B, dtype=bool)
errors_n = np.zeros(wfs.bd.mynbands)
# Arrays needed for DIIS step
if self.niter > 1:
psit_diis_nxG = wfs.empty(B * self.niter, q=kpt.q)
R_diis_nxG = wfs.empty(B * self.niter, q=kpt.q)
# P_diis_anxi = wfs.pt.dict(B * self.niter)
eig_n = np.zeros(self.niter) # eigenvalues for diagonalization
# not needed in any step
error = 0.0
for n1 in range(0, wfs.bd.mynbands, B):
state_done[:] = False
n2 = n1 + B
if n2 > wfs.bd.mynbands:
n2 = wfs.bd.mynbands
B = n2 - n1
P_axi = dict((a, P_xi[:B]) for a, P_xi in P_axi.items())
dR_xG = dR_xG[:B]
n_x = range(n1, n2)
psit_xG = psit_nG[n1:n2]
self.timer.start('Calculate residuals')
if self.keep_htpsit:
R_xG = R_nG[n1:n2]
else:
R_xG = wfs.empty(B, q=kpt.q)
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit_xG, R_xG)
wfs.pt.integrate(psit_xG, P_axi, kpt.q)
self.calculate_residuals(kpt, wfs, hamiltonian, psit_xG,
P_axi, kpt.eps_n[n_x], R_xG, n_x)
self.timer.stop('Calculate residuals')
errors_x[:] = 0.0
for n in range(n1, n2):
if kpt.f_n is None:
weight = kpt.weight
else:
weight = kpt.f_n[n]
if self.nbands_converge != 'occupied':
if wfs.bd.global_index(n) < self.nbands_converge:
weight = kpt.weight
else:
weight = 0.0
errors_x[n - n1] = weight * integrate(R_xG[n - n1],
R_xG[n - n1])
errors_n[n] = errors_x[n - n1]
comm.sum(errors_x)
error += np.sum(errors_x)
# Insert first vectors and residuals for DIIS step
if self.niter > 1:
# Save the previous vectors contiguously for each band
# in the block
psit_diis_nxG[:B * self.niter:self.niter] = psit_xG
R_diis_nxG[:B * self.niter:self.niter] = R_xG
# Precondition the residual:
self.timer.start('precondition')
# ekin_x = self.preconditioner.calculate_kinetic_energy(
# R_xG, kpt)
ekin_x = self.preconditioner.calculate_kinetic_energy(
psit_xG, kpt)
dpsit_xG = self.preconditioner(R_xG, kpt, ekin_x)
self.timer.stop('precondition')
# Calculate the residual of dpsit_G, dR_G = (H - e S) dpsit_G:
# self.timer.start('Apply Hamiltonian')
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, dpsit_xG, dR_xG)
# self.timer.stop('Apply Hamiltonian')
self.timer.start('projections')
wfs.pt.integrate(dpsit_xG, P_axi, kpt.q)
self.timer.stop('projections')
if self.use_rayleigh:
self.timer.start('Minimize Rayleigh')
i1 = wfs.integrate(psit_xG, dR_xG,
global_integral=False).item()
i2 = wfs.integrate(dpsit_xG, dR_xG,
global_integral=False).item()
i3 = wfs.integrate(dpsit_xG, psit_xG,
global_integral=False).item()
i4 = wfs.integrate(dpsit_xG, dpsit_xG,
global_integral=False).item()
for a, dP_xi in P_axi.items():
P_i = kpt.P_ani[a][n1]
dP_i = dP_xi[0]
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
dO_ii = wfs.setups[a].dO_ii
i1 += np.dot(P_i,
np.dot(dH_ii, dP_i.conj())).item()
i2 += np.dot(dP_i,
np.dot(dH_ii, dP_i.conj())).item()
i3 += np.dot(dP_i,
np.dot(dO_ii, P_i.conj())).item()
i4 += np.dot(dP_i,
np.dot(dO_ii, dP_i.conj())).item()
i1 = comm.sum(i1)
i2 = comm.sum(i2)
i3 = comm.sum(i3)
i4 = comm.sum(i4)
a = np.real(i2 * i3 - i1 * i4)
b = np.real(i2 - kpt.eps_n[n1] * i4)
c = np.real(i1 - kpt.eps_n[n1] * i3)
# print "A,B,C", a,b,c
lam_x = np.array((-2.0 * c / (b + np.sqrt(b**2 - 4.0 * a * c)),))
self.timer.stop('Minimize Rayleigh')
self.timer.start('Calculate residuals')
self.calculate_residuals(kpt, wfs, hamiltonian, dpsit_xG,
P_axi, kpt.eps_n[n_x], dR_xG, n_x,
calculate_change=True)
self.timer.stop('Calculate residuals')
else:
self.timer.start('Calculate residuals')
self.calculate_residuals(kpt, wfs, hamiltonian, dpsit_xG,
P_axi, kpt.eps_n[n_x], dR_xG, n_x,
calculate_change=True)
self.timer.stop('Calculate residuals')
# Find lam that minimizes the norm of R'_G = R_G + lam dR_G
self.timer.start('Find lambda')
RdR_x = np.array([integrate(dR_G, R_G)
for R_G, dR_G in zip(R_xG, dR_xG)])
dRdR_x = np.array([integrate(dR_G, dR_G) for dR_G in dR_xG])
comm.sum(RdR_x)
comm.sum(dRdR_x)
lam_x = -RdR_x / dRdR_x
self.timer.stop('Find lambda')
# print "Lam_x:", lam_x
# Limit abs(lam) to [0.15, 1.0]
if self.limit_lambda:
upper = self.limit_lambda['upper']
lower = self.limit_lambda['lower']
if self.limit_lambda.get('absolute', False):
lam_x = np.where(np.abs(lam_x) < lower,
lower * np.sign(lam_x), lam_x)
lam_x = np.where(np.abs(lam_x) > upper,
upper * np.sign(lam_x), lam_x)
else:
lam_x = np.where(lam_x < lower, lower, lam_x)
lam_x = np.where(lam_x > upper, upper, lam_x)
# lam_x[:] = 0.1
# New trial wavefunction and residual
self.timer.start('Update psi')
for lam, psit_G, dpsit_G, R_G, dR_G in zip(lam_x, psit_xG,
dpsit_xG, R_xG, dR_xG):
axpy(lam, dpsit_G, psit_G) # psit_G += lam * dpsit_G
axpy(lam, dR_G, R_G) # R_G += lam** dR_G
self.timer.stop('Update psi')
self.timer.start('DIIS step')
# DIIS step
for nit in range(1, self.niter):
# Do not perform DIIS if error is small
# if abs(error_block / B) < self.rtol:
# break
# Update the subspace
psit_diis_nxG[nit:B * self.niter:self.niter] = psit_xG
R_diis_nxG[nit:B * self.niter:self.niter] = R_xG
# XXX Only integrals of nit old psits would be needed
# self.timer.start('projections')
# wfs.pt.integrate(psit_diis_nxG, P_diis_anxi, kpt.q)
# self.timer.stop('projections')
if nit > 1 or self.limit_lambda:
for ib in range(B):
if state_done[ib]:
continue
istart = ib * self.niter
iend = istart + nit + 1
# Residual matrix
self.timer.start('Construct matrix')
R_nn = wfs.integrate(R_diis_nxG[istart:iend],
R_diis_nxG[istart:iend],
global_integral=True)
# Full matrix
A_nn = -np.ones((nit + 2, nit + 2), wfs.dtype)
A_nn[:nit+1, :nit+1] = R_nn[:]
A_nn[-1,-1] = 0.0
x_n = np.zeros(nit + 2, wfs.dtype)
x_n[-1] = -1.0
self.timer.stop('Construct matrix')
self.timer.start('Linear solve')
alpha_i = np.linalg.solve(A_nn, x_n)[:-1]
self.timer.stop('Linear solve')
self.timer.start('Update trial vectors')
psit_xG[ib] = alpha_i[nit] * psit_diis_nxG[istart + nit]
R_xG[ib] = alpha_i[nit] * R_diis_nxG[istart + nit]
for i in range(nit):
# axpy(alpha_i[i], psit_diis_nxG[istart + i],
# psit_diis_nxG[istart + nit])
# axpy(alpha_i[i], R_diis_nxG[istart + i],
# R_diis_nxG[istart + nit])
axpy(alpha_i[i], psit_diis_nxG[istart + i],
psit_xG[ib])
axpy(alpha_i[i], R_diis_nxG[istart + i],
R_xG[ib])
self.timer.stop('Update trial vectors')
if nit < self.niter - 1:
self.timer.start('precondition')
# ekin_x = self.preconditioner.calculate_kinetic_energy(
# R_xG, kpt)
dpsit_xG = self.preconditioner(R_xG, kpt, ekin_x)
self.timer.stop('precondition')
for psit_G, lam, dpsit_G in zip(psit_xG, lam_x, dpsit_xG):
axpy(lam, dpsit_G, psit_G)
# Calculate the new residuals
self.timer.start('Calculate residuals')
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit_xG,
R_xG)
wfs.pt.integrate(psit_xG, P_axi, kpt.q)
self.calculate_residuals(kpt, wfs, hamiltonian, psit_xG,
P_axi, kpt.eps_n[n_x], R_xG, n_x,
calculate_change=True)
self.timer.stop('Calculate residuals')
self.timer.start('Calculate errors')
errors_new_x = np.zeros(B)
# errors_x[:] = 0.0
for n in range(n1, n2):
if kpt.f_n is None:
weight = kpt.weight
else:
weight = kpt.f_n[n]
if self.nbands_converge != 'occupied':
if wfs.bd.global_index(n) < self.nbands_converge:
weight = kpt.weight
else:
weight = 0.0
errors_new_x[n-n1] += weight * integrate(R_xG[n - n1],
R_xG[n - n1])
comm.sum(errors_x)
self.timer.stop('Calculate errors')
self.timer.stop('DIIS step')
# Final trial step
self.timer.start('precondition')
# ekin_x = self.preconditioner.calculate_kinetic_energy(
# R_xG, kpt)
dpsit_xG = self.preconditioner(R_xG, kpt, ekin_x)
self.timer.stop('precondition')
self.timer.start('Update psi')
if self.trial_step is not None:
lam_x[:] = self.trial_step
for lam, psit_G, dpsit_G in zip(lam_x, psit_xG, dpsit_xG):
axpy(lam, dpsit_G, psit_G) # psit_G += lam * dpsit_G
self.timer.stop('Update psi')
# norm = wfs.integrate(psit_xG[0], psit_xG[0])
# wfs.pt.integrate(psit_xG, P_axi, kpt.q)
# for a, P_xi in P_axi.items():
# dO_ii = wfs.setups[a].dO_ii
# norm += np.vdot(P_xi[0], np.inner(dO_ii, P_xi[0]))
# norm = comm.sum(np.real(norm).item())
# psit_xG /= np.sqrt(norm)
self.timer.stop('RMM-DIIS')
return error, psit_nG
def solve(self,
phi,
rho,
charge=None,
eps=None,
maxcharge=1e-6,
zero_initial_phi=False):
if eps is None:
eps = self.eps
actual_charge = self.gd.integrate(rho)
background = (actual_charge / self.gd.dv /
self.gd.get_size_of_global_array().prod())
if charge is None:
charge = actual_charge
if abs(charge) <= maxcharge:
# System is charge neutral. Use standard solver
return self.solve_neutral(phi, rho - background, eps=eps)
elif abs(charge) > maxcharge and self.gd.pbc_c.all():
# System is charged and periodic. Subtract a homogeneous
# background charge
if self.charged_periodic_correction is None:
print "+-----------------------------------------------------+"
print "| Calculating charged periodic correction using the |"
print "| Ewald potential from a lattice of probe charges in |"
print "| a homogenous background density |"
print "+-----------------------------------------------------+"
self.charged_periodic_correction = madelung(self.gd.cell_cv)
print "Potential shift will be ", \
self.charged_periodic_correction , "Ha."
# Set initial guess for potential
if zero_initial_phi:
phi[:] = 0.0
else:
phi -= charge * self.charged_periodic_correction
iters = self.solve_neutral(phi, rho - background, eps=eps)
phi += charge * self.charged_periodic_correction
return iters
elif abs(charge) > maxcharge and not self.gd.pbc_c.any():
# The system is charged and in a non-periodic unit cell.
# Determine the potential by 1) subtract a gaussian from the
# density, 2) determine potential from the neutralized density
# and 3) add the potential from the gaussian density.
# Load necessary attributes
self.load_gauss()
# Remove monopole moment
q = actual_charge / np.sqrt(4 * pi) # Monopole moment
rho_neutral = rho - q * self.rho_gauss # neutralized density
# Set initial guess for potential
if zero_initial_phi:
phi[:] = 0.0
else:
axpy(-q, self.phi_gauss, phi) #phi -= q * self.phi_gauss
# Determine potential from neutral density using standard solver
niter = self.solve_neutral(phi, rho_neutral, eps=eps)
# correct error introduced by removing monopole
axpy(q, self.phi_gauss, phi) #phi += q * self.phi_gauss
return niter
else:
# System is charged with mixed boundaryconditions
raise NotImplementedError
def solve(self, phi, rho, charge=None, eps=None, maxcharge=1e-6,
zero_initial_phi=False):
assert np.all(phi.shape == self.gd.n_c)
assert np.all(rho.shape == self.gd.n_c)
if eps is None:
eps = self.eps
actual_charge = self.gd.integrate(rho)
background = (actual_charge / self.gd.dv /
self.gd.get_size_of_global_array().prod())
if self.remove_moment:
assert not self.gd.pbc_c.any()
if not hasattr(self, 'gauss'):
self.gauss = Gaussian(self.gd)
rho_neutral = rho.copy()
phi_cor_L = []
for L in range(self.remove_moment):
phi_cor_L.append(self.gauss.remove_moment(rho_neutral, L))
# Remove multipoles for better initial guess
for phi_cor in phi_cor_L:
phi -= phi_cor
niter = self.solve_neutral(phi, rho_neutral, eps=eps)
# correct error introduced by removing multipoles
for phi_cor in phi_cor_L:
phi += phi_cor
return niter
if charge is None:
charge = actual_charge
if abs(charge) <= maxcharge:
# System is charge neutral. Use standard solver
return self.solve_neutral(phi, rho - background, eps=eps)
elif abs(charge) > maxcharge and self.gd.pbc_c.all():
# System is charged and periodic. Subtract a homogeneous
# background charge
# Set initial guess for potential
if zero_initial_phi:
phi[:] = 0.0
iters = self.solve_neutral(phi, rho - background, eps=eps)
return iters
elif abs(charge) > maxcharge and not self.gd.pbc_c.any():
# The system is charged and in a non-periodic unit cell.
# Determine the potential by 1) subtract a gaussian from the
# density, 2) determine potential from the neutralized density
# and 3) add the potential from the gaussian density.
# Load necessary attributes
# use_charge_center: The monopole will be removed at the
# center of the majority charge, which prevents artificial
# dipoles.
# Due to the shape of the Gaussian and it's Fourier-Transform,
# the Gaussian representing the charge should stay at least
# 7 gpts from the borders - see:
# https://listserv.fysik.dtu.dk/pipermail/gpaw-developers/2015-July/005806.html
if self.use_charge_center:
charge_sign = actual_charge / abs(actual_charge)
rho_sign = rho * charge_sign
rho_sign[np.where(rho_sign < 0)] = 0
absolute_charge = self.gd.integrate(rho_sign)
center = - self.gd.calculate_dipole_moment(rho_sign) \
/ absolute_charge
border_offset = np.inner(self.gd.h_cv, np.array((7, 7, 7)))
borders = np.inner(self.gd.h_cv, self.gd.N_c)
borders -= border_offset
if np.any(center > borders) or np.any(center < border_offset):
raise RuntimeError(
'Poisson solver: center of charge outside' + \
' borders - please increase box')
center[np.where(center > borders)] = borders
self.load_gauss(center=center)
else:
self.load_gauss()
# Remove monopole moment
q = actual_charge / np.sqrt(4 * pi) # Monopole moment
rho_neutral = rho - q * self.rho_gauss # neutralized density
# Set initial guess for potential
if zero_initial_phi:
phi[:] = 0.0
else:
axpy(-q, self.phi_gauss, phi) # phi -= q * self.phi_gauss
# Determine potential from neutral density using standard solver
niter = self.solve_neutral(phi, rho_neutral, eps=eps)
# correct error introduced by removing monopole
axpy(q, self.phi_gauss, phi) # phi += q * self.phi_gauss
return niter
else:
# System is charged with mixed boundaryconditions
msg = ('Charged systems with mixed periodic/zero'
' boundary conditions')
raise NotImplementedError(msg)
nt_G = calc.density.gd.zeros()
bfs = wfs.basis_functions
nao = wfs.setups.nao
f_n = kpt.f_n
rho_MM = np.zeros((nao, nao))
wfs.calculate_density_matrix(kpt.f_n, kpt.C_nM, rho_MM)
bfs.construct_density(rho_MM, nt_G, -1)
nbands = wfs.bd.nbands
psit_nG = wfs.gd.zeros(nbands)
bfs.lcao_to_grid(kpt.C_nM, psit_nG, -1)
nt2_G = calc.density.gd.zeros()
for f, psit_G in zip(f_n, psit_nG):
axpy(f, psit_G**2, nt2_G)
identity_MM = np.identity(nao)
Phit_MG = calc.wfs.gd.zeros(nao)
bfs.lcao_to_grid(identity_MM, Phit_MG, -1)
nt3_G = calc.density.gd.zeros()
for M1, Phit1_G in enumerate(Phit_MG):
for M2, Phit2_G in enumerate(Phit_MG):
nt3_G += rho_MM[M1, M2] * Phit1_G * Phit2_G
err1_G = nt2_G - nt_G
err2_G = nt3_G - nt_G
maxerr1 = np.abs(err1_G).max()
def calculate(self, seperate_spin=None):
"""Calculate the non-interacting density response function. """
calc = self.calc
kd = self.kd
gd = self.gd
sdisp_cd = gd.sdisp_cd
ibzk_kc = kd.ibzk_kc
bzk_kc = kd.bzk_kc
kq_k = self.kq_k
f_skn = self.f_skn
e_skn = self.e_skn
# Matrix init
chi0_wGG = np.zeros((self.Nw_local, self.npw, self.npw), dtype=complex)
if self.hilbert_trans:
specfunc_wGG = np.zeros((self.NwS_local, self.npw, self.npw), dtype=complex)
# Prepare for the derivative of pseudo-wavefunction
if self.optical_limit:
d_c = [Gradient(gd, i, n=4, dtype=complex).apply for i in range(3)]
dpsit_g = gd.empty(dtype=complex)
tmp = np.zeros((3), dtype=complex)
rhoG0_v = np.zeros(3, dtype=complex)
self.chi0G0_wGv = np.zeros((self.Nw_local, self.npw, 3), dtype=complex)
self.chi00G_wGv = np.zeros((self.Nw_local, self.npw, 3), dtype=complex)
specfuncG0_wGv = np.zeros((self.NwS_local, self.npw, 3), dtype=complex)
specfunc0G_wGv = np.zeros((self.NwS_local, self.npw, 3), dtype=complex)
use_zher = False
if self.eta < 1e-5:
use_zher = True
rho_G = np.zeros(self.npw, dtype=complex)
t0 = time()
if seperate_spin is None:
spinlist = np.arange(self.nspins)
else:
spinlist = [seperate_spin]
for spin in spinlist:
if not (f_skn[spin] > self.ftol).any():
self.chi0_wGG = chi0_wGG
continue
for k in range(self.kstart, self.kend):
k_pad = False
if k >= self.kd.nbzkpts:
k = 0
k_pad = True
# Find corresponding kpoint in IBZ
ibzkpt1 = kd.bz2ibz_k[k]
if self.optical_limit:
ibzkpt2 = ibzkpt1
else:
ibzkpt2 = kd.bz2ibz_k[kq_k[k]]
if self.pwmode:
N_c = self.gd.N_c
k_c = self.kd.ibzk_kc[ibzkpt1]
eikr1_R = np.exp(2j * pi * np.dot(np.indices(N_c).T, k_c / N_c).T)
k_c = self.kd.ibzk_kc[ibzkpt2]
eikr2_R = np.exp(2j * pi * np.dot(np.indices(N_c).T, k_c / N_c).T)
index1_g, phase1_g = kd.get_transform_wavefunction_index(self.gd.N_c - (self.pbc == False), k)
index2_g, phase2_g = kd.get_transform_wavefunction_index(self.gd.N_c - (self.pbc == False), kq_k[k])
for n in range(self.nvalbands):
if self.calc.wfs.world.size == 1:
if self.f_skn[spin][ibzkpt1, n] - self.ftol < 0:
continue
t1 = time()
if self.pwmode:
u = self.kd.get_rank_and_index(spin, ibzkpt1)[1]
psitold_g = calc.wfs._get_wave_function_array(u, n, realspace=True, phase=eikr1_R)
else:
u = None
psitold_g = self.get_wavefunction(ibzkpt1, n, True, spin=spin)
psit1new_g = kd.transform_wave_function(psitold_g, k, index1_g, phase1_g)
P1_ai = self.pawstuff(psit1new_g, k, n, spin, u, ibzkpt1)
psit1_g = psit1new_g.conj() * self.expqr_g
for m in self.mlist:
if self.nbands > 1000 and m % 200 == 0:
print(" ", k, n, m, time() - t0, file=self.txt)
check_focc = (f_skn[spin][ibzkpt1, n] - f_skn[spin][ibzkpt2, m]) > self.ftol
if not self.pwmode:
psitold_g = self.get_wavefunction(ibzkpt2, m, check_focc, spin=spin)
if check_focc:
if self.pwmode:
u = self.kd.get_rank_and_index(spin, ibzkpt2)[1]
psitold_g = calc.wfs._get_wave_function_array(u, m, realspace=True, phase=eikr2_R)
psit2_g = kd.transform_wave_function(psitold_g, kq_k[k], index2_g, phase2_g)
# zero padding is included through the FFT
rho_g = np.fft.fftn(psit2_g * psit1_g, s=self.nGrpad) * self.vol / self.nG0rpad
# Here, planewave cutoff is applied
rho_G = rho_g.ravel()[self.Gindex_G]
if self.optical_limit:
phase_cd = np.exp(2j * pi * sdisp_cd * kd.bzk_kc[kq_k[k], :, np.newaxis])
for ix in range(3):
d_c[ix](psit2_g, dpsit_g, phase_cd)
tmp[ix] = gd.integrate(psit1_g * dpsit_g)
rho_G[0] = -1j * np.dot(self.qq_v, tmp)
for ix in range(3):
q2_c = np.diag((1, 1, 1))[ix] * self.qopt
qq2_v = np.dot(q2_c, self.bcell_cv) # summation over c
rhoG0_v[ix] = -1j * np.dot(qq2_v, tmp)
P2_ai = self.pawstuff(psit2_g, kq_k[k], m, spin, u, ibzkpt2)
for a, id in enumerate(calc.wfs.setups.id_a):
P_p = np.outer(P1_ai[a].conj(), P2_ai[a]).ravel()
gemv(1.0, self.phi_aGp[a], P_p, 1.0, rho_G)
if self.optical_limit:
gemv(1.0, self.phiG0_avp[a], P_p, 1.0, rhoG0_v)
if self.optical_limit:
if (
np.abs(self.enoshift_skn[spin][ibzkpt2, m] - self.enoshift_skn[spin][ibzkpt1, n])
> 0.1 / Hartree
):
rho_G[0] /= (
self.enoshift_skn[spin][ibzkpt2, m] - self.enoshift_skn[spin][ibzkpt1, n]
)
rhoG0_v /= self.enoshift_skn[spin][ibzkpt2, m] - self.enoshift_skn[spin][ibzkpt1, n]
else:
rho_G[0] = 0.0
rhoG0_v[:] = 0.0
if k_pad:
rho_G[:] = 0.0
if self.optical_limit:
rho0G_Gv = np.outer(rho_G.conj(), rhoG0_v)
rhoG0_Gv = np.outer(rho_G, rhoG0_v.conj())
rho0G_Gv[0, :] = rhoG0_v * rhoG0_v.conj()
rhoG0_Gv[0, :] = rhoG0_v * rhoG0_v.conj()
if not self.hilbert_trans:
if not use_zher:
rho_GG = np.outer(rho_G, rho_G.conj())
for iw in range(self.Nw_local):
w = self.w_w[iw + self.wstart] / Hartree
coef = 1.0 / (
w + e_skn[spin][ibzkpt1, n] - e_skn[spin][ibzkpt2, m] + 1j * self.eta
) - 1.0 / (w - e_skn[spin][ibzkpt1, n] + e_skn[spin][ibzkpt2, m] + 1j * self.eta)
C = (f_skn[spin][ibzkpt1, n] - f_skn[spin][ibzkpt2, m]) * coef
if use_zher:
czher(C.real, rho_G.conj(), chi0_wGG[iw])
else:
axpy(C, rho_GG, chi0_wGG[iw])
if self.optical_limit:
axpy(C, rho0G_Gv, self.chi00G_wGv[iw])
axpy(C, rhoG0_Gv, self.chi0G0_wGv[iw])
else:
rho_GG = np.outer(rho_G, rho_G.conj())
focc = f_skn[spin][ibzkpt1, n] - f_skn[spin][ibzkpt2, m]
w0 = e_skn[spin][ibzkpt2, m] - e_skn[spin][ibzkpt1, n]
scal(focc, rho_GG)
if self.optical_limit:
scal(focc, rhoG0_Gv)
scal(focc, rho0G_Gv)
# calculate delta function
w0_id = int(w0 / self.dw)
if w0_id + 1 < self.NwS:
# rely on the self.NwS_local is equal in each node!
if self.wScomm.rank == w0_id // self.NwS_local:
alpha = (w0_id + 1 - w0 / self.dw) / self.dw
axpy(alpha, rho_GG, specfunc_wGG[w0_id % self.NwS_local])
if self.optical_limit:
axpy(alpha, rho0G_Gv, specfunc0G_wGv[w0_id % self.NwS_local])
axpy(alpha, rhoG0_Gv, specfuncG0_wGv[w0_id % self.NwS_local])
if self.wScomm.rank == (w0_id + 1) // self.NwS_local:
alpha = (w0 / self.dw - w0_id) / self.dw
axpy(alpha, rho_GG, specfunc_wGG[(w0_id + 1) % self.NwS_local])
if self.optical_limit:
axpy(alpha, rho0G_Gv, specfunc0G_wGv[(w0_id + 1) % self.NwS_local])
axpy(alpha, rhoG0_Gv, specfuncG0_wGv[(w0_id + 1) % self.NwS_local])
# deltaw = delta_function(w0, self.dw, self.NwS, self.sigma)
# for wi in range(self.NwS_local):
# if deltaw[wi + self.wS1] > 1e-8:
# specfunc_wGG[wi] += tmp_GG * deltaw[wi + self.wS1]
if self.kd.nbzkpts == 1:
if n == 0:
dt = time() - t0
totaltime = dt * self.nvalbands * self.nspins
self.printtxt("Finished n 0 in %d seconds, estimate %d seconds left." % (dt, totaltime))
if rank == 0 and self.nvalbands // 5 > 0:
if n > 0 and n % (self.nvalbands // 5) == 0:
dt = time() - t0
self.printtxt(
"Finished n %d in %d seconds, estimate %d seconds left." % (n, dt, totaltime - dt)
)
if calc.wfs.world.size != 1:
self.kcomm.barrier()
if k == 0:
dt = time() - t0
totaltime = dt * self.nkpt_local * self.nspins
self.printtxt("Finished k 0 in %d seconds, estimate %d seconds left." % (dt, totaltime))
if rank == 0 and self.nkpt_local // 5 > 0:
if k > 0 and k % (self.nkpt_local // 5) == 0:
dt = time() - t0
self.printtxt(
"Finished k %d in %d seconds, estimate %d seconds left. " % (k, dt, totaltime - dt)
)
self.printtxt("Finished summation over k")
self.kcomm.barrier()
# Hilbert Transform
if not self.hilbert_trans:
for iw in range(self.Nw_local):
self.kcomm.sum(chi0_wGG[iw])
if self.optical_limit:
self.kcomm.sum(self.chi0G0_wGv[iw])
self.kcomm.sum(self.chi00G_wGv[iw])
if use_zher:
assert (np.abs(chi0_wGG[0, 1:, 0]) < 1e-10).all()
for iw in range(self.Nw_local):
chi0_wGG[iw] += chi0_wGG[iw].conj().T
for iG in range(self.npw):
chi0_wGG[iw, iG, iG] /= 2.0
assert np.abs(np.imag(chi0_wGG[iw, iG, iG])) < 1e-10
else:
for iw in range(self.NwS_local):
self.kcomm.sum(specfunc_wGG[iw])
if self.optical_limit:
self.kcomm.sum(specfuncG0_wGv[iw])
self.kcomm.sum(specfunc0G_wGv[iw])
if self.wScomm.size == 1:
chi0_wGG = hilbert_transform(
specfunc_wGG, self.w_w, self.Nw, self.dw, self.eta, self.full_hilbert_trans
)[self.wstart : self.wend]
self.printtxt("Finished hilbert transform !")
del specfunc_wGG
else:
# redistribute specfunc_wGG to all nodes
size = self.comm.size
assert self.NwS % size == 0
NwStmp1 = (rank % self.kcomm.size) * self.NwS // size
NwStmp2 = (rank % self.kcomm.size + 1) * self.NwS // size
specfuncnew_wGG = specfunc_wGG[NwStmp1:NwStmp2]
del specfunc_wGG
coords = np.zeros(self.wcomm.size, dtype=int)
nG_local = self.npw ** 2 // self.wcomm.size
if self.wcomm.rank == self.wcomm.size - 1:
nG_local = self.npw ** 2 - (self.wcomm.size - 1) * nG_local
self.wcomm.all_gather(np.array([nG_local]), coords)
specfunc_Wg = SliceAlongFrequency(specfuncnew_wGG, coords, self.wcomm)
self.printtxt("Finished Slice Along Frequency !")
chi0_Wg = hilbert_transform(specfunc_Wg, self.w_w, self.Nw, self.dw, self.eta, self.full_hilbert_trans)[
: self.Nw
]
self.printtxt("Finished hilbert transform !")
self.comm.barrier()
del specfunc_Wg
chi0_wGG = SliceAlongOrbitals(chi0_Wg, coords, self.wcomm)
self.printtxt("Finished Slice along orbitals !")
self.comm.barrier()
del chi0_Wg
if self.optical_limit:
specfuncG0_WGv = np.zeros((self.NwS, self.npw, 3), dtype=complex)
specfunc0G_WGv = np.zeros((self.NwS, self.npw, 3), dtype=complex)
self.wScomm.all_gather(specfunc0G_wGv, specfunc0G_WGv)
self.wScomm.all_gather(specfuncG0_wGv, specfuncG0_WGv)
specfunc0G_wGv = specfunc0G_WGv
specfuncG0_wGv = specfuncG0_WGv
if self.optical_limit:
self.chi00G_wGv = hilbert_transform(
specfunc0G_wGv, self.w_w, self.Nw, self.dw, self.eta, self.full_hilbert_trans
)[self.wstart : self.wend]
self.chi0G0_wGv = hilbert_transform(
specfuncG0_wGv, self.w_w, self.Nw, self.dw, self.eta, self.full_hilbert_trans
)[self.wstart : self.wend]
if self.optical_limit:
self.chi00G_wGv /= self.vol
self.chi0G0_wGv /= self.vol
self.chi0_wGG = chi0_wGG
self.chi0_wGG /= self.vol
self.printtxt("")
self.printtxt("Finished chi0 !")
# Check gemm for transa='n' a2 = np.arange(7 * 5 * 1 * 3).reshape(7, 5, 1, 3) * (-1. + 4.j) + 3. c = np.tensordot(a, a2, [1, 0]) gemm(1., a2, a, -1., c, 'n') assert not c.any() # Check gemm for transa='c' a = np.arange(4 * 5 * 1 * 3).reshape(4, 5, 1, 3) * (3. - 2.j) + 4. c = np.tensordot(a, a2.conj(), [[1, 2, 3], [1, 2, 3]]) gemm(1., a2, a, -1., c, 'c') assert not c.any() # Check axpy c = 5.j * a axpy(-5.j, a, c) assert not c.any() # Check rk c = np.tensordot(a, a.conj(), [[1, 2, 3], [1, 2, 3]]) rk(1., a, -1., c) tri2full(c) assert not c.any() # Check gemmdot for transa='c' c = np.tensordot(a, a2.conj(), [-1, -1]) gemmdot(a, a2, beta=-1., out=c, trans='c') assert not c.any() # Check gemmdot for transa='n' a2.shape = 3, 7, 5, 1
def calculate(self, spin=0):
"""Calculate the non-interacting density response function. """
calc = self.calc
kd = self.kd
gd = self.gd
sdisp_cd = gd.sdisp_cd
ibzk_kc = self.ibzk_kc
bzk_kc = self.bzk_kc
kq_k = self.kq_k
pt = self.pt
f_kn = self.f_kn
e_kn = self.e_kn
# Matrix init
chi0_wGG = np.zeros((self.Nw_local, self.npw, self.npw), dtype=complex)
if not (f_kn > self.ftol).any():
self.chi0_wGG = chi0_wGG
return
if self.hilbert_trans:
specfunc_wGG = np.zeros((self.NwS_local, self.npw, self.npw), dtype = complex)
# Prepare for the derivative of pseudo-wavefunction
if self.optical_limit:
d_c = [Gradient(gd, i, n=4, dtype=complex).apply for i in range(3)]
dpsit_g = gd.empty(dtype=complex)
tmp = np.zeros((3), dtype=complex)
rho_G = np.zeros(self.npw, dtype=complex)
t0 = time()
t_get_wfs = 0
for k in range(self.kstart, self.kend):
# Find corresponding kpoint in IBZ
ibzkpt1 = kd.kibz_k[k]
if self.optical_limit:
ibzkpt2 = ibzkpt1
else:
ibzkpt2 = kd.kibz_k[kq_k[k]]
for n in range(self.nstart, self.nend):
# print >> self.txt, k, n, t_get_wfs, time() - t0
t1 = time()
psitold_g = self.get_wavefunction(ibzkpt1, n, True, spin=spin)
t_get_wfs += time() - t1
psit1new_g = kd.transform_wave_function(psitold_g, k)
P1_ai = pt.dict()
pt.integrate(psit1new_g, P1_ai, k)
psit1_g = psit1new_g.conj() * self.expqr_g
for m in range(self.nbands):
if self.hilbert_trans:
check_focc = (f_kn[ibzkpt1, n] - f_kn[ibzkpt2, m]) > self.ftol
else:
check_focc = np.abs(f_kn[ibzkpt1, n] - f_kn[ibzkpt2, m]) > self.ftol
t1 = time()
psitold_g = self.get_wavefunction(ibzkpt2, m, check_focc, spin=spin)
t_get_wfs += time() - t1
if check_focc:
psit2_g = kd.transform_wave_function(psitold_g, kq_k[k])
P2_ai = pt.dict()
pt.integrate(psit2_g, P2_ai, kq_k[k])
# fft
tmp_g = np.fft.fftn(psit2_g*psit1_g) * self.vol / self.nG0
for iG in range(self.npw):
index = self.Gindex_G[iG]
rho_G[iG] = tmp_g[index[0], index[1], index[2]]
if self.optical_limit:
phase_cd = np.exp(2j * pi * sdisp_cd * bzk_kc[kq_k[k], :, np.newaxis])
for ix in range(3):
d_c[ix](psit2_g, dpsit_g, phase_cd)
tmp[ix] = gd.integrate(psit1_g * dpsit_g)
rho_G[0] = -1j * np.dot(self.qq_v, tmp)
# PAW correction
for a, id in enumerate(calc.wfs.setups.id_a):
P_p = np.outer(P1_ai[a].conj(), P2_ai[a]).ravel()
gemv(1.0, self.phi_aGp[a], P_p, 1.0, rho_G)
if self.optical_limit:
rho_G[0] /= e_kn[ibzkpt2, m] - e_kn[ibzkpt1, n]
rho_GG = np.outer(rho_G, rho_G.conj())
if not self.hilbert_trans:
for iw in range(self.Nw_local):
w = self.w_w[iw + self.wstart] / Hartree
C = (f_kn[ibzkpt1, n] - f_kn[ibzkpt2, m]) / (
w + e_kn[ibzkpt1, n] - e_kn[ibzkpt2, m] + 1j * self.eta)
axpy(C, rho_GG, chi0_wGG[iw])
else:
focc = f_kn[ibzkpt1,n] - f_kn[ibzkpt2,m]
w0 = e_kn[ibzkpt2,m] - e_kn[ibzkpt1,n]
scal(focc, rho_GG)
# calculate delta function
w0_id = int(w0 / self.dw)
if w0_id + 1 < self.NwS:
# rely on the self.NwS_local is equal in each node!
if self.wScomm.rank == w0_id // self.NwS_local:
alpha = (w0_id + 1 - w0/self.dw) / self.dw
axpy(alpha, rho_GG, specfunc_wGG[w0_id % self.NwS_local] )
if self.wScomm.rank == (w0_id+1) // self.NwS_local:
alpha = (w0 / self.dw - w0_id) / self.dw
axpy(alpha, rho_GG, specfunc_wGG[(w0_id+1) % self.NwS_local] )
# deltaw = delta_function(w0, self.dw, self.NwS, self.sigma)
# for wi in range(self.NwS_local):
# if deltaw[wi + self.wS1] > 1e-8:
# specfunc_wGG[wi] += tmp_GG * deltaw[wi + self.wS1]
if self.nkpt == 1:
if n == 0:
dt = time() - t0
totaltime = dt * self.nband_local
self.printtxt('Finished n 0 in %f seconds, estimated %f seconds left.' %(dt, totaltime) )
if rank == 0 and self.nband_local // 5 > 0:
if n > 0 and n % (self.nband_local // 5) == 0:
dt = time() - t0
self.printtxt('Finished n %d in %f seconds, estimated %f seconds left.'%(n, dt, totaltime-dt))
if calc.wfs.world.size != 1:
self.kcomm.barrier()
if k == 0:
dt = time() - t0
totaltime = dt * self.nkpt_local
self.printtxt('Finished k 0 in %f seconds, estimated %f seconds left.' %(dt, totaltime))
if rank == 0 and self.nkpt_local // 5 > 0:
if k > 0 and k % (self.nkpt_local // 5) == 0:
dt = time() - t0
self.printtxt('Finished k %d in %f seconds, estimated %f seconds left. '%(k, dt, totaltime - dt) )
self.printtxt('Finished summation over k')
self.kcomm.barrier()
del rho_GG, rho_G
# Hilbert Transform
if not self.hilbert_trans:
self.kcomm.sum(chi0_wGG)
else:
self.kcomm.sum(specfunc_wGG)
if self.wScomm.size == 1:
if not self.full_hilbert_trans:
chi0_wGG = hilbert_transform(specfunc_wGG, self.Nw, self.dw, self.eta)[self.wstart:self.wend]
else:
chi0_wGG = full_hilbert_transform(specfunc_wGG, self.Nw, self.dw, self.eta)[self.wstart:self.wend]
self.printtxt('Finished hilbert transform !')
del specfunc_wGG
else:
# redistribute specfunc_wGG to all nodes
assert self.NwS % size == 0
NwStmp1 = (rank % self.kcomm.size) * self.NwS // size
NwStmp2 = (rank % self.kcomm.size + 1) * self.NwS // size
specfuncnew_wGG = specfunc_wGG[NwStmp1:NwStmp2]
del specfunc_wGG
coords = np.zeros(self.wcomm.size, dtype=int)
nG_local = self.npw**2 // self.wcomm.size
if self.wcomm.rank == self.wcomm.size - 1:
nG_local = self.npw**2 - (self.wcomm.size - 1) * nG_local
self.wcomm.all_gather(np.array([nG_local]), coords)
specfunc_Wg = SliceAlongFrequency(specfuncnew_wGG, coords, self.wcomm)
self.printtxt('Finished Slice Along Frequency !')
if not self.full_hilbert_trans:
chi0_Wg = hilbert_transform(specfunc_Wg, self.Nw, self.dw, self.eta)[:self.Nw]
else:
chi0_Wg = full_hilbert_transform(specfunc_Wg, self.Nw, self.dw, self.eta)[:self.Nw]
self.printtxt('Finished hilbert transform !')
self.comm.barrier()
del specfunc_Wg
chi0_wGG = SliceAlongOrbitals(chi0_Wg, coords, self.wcomm)
self.printtxt('Finished Slice along orbitals !')
self.comm.barrier()
del chi0_Wg
self.chi0_wGG = chi0_wGG / self.vol
self.printtxt('')
self.printtxt('Finished chi0 !')
return
def mix(self, nt_G, D_ap):
if self.step > 2:
del self.d_nt_G[0]
for d_Dp in self.d_D_ap:
del d_Dp[0]
if self.step > 0:
self.d_nt_G.append(nt_G - self.nt_iG[-1])
for d_Dp, D_p, D_ip in zip(self.d_D_ap, D_ap, self.D_iap):
d_Dp.append(D_p - D_ip[-1])
fmin_G = self.gd.integrate(self.d_nt_G[-1] * self.d_nt_G[-1])
self.dNt = self.gd.integrate(np.fabs(self.d_nt_G[-1]))
if self.verbose:
print 'Mixer: broydn: fmin_G = %f fmin_D = %f'% fmin_G
if self.step == 0:
self.eta_G = np.empty(nt_G.shape)
self.eta_D = []
for D_p in D_ap:
self.eta_D.append(0)
self.u_D.append([])
self.D_iap.append([])
self.d_D_ap.append([])
else:
if self.step >= 2:
del self.c_G[:]
if len(self.v_G) >= self.nmaxold:
del self.u_G[0]
del self.v_G[0]
for u_D in self.u_D:
del u_D[0]
temp_nt_G = self.d_nt_G[1] - self.d_nt_G[0]
self.v_G.append(temp_nt_G / self.gd.integrate(temp_nt_G
* temp_nt_G))
if len(self.v_G) < self.nmaxold:
nstep = self.step - 1
else:
nstep = self.nmaxold
for i in range(nstep):
self.c_G.append(self.gd.integrate(self.v_G[i] *
self.d_nt_G[1]))
self.u_G.append(self.beta * temp_nt_G + self.nt_iG[1] - self.nt_iG[0])
for d_Dp, u_D, D_ip in zip(self.d_D_ap, self.u_D, self.D_iap):
temp_D_ap = d_Dp[1] - d_Dp[0]
u_D.append(self.beta * temp_D_ap + D_ip[1] - D_ip[0])
usize = len(self.u_G)
for i in range(usize - 1):
a_G = self.gd.integrate(self.v_G[i] * temp_nt_G)
axpy(-a_G, self.u_G[i], self.u_G[usize - 1])
for u_D in self.u_D:
axpy(-a_G, u_D[i], u_D[usize - 1])
self.eta_G = self.beta * self.d_nt_G[-1]
for i, d_Dp in enumerate(self.d_D_ap):
self.eta_D[i] = self.beta * d_Dp[-1]
usize = len(self.u_G)
for i in range(usize):
axpy(-self.c_G[i], self.u_G[i], self.eta_G)
for eta_D, u_D in zip(self.eta_D, self.u_D):
axpy(-self.c_G[i], u_D[i], eta_D)
axpy(-1.0, self.d_nt_G[-1], nt_G)
axpy(1.0, self.eta_G, nt_G)
for D_p, d_Dp, eta_D in zip(D_ap, self.d_D_ap, self.eta_D):
axpy(-1.0, d_Dp[-1], D_p)
axpy(1.0, eta_D, D_p)
if self.step >= 2:
del self.nt_iG[0]
for D_ip in self.D_iap:
del D_ip[0]
self.nt_iG.append(np.copy(nt_G))
for D_ip, D_p in zip(self.D_iap, D_ap):
D_ip.append(np.copy(D_p))
self.step += 1
def mix(self, nt_G, D_ap, phase_cd=None):
iold = len(self.nt_iG)
if iold > 0:
if iold > self.nmaxold:
# Throw away too old stuff:
del self.nt_iG[0]
del self.R_iG[0]
del self.D_iap[0]
del self.dD_iap[0]
# for D_p, D_ip, dD_ip in self.D_a:
# del D_ip[0]
# del dD_ip[0]
iold = self.nmaxold
# Calculate new residual (difference between input and output)
R_G = nt_G - self.nt_iG[-1]
# Use np.absolute instead of np.fabs
self.dNt = self.gd.integrate(np.absolute(R_G))
self.R_iG.append(R_G)
self.dD_iap.append([])
for D_p, D_ip in zip(D_ap, self.D_iap[-1]):
self.dD_iap[-1].append(D_p - D_ip)
# Update matrix:
A_ii = np.zeros((iold, iold))
i1 = 0
i2 = iold - 1
if self.metric is None:
mR_G = R_G
else:
mR_G = self.mR_G
self.metric(R_G, mR_G, phase_cd=phase_cd)
for R_1G in self.R_iG:
# Inner product between new and old residues
# XXX For now, use only real part of residues
# For complex quantities a .conjugate should be added ??
a = self.gd.comm.sum(np.vdot(R_1G.real, mR_G.real))
if self.dtype == complex:
a += self.gd.comm.sum(np.vdot(R_1G.imag, mR_G.imag))
A_ii[i1, i2] = a
A_ii[i2, i1] = a
i1 += 1
A_ii[:i2, :i2] = self.A_ii[-i2:, -i2:]
self.A_ii = A_ii
try:
B_ii = np.linalg.inv(A_ii)
except np.linalg.LinAlgError:
alpha_i = np.zeros(iold)
alpha_i[-1] = 1.0
else:
alpha_i = B_ii.sum(1)
try:
# Normalize:
alpha_i /= alpha_i.sum()
except ZeroDivisionError:
alpha_i[:] = 0.0
alpha_i[-1] = 1.0
# Calculate new input density:
nt_G[:] = 0.0
for D in D_ap:
D[:] = 0.0
beta = self.beta
for i, alpha in enumerate(alpha_i):
axpy(alpha, self.nt_iG[i], nt_G)
axpy(alpha * beta, self.R_iG[i], nt_G)
for D_p, D_ip, dD_ip in zip(D_ap, self.D_iap[i],
self.dD_iap[i]):
axpy(alpha, D_ip, D_p)
axpy(alpha * beta, dD_ip, D_p)
# Store new input density (and new atomic density matrices):
self.nt_iG.append(nt_G.copy())
self.D_iap.append([])
for D_p in D_ap:
self.D_iap[-1].append(D_p.copy())
def add_orbital_density(self, nt_G, kpt, n):
axpy(1.0, abs(self.pd.ifft(kpt.psit_nG[n], kpt.q))**2, nt_G)
def multi_zaxpy(a,x,y, nvec):
for i in range(nvec):
axpy(a[i]*(1+0J), x[i], y[i])
def solve(self, phi, rho, charge=None, eps=None, maxcharge=1e-6,
zero_initial_phi=False):
if eps is None:
eps = self.eps
actual_charge = self.gd.integrate(rho)
background = (actual_charge / self.gd.dv /
self.gd.get_size_of_global_array().prod())
if charge is None:
charge = actual_charge
if abs(charge) <= maxcharge:
# System is charge neutral. Use standard solver
return self.solve_neutral(phi, rho - background, eps=eps)
elif abs(charge) > maxcharge and self.gd.pbc_c.all():
# System is charged and periodic. Subtract a homogeneous
# background charge
if self.charged_periodic_correction is None:
print "+-----------------------------------------------------+"
print "| Calculating charged periodic correction using the |"
print "| Ewald potential from a lattice of probe charges in |"
print "| a homogenous background density |"
print "+-----------------------------------------------------+"
self.charged_periodic_correction = madelung(self.gd.cell_cv)
print "Potential shift will be ", \
self.charged_periodic_correction , "Ha."
# Set initial guess for potential
if zero_initial_phi:
phi[:] = 0.0
else:
phi -= charge * self.charged_periodic_correction
iters = self.solve_neutral(phi, rho - background, eps=eps)
phi += charge * self.charged_periodic_correction
return iters
elif abs(charge) > maxcharge and not self.gd.pbc_c.any():
# The system is charged and in a non-periodic unit cell.
# Determine the potential by 1) subtract a gaussian from the
# density, 2) determine potential from the neutralized density
# and 3) add the potential from the gaussian density.
# Load necessary attributes
self.load_gauss()
# Remove monopole moment
q = actual_charge / np.sqrt(4 * pi) # Monopole moment
rho_neutral = rho - q * self.rho_gauss # neutralized density
# Set initial guess for potential
if zero_initial_phi:
phi[:] = 0.0
else:
axpy(-q, self.phi_gauss, phi) #phi -= q * self.phi_gauss
# Determine potential from neutral density using standard solver
niter = self.solve_neutral(phi, rho_neutral, eps=eps)
# correct error introduced by removing monopole
axpy(q, self.phi_gauss, phi) #phi += q * self.phi_gauss
return niter
else:
# System is charged with mixed boundaryconditions
raise NotImplementedError
def multi_zaxpy(a, x, y, nvec):
for i in range(nvec):
axpy(a[i] * (1 + 0J), x[i], y[i])
def mix(self, nt_G, D_ap):
if self.step > 2:
del self.d_nt_G[0]
for d_Dp in self.d_D_ap:
del d_Dp[0]
if self.step > 0:
self.d_nt_G.append(nt_G - self.nt_iG[-1])
for d_Dp, D_p, D_ip in zip(self.d_D_ap, D_ap, self.D_iap):
d_Dp.append(D_p - D_ip[-1])
fmin_G = self.gd.integrate(self.d_nt_G[-1] * self.d_nt_G[-1])
self.dNt = self.gd.integrate(np.fabs(self.d_nt_G[-1]))
if self.verbose:
print('Mixer: broydn: fmin_G = %f fmin_D = %f' % fmin_G)
if self.step == 0:
self.eta_G = np.empty(nt_G.shape)
self.eta_D = []
for D_p in D_ap:
self.eta_D.append(0)
self.u_D.append([])
self.D_iap.append([])
self.d_D_ap.append([])
else:
if self.step >= 2:
del self.c_G[:]
if len(self.v_G) >= self.nmaxold:
del self.u_G[0]
del self.v_G[0]
for u_D in self.u_D:
del u_D[0]
temp_nt_G = self.d_nt_G[1] - self.d_nt_G[0]
self.v_G.append(temp_nt_G /
self.gd.integrate(temp_nt_G * temp_nt_G))
if len(self.v_G) < self.nmaxold:
nstep = self.step - 1
else:
nstep = self.nmaxold
for i in range(nstep):
self.c_G.append(
self.gd.integrate(self.v_G[i] * self.d_nt_G[1]))
self.u_G.append(self.beta * temp_nt_G + self.nt_iG[1] -
self.nt_iG[0])
for d_Dp, u_D, D_ip in zip(self.d_D_ap, self.u_D, self.D_iap):
temp_D_ap = d_Dp[1] - d_Dp[0]
u_D.append(self.beta * temp_D_ap + D_ip[1] - D_ip[0])
usize = len(self.u_G)
for i in range(usize - 1):
a_G = self.gd.integrate(self.v_G[i] * temp_nt_G)
axpy(-a_G, self.u_G[i], self.u_G[usize - 1])
for u_D in self.u_D:
axpy(-a_G, u_D[i], u_D[usize - 1])
self.eta_G = self.beta * self.d_nt_G[-1]
for i, d_Dp in enumerate(self.d_D_ap):
self.eta_D[i] = self.beta * d_Dp[-1]
usize = len(self.u_G)
for i in range(usize):
axpy(-self.c_G[i], self.u_G[i], self.eta_G)
for eta_D, u_D in zip(self.eta_D, self.u_D):
axpy(-self.c_G[i], u_D[i], eta_D)
axpy(-1.0, self.d_nt_G[-1], nt_G)
axpy(1.0, self.eta_G, nt_G)
for D_p, d_Dp, eta_D in zip(D_ap, self.d_D_ap, self.eta_D):
axpy(-1.0, d_Dp[-1], D_p)
axpy(1.0, eta_D, D_p)
if self.step >= 2:
del self.nt_iG[0]
for D_ip in self.D_iap:
del D_ip[0]
self.nt_iG.append(np.copy(nt_G))
for D_ip, D_p in zip(self.D_iap, D_ap):
D_ip.append(np.copy(D_p))
self.step += 1
for i in range(3):
for j in range(3):
a[i, j] = a[j, i].conj()
a[i, i] = np.real(a[i, i])
b = alpha * np.outer(x.conj(), x) + a
czher(alpha, x, a)
for i in range(3):
for j in range(i, 3):
a[j, i] = a[i, j].conj()
assert np.abs(b - a).sum() < 1e-14
# testing speed
t_czher = 0
t_axpy = 0
for i in np.arange(1000):
t0 = time()
czher(alpha, x, a)
t_czher += time() - t0
t0 = time()
xx = np.outer(x.conj(), x)
axpy(alpha, xx, a)
t_axpy += time() - t0
print("t_czher:", t_czher)
print("t_axpy:", t_axpy)
def iterate_one_k_point(self, ham, wfs, kpt):
"""Do a single RMM-DIIS iteration for the kpoint"""
self.subspace_diagonalize(ham, wfs, kpt)
psit = kpt.psit
# psit2 = psit.new(buf=wfs.work_array)
P = kpt.projections
P2 = P.new()
# dMP = P.new()
# M_nn = wfs.work_matrix_nn
# dS = wfs.setups.dS
R = psit.new(buf=self.Htpsit_nG)
self.timer.start('RMM-DIIS')
if self.keep_htpsit:
with self.timer('Calculate residuals'):
self.calculate_residuals(kpt, wfs, ham, psit, P, kpt.eps_n, R,
P2)
def integrate(a_G, b_G):
return np.real(wfs.integrate(a_G, b_G, global_integral=False))
comm = wfs.gd.comm
B = self.blocksize
dR = R.new(dist=None, nbands=B)
dpsit = dR.new()
P = P.new(bcomm=None, nbands=B)
P2 = P.new()
errors_x = np.zeros(B)
# Arrays needed for DIIS step
if self.niter > 1:
psit_diis_nxG = wfs.empty(B * self.niter, q=kpt.q)
R_diis_nxG = wfs.empty(B * self.niter, q=kpt.q)
weights = self.weights(kpt)
Ht = partial(wfs.apply_pseudo_hamiltonian, kpt, ham)
error = 0.0
for n1 in range(0, wfs.bd.mynbands, B):
n2 = n1 + B
if n2 > wfs.bd.mynbands:
n2 = wfs.bd.mynbands
B = n2 - n1
P = P.new(nbands=B)
P2 = P.new()
dR = dR.new(nbands=B, dist=None)
dpsit = dR.new()
n_x = np.arange(n1, n2)
psitb = psit.view(n1, n2)
with self.timer('Calculate residuals'):
Rb = R.view(n1, n2)
if not self.keep_htpsit:
psitb.apply(Ht, out=Rb)
psitb.matrix_elements(wfs.pt, out=P)
self.calculate_residuals(kpt, wfs, ham, psitb, P,
kpt.eps_n[n_x], Rb, P2, n_x)
errors_x[:] = 0.0
for n in range(n1, n2):
weight = weights[n]
errors_x[n - n1] = weight * integrate(Rb.array[n - n1],
Rb.array[n - n1])
comm.sum(errors_x)
error += np.sum(errors_x)
# Insert first vectors and residuals for DIIS step
if self.niter > 1:
# Save the previous vectors contiguously for each band
# in the block
psit_diis_nxG[:B * self.niter:self.niter] = psitb.array
R_diis_nxG[:B * self.niter:self.niter] = Rb.array
# Precondition the residual:
with self.timer('precondition'):
ekin_x = self.preconditioner.calculate_kinetic_energy(
psitb.array, kpt)
self.preconditioner(Rb.array, kpt, ekin_x, out=dpsit.array)
# Calculate the residual of dpsit_G, dR_G = (H - e S) dpsit_G:
# self.timer.start('Apply Hamiltonian')
dpsit.apply(Ht, out=dR)
# self.timer.stop('Apply Hamiltonian')
with self.timer('projections'):
dpsit.matrix_elements(wfs.pt, out=P)
with self.timer('Calculate residuals'):
self.calculate_residuals(kpt,
wfs,
ham,
dpsit,
P,
kpt.eps_n[n_x],
dR,
P2,
n_x,
calculate_change=True)
# Find lam that minimizes the norm of R'_G = R_G + lam dR_G
with self.timer('Find lambda'):
RdR_x = np.array([
integrate(dR_G, R_G)
for R_G, dR_G in zip(Rb.array, dR.array)
])
dRdR_x = np.array([integrate(dR_G, dR_G) for dR_G in dR.array])
comm.sum(RdR_x)
comm.sum(dRdR_x)
lam_x = -RdR_x / dRdR_x
# Limit abs(lam) to [0.15, 1.0]
if self.limit_lambda:
upper = self.limit_lambda['upper']
lower = self.limit_lambda['lower']
if self.limit_lambda.get('absolute', False):
lam_x = np.where(
np.abs(lam_x) < lower, lower * np.sign(lam_x), lam_x)
lam_x = np.where(
np.abs(lam_x) > upper, upper * np.sign(lam_x), lam_x)
else:
lam_x = np.where(lam_x < lower, lower, lam_x)
lam_x = np.where(lam_x > upper, upper, lam_x)
# lam_x[:] = 0.1
# New trial wavefunction and residual
with self.timer('Update psi'):
for lam, psit_G, dpsit_G, R_G, dR_G in zip(
lam_x, psitb.array, dpsit.array, Rb.array, dR.array):
axpy(lam, dpsit_G, psit_G) # psit_G += lam * dpsit_G
axpy(lam, dR_G, R_G) # R_G += lam** dR_G
self.timer.start('DIIS step')
# DIIS step
for nit in range(1, self.niter):
# Do not perform DIIS if error is small
# if abs(error_block / B) < self.rtol:
# break
# Update the subspace
psit_diis_nxG[nit:B * self.niter:self.niter] = psitb.array
R_diis_nxG[nit:B * self.niter:self.niter] = Rb.array
# XXX Only integrals of nit old psits would be needed
# self.timer.start('projections')
# wfs.pt.integrate(psit_diis_nxG, P_diis_anxi, kpt.q)
# self.timer.stop('projections')
if nit > 1 or self.limit_lambda:
for ib in range(B):
istart = ib * self.niter
iend = istart + nit + 1
# Residual matrix
self.timer.start('Construct matrix')
R_nn = wfs.integrate(R_diis_nxG[istart:iend],
R_diis_nxG[istart:iend],
global_integral=True)
# Full matrix
A_nn = -np.ones((nit + 2, nit + 2), wfs.dtype)
A_nn[:nit + 1, :nit + 1] = R_nn[:]
A_nn[-1, -1] = 0.0
x_n = np.zeros(nit + 2, wfs.dtype)
x_n[-1] = -1.0
self.timer.stop('Construct matrix')
with self.timer('Linear solve'):
alpha_i = np.linalg.solve(A_nn, x_n)[:-1]
self.timer.start('Update trial vectors')
psitb.array[ib] = alpha_i[nit] * psit_diis_nxG[istart +
nit]
Rb.array[ib] = alpha_i[nit] * R_diis_nxG[istart + nit]
for i in range(nit):
# axpy(alpha_i[i], psit_diis_nxG[istart + i],
# psit_diis_nxG[istart + nit])
# axpy(alpha_i[i], R_diis_nxG[istart + i],
# R_diis_nxG[istart + nit])
axpy(alpha_i[i], psit_diis_nxG[istart + i],
psitb.array[ib])
axpy(alpha_i[i], R_diis_nxG[istart + i],
Rb.array[ib])
self.timer.stop('Update trial vectors')
if nit < self.niter - 1:
with self.timer('precondition'):
self.preconditioner(Rb.array,
kpt,
ekin_x,
out=dpsit.array)
for psit_G, lam, dpsit_G in zip(psitb.array, lam_x,
dpsit.array):
axpy(lam, dpsit_G, psit_G)
# Calculate the new residuals
self.timer.start('Calculate residuals')
psitb.apply(Ht, out=Rb)
psitb.matrix_elements(wfs.pt, out=P)
self.calculate_residuals(kpt,
wfs,
ham,
psitb,
P,
kpt.eps_n[n_x],
Rb,
P2,
n_x,
calculate_change=True)
self.timer.stop('Calculate residuals')
self.timer.stop('DIIS step')
# Final trial step
with self.timer('precondition'):
self.preconditioner(Rb.array, kpt, ekin_x, out=dpsit.array)
self.timer.start('Update psi')
if self.trial_step is not None:
lam_x[:] = self.trial_step
for lam, psit_G, dpsit_G in zip(lam_x, psitb.array, dpsit.array):
axpy(lam, dpsit_G, psit_G) # psit_G += lam * dpsit_G
self.timer.stop('Update psi')
self.timer.stop('RMM-DIIS')
return error
# Check gemm for transa='n' a2 = np.arange(7 * 5 * 1 * 3).reshape(7, 5, 1, 3) * (-1. + 4.j) + 3. c = np.tensordot(a, a2, [1, 0]) gemm(1., a2, a, -1., c, 'n') assert not c.any() # Check gemm for transa='c' a = np.arange(4 * 5 * 1 * 3).reshape(4, 5, 1, 3) * (3. - 2.j) + 4. c = np.tensordot(a, a2.conj(), [[1, 2, 3], [1, 2, 3]]) gemm(1., a2, a, -1., c, 'c') assert not c.any() # Check axpy c = 5.j * a axpy(-5.j, a, c) assert not c.any() # Check rk c = np.tensordot(a, a.conj(), [[1, 2, 3], [1, 2, 3]]) rk(1., a, -1., c) tri2full(c) assert not c.any() # Check gemmdot for transa='c' c = np.tensordot(a, a2.conj(), [-1, -1]) gemmdot(a, a2, beta=-1., out=c, trans='c') assert not c.any() # Check gemmdot for transa='n' a2.shape = 3, 7, 5, 1
def mix(self, nt_G, D_ap, phase_cd=None):
iold = len(self.nt_iG)
if iold > 0:
if iold > self.nmaxold:
# Throw away too old stuff:
del self.nt_iG[0]
del self.R_iG[0]
del self.D_iap[0]
del self.dD_iap[0]
# for D_p, D_ip, dD_ip in self.D_a:
# del D_ip[0]
# del dD_ip[0]
iold = self.nmaxold
# Calculate new residual (difference between input and output)
R_G = nt_G - self.nt_iG[-1]
# Use np.absolute instead of np.fabs
self.dNt = self.gd.integrate(np.absolute(R_G))
self.R_iG.append(R_G)
self.dD_iap.append([])
for D_p, D_ip in zip(D_ap, self.D_iap[-1]):
self.dD_iap[-1].append(D_p - D_ip)
# Update matrix:
A_ii = np.zeros((iold, iold))
i1 = 0
i2 = iold - 1
if self.metric is None:
mR_G = R_G
else:
mR_G = self.mR_G
self.metric(R_G, mR_G, phase_cd=phase_cd)
for R_1G in self.R_iG:
# Inner product between new and old residues
# XXX For now, use only real part of residues
# For complex quantities a .conjugate should be added ??
a = self.gd.comm.sum(np.vdot(R_1G.real, mR_G.real))
if self.dtype == complex:
a += self.gd.comm.sum(np.vdot(R_1G.imag, mR_G.imag))
A_ii[i1, i2] = a
A_ii[i2, i1] = a
i1 += 1
A_ii[:i2, :i2] = self.A_ii[-i2:, -i2:]
self.A_ii = A_ii
try:
B_ii = np.linalg.inv(A_ii)
except np.linalg.LinAlgError:
alpha_i = np.zeros(iold)
alpha_i[-1] = 1.0
else:
alpha_i = B_ii.sum(1)
try:
# Normalize:
alpha_i /= alpha_i.sum()
except ZeroDivisionError:
alpha_i[:] = 0.0
alpha_i[-1] = 1.0
# Calculate new input density:
nt_G[:] = 0.0
for D in D_ap:
D[:] = 0.0
beta = self.beta
for i, alpha in enumerate(alpha_i):
axpy(alpha, self.nt_iG[i], nt_G)
axpy(alpha * beta, self.R_iG[i], nt_G)
for D_p, D_ip, dD_ip in zip(D_ap, self.D_iap[i],
self.dD_iap[i]):
axpy(alpha, D_ip, D_p)
axpy(alpha * beta, dD_ip, D_p)
# Store new input density (and new atomic density matrices):
self.nt_iG.append(nt_G.copy())
self.D_iap.append([])
for D_p in D_ap:
self.D_iap[-1].append(D_p.copy())
def add_orbital_density(self, nt_G, kpt, n):
if self.dtype == float:
axpy(1.0, kpt.psit_nG[n]**2, nt_G)
else:
axpy(1.0, kpt.psit_nG[n].real**2, nt_G)
axpy(1.0, kpt.psit_nG[n].imag**2, nt_G)
def mix(self, nt_G, D_ap):
iold = len(self.nt_iG)
if iold > 0:
if iold > self.nmaxold:
# Throw away too old stuff:
del self.nt_iG[0]
del self.R_iG[0]
del self.D_iap[0]
del self.dD_iap[0]
# for D_p, D_ip, dD_ip in self.D_a:
# del D_ip[0]
# del dD_ip[0]
iold = self.nmaxold
# Calculate new residual (difference between input and
# output density):
R_G = nt_G - self.nt_iG[-1]
self.dNt = self.calculate_charge_sloshing(R_G)
self.R_iG.append(R_G)
self.dD_iap.append([])
for D_p, D_ip in zip(D_ap, self.D_iap[-1]):
self.dD_iap[-1].append(D_p - D_ip)
# Update matrix:
A_ii = np.zeros((iold, iold))
i2 = iold - 1
if self.metric is None:
mR_G = R_G
else:
mR_G = self.mR_G
self.metric(R_G, mR_G)
for i1, R_1G in enumerate(self.R_iG):
a = self.gd.comm.sum(self.dotprod(R_1G, mR_G, self.dD_iap[i1],
self.dD_iap[-1]))
A_ii[i1, i2] = a
A_ii[i2, i1] = a
A_ii[:i2, :i2] = self.A_ii[-i2:, -i2:]
self.A_ii = A_ii
try:
B_ii = np.linalg.inv(A_ii)
except np.linalg.LinAlgError:
alpha_i = np.zeros(iold)
alpha_i[-1] = 1.0
else:
alpha_i = B_ii.sum(1)
try:
# Normalize:
alpha_i /= alpha_i.sum()
except ZeroDivisionError:
alpha_i[:] = 0.0
alpha_i[-1] = 1.0
# Calculate new input density:
nt_G[:] = 0.0
#for D_p, D_ip, dD_ip in self.D_a:
for D in D_ap:
D[:] = 0.0
beta = self.beta
for i, alpha in enumerate(alpha_i):
axpy(alpha, self.nt_iG[i], nt_G)
axpy(alpha * beta, self.R_iG[i], nt_G)
for D_p, D_ip, dD_ip in zip(D_ap, self.D_iap[i],
self.dD_iap[i]):
axpy(alpha, D_ip, D_p)
axpy(alpha * beta, dD_ip, D_p)
# Store new input density (and new atomic density matrices):
self.nt_iG.append(nt_G.copy())
self.D_iap.append([])
for D_p in D_ap:
self.D_iap[-1].append(D_p.copy())
def add_orbital_density(self, nt_G, kpt, n):
if self.dtype == float:
axpy(1.0, kpt.psit_nG[n]**2, nt_G)
else:
axpy(1.0, kpt.psit_nG[n].real**2, nt_G)
axpy(1.0, kpt.psit_nG[n].imag**2, nt_G)
def iterate_one_k_point(self, hamiltonian, wfs, kpt):
"""Do conjugate gradient iterations for the k-point"""
niter = self.niter
phi_G = wfs.empty(q=kpt.q)
phi_old_G = wfs.empty(q=kpt.q)
comm = wfs.gd.comm
psit_nG, Htpsit_nG = self.subspace_diagonalize(hamiltonian, wfs, kpt)
# Note that psit_nG is now in self.operator.work1_nG and
# Htpsit_nG is in kpt.psit_nG!
R_nG = reshape(self.Htpsit_nG, psit_nG.shape)
Htphi_G = R_nG[0]
R_nG[:] = Htpsit_nG
self.timer.start('Residuals')
self.calculate_residuals(kpt, wfs, hamiltonian, psit_nG,
kpt.P_ani, kpt.eps_n, R_nG)
self.timer.stop('Residuals')
self.timer.start('CG')
total_error = 0.0
for n in range(self.nbands):
if extra_parameters.get('PK', False):
N = n+1
else:
N = psit_nG.shape[0]+1
R_G = R_nG[n]
Htpsit_G = Htpsit_nG[n]
gamma_old = 1.0
phi_old_G[:] = 0.0
error = np.real(wfs.integrate(R_G, R_G))
for nit in range(niter):
if (error * Hartree**2 < self.tolerance / self.nbands):
break
ekin = self.preconditioner.calculate_kinetic_energy(
psit_nG[n:n + 1], kpt)
pR_G = self.preconditioner(R_nG[n:n + 1], kpt, ekin)
# New search direction
gamma = comm.sum(np.vdot(pR_G, R_G).real)
phi_G[:] = -pR_G - gamma / gamma_old * phi_old_G
gamma_old = gamma
phi_old_G[:] = phi_G[:]
# Calculate projections
P2_ai = wfs.pt.dict()
wfs.pt.integrate(phi_G, P2_ai, kpt.q)
# Orthonormalize phi_G to all bands
self.timer.start('CG: orthonormalize')
self.timer.start('CG: overlap')
overlap_n = wfs.integrate(psit_nG[:N], phi_G,
global_integral=False)
self.timer.stop('CG: overlap')
self.timer.start('CG: overlap2')
for a, P2_i in P2_ai.items():
P_ni = kpt.P_ani[a]
dO_ii = wfs.setups[a].dO_ii
gemv(1.0, P_ni[:N].conjugate(), np.inner(dO_ii, P2_i),
1.0, overlap_n)
self.timer.stop('CG: overlap2')
comm.sum(overlap_n)
# phi_G -= overlap_n * kpt.psit_nG
wfs.matrixoperator.gd.gemv(-1.0, psit_nG[:N], overlap_n,
1.0, phi_G, 'n')
for a, P2_i in P2_ai.items():
P_ni = kpt.P_ani[a]
gemv(-1.0, P_ni[:N], overlap_n, 1.0, P2_i, 'n')
norm = wfs.integrate(phi_G, phi_G, global_integral=False)
for a, P2_i in P2_ai.items():
dO_ii = wfs.setups[a].dO_ii
norm += np.vdot(P2_i, np.inner(dO_ii, P2_i))
norm = comm.sum(np.real(norm).item())
phi_G /= sqrt(norm)
for P2_i in P2_ai.values():
P2_i /= sqrt(norm)
self.timer.stop('CG: orthonormalize')
# find optimum linear combination of psit_G and phi_G
an = kpt.eps_n[n]
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian,
phi_G.reshape((1,) + phi_G.shape),
Htphi_G.reshape((1,) +
Htphi_G.shape))
b = wfs.integrate(phi_G, Htpsit_G, global_integral=False)
c = wfs.integrate(phi_G, Htphi_G, global_integral=False)
for a, P2_i in P2_ai.items():
P_i = kpt.P_ani[a][n]
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
b += dot(P2_i, dot(dH_ii, P_i.conj()))
c += dot(P2_i, dot(dH_ii, P2_i.conj()))
b = comm.sum(np.real(b).item())
c = comm.sum(np.real(c).item())
theta = 0.5 * atan2(2 * b, an - c)
enew = (an * cos(theta)**2 +
c * sin(theta)**2 +
b * sin(2.0 * theta))
# theta can correspond either minimum or maximum
if (enew - kpt.eps_n[n]) > 0.0: # we were at maximum
theta += pi / 2.0
enew = (an * cos(theta)**2 +
c * sin(theta)**2 +
b * sin(2.0 * theta))
kpt.eps_n[n] = enew
psit_nG[n] *= cos(theta)
# kpt.psit_nG[n] += sin(theta) * phi_G
axpy(sin(theta), phi_G, psit_nG[n])
for a, P2_i in P2_ai.items():
P_i = kpt.P_ani[a][n]
P_i *= cos(theta)
P_i += sin(theta) * P2_i
if nit < niter - 1:
Htpsit_G *= cos(theta)
# Htpsit_G += sin(theta) * Htphi_G
axpy(sin(theta), Htphi_G, Htpsit_G)
#adjust residuals
R_G[:] = Htpsit_G - kpt.eps_n[n] * psit_nG[n]
coef_ai = wfs.pt.dict()
for a, coef_i in coef_ai.items():
P_i = kpt.P_ani[a][n]
dO_ii = wfs.setups[a].dO_ii
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
coef_i[:] = (dot(P_i, dH_ii) -
dot(P_i * kpt.eps_n[n], dO_ii))
wfs.pt.add(R_G, coef_ai, kpt.q)
error_new = np.real(wfs.integrate(R_G, R_G))
if error_new / error < self.rtol:
# print >> self.f, "cg:iters", n, nit+1
break
if (self.nbands_converge == 'occupied' and
kpt.f_n is not None and kpt.f_n[n] == 0.0):
# print >> self.f, "cg:iters", n, nit+1
break
error = error_new
if kpt.f_n is None:
weight = 1.0
else:
weight = kpt.f_n[n]
if self.nbands_converge != 'occupied':
weight = kpt.weight * float(n < self.nbands_converge)
total_error += weight * error
# if nit == 3:
# print >> self.f, "cg:iters", n, nit+1
self.timer.stop('CG')
return total_error, psit_nG