def update_hilbert(self, n_mG, deps_m, df_m, chi0_wGG):
"""Update spectral function.
Updates spectral function A_wGG and saves it to chi0_wGG for
later hilbert-transform."""
self.timer.start('prep')
beta = (2**0.5 - 1) * self.domega0 / self.omega2
o_m = abs(deps_m)
w_m = (o_m / (self.domega0 + beta * o_m)).astype(int)
o1_m = self.omega_w[w_m]
o2_m = self.omega_w[w_m + 1]
p_m = self.prefactor * abs(df_m) / (o2_m - o1_m)**2 # XXX abs()?
p1_m = p_m * (o2_m - o_m)
p2_m = p_m * (o_m - o1_m)
self.timer.stop('prep')
if self.blockcomm.size > 1:
for p1, p2, n_G, w in zip(p1_m, p2_m, n_mG, w_m):
myn_G = n_G[self.Ga:self.Gb].reshape((-1, 1))
gemm(p1, n_G.reshape((-1, 1)), myn_G, 1.0, chi0_wGG[w], 'c')
gemm(p2, n_G.reshape((-1, 1)), myn_G, 1.0, chi0_wGG[w + 1],
'c')
return
for p1, p2, n_G, w in zip(p1_m, p2_m, n_mG, w_m):
czher(p1, n_G.conj(), chi0_wGG[w])
czher(p2, n_G.conj(), chi0_wGG[w + 1])
def update_hilbert(self, n_mG, deps_m, wd, chi0_wGG):
"""Update spectral function.
Updates spectral function A_wGG and saves it to chi0_wGG for
later hilbert-transform."""
self.timer.start('prep')
omega_w = wd.get_data()
deps_m += self.eshift * np.sign(deps_m)
o_m = abs(deps_m)
w_m = wd.get_closest_index(o_m)
o1_m = omega_w[w_m]
o2_m = omega_w[w_m + 1]
p_m = np.abs(1 / (o2_m - o1_m)**2)
p1_m = p_m * (o2_m - o_m)
p2_m = p_m * (o_m - o1_m)
self.timer.stop('prep')
if self.blockcomm.size > 1:
for p1, p2, n_G, w in zip(p1_m, p2_m, n_mG, w_m):
if w + 1 < wd.wmax: # The last frequency is not reliable
myn_G = n_G[self.Ga:self.Gb].reshape((-1, 1))
gemm(p1, n_G.reshape((-1, 1)), myn_G,
1.0, chi0_wGG[w], 'c')
gemm(p2, n_G.reshape((-1, 1)), myn_G,
1.0, chi0_wGG[w + 1], 'c')
return
for p1, p2, n_G, w in zip(p1_m, p2_m, n_mG, w_m):
if w + 1 < wd.wmax: # The last frequency is not reliable
czher(p1, n_G.conj(), chi0_wGG[w])
czher(p2, n_G.conj(), chi0_wGG[w + 1])
def update_hilbert(self, n_mG, deps_m, df_m, chi0_wGG):
self.timer.start("prep")
beta = (2 ** 0.5 - 1) * self.domega0 / self.omega2
o_m = abs(deps_m)
w_m = (o_m / (self.domega0 + beta * o_m)).astype(int)
o1_m = self.omega_w[w_m]
o2_m = self.omega_w[w_m + 1]
p_m = self.prefactor * abs(df_m) / (o2_m - o1_m) ** 2 # XXX abs()?
p1_m = p_m * (o2_m - o_m)
p2_m = p_m * (o_m - o1_m)
self.timer.stop("prep")
if self.blockcomm.size > 1:
for p1, p2, n_G, w in zip(p1_m, p2_m, n_mG, w_m):
myn_G = n_G[self.Ga : self.Gb].reshape((-1, 1))
gemm(p1, n_G.reshape((-1, 1)), myn_G, 1.0, chi0_wGG[w], "c")
gemm(p2, n_G.reshape((-1, 1)), myn_G, 1.0, chi0_wGG[w + 1], "c")
# chi0_wGG[w + 1] += p2 * np.outer(myn_G, n_G.conj())
return
for p1, p2, n_G, w in zip(p1_m, p2_m, n_mG, w_m):
czher(p1, n_G.conj(), chi0_wGG[w])
czher(p2, n_G.conj(), chi0_wGG[w + 1])
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 !")
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 !')
from gpaw.utilities.blas import czher, axpy
import numpy as np
from time import time
alpha = 0.5
x = np.random.rand(3) + 1j * np.random.rand(3)
a = np.random.rand(9).reshape(3, 3) + np.random.rand(9).reshape(3, 3) * 1j
# make a hermitian
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
from gpaw.utilities.blas import czher, axpy
import numpy as np
from time import time
alpha = 0.5
x = np.random.rand(3) + 1j * np.random.rand(3)
a = np.random.rand(9).reshape(3,3) + np.random.rand(9).reshape(3,3) * 1j
# make a hermitian
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
def spectral_function_integration(self, domain=None, integrand=None,
x=None, kwargs=None, out_wxx=None):
"""Integrate response function.
Assume that the integral has the
form of a response function. For the linear tetrahedron
method it is possible calculate frequency dependent weights
and do a point summation using these weights."""
if out_wxx is None:
raise NotImplementedError
nG = out_wxx.shape[2]
mynG = (nG + self.blockcomm.size - 1) // self.blockcomm.size
self.Ga = min(self.blockcomm.rank * mynG, nG)
self.Gb = min(self.Ga + mynG, nG)
# assert mynG * (self.blockcomm.size - 1) < nG, \
# print('mynG', mynG, 'nG', nG, 'nblocks', self.blockcomm.size)
# Input domain
td = self.tesselate(domain[0])
args = domain[1:]
get_matrix_element, get_eigenvalues = integrand
# The kwargs contain any constant
# arguments provided by the user
if kwargs is not None:
get_matrix_element = partial(get_matrix_element,
**kwargs[0])
get_eigenvalues = partial(get_eigenvalues,
**kwargs[1])
# Relevant quantities
bzk_kc = td.points
nk = len(bzk_kc)
with self.timer('pts'):
# Point to simplex
pts_k = [[] for n in range(nk)]
for s, K_k in enumerate(td.simplices):
A_kv = np.append(td.points[K_k],
np.ones(4)[:, np.newaxis], axis=1)
D_kv = np.append((A_kv[:, :-1]**2).sum(1)[:, np.newaxis],
A_kv, axis=1)
a = np.linalg.det(D_kv[:, np.arange(5) != 0])
if np.abs(a) < 1e-10:
continue
for K in K_k:
pts_k[K].append(s)
# Change to numpy arrays:
for k in range(nk):
pts_k[k] = np.array(pts_k[k], int)
with self.timer('neighbours'):
# Nearest neighbours
neighbours_k = [None for n in range(nk)]
for k in range(nk):
neighbours_k[k] = np.unique(td.simplices[pts_k[k]])
# Distribute everything
myterms_t = self.distribute_domain(list(args) +
[list(range(nk))])
with self.timer('eigenvalues'):
# Store eigenvalues
deps_tMk = None # t for term
shape = [len(domain_l) for domain_l in args]
nterms = int(np.prod(shape))
for t in range(nterms):
if len(shape) == 0:
arguments = ()
else:
arguments = np.unravel_index(t, shape)
for K in range(nk):
k_c = bzk_kc[K]
deps_M = -get_eigenvalues(k_c, *arguments)
if deps_tMk is None:
deps_tMk = np.zeros([nterms] +
list(deps_M.shape) +
[nk], float)
deps_tMk[t, :, K] = deps_M
omega_w = x.get_data()
# Calculate integrations weight
pb = ProgressBar(self.fd)
for _, arguments in pb.enumerate(myterms_t):
K = arguments[-1]
if len(shape) == 0:
t = 0
else:
t = np.ravel_multi_index(arguments[:-1], shape)
deps_Mk = deps_tMk[t]
teteps_Mk = deps_Mk[:, neighbours_k[K]]
i0_M, i1_M = x.get_index_range(teteps_Mk.min(1), teteps_Mk.max(1))
n_MG = get_matrix_element(bzk_kc[K],
*arguments[:-1])
for n_G, deps_k, i0, i1 in zip(n_MG, deps_Mk,
i0_M, i1_M):
if i0 == i1:
continue
W_w = self.get_kpoint_weight(K, deps_k,
pts_k, omega_w[i0:i1],
td)
for iw, weight in enumerate(W_w):
if self.blockcomm.size > 1:
myn_G = n_G[self.Ga:self.Gb].reshape((-1, 1))
gemm(weight, n_G.reshape((-1, 1)), myn_G,
1.0, out_wxx[i0 + iw], 'c')
else:
czher(weight, n_G.conj(), out_wxx[i0 + iw])
self.kncomm.sum(out_wxx)
if self.blockcomm.size == 1:
# Fill in upper/lower triangle also:
nx = out_wxx.shape[1]
il = np.tril_indices(nx, -1)
iu = il[::-1]
for out_xx in out_wxx:
out_xx[il] = out_xx[iu].conj()