def vxc(paw, xc=None, coredensity=True):
"""Calculate XC-contribution to eigenvalues."""
ham = paw.hamiltonian
dens = paw.density
wfs = paw.wfs
if xc is None:
xc = ham.xc
elif isinstance(xc, str):
xc = XC(xc)
if dens.nt_sg is None:
dens.interpolate_pseudo_density()
thisisatest = not True
if xc.orbital_dependent:
paw.get_xc_difference(xc)
# Calculate XC-potential:
vxct_sg = ham.finegd.zeros(wfs.nspins)
xc.calculate(dens.finegd, dens.nt_sg, vxct_sg)
vxct_sG = ham.gd.empty(wfs.nspins)
ham.restrict(vxct_sg, vxct_sG)
if thisisatest:
vxct_sG[:] = 1
# ... and PAW corrections:
dvxc_asii = {}
for a, D_sp in dens.D_asp.items():
dvxc_sp = np.zeros_like(D_sp)
xc.calculate_paw_correction(wfs.setups[a], D_sp, dvxc_sp, a=a,
addcoredensity=coredensity)
dvxc_asii[a] = [unpack(dvxc_p) for dvxc_p in dvxc_sp]
if thisisatest:
dvxc_asii[a] = [wfs.setups[a].dO_ii]
vxc_un = np.empty((wfs.kd.mynks, wfs.bd.mynbands))
for u, vxc_n in enumerate(vxc_un):
kpt = wfs.kpt_u[u]
vxct_G = vxct_sG[kpt.s]
for n in range(wfs.bd.mynbands):
psit_G = wfs._get_wave_function_array(u, n, realspace=True)
vxc_n[n] = wfs.gd.integrate((psit_G * psit_G.conj()).real,
vxct_G, global_integral=False)
for a, dvxc_sii in dvxc_asii.items():
P_ni = kpt.P_ani[a]
vxc_n += (np.dot(P_ni, dvxc_sii[kpt.s]) *
P_ni.conj()).sum(1).real
wfs.gd.comm.sum(vxc_un)
vxc_skn = wfs.kd.collect(vxc_un)
if xc.orbital_dependent:
vxc_skn += xc.exx_skn
return vxc_skn * Hartree
from gpaw.xc import XC
from gpaw.test import equal
x = 0.000001
ra.seed(8)
for xc in ['LDA', 'PBE']:
print(xc)
xc = XC(xc)
s = create_setup('N', xc)
ni = s.ni
nii = ni * (ni + 1) // 2
D_p = 0.1 * ra.random(nii) + 0.2
H_p = np.zeros(nii)
E = xc.calculate_paw_correction(s, D_p.reshape(1, -1), H_p.reshape(1, -1))
dD_p = x * ra.random(nii)
dE = np.dot(H_p, dD_p) / x
D_p += dD_p
Ep = xc.calculate_paw_correction(s, D_p.reshape(1, -1))
D_p -= 2 * dD_p
Em = xc.calculate_paw_correction(s, D_p.reshape(1, -1))
print(dE, dE - 0.5 * (Ep - Em) / x)
equal(dE, 0.5 * (Ep - Em) / x, 1e-6)
Ems = xc.calculate_paw_correction(s, np.array([0.5 * D_p, 0.5 * D_p]))
print(Em - Ems)
equal(Em, Ems, 1.0e-12)
D_sp = 0.1 * ra.random((2, nii)) + 0.2
H_sp = np.zeros((2, nii))
'GGA_X_PBE+GGA_C_PBE', 'GGA_X_PBE_R+GGA_C_PBE',
'GGA_X_B88+GGA_C_P86', 'GGA_X_B88+GGA_C_LYP',
'GGA_X_FT97_A+GGA_C_LYP'
]
x = 0.000001
for xcname in libxc_set:
ra.seed(8)
xc = XC(xcname)
s = create_setup('N', xc)
ni = s.ni
nii = ni * (ni + 1) // 2
D_p = 0.1 * ra.random(nii) + 0.4
H_p = np.zeros(nii)
E1 = xc.calculate_paw_correction(s, D_p.reshape(1, -1), H_p.reshape(1, -1))
dD_p = x * ra.random(nii)
D_p += dD_p
dE = np.dot(H_p, dD_p) / x
E2 = xc.calculate_paw_correction(s, D_p.reshape(1, -1))
print xcname, dE, (E2 - E1) / x
equal(dE, (E2 - E1) / x, 0.003)
E2s = xc.calculate_paw_correction(s,
np.array([0.5 * D_p, 0.5 * D_p]), np.array([H_p, H_p]))
print E2, E2s
equal(E2, E2s, 1.0e-12)
if xcname in reference: # compare with old gpaw
print 'A:', E2, reference[xcname]
equal(E2, reference[xcname], tolerance)
class C_XC(Contribution):
def __init__(self, nlfunc, weight, functional = 'LDA'):
Contribution.__init__(self, nlfunc, weight)
self.functional = functional
def get_name(self):
return 'XC'
def get_desc(self):
return "("+self.functional+")"
def initialize(self):
self.xc = XC(self.functional)
self.vt_sg = self.nlfunc.finegd.empty(self.nlfunc.nspins)
self.e_g = self.nlfunc.finegd.empty()
def initialize_1d(self):
self.ae = self.nlfunc.ae
self.xc = XC(self.functional)
self.v_g = np.zeros(self.ae.N)
def calculate_spinpaired(self, e_g, n_g, v_g):
self.e_g[:] = 0.0
self.vt_sg[:] = 0.0
self.xc.calculate(self.nlfunc.finegd, n_g[None, ...], self.vt_sg,
self.e_g)
v_g += self.weight * self.vt_sg[0]
e_g += self.weight * self.e_g
def calculate_spinpolarized(self, e_g, n_sg, v_sg):
self.e_g[:] = 0.0
self.vt_sg[:] = 0.0
self.xc.calculate(self.nlfunc.finegd, n_sg, self.vt_sg, self.e_g)
#self.xc.get_energy_and_potential(na_g, self.vt_sg[0], nb_g, self.vt_sg[1], e_g=self.e_g)
v_sg[0] += self.weight * self.vt_sg[0]
v_sg[1] += self.weight * self.vt_sg[1]
e_g += self.weight * self.e_g
def calculate_energy_and_derivatives(self, setup, D_sp, H_sp, a, addcoredensity=True):
E = self.xc.calculate_paw_correction(setup, D_sp, H_sp, True, a)
E += setup.xc_correction.Exc0
print("E", E)
return E
def add_xc_potential_and_energy_1d(self, v_g):
self.v_g[:] = 0.0
Exc = self.xc.calculate_spherical(self.ae.rgd,
self.ae.n.reshape((1, -1)),
self.v_g.reshape((1, -1)))
v_g += self.weight * self.v_g
return self.weight * Exc
def add_smooth_xc_potential_and_energy_1d(self, vt_g):
self.v_g[:] = 0.0
Exc = self.xc.calculate_spherical(self.ae.rgd,
self.ae.nt.reshape((1, -1)),
self.v_g.reshape((1, -1)))
vt_g += self.weight * self.v_g
return self.weight * Exc
def initialize_from_atomic_orbitals(self, basis_functions):
# LDA needs only density, which is already initialized
pass
def add_extra_setup_data(self, dict):
# LDA has not any special data
pass
def write(self, writer, natoms):
# LDA has not any special data to be written
pass
def read(self, reader):
# LDA has not any special data to be read
pass
v_g = np.zeros((1, n, n, n))
P_ni = 0.2 * ra.random((20, ni))
P_ni[:, nao:] = 0.0
D_ii = np.dot(np.transpose(P_ni), P_ni)
D_p = pack(D_ii)
p = 0
for i1 in range(nao):
for i2 in range(i1, nao):
n_g += D_p[p] * psit_ig[i1] * psit_ig[i2]
p += 1
p += ni - nao
p = create_localized_functions([s.nct], gd, (0.5, 0.5, 0.5))
p.add(n_g[0], np.ones(1))
e_g = gd.zeros()
xc.calculate(gd, n_g, v_g, e_g)
r2_g = np.sum((np.indices((n, n, n)) - n / 2)**2, axis=0)
dv_g = gd.dv * np.less(r2_g, (rcut / a * n)**2)
E2 = -np.dot(e_g.ravel(), dv_g.ravel())
s.xc_correction.n_qg[:] = 0.0
s.xc_correction.nc_g[:] = 0.0
E1 = (xc.calculate_paw_correction(s, D_p.reshape(1, -1)) +
s.xc_correction.Exc0)
print(name, E1, E2, E1 - E2)
equal(E1, E2, 0.0013)
class C_XC(Contribution):
def __init__(self, nlfunc, weight, functional='LDA'):
Contribution.__init__(self, nlfunc, weight)
self.functional = functional
def get_name(self):
return 'XC'
def get_desc(self):
return "(" + self.functional + ")"
def initialize(self):
self.xc = XC(self.functional)
self.vt_sg = self.nlfunc.finegd.empty(self.nlfunc.nspins)
self.e_g = self.nlfunc.finegd.empty()
def initialize_1d(self):
self.ae = self.nlfunc.ae
self.xc = XC(self.functional)
self.v_g = np.zeros(self.ae.N)
def calculate_spinpaired(self, e_g, n_g, v_g):
self.e_g[:] = 0.0
self.vt_sg[:] = 0.0
self.xc.calculate(self.nlfunc.finegd, n_g[None, ...], self.vt_sg,
self.e_g)
v_g += self.weight * self.vt_sg[0]
e_g += self.weight * self.e_g
def calculate_spinpolarized(self, e_g, n_sg, v_sg):
self.e_g[:] = 0.0
self.vt_sg[:] = 0.0
self.xc.calculate(self.nlfunc.finegd, n_sg, self.vt_sg, self.e_g)
#self.xc.get_energy_and_potential(na_g, self.vt_sg[0], nb_g, self.vt_sg[1], e_g=self.e_g)
v_sg[0] += self.weight * self.vt_sg[0]
v_sg[1] += self.weight * self.vt_sg[1]
e_g += self.weight * self.e_g
def calculate_energy_and_derivatives(self,
setup,
D_sp,
H_sp,
a,
addcoredensity=True):
E = self.xc.calculate_paw_correction(setup, D_sp, H_sp, True, a)
E += setup.xc_correction.Exc0
print("E", E)
return E
def add_xc_potential_and_energy_1d(self, v_g):
self.v_g[:] = 0.0
Exc = self.xc.calculate_spherical(self.ae.rgd,
self.ae.n.reshape((1, -1)),
self.v_g.reshape((1, -1)))
v_g += self.weight * self.v_g
return self.weight * Exc
def add_smooth_xc_potential_and_energy_1d(self, vt_g):
self.v_g[:] = 0.0
Exc = self.xc.calculate_spherical(self.ae.rgd,
self.ae.nt.reshape((1, -1)),
self.v_g.reshape((1, -1)))
vt_g += self.weight * self.v_g
return self.weight * Exc
def initialize_from_atomic_orbitals(self, basis_functions):
# LDA needs only density, which is already initialized
pass
def add_extra_setup_data(self, dict):
# LDA has not any special data
pass
def write(self, writer, natoms):
# LDA has not any special data to be written
pass
def read(self, reader):
# LDA has not any special data to be read
pass
x = 0.0000001
ra.seed(8)
for xc in ['LDA']:#, 'PBE']:
print(xc)
xc = XC(xc)
s = create_setup('N', xc)
ni = s.ni
D_sp = np.array([pack(np.outer(P_i, P_i))
for P_i in 0.2 * ra.random((2, ni)) - 0.1])
D_sp[1] += D_sp[0]
nii = ni * (ni + 1) // 2
E = xc.calculate_paw_correction(s, D_sp)
xc = NonCollinearFunctional(xc)
Dnc_sp = np.zeros((4, nii))
Dnc_sp[0] = D_sp.sum(0)
Dnc_sp[3] = D_sp[0] - D_sp[1]
Enc = xc.calculate_paw_correction(s, Dnc_sp)
print(E, E-Enc)
assert abs(E - Enc) < 1e-11
Dnc_sp[1] = 0.1 * Dnc_sp[3]
Dnc_sp[2] = 0.2 * Dnc_sp[3]
Dnc_sp[3] *= (1 - 0.1**2 - 0.2**2)**0.5
H_sp = 0 * Dnc_sp
Enc = xc.calculate_paw_correction(s, Dnc_sp, H_sp)
class OmegaMatrix:
"""
Omega matrix in Casidas linear response formalism
Parameters
- calculator: the calculator object the ground state calculation
- kss: the Kohn-Sham singles object
- xc: the exchange correlation approx. to use
- derivativeLevel: which level i of d^i Exc/dn^i to use
- numscale: numeric epsilon for derivativeLevel=0,1
- filehandle: the oject can be read from a filehandle
- txt: output stream or file name
- finegrid: level of fine grid to use. 0: nothing, 1 for poisson only,
2 everything on the fine grid
"""
def __init__(self,
calculator=None,
kss=None,
xc=None,
derivativeLevel=None,
numscale=0.001,
filehandle=None,
txt=None,
finegrid=2,
eh_comm=None,
):
if not txt and calculator:
txt = calculator.txt
self.txt = get_txt(txt, mpi.rank)
if eh_comm is None:
eh_comm = mpi.serial_comm
self.eh_comm = eh_comm
if filehandle is not None:
self.kss = kss
self.read(fh=filehandle)
return None
self.fullkss = kss
self.finegrid = finegrid
if calculator is None:
return
self.paw = calculator
wfs = self.paw.wfs
# handle different grid possibilities
self.restrict = None
# self.poisson = PoissonSolver(nn=self.paw.hamiltonian.poisson.nn)
self.poisson = calculator.hamiltonian.poisson
if finegrid:
self.poisson.set_grid_descriptor(self.paw.density.finegd)
self.poisson.initialize()
self.gd = self.paw.density.finegd
if finegrid == 1:
self.gd = wfs.gd
else:
self.poisson.set_grid_descriptor(wfs.gd)
self.poisson.initialize()
self.gd = wfs.gd
self.restrict = Transformer(self.paw.density.finegd, wfs.gd,
self.paw.input_parameters.stencils[1]
).apply
if xc == 'RPA':
xc = None # enable RPA as keyword
if xc is not None:
self.xc = XC(xc)
self.xc.initialize(self.paw.density, self.paw.hamiltonian,
wfs, self.paw.occupations)
# check derivativeLevel
if derivativeLevel is None:
derivativeLevel = \
self.xc.get_functional().get_max_derivative_level()
self.derivativeLevel = derivativeLevel
# change the setup xc functional if needed
# the ground state calculation may have used another xc
if kss.npspins > kss.nvspins:
spin_increased = True
else:
spin_increased = False
else:
self.xc = None
self.numscale = numscale
self.singletsinglet = False
if kss.nvspins < 2 and kss.npspins < 2:
# this will be a singlet to singlet calculation only
self.singletsinglet = True
nij = len(kss)
self.Om = np.zeros((nij, nij))
self.get_full()
def get_full(self):
self.paw.timer.start('Omega RPA')
self.get_rpa()
self.paw.timer.stop()
if self.xc is not None:
self.paw.timer.start('Omega XC')
self.get_xc()
self.paw.timer.stop()
self.eh_comm.sum(self.Om)
self.full = self.Om
def get_xc(self):
"""Add xc part of the coupling matrix"""
# shorthands
paw = self.paw
wfs = paw.wfs
gd = paw.density.finegd
comm = gd.comm
eh_comm = self.eh_comm
fg = self.finegrid is 2
kss = self.fullkss
nij = len(kss)
Om_xc = self.Om
# initialize densities
# nt_sg is the smooth density on the fine grid with spin index
if kss.nvspins == 2:
# spin polarised ground state calc.
nt_sg = paw.density.nt_sg
else:
# spin unpolarised ground state calc.
if kss.npspins == 2:
# construct spin polarised densities
nt_sg = np.array([.5 * paw.density.nt_sg[0],
.5 * paw.density.nt_sg[0]])
else:
nt_sg = paw.density.nt_sg
# check if D_sp have been changed before
D_asp = self.paw.density.D_asp
for a, D_sp in D_asp.items():
if len(D_sp) != kss.npspins:
if len(D_sp) == 1:
D_asp[a] = np.array([0.5 * D_sp[0], 0.5 * D_sp[0]])
else:
D_asp[a] = np.array([D_sp[0] + D_sp[1]])
# restrict the density if needed
if fg:
nt_s = nt_sg
else:
nt_s = self.gd.zeros(nt_sg.shape[0])
for s in range(nt_sg.shape[0]):
self.restrict(nt_sg[s], nt_s[s])
gd = paw.density.gd
# initialize vxc or fxc
if self.derivativeLevel == 0:
raise NotImplementedError
if kss.npspins == 2:
v_g = nt_sg[0].copy()
else:
v_g = nt_sg.copy()
elif self.derivativeLevel == 1:
pass
elif self.derivativeLevel == 2:
fxc_sg = np.zeros(nt_sg.shape)
self.xc.calculate_fxc(gd, nt_sg, fxc_sg)
else:
raise ValueError('derivativeLevel can only be 0,1,2')
# self.paw.my_nuclei = []
ns = self.numscale
xc = self.xc
print('XC', nij, 'transitions', file=self.txt)
for ij in range(eh_comm.rank, nij, eh_comm.size):
print('XC kss[' + '%d' % ij + ']', file=self.txt)
timer = Timer()
timer.start('init')
timer2 = Timer()
if self.derivativeLevel >= 1:
# vxc is available
# We use the numerical two point formula for calculating
# the integral over fxc*n_ij. The results are
# vvt_s smooth integral
# nucleus.I_sp atom based correction matrices (pack2)
# stored on each nucleus
timer2.start('init v grids')
vp_s = np.zeros(nt_s.shape, nt_s.dtype.char)
vm_s = np.zeros(nt_s.shape, nt_s.dtype.char)
if kss.npspins == 2: # spin polarised
nv_s = nt_s.copy()
nv_s[kss[ij].pspin] += ns * kss[ij].get(fg)
xc.calculate(gd, nv_s, vp_s)
nv_s = nt_s.copy()
nv_s[kss[ij].pspin] -= ns * kss[ij].get(fg)
xc.calculate(gd, nv_s, vm_s)
else: # spin unpolarised
nv = nt_s + ns * kss[ij].get(fg)
xc.calculate(gd, nv, vp_s)
nv = nt_s - ns * kss[ij].get(fg)
xc.calculate(gd, nv, vm_s)
vvt_s = (0.5 / ns) * (vp_s - vm_s)
timer2.stop()
# initialize the correction matrices
timer2.start('init v corrections')
I_asp = {}
for a, P_ni in wfs.kpt_u[kss[ij].spin].P_ani.items():
# create the modified density matrix
Pi_i = P_ni[kss[ij].i]
Pj_i = P_ni[kss[ij].j]
P_ii = np.outer(Pi_i, Pj_i)
# we need the symmetric form, hence we can pack
P_p = pack(P_ii)
D_sp = self.paw.density.D_asp[a].copy()
D_sp[kss[ij].pspin] -= ns * P_p
setup = wfs.setups[a]
I_sp = np.zeros_like(D_sp)
self.xc.calculate_paw_correction(setup, D_sp, I_sp)
I_sp *= -1.0
D_sp = self.paw.density.D_asp[a].copy()
D_sp[kss[ij].pspin] += ns * P_p
self.xc.calculate_paw_correction(setup, D_sp, I_sp)
I_sp /= 2.0 * ns
I_asp[a] = I_sp
timer2.stop()
timer.stop()
t0 = timer.get_time('init')
timer.start(ij)
for kq in range(ij, nij):
weight = self.weight_Kijkq(ij, kq)
if self.derivativeLevel == 0:
# only Exc is available
if kss.npspins == 2: # spin polarised
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] += kss[ij].get(fg)
nv_g[kss[kq].pspin] += kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(
nv_g[0], v_g, nv_g[1], v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] += kss[ij].get(fg)
nv_g[kss[kq].pspin] -= kss[kq].get(fg)
Excpm = xc.get_energy_and_potential(
nv_g[0], v_g, nv_g[1], v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] -=\
kss[ij].get(fg)
nv_g[kss[kq].pspin] +=\
kss[kq].get(fg)
Excmp = xc.get_energy_and_potential(
nv_g[0], v_g, nv_g[1], v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] -= \
kss[ij].get(fg)
nv_g[kss[kq].pspin] -=\
kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(
nv_g[0], v_g, nv_g[1], v_g)
else: # spin unpolarised
nv_g = nt_sg + ns * kss[ij].get(fg)\
+ ns * kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(nv_g, v_g)
nv_g = nt_sg + ns * kss[ij].get(fg)\
- ns * kss[kq].get(fg)
Excpm = xc.get_energy_and_potential(nv_g, v_g)
nv_g = nt_sg - ns * kss[ij].get(fg)\
+ ns * kss[kq].get(fg)
Excmp = xc.get_energy_and_potential(nv_g, v_g)
nv_g = nt_sg - ns * kss[ij].get(fg)\
- ns * kss[kq].get(fg)
Excmm = xc.get_energy_and_potential(nv_g, v_g)
Om_xc[ij, kq] += weight *\
0.25 * \
(Excpp - Excmp - Excpm + Excmm) / (ns * ns)
elif self.derivativeLevel == 1:
# vxc is available
timer2.start('integrate')
Om_xc[ij, kq] += weight *\
self.gd.integrate(kss[kq].get(fg) *
vvt_s[kss[kq].pspin])
timer2.stop()
timer2.start('integrate corrections')
Exc = 0.
for a, P_ni in wfs.kpt_u[kss[kq].spin].P_ani.items():
# create the modified density matrix
Pk_i = P_ni[kss[kq].i]
Pq_i = P_ni[kss[kq].j]
P_ii = np.outer(Pk_i, Pq_i)
# we need the symmetric form, hence we can pack
# use pack as I_sp used pack2
P_p = pack(P_ii)
Exc += np.dot(I_asp[a][kss[kq].pspin], P_p)
Om_xc[ij, kq] += weight * self.gd.comm.sum(Exc)
timer2.stop()
elif self.derivativeLevel == 2:
# fxc is available
if kss.npspins == 2: # spin polarised
Om_xc[ij, kq] += weight *\
gd.integrate(kss[ij].get(fg) *
kss[kq].get(fg) *
fxc_sg[kss[ij].pspin, kss[kq].pspin])
else: # spin unpolarised
Om_xc[ij, kq] += weight *\
gd.integrate(kss[ij].get(fg) *
kss[kq].get(fg) *
fxc_sg)
# XXX still numeric derivatives for local terms
timer2.start('integrate corrections')
Exc = 0.
for a, P_ni in wfs.kpt_u[kss[kq].spin].P_ani.items():
# create the modified density matrix
Pk_i = P_ni[kss[kq].i]
Pq_i = P_ni[kss[kq].j]
P_ii = np.outer(Pk_i, Pq_i)
# we need the symmetric form, hence we can pack
# use pack as I_sp used pack2
P_p = pack(P_ii)
Exc += np.dot(I_asp[a][kss[kq].pspin], P_p)
Om_xc[ij, kq] += weight * self.gd.comm.sum(Exc)
timer2.stop()
if ij != kq:
Om_xc[kq, ij] = Om_xc[ij, kq]
timer.stop()
# timer2.write()
if ij < (nij - 1):
print('XC estimated time left',
self.time_left(timer, t0, ij, nij), file=self.txt)
def Coulomb_integral_kss(self, kss_ij, kss_kq, phit, rhot,
timer=None):
# smooth part
if timer:
timer.start('integrate')
I = self.gd.integrate(rhot * phit)
if timer:
timer.stop()
timer.start('integrate corrections 2')
wfs = self.paw.wfs
Pij_ani = wfs.kpt_u[kss_ij.spin].P_ani
Pkq_ani = wfs.kpt_u[kss_kq.spin].P_ani
# Add atomic corrections
Ia = 0.0
for a, Pij_ni in Pij_ani.items():
Pi_i = Pij_ni[kss_ij.i]
Pj_i = Pij_ni[kss_ij.j]
Dij_ii = np.outer(Pi_i, Pj_i)
Dij_p = pack(Dij_ii)
Pk_i = Pkq_ani[a][kss_kq.i]
Pq_i = Pkq_ani[a][kss_kq.j]
Dkq_ii = np.outer(Pk_i, Pq_i)
Dkq_p = pack(Dkq_ii)
C_pp = wfs.setups[a].M_pp
# ----
# 2 > P P C P P
# ---- ip jr prst ks qt
# prst
Ia += 2.0 * np.dot(Dkq_p, np.dot(C_pp, Dij_p))
I += self.gd.comm.sum(Ia)
if timer:
timer.stop()
return I
def get_rpa(self):
"""calculate RPA part of the omega matrix"""
# shorthands
kss = self.fullkss
finegrid = self.finegrid
wfs = self.paw.wfs
eh_comm = self.eh_comm
# calculate omega matrix
nij = len(kss)
print('RPA', nij, 'transitions', file=self.txt)
Om = self.Om
for ij in range(eh_comm.rank, nij, eh_comm.size):
print('RPA kss[' + '%d' % ij + ']=', kss[ij], file=self.txt)
timer = Timer()
timer.start('init')
timer2 = Timer()
# smooth density including compensation charges
timer2.start('with_compensation_charges 0')
rhot_p = kss[ij].with_compensation_charges(
finegrid is not 0)
timer2.stop()
# integrate with 1/|r_1-r_2|
timer2.start('poisson')
phit_p = np.zeros(rhot_p.shape, rhot_p.dtype.char)
self.poisson.solve(phit_p, rhot_p, charge=None)
timer2.stop()
timer.stop()
t0 = timer.get_time('init')
timer.start(ij)
if finegrid == 1:
rhot = kss[ij].with_compensation_charges()
phit = self.gd.zeros()
# print "shapes 0=",phit.shape,rhot.shape
self.restrict(phit_p, phit)
else:
phit = phit_p
rhot = rhot_p
for kq in range(ij, nij):
if kq != ij:
# smooth density including compensation charges
timer2.start('kq with_compensation_charges')
rhot = kss[kq].with_compensation_charges(
finegrid is 2)
timer2.stop()
pre = 2 * sqrt(kss[ij].get_energy() * kss[kq].get_energy() *
kss[ij].get_weight() * kss[kq].get_weight())
I = self.Coulomb_integral_kss(kss[ij], kss[kq],
rhot, phit, timer2)
Om[ij, kq] = pre * I
if ij == kq:
Om[ij, kq] += kss[ij].get_energy() ** 2
else:
Om[kq, ij] = Om[ij, kq]
timer.stop()
# timer2.write()
if ij < (nij - 1):
t = timer.get_time(ij) # time for nij-ij calculations
t = .5 * t * \
(nij - ij) # estimated time for n*(n+1)/2, n=nij-(ij+1)
print('RPA estimated time left',
self.timestring(t0 * (nij - ij - 1) + t), file=self.txt)
def singlets_triplets(self):
"""Split yourself into singlet and triplet transitions"""
assert(self.fullkss.npspins == 2)
assert(self.fullkss.nvspins == 1)
# strip kss from down spins
skss = KSSingles()
tkss = KSSingles()
map = []
for ij, ks in enumerate(self.fullkss):
if ks.pspin == ks.spin:
skss.append((ks + ks) / sqrt(2))
tkss.append((ks - ks) / sqrt(2))
map.append(ij)
nkss = len(skss)
# define the singlet and the triplet omega-matrixes
sOm = OmegaMatrix(kss=skss)
sOm.full = np.empty((nkss, nkss))
tOm = OmegaMatrix(kss=tkss)
tOm.full = np.empty((nkss, nkss))
for ij in range(nkss):
for kl in range(nkss):
sOm.full[ij, kl] = (self.full[map[ij], map[kl]] +
self.full[map[ij], nkss + map[kl]])
tOm.full[ij, kl] = (self.full[map[ij], map[kl]] -
self.full[map[ij], nkss + map[kl]])
return sOm, tOm
def timestring(self, t):
ti = int(t + 0.5)
td = ti // 86400
st = ''
if td > 0:
st += '%d' % td + 'd'
ti -= td * 86400
th = ti // 3600
if th > 0:
st += '%d' % th + 'h'
ti -= th * 3600
tm = ti // 60
if tm > 0:
st += '%d' % tm + 'm'
ti -= tm * 60
st += '%d' % ti + 's'
return st
def time_left(self, timer, t0, ij, nij):
t = timer.get_time(ij) # time for nij-ij calculations
t = .5 * t * (nij - ij) # estimated time for n*(n+1)/2, n=nij-(ij+1)
return self.timestring(t0 * (nij - ij - 1) + t)
def get_map(self, istart=None, jend=None, energy_range=None):
"""Return the reduction map for the given requirements"""
self.istart = istart
self.jend = jend
if istart is None and jend is None and energy_range is None:
return None, self.fullkss
# reduce the matrix
print('# diagonalize: %d transitions original'
% len(self.fullkss), file=self.txt)
if energy_range is None:
if istart is None:
istart = self.kss.istart
if self.fullkss.istart > istart:
raise RuntimeError('istart=%d has to be >= %d' %
(istart, self.kss.istart))
if jend is None:
jend = self.kss.jend
if self.fullkss.jend < jend:
raise RuntimeError('jend=%d has to be <= %d' %
(jend, self.kss.jend))
else:
try:
emin, emax = energy_range
except:
emax = energy_range
emin = 0.
emin /= Hartree
emax /= Hartree
map = []
kss = KSSingles()
for ij, k in zip(range(len(self.fullkss)), self.fullkss):
if energy_range is None:
if k.i >= istart and k.j <= jend:
kss.append(k)
map.append(ij)
else:
if k.energy >= emin and k.energy < emax:
kss.append(k)
map.append(ij)
kss.update()
print('# diagonalize: %d transitions now' % len(kss), file=self.txt)
return map, kss
def diagonalize(self, istart=None, jend=None, energy_range=None,
TDA=False):
"""Evaluate Eigenvectors and Eigenvalues:"""
if TDA:
raise NotImplementedError
map, kss = self.get_map(istart, jend, energy_range)
nij = len(kss)
if map is None:
evec = self.full.copy()
else:
evec = np.zeros((nij, nij))
for ij in range(nij):
for kq in range(nij):
evec[ij, kq] = self.full[map[ij], map[kq]]
assert(len(evec) > 0)
self.eigenvectors = evec
self.eigenvalues = np.zeros((len(kss)))
self.kss = kss
diagonalize(self.eigenvectors, self.eigenvalues)
def Kss(self, kss=None):
"""Set and get own Kohn-Sham singles"""
if kss is not None:
self.fullkss = kss
if(hasattr(self, 'fullkss')):
return self.fullkss
else:
return None
def read(self, filename=None, fh=None):
"""Read myself from a file"""
if fh is None:
f = open(filename, 'r')
else:
f = fh
f.readline()
nij = int(f.readline())
full = np.zeros((nij, nij))
for ij in range(nij):
l = f.readline().split()
for kq in range(ij, nij):
full[ij, kq] = float(l[kq - ij])
full[kq, ij] = full[ij, kq]
self.full = full
if fh is None:
f.close()
def write(self, filename=None, fh=None):
"""Write current state to a file."""
if mpi.rank == mpi.MASTER:
if fh is None:
f = open(filename, 'w')
else:
f = fh
f.write('# OmegaMatrix\n')
nij = len(self.fullkss)
f.write('%d\n' % nij)
for ij in range(nij):
for kq in range(ij, nij):
f.write(' %g' % self.full[ij, kq])
f.write('\n')
if fh is None:
f.close()
def weight_Kijkq(self, ij, kq):
"""weight for the coupling matrix terms"""
kss = self.fullkss
return 2. * sqrt(kss[ij].get_energy() * kss[kq].get_energy() *
kss[ij].get_weight() * kss[kq].get_weight())
def __str__(self):
str = '<OmegaMatrix> '
if hasattr(self, 'eigenvalues'):
str += 'dimension ' + ('%d' % len(self.eigenvalues))
str += '\neigenvalues: '
for ev in self.eigenvalues:
str += ' ' + ('%f' % (sqrt(ev) * Hartree))
return str
def vxc(paw, xc=None, coredensity=True):
"""Calculate XC-contribution to eigenvalues."""
ham = paw.hamiltonian
dens = paw.density
wfs = paw.wfs
if xc is None:
xc = ham.xc
elif isinstance(xc, str):
xc = XC(xc)
if dens.nt_sg is None:
dens.interpolate_pseudo_density()
thisisatest = not True
if xc.orbital_dependent:
paw.get_xc_difference(xc)
# Calculate XC-potential:
vxct_sg = ham.finegd.zeros(wfs.nspins)
xc.calculate(dens.finegd, dens.nt_sg, vxct_sg)
vxct_sG = ham.gd.empty(wfs.nspins)
ham.restrict(vxct_sg, vxct_sG)
if thisisatest:
vxct_sG[:] = 1
# ... and PAW corrections:
dvxc_asii = {}
for a, D_sp in dens.D_asp.items():
dvxc_sp = np.zeros_like(D_sp)
xc.calculate_paw_correction(wfs.setups[a],
D_sp,
dvxc_sp,
a=a,
addcoredensity=coredensity)
dvxc_asii[a] = [unpack(dvxc_p) for dvxc_p in dvxc_sp]
if thisisatest:
dvxc_asii[a] = [wfs.setups[a].dO_ii]
vxc_un = np.empty((wfs.kd.mynks, wfs.bd.mynbands))
for u, vxc_n in enumerate(vxc_un):
kpt = wfs.kpt_u[u]
vxct_G = vxct_sG[kpt.s]
for n in range(wfs.bd.mynbands):
psit_G = wfs._get_wave_function_array(u, n, realspace=True)
vxc_n[n] = wfs.gd.integrate((psit_G * psit_G.conj()).real,
vxct_G,
global_integral=False)
for a, dvxc_sii in dvxc_asii.items():
P_ni = kpt.P_ani[a]
vxc_n += (np.dot(P_ni, dvxc_sii[kpt.s]) * P_ni.conj()).sum(1).real
wfs.gd.comm.sum(vxc_un)
vxc_skn = wfs.kd.collect(vxc_un)
if xc.orbital_dependent:
vxc_skn += xc.exx_skn
return vxc_skn * Hartree
class OmegaMatrix:
"""
Omega matrix in Casidas linear response formalism
Parameters
- calculator: the calculator object the ground state calculation
- kss: the Kohn-Sham singles object
- xc: the exchange correlation approx. to use
- derivativeLevel: which level i of d^i Exc/dn^i to use
- numscale: numeric epsilon for derivativeLevel=0,1
- filehandle: the oject can be read from a filehandle
- txt: output stream or file name
- finegrid: level of fine grid to use. 0: nothing, 1 for poisson only,
2 everything on the fine grid
"""
def __init__(self,
calculator=None,
kss=None,
xc=None,
derivativeLevel=None,
numscale=0.001,
filehandle=None,
txt=None,
finegrid=2,
eh_comm=None,
):
if not txt and calculator:
txt = calculator.txt
self.txt, firsttime = initialize_text_stream(txt, mpi.rank)
if eh_comm == None:
eh_comm = mpi.serial_comm
self.eh_comm = eh_comm
if filehandle is not None:
self.kss = kss
self.read(fh=filehandle)
return None
self.fullkss = kss
self.finegrid = finegrid
if calculator is None:
return
self.paw = calculator
wfs = self.paw.wfs
# handle different grid possibilities
self.restrict = None
self.poisson = PoissonSolver(nn=self.paw.hamiltonian.poisson.nn)
if finegrid:
self.poisson.set_grid_descriptor(self.paw.density.finegd)
self.poisson.initialize()
self.gd = self.paw.density.finegd
if finegrid == 1:
self.gd = wfs.gd
else:
self.poisson.set_grid_descriptor(wfs.gd)
self.poisson.initialize()
self.gd = wfs.gd
self.restrict = Transformer(self.paw.density.finegd, wfs.gd,
self.paw.input_parameters.stencils[1]
).apply
if xc == 'RPA':
xc = None # enable RPA as keyword
if xc is not None:
self.xc = XC(xc)
self.xc.initialize(self.paw.density, self.paw.hamiltonian,
wfs, self.paw.occupations)
# check derivativeLevel
if derivativeLevel is None:
derivativeLevel= \
self.xc.get_functional().get_max_derivative_level()
self.derivativeLevel = derivativeLevel
# change the setup xc functional if needed
# the ground state calculation may have used another xc
if kss.npspins > kss.nvspins:
spin_increased = True
else:
spin_increased = False
else:
self.xc = None
self.numscale = numscale
self.singletsinglet = False
if kss.nvspins<2 and kss.npspins<2:
# this will be a singlet to singlet calculation only
self.singletsinglet=True
nij = len(kss)
self.Om = np.zeros((nij,nij))
self.get_full()
def get_full(self):
self.paw.timer.start('Omega RPA')
self.get_rpa()
self.paw.timer.stop()
if self.xc is not None:
self.paw.timer.start('Omega XC')
self.get_xc()
self.paw.timer.stop()
self.eh_comm.sum(self.Om)
self.full = self.Om
def get_xc(self):
"""Add xc part of the coupling matrix"""
# shorthands
paw = self.paw
wfs = paw.wfs
gd = paw.density.finegd
comm = gd.comm
eh_comm = self.eh_comm
fg = self.finegrid is 2
kss = self.fullkss
nij = len(kss)
Om_xc = self.Om
# initialize densities
# nt_sg is the smooth density on the fine grid with spin index
if kss.nvspins==2:
# spin polarised ground state calc.
nt_sg = paw.density.nt_sg
else:
# spin unpolarised ground state calc.
if kss.npspins==2:
# construct spin polarised densities
nt_sg = np.array([.5*paw.density.nt_sg[0],
.5*paw.density.nt_sg[0]])
else:
nt_sg = paw.density.nt_sg
# check if D_sp have been changed before
D_asp = self.paw.density.D_asp
for a, D_sp in D_asp.items():
if len(D_sp) != kss.npspins:
if len(D_sp) == 1:
D_asp[a] = np.array([0.5 * D_sp[0], 0.5 * D_sp[0]])
else:
D_asp[a] = np.array([D_sp[0] + D_sp[1]])
# restrict the density if needed
if fg:
nt_s = nt_sg
else:
nt_s = self.gd.zeros(nt_sg.shape[0])
for s in range(nt_sg.shape[0]):
self.restrict(nt_sg[s], nt_s[s])
gd = paw.density.gd
# initialize vxc or fxc
if self.derivativeLevel==0:
raise NotImplementedError
if kss.npspins==2:
v_g=nt_sg[0].copy()
else:
v_g=nt_sg.copy()
elif self.derivativeLevel==1:
pass
elif self.derivativeLevel==2:
fxc_sg = np.zeros(nt_sg.shape)
self.xc.calculate_fxc(gd, nt_sg, fxc_sg)
else:
raise ValueError('derivativeLevel can only be 0,1,2')
## self.paw.my_nuclei = []
ns=self.numscale
xc=self.xc
print >> self.txt, 'XC',nij,'transitions'
for ij in range(eh_comm.rank, nij, eh_comm.size):
print >> self.txt,'XC kss['+'%d'%ij+']'
timer = Timer()
timer.start('init')
timer2 = Timer()
if self.derivativeLevel >= 1:
# vxc is available
# We use the numerical two point formula for calculating
# the integral over fxc*n_ij. The results are
# vvt_s smooth integral
# nucleus.I_sp atom based correction matrices (pack2)
# stored on each nucleus
timer2.start('init v grids')
vp_s=np.zeros(nt_s.shape,nt_s.dtype.char)
vm_s=np.zeros(nt_s.shape,nt_s.dtype.char)
if kss.npspins == 2: # spin polarised
nv_s = nt_s.copy()
nv_s[kss[ij].pspin] += ns * kss[ij].get(fg)
xc.calculate(gd, nv_s, vp_s)
nv_s = nt_s.copy()
nv_s[kss[ij].pspin] -= ns * kss[ij].get(fg)
xc.calculate(gd, nv_s, vm_s)
else: # spin unpolarised
nv = nt_s + ns * kss[ij].get(fg)
xc.calculate(gd, nv, vp_s)
nv = nt_s - ns * kss[ij].get(fg)
xc.calculate(gd, nv, vm_s)
vvt_s = (0.5 / ns) * (vp_s - vm_s)
timer2.stop()
# initialize the correction matrices
timer2.start('init v corrections')
I_asp = {}
for a, P_ni in wfs.kpt_u[kss[ij].spin].P_ani.items():
# create the modified density matrix
Pi_i = P_ni[kss[ij].i]
Pj_i = P_ni[kss[ij].j]
P_ii = np.outer(Pi_i, Pj_i)
# we need the symmetric form, hence we can pack
P_p = pack(P_ii)
D_sp = self.paw.density.D_asp[a].copy()
D_sp[kss[ij].pspin] -= ns * P_p
setup = wfs.setups[a]
I_sp = np.zeros_like(D_sp)
self.xc.calculate_paw_correction(setup, D_sp, I_sp)
I_sp *= -1.0
D_sp = self.paw.density.D_asp[a].copy()
D_sp[kss[ij].pspin] += ns * P_p
self.xc.calculate_paw_correction(setup, D_sp, I_sp)
I_sp /= 2.0 * ns
I_asp[a] = I_sp
timer2.stop()
timer.stop()
t0 = timer.get_time('init')
timer.start(ij)
for kq in range(ij,nij):
weight = self.weight_Kijkq(ij, kq)
if self.derivativeLevel == 0:
# only Exc is available
if kss.npspins==2: # spin polarised
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] += kss[ij].get(fg)
nv_g[kss[kq].pspin] += kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(
nv_g[0], v_g, nv_g[1], v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] += kss[ij].get(fg)
nv_g[kss[kq].pspin] -= kss[kq].get(fg)
Excpm = xc.get_energy_and_potential(\
nv_g[0],v_g,nv_g[1],v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] -=\
kss[ij].get(fg)
nv_g[kss[kq].pspin] +=\
kss[kq].get(fg)
Excmp = xc.get_energy_and_potential(\
nv_g[0],v_g,nv_g[1],v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] -= \
kss[ij].get(fg)
nv_g[kss[kq].pspin] -=\
kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(\
nv_g[0],v_g,nv_g[1],v_g)
else: # spin unpolarised
nv_g=nt_sg + ns*kss[ij].get(fg)\
+ ns*kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(nv_g,v_g)
nv_g=nt_sg + ns*kss[ij].get(fg)\
- ns*kss[kq].get(fg)
Excpm = xc.get_energy_and_potential(nv_g,v_g)
nv_g=nt_sg - ns*kss[ij].get(fg)\
+ ns*kss[kq].get(fg)
Excmp = xc.get_energy_and_potential(nv_g,v_g)
nv_g=nt_sg - ns*kss[ij].get(fg)\
- ns*kss[kq].get(fg)
Excmm = xc.get_energy_and_potential(nv_g,v_g)
Om_xc[ij,kq] += weight *\
0.25*(Excpp-Excmp-Excpm+Excmm)/(ns*ns)
elif self.derivativeLevel == 1:
# vxc is available
timer2.start('integrate')
Om_xc[ij,kq] += weight*\
self.gd.integrate(kss[kq].get(fg)*
vvt_s[kss[kq].pspin])
timer2.stop()
timer2.start('integrate corrections')
Exc = 0.
for a, P_ni in wfs.kpt_u[kss[kq].spin].P_ani.items():
# create the modified density matrix
Pk_i = P_ni[kss[kq].i]
Pq_i = P_ni[kss[kq].j]
P_ii = np.outer(Pk_i, Pq_i)
# we need the symmetric form, hence we can pack
# use pack as I_sp used pack2
P_p = pack(P_ii)
Exc += np.dot(I_asp[a][kss[kq].pspin], P_p)
Om_xc[ij, kq] += weight * self.gd.comm.sum(Exc)
timer2.stop()
elif self.derivativeLevel == 2:
# fxc is available
if kss.npspins==2: # spin polarised
Om_xc[ij,kq] += weight *\
gd.integrate(kss[ij].get(fg) *
kss[kq].get(fg) *
fxc_sg[kss[ij].pspin, kss[kq].pspin])
else: # spin unpolarised
Om_xc[ij,kq] += weight *\
gd.integrate(kss[ij].get(fg) *
kss[kq].get(fg) *
fxc_sg)
# XXX still numeric derivatives for local terms
timer2.start('integrate corrections')
Exc = 0.
for a, P_ni in wfs.kpt_u[kss[kq].spin].P_ani.items():
# create the modified density matrix
Pk_i = P_ni[kss[kq].i]
Pq_i = P_ni[kss[kq].j]
P_ii = np.outer(Pk_i, Pq_i)
# we need the symmetric form, hence we can pack
# use pack as I_sp used pack2
P_p = pack(P_ii)
Exc += np.dot(I_asp[a][kss[kq].pspin], P_p)
Om_xc[ij, kq] += weight * self.gd.comm.sum(Exc)
timer2.stop()
if ij != kq:
Om_xc[kq,ij] = Om_xc[ij,kq]
timer.stop()
## timer2.write()
if ij < (nij-1):
print >> self.txt,'XC estimated time left',\
self.time_left(timer, t0, ij, nij)
def Coulomb_integral_kss(self, kss_ij, kss_kq, phit, rhot,
timer=None):
# smooth part
if timer:
timer.start('integrate')
I = self.gd.integrate(rhot * phit)
if timer:
timer.stop()
timer.start('integrate corrections 2')
wfs = self.paw.wfs
Pij_ani = wfs.kpt_u[kss_ij.spin].P_ani
Pkq_ani = wfs.kpt_u[kss_kq.spin].P_ani
# Add atomic corrections
Ia = 0.0
for a, Pij_ni in Pij_ani.items():
Pi_i = Pij_ni[kss_ij.i]
Pj_i = Pij_ni[kss_ij.j]
Dij_ii = np.outer(Pi_i, Pj_i)
Dij_p = pack(Dij_ii)
Pk_i = Pkq_ani[a][kss_kq.i]
Pq_i = Pkq_ani[a][kss_kq.j]
Dkq_ii = np.outer(Pk_i, Pq_i)
Dkq_p = pack(Dkq_ii)
C_pp = wfs.setups[a].M_pp
# ----
# 2 > P P C P P
# ---- ip jr prst ks qt
# prst
Ia += 2.0*np.dot(Dkq_p, np.dot(C_pp, Dij_p))
I += self.gd.comm.sum(Ia)
if timer:
timer.stop()
return I
def get_rpa(self):
"""calculate RPA part of the omega matrix"""
# shorthands
kss=self.fullkss
finegrid=self.finegrid
wfs = self.paw.wfs
eh_comm = self.eh_comm
# calculate omega matrix
nij = len(kss)
print >> self.txt,'RPA',nij,'transitions'
Om = self.Om
for ij in range(eh_comm.rank, nij, eh_comm.size):
print >> self.txt,'RPA kss['+'%d'%ij+']=', kss[ij]
timer = Timer()
timer.start('init')
timer2 = Timer()
# smooth density including compensation charges
timer2.start('with_compensation_charges 0')
rhot_p = kss[ij].with_compensation_charges(
finegrid is not 0)
timer2.stop()
# integrate with 1/|r_1-r_2|
timer2.start('poisson')
phit_p = np.zeros(rhot_p.shape, rhot_p.dtype.char)
self.poisson.solve(phit_p, rhot_p, charge=None)
timer2.stop()
timer.stop()
t0 = timer.get_time('init')
timer.start(ij)
if finegrid == 1:
rhot = kss[ij].with_compensation_charges()
phit = self.gd.zeros()
## print "shapes 0=",phit.shape,rhot.shape
self.restrict(phit_p,phit)
else:
phit = phit_p
rhot = rhot_p
for kq in range(ij,nij):
if kq != ij:
# smooth density including compensation charges
timer2.start('kq with_compensation_charges')
rhot = kss[kq].with_compensation_charges(
finegrid is 2)
timer2.stop()
pre = 2 * sqrt(kss[ij].get_energy() * kss[kq].get_energy() *
kss[ij].get_weight() * kss[kq].get_weight() )
I = self.Coulomb_integral_kss(kss[ij], kss[kq],
rhot, phit, timer2)
Om[ij,kq] = pre * I
if ij == kq:
Om[ij,kq] += kss[ij].get_energy()**2
else:
Om[kq,ij]=Om[ij,kq]
timer.stop()
## timer2.write()
if ij < (nij-1):
t = timer.get_time(ij) # time for nij-ij calculations
t = .5*t*(nij-ij) # estimated time for n*(n+1)/2, n=nij-(ij+1)
print >> self.txt,'RPA estimated time left',\
self.timestring(t0*(nij-ij-1)+t)
def singlets_triplets(self):
"""Split yourself into singlet and triplet transitions"""
assert(self.fullkss.npspins == 2)
assert(self.fullkss.nvspins == 1)
# strip kss from down spins
skss = KSSingles()
tkss = KSSingles()
map = []
for ij, ks in enumerate(self.fullkss):
if ks.pspin == ks.spin:
skss.append((ks + ks) / sqrt(2))
tkss.append((ks - ks) / sqrt(2))
map.append(ij)
nkss = len(skss)
# define the singlet and the triplet omega-matrixes
sOm = OmegaMatrix(kss=skss)
sOm.full = np.empty((nkss, nkss))
tOm = OmegaMatrix(kss=tkss)
tOm.full = np.empty((nkss, nkss))
for ij in range(nkss):
for kl in range(nkss):
sOm.full[ij, kl] = (self.full[map[ij], map[kl]] +
self.full[map[ij], nkss + map[kl]])
tOm.full[ij, kl] = (self.full[map[ij], map[kl]] -
self.full[map[ij], nkss + map[kl]])
return sOm, tOm
def timestring(self, t):
ti = int(t + 0.5)
td = ti // 86400
st = ''
if td > 0:
st += '%d' % td + 'd'
ti -= td * 86400
th = ti // 3600
if th > 0:
st += '%d' % th + 'h'
ti -= th * 3600
tm = ti // 60
if tm > 0:
st += '%d' % tm + 'm'
ti -= tm * 60
st += '%d' % ti + 's'
return st
def time_left(self, timer, t0, ij, nij):
t = timer.get_time(ij) # time for nij-ij calculations
t = .5 * t * (nij - ij) # estimated time for n*(n+1)/2, n=nij-(ij+1)
return self.timestring(t0 * (nij - ij - 1) + t)
def get_map(self, istart=None, jend=None, energy_range=None):
"""Return the reduction map for the given requirements"""
self.istart = istart
self.jend = jend
if istart is None and jend is None and energy_range is None:
return None, self.fullkss
# reduce the matrix
print >> self.txt,'# diagonalize: %d transitions original'\
% len(self.fullkss)
if energy_range is None:
if istart is None: istart = self.kss.istart
if self.fullkss.istart > istart:
raise RuntimeError('istart=%d has to be >= %d' %
(istart, self.kss.istart))
if jend is None: jend = self.kss.jend
if self.fullkss.jend < jend:
raise RuntimeError('jend=%d has to be <= %d' %
(jend, self.kss.jend))
else:
try:
emin, emax = energy_range
except:
emax = energy_range
emin = 0.
emin /= Hartree
emax /= Hartree
map= []
kss = KSSingles()
for ij, k in zip(range(len(self.fullkss)), self.fullkss):
if energy_range is None:
if k.i >= istart and k.j <= jend:
kss.append(k)
map.append(ij)
else:
if k.energy >= emin and k.energy < emax:
kss.append(k)
map.append(ij)
kss.update()
print >> self.txt, '# diagonalize: %d transitions now' % len(kss)
return map, kss
def diagonalize(self, istart=None, jend=None, energy_range=None,
TDA=False):
"""Evaluate Eigenvectors and Eigenvalues:"""
if TDA:
raise NotImplementedError
map, kss = self.get_map(istart, jend, energy_range)
nij = len(kss)
if map is None:
evec = self.full.copy()
else:
evec = np.zeros((nij,nij))
for ij in range(nij):
for kq in range(nij):
evec[ij,kq] = self.full[map[ij],map[kq]]
assert(len(evec) > 0)
self.eigenvectors = evec
self.eigenvalues = np.zeros((len(kss)))
self.kss = kss
diagonalize(self.eigenvectors, self.eigenvalues)
def Kss(self, kss=None):
"""Set and get own Kohn-Sham singles"""
if kss is not None:
self.fullkss = kss
if(hasattr(self,'fullkss')):
return self.fullkss
else:
return None
def read(self, filename=None, fh=None):
"""Read myself from a file"""
if fh is None:
f = open(filename, 'r')
else:
f = fh
f.readline()
nij = int(f.readline())
full = np.zeros((nij,nij))
for ij in range(nij):
l = f.readline().split()
for kq in range(ij,nij):
full[ij,kq] = float(l[kq-ij])
full[kq,ij] = full[ij,kq]
self.full = full
if fh is None:
f.close()
def write(self, filename=None, fh=None):
"""Write current state to a file."""
if mpi.rank == mpi.MASTER:
if fh is None:
f = open(filename, 'w')
else:
f = fh
f.write('# OmegaMatrix\n')
nij = len(self.fullkss)
f.write('%d\n' % nij)
for ij in range(nij):
for kq in range(ij,nij):
f.write(' %g' % self.full[ij,kq])
f.write('\n')
if fh is None:
f.close()
def weight_Kijkq(self, ij, kq):
"""weight for the coupling matrix terms"""
kss = self.fullkss
return 2.*sqrt( kss[ij].get_energy() * kss[kq].get_energy() *
kss[ij].get_weight() * kss[kq].get_weight() )
def __str__(self):
str='<OmegaMatrix> '
if hasattr(self,'eigenvalues'):
str += 'dimension '+ ('%d'%len(self.eigenvalues))
str += "\neigenvalues: "
for ev in self.eigenvalues:
str += ' ' + ('%f'%(sqrt(ev) * Hartree))
return str
'LDA_X', 'LDA_X+LDA_C_PW', 'LDA_X+LDA_C_VWN', 'LDA_X+LDA_C_PZ',
'GGA_X_PBE+GGA_C_PBE', 'GGA_X_PBE_R+GGA_C_PBE', 'GGA_X_B88+GGA_C_P86',
'GGA_X_B88+GGA_C_LYP', 'GGA_X_FT97_A+GGA_C_LYP'
]
x = 0.000001
for xcname in libxc_set:
ra.seed(8)
xc = XC(xcname)
s = create_setup('N', xc)
ni = s.ni
nii = ni * (ni + 1) // 2
D_p = 0.1 * ra.random(nii) + 0.4
H_p = np.zeros(nii)
E1 = xc.calculate_paw_correction(s, D_p.reshape(1, -1), H_p.reshape(1, -1))
dD_p = x * ra.random(nii)
D_p += dD_p
dE = np.dot(H_p, dD_p) / x
E2 = xc.calculate_paw_correction(s, D_p.reshape(1, -1))
print(xcname, dE, (E2 - E1) / x)
equal(dE, (E2 - E1) / x, 0.003)
E2s = xc.calculate_paw_correction(s, np.array([0.5 * D_p, 0.5 * D_p]),
np.array([H_p, H_p]))
print(E2, E2s)
equal(E2, E2s, 1.0e-12)
if xcname in reference: # compare with old gpaw
print('A:', E2, reference[xcname])
equal(E2, reference[xcname], tolerance)
v_g = np.zeros((1, n, n, n))
P_ni = 0.2 * ra.random((20, ni))
P_ni[:, nao:] = 0.0
D_ii = np.dot(np.transpose(P_ni), P_ni)
D_p = pack(D_ii)
p = 0
for i1 in range(nao):
for i2 in range(i1, nao):
n_g += D_p[p] * psit_ig[i1] * psit_ig[i2]
p += 1
p += ni - nao
p = create_localized_functions([s.nct], gd, (0.5, 0.5, 0.5))
p.add(n_g[0], np.ones(1))
e_g = gd.zeros()
xc.calculate(gd, n_g, v_g, e_g)
r2_g = np.sum((np.indices((n, n, n)) - n / 2)**2, axis=0)
dv_g = gd.dv * np.less(r2_g, (rcut / a * n)**2)
E2 = -np.dot(e_g.ravel(), dv_g.ravel())
s.xc_correction.n_qg[:] = 0.0
s.xc_correction.nc_g[:] = 0.0
E1 = (xc.calculate_paw_correction(s, D_p.reshape(1, -1))
+ s.xc_correction.Exc0)
print(name, E1, E2, E1 - E2)
equal(E1, E2, 0.0013)
from gpaw.utilities import pack
x = 0.0000001
ra.seed(8)
for xc in ['LDA']: #, 'PBE']:
print(xc)
xc = XC(xc)
s = create_setup('N', xc)
ni = s.ni
D_sp = np.array(
[pack(np.outer(P_i, P_i)) for P_i in 0.2 * ra.random((2, ni)) - 0.1])
D_sp[1] += D_sp[0]
nii = ni * (ni + 1) // 2
E = xc.calculate_paw_correction(s, D_sp)
xc = NonCollinearFunctional(xc)
Dnc_sp = np.zeros((4, nii))
Dnc_sp[0] = D_sp.sum(0)
Dnc_sp[3] = D_sp[0] - D_sp[1]
Enc = xc.calculate_paw_correction(s, Dnc_sp)
print(E, E - Enc)
assert abs(E - Enc) < 1e-11
Dnc_sp[1] = 0.1 * Dnc_sp[3]
Dnc_sp[2] = 0.2 * Dnc_sp[3]
Dnc_sp[3] *= (1 - 0.1**2 - 0.2**2)**0.5
H_sp = 0 * Dnc_sp
Enc = xc.calculate_paw_correction(s, Dnc_sp, H_sp)
n_g = np.zeros((1, n, n, n))
v_g = np.zeros((1, n, n, n))
P_ni = 0.2 * ra.random((20, ni))
P_ni[:, nao:] = 0.0
D_ii = np.dot(np.transpose(P_ni), P_ni)
D_p = pack(D_ii)
p = 0
for i1 in range(nao):
for i2 in range(i1, nao):
n_g += D_p[p] * psit_ig[i1] * psit_ig[i2]
p += 1
p += ni - nao
p = create_localized_functions([s.nct], gd, (0.5, 0.5, 0.5))
p.add(n_g[0], np.ones(1))
e_g = gd.zeros()
xc.calculate(gd, n_g, v_g, e_g)
r2_g = np.sum((np.indices((n, n, n)) - n / 2) ** 2, axis=0)
dv_g = gd.dv * np.less(r2_g, (rcut / a * n) ** 2)
E2 = -np.dot(e_g.ravel(), dv_g.ravel())
s.xc_correction.n_qg[:] = 0.0
s.xc_correction.nc_g[:] = 0.0
E1 = xc.calculate_paw_correction(s, D_p.reshape(1, -1)) + s.xc_correction.Exc0
print name, E1, E2, E1 - E2
equal(E1, E2, 0.0013)