def __init__(self, width, folding='Gauss'):
self.width = width
if folding == 'Gauss':
self.func = Gauss(width)
elif folding == 'Lorentz':
self.func = Lorentz(width)
elif folding == None:
self.func = None
else:
raise RuntimeError('unknown folding "' + folding + '"')
def __init__(self, width,
folding='Gauss'):
self.width = width
if folding == 'Gauss':
self.func = Gauss(width)
elif folding == 'Lorentz':
self.func = Lorentz(width)
elif folding == 'ComplexGauss':
self.func = ComplexGauss(width)
elif folding == 'ComplexLorentz':
self.func = ComplexLorentz(width)
elif folding == 'RealLorentzPole':
self.func = LorentzPole(width, imag=False)
elif folding == 'ImaginaryLorentzPole':
self.func = LorentzPole(width, imag=True)
elif folding == 'Voigt':
self.func = Voigt(width)
else:
raise RuntimeError('unknown folding "' + folding + '"')
from math import exp, pi, sqrt
import numpy as np
from gpaw.gauss import Gauss
from gpaw.test import equal
from gpaw.utilities.folder import Folder, Lorentz, Voigt # noqa
# Gauss and Lorentz functions
width = 0.5
x = 1.5
equal(Gauss(width).get(x),
exp(- x**2 / 2 / width**2) / sqrt(2 * pi) / width,
1.e-15)
equal(Gauss(width).fwhm, width * np.sqrt(8 * np.log(2)), 1.e-15)
equal(Lorentz(width).get(x),
width / (x**2 + width**2) / pi,
1.e-15)
equal(Lorentz(width).fwhm, width * 2, 1.e-15)
# folder function
for func in [Gauss, Lorentz, Voigt]:
folder = Folder(width, func(width).__class__.__name__)
x = [0, 2]
y = [[2, 0, 1], [1, 1, 1]]
xl, yl = folder.fold(x, y, dx=.7)
print('From analyse :', Eanalyse, oszanalyse)
equal(E, Eanalyse, 1e-3) # Written precision in analyse
equal(osz[0], oszanalyse, 1e-3)
E2 = lr2[n].get_energy() * Hartree
osz2 = lr2[n].get_oscillator_strength()
print('Written and read object:', E2, osz2[0])
# Compare values of original and written/read objects
equal(E, E2, 1e-4)
for i in range(len(osz)):
equal(osz[i], osz2[i], 1.7e-4)
width = 0.05
photoabsorption_spectrum(lr,
spectrum_file='lrtddft3-spectrum.dat',
width=width)
# We need to be able to check the heights in the spectrum
weight = Gauss(width).get(0)
spectrum = np.loadtxt('lrtddft3-spectrum.dat', usecols=(0, 1))
idx = (spectrum[:, 0] >= E - 0.1) & (spectrum[:, 0] <= E + 0.1)
peak = np.argmax(spectrum[idx, 1]) + np.nonzero(idx)[0][0]
Espec = spectrum[peak, 0]
oszspec = spectrum[peak, 1] / weight
print('Values from spectrum :', Espec, oszspec)
# Compare calculated values with values written to file
equal(E, Espec, 1e-2) # The spectrum has a low sampling
equal(osz[0], oszspec, 1e-2)
def to_file(self,
ldbe,
filename=None,
width=None,
shift=True,
bound=False):
"""Write the LDOS to a file.
If a width is given, the LDOS will be Gaussian folded and shifted to set
Fermi energy to 0 eV. The latter can be avoided by setting shift=False.
If you use fixmagmom=true, you will get two fermi-levels, one for each
spin-setting. Normaly these will shifted individually to 0 eV. If you
want to shift them as pair to the higher energy use bound=True.
"""
f = paropen(filename, 'w')
def append_weight_strings(ldbe, data):
s = ''
for key in ldbe:
for l in 'spd':
data.append(key + '(' + l + ')-weight')
if len(key) == 1:
key = ' ' + key
s += ' ' + key + ':s p d '
return s
wfs = self.paw.wfs
if width is None:
# unfolded ldos
fmf = FMF(['Raw LDOS obtained from projector weights'])
print >> f, fmf.header(),
data = ['energy: energy [eV]',
'occupation number: occ',
'spin index: s',
'k-point index: k',
'band index: n',
'k-point weight: weight']
string = '# e_i[eV] occ s k n kptwght '
string += append_weight_strings(ldbe, data)
data.append('summed weights: sum')
string += ' sum'
print >> f, fmf.data(data),
print >> f, string
for k in range(wfs.nibzkpts):
for s in range(wfs.nspins):
e_n = self.paw.get_eigenvalues(kpt=k, spin=s)
f_n = self.paw.get_occupation_numbers(kpt=k, spin=s)
if e_n is None:
continue
w = wfs.weight_k[k]
for n in range(wfs.bd.nbands):
sum = 0.0
print >> f, '%10.5f %6.4f %2d %5d' % (e_n[n], f_n[n],
s, k),
print >> f, '%6d %8.4f' % (n, w),
for key in ldbe:
spd = ldbe[key][s, k, n]
for l in range(3):
sum += spd[l]
print >> f, '%8.4f' % spd[l],
print >> f, '%8.4f' % sum
else:
# folded ldos
fmf = FMF(['Folded raw LDOS obtained from projector weights'])
print >> f, fmf.header(),
gauss = Gauss(width)
print >> f, fmf.field('folding',
['function: Gauss',
'width: ' + str(width) + ' [eV]']),
data = ['energy: energy [eV]',
'spin index: s',
'k-point index: k',
'band index: n',
'k-point weight: weight']
# minimal and maximal energies
emin = 1.e32
emax = -1.e32
for k in range(wfs.nibzkpts):
for s in range(wfs.nspins):
e_n = self.paw.get_eigenvalues(kpt=k, spin=s,
broadcast=True)
emin = min(e_n.min(), emin)
emax = max(e_n.max(), emax)
emin -= 4 * width
emax += 4 * width
# Fermi energy
try:
if self.paw.occupations.fixmagmom:
efermi = self.paw.get_fermi_levels()
else:
efermi = self.paw.get_fermi_level()
except:
# set Fermi level half way between H**O and LUMO
hl = self.paw.occupations.get_homo_lumo(wfs)
efermi = (hl[0] + hl[1]) * Hartree / 2
eshift = 0.0
if shift and not self.paw.occupations.fixmagmom:
eshift = -efermi
# set de to sample 4 points in the width
de = width / 4
string = '# e[eV] s '
string += append_weight_strings(ldbe, data)
for s in range(wfs.nspins):
if self.paw.occupations.fixmagmom:
if not bound:
eshift = - efermi[s]
else:
eshift = - efermi.max()
print >> f, fmf.data(data),
print >> f, '# Gauss folded, width=%g [eV]' % width
if shift:
print >> f, '# shifted to Fermi energy = 0'
print >> f, '# Fermi energy was',
else:
print >> f, '# Fermi energy',
print >> f, efermi, 'eV'
print >> f, string
# loop over energies
emax=emax+.5*de
e=emin
while e<emax:
val = {}
for key in ldbe:
val[key] = np.zeros((3))
for k in range(wfs.nibzkpts):
w = wfs.kpt_u[k].weight
e_n = self.paw.get_eigenvalues(kpt=k, spin=s,
broadcast=True)
for n in range(wfs.bd.nbands):
w_i = w * gauss.get(e_n[n] - e)
for key in ldbe:
val[key] += w_i * ldbe[key][s, k, n]
print >> f, '%10.5f %2d' % (e + eshift, s),
for key in val:
spd = val[key]
for l in range(3):
print >> f, '%8.4f' % spd[l],
print >> f
e += de
f.close()
def to_file(self,
ldbe,
filename=None,
width=None,
shift=True,
bound=False):
"""Write the LDOS to a file.
If a width is given, the LDOS will be Gaussian folded and shifted to set
Fermi energy to 0 eV. The latter can be avoided by setting shift=False.
If you use fixmagmom=true, you will get two fermi-levels, one for each
spin-setting. Normaly these will shifted individually to 0 eV. If you
want to shift them as pair to the higher energy use bound=True.
"""
f = paropen(filename, 'w')
def append_weight_strings(ldbe, data):
s = ''
for key in ldbe:
for l in 'spd':
data.append(key + '(' + l + ')-weight')
if len(key) == 1:
key = ' ' + key
s += ' ' + key + ':s p d '
return s
wfs = self.paw.wfs
if width is None:
# unfolded ldos
fmf = FMF(['Raw LDOS obtained from projector weights'])
print(fmf.header(), end=' ', file=f)
data = [
'energy: energy [eV]', 'occupation number: occ',
'spin index: s', 'k-point index: k', 'band index: n',
'k-point weight: weight'
]
string = '# e_i[eV] occ s k n kptwght '
string += append_weight_strings(ldbe, data)
data.append('summed weights: sum')
string += ' sum'
print(fmf.data(data), end=' ', file=f)
print(string, file=f)
for k in range(wfs.kd.nibzkpts):
for s in range(wfs.nspins):
e_n = self.paw.get_eigenvalues(kpt=k, spin=s)
f_n = self.paw.get_occupation_numbers(kpt=k, spin=s)
if e_n is None:
continue
w = wfs.kd.weight_k[k]
for n in range(wfs.bd.nbands):
sum = 0.0
print('%10.5f %6.4f %2d %5d' % (e_n[n], f_n[n], s, k),
end=' ',
file=f)
print('%6d %8.4f' % (n, w), end=' ', file=f)
for key in ldbe:
spd = ldbe[key][s, k, n]
for l in range(3):
sum += spd[l]
print('%8.4f' % spd[l], end=' ', file=f)
print('%8.4f' % sum, file=f)
else:
# folded ldos
fmf = FMF(['Folded raw LDOS obtained from projector weights'])
print(fmf.header(), end=' ', file=f)
gauss = Gauss(width)
print(fmf.field(
'folding',
['function: Gauss', 'width: ' + str(width) + ' [eV]']),
end=' ',
file=f)
data = [
'energy: energy [eV]', 'spin index: s', 'k-point index: k',
'band index: n', 'k-point weight: weight'
]
# minimal and maximal energies
emin = 1.e32
emax = -1.e32
for k in range(wfs.kd.nibzkpts):
for s in range(wfs.nspins):
e_n = self.paw.get_eigenvalues(kpt=k,
spin=s,
broadcast=True)
emin = min(e_n.min(), emin)
emax = max(e_n.max(), emax)
emin -= 4 * width
emax += 4 * width
# Fermi energy
try:
if self.paw.occupations.fixmagmom:
efermi = self.paw.get_fermi_levels()
else:
efermi = self.paw.get_fermi_level()
except:
# set Fermi level half way between H**O and LUMO
hl = wfs.get_homo_lumo()
efermi = (hl[0] + hl[1]) * Hartree / 2
eshift = 0.0
if shift and not self.paw.occupations.fixmagmom:
eshift = -efermi
# set de to sample 4 points in the width
de = width / 4
string = '# e[eV] s '
string += append_weight_strings(ldbe, data)
for s in range(wfs.nspins):
if self.paw.occupations.fixmagmom:
if not bound:
eshift = -efermi[s]
else:
eshift = -efermi.max()
print(fmf.data(data), end=' ', file=f)
print('# Gauss folded, width=%g [eV]' % width, file=f)
if shift:
print('# shifted to Fermi energy = 0', file=f)
print('# Fermi energy was', end=' ', file=f)
else:
print('# Fermi energy', end=' ', file=f)
print(efermi, 'eV', file=f)
print(string, file=f)
# loop over energies
emax = emax + .5 * de
e = emin
while e < emax:
val = {}
for key in ldbe:
val[key] = np.zeros((3))
for k in range(wfs.kd.nibzkpts):
w = wfs.kpt_u[k].weight
e_n = self.paw.get_eigenvalues(kpt=k,
spin=s,
broadcast=True)
for n in range(wfs.bd.nbands):
w_i = w * gauss.get(e_n[n] - e)
for key in ldbe:
val[key] += w_i * ldbe[key][s, k, n]
print('%10.5f %2d' % (e + eshift, s), end=' ', file=f)
for key in val:
spd = val[key]
for l in range(3):
print('%8.4f' % spd[l], end=' ', file=f)
print(file=f)
e += de
f.close()
import os
from math import exp, pi, sqrt
import numpy as np
from gpaw.gauss import Gauss, Lorentz
from gpaw.test import equal
from gpaw.utilities.folder import Folder
# Gauss and Lorentz functions
width = 0.5
x = 1.5
equal(Gauss(width).get(x),
exp(- x**2 / 2 / width**2) / sqrt(2 * pi) / width,
1.e-15)
equal(Lorentz(width).get(x),
width / (x**2 + width**2) / pi,
1.e-15)
# folder function
for name in ['Gauss', 'Lorentz']:
folder = Folder(width, name)
x = [0, 2]
y = [[2, 0, 1], [1, 1, 1]]
xl, yl = folder.fold(x, y, dx=.7)
# check first value
from math import exp, pi, sqrt
import numpy as np
from gpaw.gauss import Gauss, Lorentz
from gpaw.test import equal
from gpaw.utilities.folder import Folder, Voigt
# Gauss and Lorentz functions
width = 0.5
x = 1.5
equal(Gauss(width).get(x),
exp(- x**2 / 2 / width**2) / sqrt(2 * pi) / width,
1.e-15)
equal(Lorentz(width).get(x),
width / (x**2 + width**2) / pi,
1.e-15)
# folder function
for name in ['Gauss', 'Lorentz', 'Voigt']:
folder = Folder(width, name)
x = [0, 2]
y = [[2, 0, 1], [1, 1, 1]]
xl, yl = folder.fold(x, y, dx=.7)
# check first value
exec('func = {0}(width)'.format(name))