def Eindex(self, E):
""" Return the closest energy index corresponding to the energy ``E``
Parameters
----------
E : float or int
if ``int``, return it-self, else return the energy index which is
closests to the energy.
"""
if isinstance(E, Integral):
return E
elif isinstance(E, _str):
# This will always be converted to a float
E = float(E)
idxE = np.abs(self.E - E).argmin()
ret_E = self.E[idxE]
if abs(ret_E - E) > 5e-3:
warn(self.__class__.__name__ + " requesting energy " +
"{0:.5f} eV, found {1:.5f} eV as the closest energy!".format(
E, ret_E))
elif abs(ret_E - E) > 1e-3:
info(self.__class__.__name__ + " requesting energy " +
"{0:.5f} eV, found {1:.5f} eV as the closest energy!".format(
E, ret_E))
return idxE
def undo_settings_group(self, group):
""" Takes the desired group of settings one step back, but the rest of the settings remain unchanged
At the moment it is a 'fake' undo function, since it actually updates the settings.
Parameters
-----------
group: str
the key of the settings group for which you want to undo its values.
"""
#Get the actual settings for that group
actualSettings = self.get_settings_group(group)
#Try to find any different values for the settings
for i in range(len(self.settings_history)):
previousSettings = self.get_settings_group(group, steps_back=i)
if previousSettings != actualSettings:
return self.update_settings(previousSettings)
else:
info(f"group={group} was never changed; cannot undo nothing.")
return self
def read_hamiltonian(self, **kwargs):
""" Returns a Hamiltonian from the underlying NetCDF file """
H = self._read_class_spin(Hamiltonian, **kwargs)
S = H._csr._D[:, H.S_idx]
Ef = self._value('Ef')[:] * Ry2eV
if Ef.size == 1:
Ef = np.tile(Ef, 2)
else:
dEf = np.diff(Ef)[0]
info(
repr(self) +
'.read_hamiltonian found a calculation with spin-dependent Fermi-levels: '
'dEf={:.4f} eV. '
'Both spin configurations are shifted to 0. This may change in future '
'versions of sisl.'.format(dEf))
sp = self._crt_grp(self, 'SPARSE')
for i in range(len(H.spin)):
# Create new container
h = np.array(sp.variables['H'][i, :], np.float64) * Ry2eV
# Correct for the Fermi-level, Ef == 0
if i < 2:
h -= Ef[i] * S[:]
H._csr._D[:, i] = h[:]
return H
def _r_basis_orb_indx(self):
f = self._tofile(self.get('SystemLabel',
default='siesta')) + '.ORB_INDX'
if isfile(f):
info(
SileInfo(
'Siesta basis information is read from {}, the radial functions are in accessible.'
.format(f)))
return orbindxSileSiesta(f).read_basis()
return None
def undo_setting(self, key):
""" Undoes only a particular setting and leaves the others unchanged
At the moment it is a 'fake' undo function, since it actually updates the settings.
Parameters
-----------
key: str
the key of the setting that you want to undo.
"""
i = self.settings_history.last_update_for(key)
if i is None:
info(f"key={key} was never changed; cannot undo nothing.")
self.update_settings(key=self.settings_history[key][i])
return self
def trigger_notification(title, message, sound="Submarine"):
""" Triggers a notification.
Will not do anything in Windows (oops!)
Parameters
-----------
title: str
message: str
sound: str
"""
if sys.platform == 'linux':
os.system(f"""notify-send "{title}" "{message}" """)
elif sys.platform == 'darwin':
sound_string = f'sound name "{sound}"' if sound else ''
os.system(f"""osascript -e 'display notification "{message}" with title "{title}" {sound_string}' """)
else:
info(f"sisl cannot issue notifications through the operating system ({sys.platform})")
def Eindex(self, E):
""" Return the closest energy index corresponding to the energy ``E``
Parameters
----------
E : float or int
if ``int``, return it-self, else return the energy index which is
closests to the energy.
"""
if isinstance(E, Integral):
return E
idxE = np.abs(self.E - E).argmin()
ret_E = self.E[idxE]
if abs(ret_E - E) > 5e-3:
warn(self.__class__.__name__ + " requesting energy " +
f"{E:.5f} eV, found {ret_E:.5f} eV as the closest energy!")
elif abs(ret_E - E) > 1e-3:
info(self.__class__.__name__ + " requesting energy " +
f"{E:.5f} eV, found {ret_E:.5f} eV as the closest energy!")
return idxE
def spoken_message(message):
""" Trigger a spoken message.
In linux espeak must be installed (sudo apt-get install espeak)
Will not do anything in Windows (oops!)
Parameters
-----------
title: str
message: str
sound: str
"""
if sys.platform == 'linux':
os.system(f"""espeak -s 150 "{message}" 2>/dev/null""")
elif sys.platform == 'darwin':
os.system(f"""osascript -e 'say "{message}"' """)
else:
info(f"sisl cannot issue notifications through the operating system ({sys.platform})")
def undo_settings(self, steps=1, run_updates=True):
""" Brings the settings back a number of steps
Parameters
------------
steps: int, optional
the number of steps you want to go back.
run_updates: bool, optional
whether we should run updates after updating the settings. If not, the settings
will be updated, but you won't see any change in the object.
"""
try:
diff = self.settings_history.diff_keys(-1, -steps - 1)
self.settings_history.undo(steps=steps)
if run_updates:
self._run_updates(diff)
except IndexError:
info(
f"This instance of {self.__class__.__name__} does not "
f"contain earlier settings as requested ({steps} step(s) back)"
)
return self
def Eindex(self, E):
""" Return the closest energy index corresponding to the energy ``E``
Parameters
----------
E : float or int or str
if `int`, return it-self, else return the energy index which is
closests to the energy.
For a `str` it will be parsed to a float and treated as such.
"""
if isinstance(E, Integral):
return E
elif isinstance(E, str):
E = float(E)
idxE = np.abs(self.E - E).argmin()
ret_E = self.E[idxE]
if abs(ret_E - E) > 5e-3:
warn(f"{self.__class__.__name__} requesting energy "
f"{E:.5f} eV, found {ret_E:.5f} eV as the closest energy!")
elif abs(ret_E - E) > 1e-3:
info(f"{self.__class__.__name__} requesting energy "
f"{E:.5f} eV, found {ret_E:.5f} eV as the closest energy!")
return idxE
def _r_dynamical_matrix_got(self, geometry, **kwargs):
""" In case the dynamical matrix is read from the file """
# Easier for creation of the sparsity pattern
from scipy.sparse import lil_matrix
# Default cutoff eV / Ang ** 2
cutoff = kwargs.get('cutoff', 1.e-4)
dtype = kwargs.get('dtype', np.float64)
nxyz = geometry.no
dyn = lil_matrix((nxyz, nxyz), dtype=dtype)
f, _ = self.step_to(self._keys['dyn'])
if not f:
info(
self.__class__.__name__ +
' tries to lookup the Dynamical matrix '
'using key "' + self._keys['dyn'] + '". '
'Use .set_dynamical_matrix_key(...) to search for different name.'
'This could not be found found in file: "{}".'.format(
self.file))
return None
# skip 1 line
self.readline()
# default range
dat = np.empty([nxyz], dtype=dtype)
i, j = 0, 0
nxyzm1 = nxyz - 1
while i < nxyz:
l = self.readline().strip()
if len(l) == 0:
break
# convert to float list
ls = [float(x) for x in l.split()]
k = min(12, nxyz - j)
# GULP only prints columns corresponding
# to a full row. Hence the remaining
# data must be nxyz - j - 1
dat[j:j + k] = ls[:k]
j += k
if j >= nxyz:
dyn[i, :] = dat[:]
# step row
i += 1
# reset column
j = 0
# clean-up for memory
del dat
# Convert to COO matrix format
dyn = dyn.tocoo()
# Construct mass ** (-.5), so we can check cutoff correctly
mass_sqrt = geometry.atoms.mass.repeat(3)**0.5
dyn.data[:] *= mass_sqrt[dyn.row] * mass_sqrt[dyn.col]
dyn.data[np_abs(dyn.data) < cutoff] = 0.
dyn.data[:] *= 1 / (mass_sqrt[dyn.row] * mass_sqrt[dyn.col])
dyn.eliminate_zeros()
return dyn
def param_circle(self, sc, N_or_dk, kR, normal, origo, loop=False):
r""" Create a parameterized k-point list where the k-points are generated on a circle around an origo
The generated circle is a perfect circle in the reciprocal space (Cartesian coordinates).
To generate a perfect circle in units of the reciprocal lattice vectors one can
generate the circle for a diagonal supercell with side-length :math:`2\pi`, see
example below.
Parameters
----------
sc : SuperCell, or SuperCellChild
the supercell used to construct the k-points
N_or_dk : int
number of k-points generated using the parameterization (if an integer),
otherwise it specifies the discretization length on the circle (in 1/Ang),
If the latter case will use less than 4 points a warning will be raised and
the number of points increased to 4.
kR : float
radius of the k-point. In 1/Ang
normal : array_like of float
normal vector to determine the circle plane
origo : array_like of float
origo of the circle used to generate the circular parameterization
loop : bool, optional
whether the first and last point are equal
Examples
--------
>>> sc = SuperCell([1, 1, 10, 90, 90, 60])
>>> bz = BrillouinZone.param_circle(sc, 10, 0.05, [0, 0, 1], [1./3, 2./3, 0])
To generate a circular set of k-points in reduced coordinates (reciprocal
>>> sc = SuperCell([1, 1, 10, 90, 90, 60])
>>> bz = BrillouinZone.param_circle(sc, 10, 0.05, [0, 0, 1], [1./3, 2./3, 0])
>>> bz_rec = BrillouinZone.param_circle(2*np.pi, 10, 0.05, [0, 0, 1], [1./3, 2./3, 0])
>>> bz.k[:, :] = bz_rec.k[:, :]
Returns
-------
BrillouinZone : with the parameterized k-points.
"""
if isinstance(N_or_dk, Integral):
N = N_or_dk
else:
# Calculate the required number of points
N = int(kR ** 2 * np.pi / N_or_dk + 0.5)
if N < 4:
N = 4
info('BrillouinZone.param_circle increased the number of circle points to 4.')
# Conversion object
bz = BrillouinZone(sc)
normal = _a.arrayd(normal)
origo = _a.arrayd(origo)
k_n = bz.tocartesian(normal)
k_o = bz.tocartesian(origo)
# Generate a preset list of k-points on the unit-circle
if loop:
radians = _a.aranged(N) / (N-1) * 2 * np.pi
else:
radians = _a.aranged(N) / N * 2 * np.pi
k = _a.emptyd([N, 3])
k[:, 0] = np.cos(radians)
k[:, 1] = np.sin(radians)
k[:, 2] = 0.
# Now generate the rotation
_, theta, phi = cart2spher(k_n)
if theta != 0:
pv = _a.arrayd([k_n[0], k_n[1], 0])
pv /= fnorm(pv)
q = Quaternion(phi, pv, rad=True) * Quaternion(theta, [0, 0, 1], rad=True)
else:
q = Quaternion(0., [0, 0, k_n[2] / abs(k_n[2])], rad=True)
# Calculate k-points
k = q.rotate(k)
k *= kR / fnorm(k).reshape(-1, 1)
k = bz.toreduced(k + k_o)
# The sum of weights is equal to the BZ area
W = np.pi * kR ** 2
w = np.repeat([W / N], N)
return BrillouinZone(sc, k, w)
def test_info_category():
with pytest.warns(sm.SislInfo):
sm.info('Information', sm.SislInfo)
def test_info_specific():
with pytest.warns(sm.SislInfo):
sm.info(sm.SislInfo('Info'))
def test_info_method():
with pytest.warns(sm.SislInfo):
sm.info('Information')
def initialize(self):
""" Initialize the internal data-arrays used for efficient calculation of the real-space quantities
This method should first be called *after* all options has been specified.
If the user hasn't specified the ``bz`` value as an option this method will update the internal
integration Brillouin zone based on the ``dk`` option.
"""
# Try and guess the directions
unfold = self._unfold
nsc = self.parent.nsc.copy()
axes = self._options['axes']
if axes is None:
if nsc[2] == 1:
axes = _a.arrayi([0, 1])
elif nsc[1] == 1:
axes = _a.arrayi([0, 2])
elif nsc[0] == 1:
axes = _a.arrayi([1, 2])
else:
raise ValueError(self.__class__.__name__ + '.initialize currently only supports a 2D real-space self-energy, hence the MonkhorstPack grid should reflect only 2 periodic directions.')
self._options['axes'] = axes
# Check that we have periodicity along the chosen axes
nsc_sum = nsc[axes].sum()
if nsc_sum == 1:
raise ValueError(self.__class__.__name__ + '.initialize found no periodic directions for the chosen integration axes: {} and {}.'.format(*nsc[axes]))
elif nsc_sum < 6:
raise ValueError((self.__class__.__name__ + '.initialize found one periodic direction '
'out of two for the chosen integration axes: {} and {}. '
'For 1D systems the regular surface self-energy method is appropriate.').format(*nsc[axes]))
if self._options['semi_axis'] is None and self._options['k_axis'] is None:
# None of the axis has been described
if nsc[axes[0]] > 3:
k_ax = axes[0]
s_ax = axes[1]
elif nsc[axes[1]] > 3:
k_ax = axes[1]
s_ax = axes[0]
else:
# Choose the direction of k to be the smallest shortest
sc = self.parent.sc.tile(unfold[axes[0]], axes[0]).tile(unfold[axes[1]], axes[1])
rcell = fnorm(sc.rcell)[axes]
k_ax = axes[np.argmax(rcell)]
if k_ax == axes[0]:
s_ax = axes[1]
else:
s_ax = axes[0]
self._options['semi_axis'] = s_ax
self._options['k_axis'] = k_ax
s_ax = 'ABC'[s_ax]
k_ax = 'ABC'[k_ax]
info(self.__class__.__name__ + '.initialize determined the semi-inf- and k-directions to be: {} and {}'.format(s_ax, k_ax))
elif self._options['k_axis'] is None:
s_ax = self._options['semi_axis']
if s_ax == axes[0]:
k_ax = axes[1]
else:
k_ax = axes[0]
self._options['k_axis'] = k_ax
k_ax = 'ABC'[k_ax]
info(self.__class__.__name__ + '.initialize determined the k direction to be: {}'.format(k_ax))
elif self._options['semi_axis'] is None:
k_ax = self._options['k_axis']
if k_ax == axes[0]:
s_ax = axes[1]
else:
s_ax = axes[0]
self._options['semi_axis'] = s_ax
s_ax = 'ABC'[s_ax]
info(self.__class__.__name__ + '.initialize determined the semi-infinite direction to be: {}'.format(s_ax))
k_ax = self._options['k_axis']
s_ax = self._options['semi_axis']
if nsc[s_ax] != 3:
raise ValueError(self.__class__.__name__ + '.initialize found the self-energy direction to be '
'incompatible with the parent object. It *must* have 3 supercells along the '
'semi-infinite direction.')
P0 = self.real_space_parent()
V_atoms = self.real_space_coupling(True)[1]
self._calc = {
# The below algorithm requires the direction to be negative
# if changed, B, C should be reversed below
'SE': RecursiveSI(self.parent, '-' + 'ABC'[s_ax], eta=self._options['eta']),
# Used to calculate the real-space self-energy
'P0': P0.Pk(), # in sparse format
'S0': P0.Sk(), # in sparse format
# Orbitals in the coupling atoms
'orbs': P0.a2o(V_atoms, True).reshape(-1, 1),
}
# Update the BrillouinZone integration grid in case it isn't specified
if self._options['bz'] is None:
# Update the integration grid
# Note this integration grid is based on the big system.
sc = self.parent.sc.tile(unfold[axes[0]], axes[0]).tile(unfold[axes[1]], axes[1])
rcell = fnorm(sc.rcell)[k_ax]
nk = [1] * 3
nk[k_ax] = int(self._options['dk'] * rcell)
self._options['bz'] = MonkhorstPack(sc, nk, trs=self._options['trs'])
info(self.__class__.__name__ + '.initialize determined the number of k-points: {}'.format(nk[k_ax]))
def _r_dynamical_matrix_got(self, geom, **kwargs):
""" In case the dynamical matrix is read from the file """
# Easier for creation of the sparsity pattern
from scipy.sparse import lil_matrix
# Default cutoff eV / Ang ** 2
cutoff = kwargs.get('cutoff', 1.e-4)
dtype = kwargs.get('dtype', np.float64)
no = geom.no
dyn = lil_matrix((no, no), dtype=dtype)
f, _ = self.step_to(self._keys['dyn'])
if not f:
info(
self.__class__.__name__ +
' tries to lookup the Dynamical matrix '
'using key "' + self._keys['dyn'] + '". '
'Use .set_dynamical_matrix_key(...) to search for different name.'
'This could not be found found in file: "{}".'.format(
self.file))
return None
# skip 1 line
self.readline()
# default range
dat = np.empty([no], dtype=dtype)
i, j = 0, 0
while True:
l = self.readline().strip()
if len(l) == 0:
break
# convert to float list
ls = [float(x) for x in l.split()]
if j + 12 <= no:
# Here the full line can fit for the same row
dat[j:j + 12] = ls[:12]
j += 12
if j >= no:
dyn[i, :] = dat[:]
# step row
i += 1
# reset column
j = 0
if i >= no:
break
else:
# add the values (12 values == 3*4)
# for atoms on each line
for k in [0, 1, 2, 3]:
dat[j:j + 3] = ls[k * 3:(k + 1) * 3]
j += 3
if j >= no:
# Clear those below the cutoff
dyn[i, :] = dat[:]
i += 1
j = 0
if i >= no:
break
# clean-up for memory
del dat
# Convert to COO matrix format
dyn = dyn.tocoo()
# Construct mass ** (-.5), so we can check cutoff correctly
mass_sqrt = np.array(geom.atoms.mass, np.float64).repeat(3)**0.5
dyn.data[:] *= mass_sqrt[dyn.row] * mass_sqrt[dyn.col]
dyn.data[np_abs(dyn.data) < cutoff] = 0.
dyn.data[:] *= 1 / (mass_sqrt[dyn.row] * mass_sqrt[dyn.col])
dyn.eliminate_zeros()
return dyn
def replace(self, k, mp):
r""" Replace a k-point with a new set of k-points from a Monkhorst-Pack grid
This method tries to replace an area corresponding to `mp.size` around the k-point `k`
such that the k-points are replaced.
This enables one to zoom in on specific points in the Brillouin zone for detailed analysis.
Parameters
----------
k : array_like
k-point in this object to replace
mp : MonkhorstPack
object containing the replacement k-points.
Examples
--------
This example creates a zoomed-in view of the :math:`\Gamma`-point by replacing it with
a 3x3x3 Monkhorst-Pack grid.
>>> sc = SuperCell(1.)
>>> mp = MonkhorstPack(sc, [3, 3, 3])
>>> mp.replace([0, 0, 0], MonkhorstPack(sc, [3, 3, 3], size=1./3))
This example creates a zoomed-in view of the :math:`\Gamma`-point by replacing it with
a 4x4x4 Monkhorst-Pack grid.
>>> sc = SuperCell(1.)
>>> mp = MonkhorstPack(sc, [3, 3, 3])
>>> mp.replace([0, 0, 0], MonkhorstPack(sc, [4, 4, 4], size=1./3))
This example creates a zoomed-in view of the :math:`\Gamma`-point by replacing it with
a 4x4x1 Monkhorst-Pack grid.
>>> sc = SuperCell(1.)
>>> mp = MonkhorstPack(sc, [3, 3, 3])
>>> mp.replace([0, 0, 0], MonkhorstPack(sc, [4, 4, 1], size=1./3))
Raises
------
SislError : if the size of the replacement `MonkhorstPack` grid is not compatible with the
k-point spacing in this object.
"""
# First we find all k-points within k +- mp.size
# Those are the points we wish to remove.
# Secondly we need to ensure that the k-points we remove are occupying *exactly*
# the Brillouin zone we wish to replace.
if not isinstance(mp, MonkhorstPack):
raise ValueError('Object `mp` is not a MonkhorstPack object')
# We can easily figure out the BZ that each k-point is averaging
k_vol = self._size / self._diag
# Compare against the size of this one
# Since we can remove more than one k-point, we require that the
# size of the replacement MP is an integer multiple of the
# k-point volumes.
k_int = mp._size / k_vol
if not np.allclose(np.rint(k_int), k_int):
raise SislError(self.__class__.__name__ + '.reduce could not replace k-point, BZ '
'volume replaced is not equivalent to the inherent k-point volume.')
k_int = np.rint(k_int)
# 1. find all k-points
k = self.in_primitive(k).reshape(1, 3)
dk = (mp._size / 2).reshape(1, 3)
# Find all points within [k - dk; k + dk]
# Since the volume of each k-point is non-zero we know that no k-points will be located
# on the boundary.
# This does remove boundary points because we shift everything into the positive
# plane.
diff_k = self.in_primitive(self.k % 1. - k % 1.)
idx = np.logical_and.reduce(np.abs(diff_k) <= dk, axis=1).nonzero()[0]
if len(idx) == 0:
raise SislError(self.__class__.__name__ + '.reduce could not find any points to replace.')
# Now we have the k-points we need to remove
# Figure out if the total weight is consistent
total_weight = self.weight[idx].sum()
replace_weight = mp.weight.sum()
if abs(total_weight - replace_weight) < 1e-8:
weight_factor = 1.
elif abs(total_weight - replace_weight * 2) < 1e-8:
weight_factor = 2.
if self._trs < 0:
info(self.__class__.__name__ + '.reduce assumes that the replaced k-point has double weights.')
else:
print('k-point to replace:')
print(' ', k.ravel())
print('delta-k:')
print(' ', dk.ravel())
print('Found k-indices that will be replaced:')
print(' ', idx)
print('k-points replaced:')
print(self.k[idx, :])
raise SislError(self.__class__.__name__ + '.reduce could not assert the weights are consistent during replacement.')
self._k = np.delete(self._k, idx, axis=0)
self._w = np.delete(self._w, idx)
# Append the new k-points and weights
self._k = np.concatenate((self._k, mp._k), axis=0)
self._w = np.concatenate((self._w, mp._w * weight_factor))
def read_grid(self, spin=0, name='gridfunc', *args, **kwargs):
""" Reads a grid in the current Siesta.grid.nc file
Enables the reading and processing of the grids created by Siesta
Parameters
----------
spin : int or array_like, optional
specify the retrieved values
name : str, optional
the name for the grid-function (do not supply for standard Siesta output)
geometry: Geometry, optional
add the Geometry to the Grid
"""
# Default to *index* variable
spin = kwargs.get('index', spin)
# Determine the name of this file
f = osp.basename(self.file)
# File names are made up of
# ElectrostaticPotential.grid.nc
# So the first one should be ElectrostaticPotential
try:
# <>.grid.nc
base = f.split('.')[-3]
except:
base = 'None'
# Unit-conversion
BohrC2AngC = Bohr2Ang**3
unit = {
'Rho': 1. / BohrC2AngC,
'DeltaRho': 1. / BohrC2AngC,
'RhoXC': 1. / BohrC2AngC,
'RhoInit': 1. / BohrC2AngC,
'Chlocal': 1. / BohrC2AngC,
'TotalCharge': 1. / BohrC2AngC,
'BaderCharge': 1. / BohrC2AngC,
'ElectrostaticPotential': Ry2eV,
'TotalPotential': Ry2eV,
'Vna': Ry2eV,
}.get(base, None)
# Fall-back
if unit is None:
unit = 1.
show_info = True
else:
show_info = False
# Swap as we swap back in the end
sc = self.read_supercell().swapaxes(0, 2)
# Create the grid
nx = len(self._dimension('n1'))
ny = len(self._dimension('n2'))
nz = len(self._dimension('n3'))
if name is None:
v = self._variable('gridfunc')
else:
v = self._variable(name)
# Create the grid, Siesta uses periodic, always
grid = Grid([nz, ny, nx],
bc=Grid.PERIODIC,
sc=sc,
dtype=v.dtype,
geometry=kwargs.get("geometry", None))
if v.ndim == 3:
grid.grid[:, :, :] = v[:, :, :] * unit
elif isinstance(spin, Integral):
grid.grid[:, :, :] = v[spin, :, :, :] * unit
else:
if len(spin) > v.shape[0]:
raise SileError(
f"{self.__class__.__name__}.read_grid requires spin to be an integer or "
"an array of length equal to the number of spin components."
)
grid.grid[:, :, :] = v[0, :, :, :] * spin[0] * unit
for i, scale in enumerate(spin[1:]):
grid.grid[:, :, :] += v[1 + i, :, :, :] * scale * unit
if show_info:
info(
f"{self.__class__.__name__}.read_grid cannot determine the units of the grid. "
"The units may not be in sisl units.")
# Read the grid, we want the z-axis to be the fastest
# looping direction, hence x,y,z == 0,1,2
return grid.swapaxes(0, 2)
def wavefunction(v,
grid,
geometry=None,
k=None,
spinor=0,
spin=None,
eta=False):
r""" Add the wave-function (`Orbital.psi`) component of each orbital to the grid
This routine calculates the real-space wave-function components in the
specified grid.
This is an *in-place* operation that *adds* to the current values in the grid.
It may be instructive to check that an eigenstate is normalized:
>>> grid = Grid(...) # doctest: +SKIP
>>> psi(state, grid) # doctest: +SKIP
>>> (np.abs(grid.grid) ** 2).sum() * grid.dvolume == 1. # doctest: +SKIP
Note: To calculate :math:`\psi(\mathbf r)` in a unit-cell different from the
originating geometry, simply pass a grid with a unit-cell smaller than the originating
supercell.
The wavefunctions are calculated in real-space via:
.. math::
\psi(\mathbf r) = \sum_i\phi_i(\mathbf r) |\psi\rangle_i \exp(-i\mathbf k \mathbf R)
While for non-collinear/spin-orbit calculations the wavefunctions are determined from the
spinor component (`spinor`)
.. math::
\psi_{\alpha/\beta}(\mathbf r) = \sum_i\phi_i(\mathbf r) |\psi_{\alpha/\beta}\rangle_i \exp(-i\mathbf k \mathbf R)
where ``spinor in [0, 1]`` determines :math:`\alpha` or :math:`\beta`, respectively.
Notes
-----
Currently this method only works for :math:`\Gamma` states
Parameters
----------
v : array_like
coefficients for the orbital expansion on the real-space grid.
If `v` is a complex array then the `grid` *must* be complex as well.
grid : Grid
grid on which the wavefunction will be plotted.
If multiple eigenstates are in this object, they will be summed.
geometry : Geometry, optional
geometry where the orbitals are defined. This geometry's orbital count must match
the number of elements in `v`.
If this is ``None`` the geometry associated with `grid` will be used instead.
k : array_like, optional
k-point associated with wavefunction, by default the inherent k-point used
to calculate the eigenstate will be used (generally shouldn't be used unless the `EigenstateElectron` object
has not been created via `Hamiltonian.eigenstate`).
spinor : int, optional
the spinor for non-collinear/spin-orbit calculations. This is only used if the
eigenstate object has been created from a parent object with a `Spin` object
contained, *and* if the spin-configuration is non-collinear or spin-orbit coupling.
Default to the first spinor component.
spin : Spin, optional
specification of the spin configuration of the orbital coefficients. This only has
influence for non-collinear wavefunctions where `spinor` choice is important.
eta : bool, optional
Display a console progressbar.
"""
if geometry is None:
geometry = grid.geometry
warn(
'wavefunction was not passed a geometry associated, will use the geometry associated with the Grid.'
)
if geometry is None:
raise SislError(
'wavefunction did not find a usable Geometry through keywords or the Grid!'
)
# In case the user has passed several vectors we sum them to plot the summed state
if v.ndim == 2:
v = v.sum(0)
if spin is None:
if len(v) // 2 == geometry.no:
# We can see from the input that the vector *must* be a non-collinear calculation
v = v.reshape(-1, 2)[:, spinor]
info(
'wavefunction assumes the input wavefunction coefficients to originate from a non-collinear calculation!'
)
elif spin.kind > Spin.POLARIZED:
# For non-collinear cases the user selects the spinor component.
v = v.reshape(-1, 2)[:, spinor]
if len(v) != geometry.no:
raise ValueError(
"wavefunction require wavefunction coefficients corresponding to number of orbitals in the geometry."
)
# Check for k-points
k = _a.asarrayd(k)
kl = (k**2).sum()**0.5
has_k = kl > 0.000001
if has_k:
raise NotImplementedError(
'wavefunction for k != Gamma does not produce correct wavefunctions!'
)
# Check that input/grid makes sense.
# If the coefficients are complex valued, then the grid *has* to be
# complex valued.
# Likewise if a k-point has been passed.
is_complex = np.iscomplexobj(v) or has_k
if is_complex and not np.iscomplexobj(grid.grid):
raise SislError(
"wavefunction input coefficients are complex, while grid only contains real."
)
if is_complex:
psi_init = _a.zerosz
else:
psi_init = _a.zerosd
# Extract sub variables used throughout the loop
shape = _a.asarrayi(grid.shape)
dcell = grid.dcell
ic = grid.sc.icell * shape.reshape(1, -1)
geom_shape = dot(ic, geometry.cell.T).T
# In the following we don't care about division
# So 1) save error state, 2) turn off divide by 0, 3) calculate, 4) turn on old error state
old_err = np.seterr(divide='ignore', invalid='ignore')
addouter = add.outer
def idx2spherical(ix, iy, iz, offset, dc, R):
""" Calculate the spherical coordinates from indices """
rx = addouter(addouter(ix * dc[0, 0], iy * dc[1, 0]),
iz * dc[2, 0] - offset[0]).ravel()
ry = addouter(addouter(ix * dc[0, 1], iy * dc[1, 1]),
iz * dc[2, 1] - offset[1]).ravel()
rz = addouter(addouter(ix * dc[0, 2], iy * dc[1, 2]),
iz * dc[2, 2] - offset[2]).ravel()
# Total size of the indices
n = rx.shape[0]
# Reduce our arrays to where the radius is "fine"
idx = indices_le(rx**2 + ry**2 + rz**2, R**2)
rx = rx[idx]
ry = ry[idx]
rz = rz[idx]
xyz_to_spherical_cos_phi(rx, ry, rz)
return n, idx, rx, ry, rz
# Figure out the max-min indices with a spacing of 1 radian
rad1 = pi / 180
theta, phi = ogrid[-pi:pi:rad1, 0:pi:rad1]
cphi, sphi = cos(phi), sin(phi)
ctheta_sphi = cos(theta) * sphi
stheta_sphi = sin(theta) * sphi
del sphi
nrxyz = (theta.size, phi.size, 3)
del theta, phi, rad1
# First we calculate the min/max indices for all atoms
idx_mm = _a.emptyi([geometry.na, 2, 3])
rxyz = _a.emptyd(nrxyz)
rxyz[..., 0] = ctheta_sphi
rxyz[..., 1] = stheta_sphi
rxyz[..., 2] = cphi
# Reshape
rxyz.shape = (-1, 3)
idx = dot(ic, rxyz.T)
idxm = idx.min(1).reshape(1, 3)
idxM = idx.max(1).reshape(1, 3)
del ctheta_sphi, stheta_sphi, cphi, idx, rxyz, nrxyz
origo = grid.sc.origo.reshape(1, -1)
for atom, ia in geometry.atom.iter(True):
if len(ia) == 0:
continue
R = atom.maxR()
# Now do it for all the atoms to get indices of the middle of
# the atoms
# The coordinates are relative to origo, so we need to shift (when writing a grid
# it is with respect to origo)
xyz = geometry.xyz[ia, :] - origo
idx = dot(ic, xyz.T).T
# Get min-max for all atoms
idx_mm[ia, 0, :] = idxm * R + idx
idx_mm[ia, 1, :] = idxM * R + idx
# Now we have min-max for all atoms
# When we run the below loop all indices can be retrieved by looking
# up in the above table.
# Before continuing, we can easily clean up the temporary arrays
del origo, idx
aranged = _a.aranged
# In case this grid does not have a Geometry associated
# We can *perhaps* easily attach a geometry with the given
# atoms in the unit-cell
sc = grid.sc.copy()
if grid.geometry is None:
# Create the actual geometry that encompass the grid
ia, xyz, _ = geometry.within_inf(sc)
if len(ia) > 0:
grid.set_geometry(Geometry(xyz, geometry.atom[ia], sc=sc))
# Instead of looping all atoms in the supercell we find the exact atoms
# and their supercell indices.
add_R = _a.zerosd(3) + geometry.maxR()
# Calculate the required additional vectors required to increase the fictitious
# supercell by add_R in each direction.
# For extremely skewed lattices this will be way too much, hence we make
# them square.
o = sc.toCuboid(True)
sc = SuperCell(o._v, origo=o.origo) + np.diag(2 * add_R)
sc.origo -= add_R
# Retrieve all atoms within the grid supercell
# (and the neighbours that connect into the cell)
IA, XYZ, ISC = geometry.within_inf(sc)
r_k = dot(geometry.rcell, k)
r_k_cell = dot(r_k, geometry.cell)
phase = 1
# Retrieve progressbar
eta = tqdm_eta(len(IA), 'wavefunction', 'atom', eta)
# Loop over all atoms in the grid-cell
for ia, xyz, isc in zip(IA, XYZ - grid.origo.reshape(1, 3), ISC):
# Get current atom
atom = geometry.atom[ia]
# Extract maximum R
R = atom.maxR()
if R <= 0.:
warn("Atom '{}' does not have a wave-function, skipping atom.".
format(atom))
eta.update()
continue
# Get indices in the supercell grid
idx = (isc.reshape(3, 1) * geom_shape).sum(0)
idxm = floor(idx_mm[ia, 0, :] + idx).astype(int32)
idxM = ceil(idx_mm[ia, 1, :] + idx).astype(int32) + 1
# Fast check whether we can skip this point
if idxm[0] >= shape[0] or idxm[1] >= shape[1] or idxm[2] >= shape[2] or \
idxM[0] <= 0 or idxM[1] <= 0 or idxM[2] <= 0:
eta.update()
continue
# Truncate values
if idxm[0] < 0:
idxm[0] = 0
if idxM[0] > shape[0]:
idxM[0] = shape[0]
if idxm[1] < 0:
idxm[1] = 0
if idxM[1] > shape[1]:
idxM[1] = shape[1]
if idxm[2] < 0:
idxm[2] = 0
if idxM[2] > shape[2]:
idxM[2] = shape[2]
# Now idxm/M contains min/max indices used
# Convert to spherical coordinates
n, idx, r, theta, phi = idx2spherical(aranged(idxm[0], idxM[0]),
aranged(idxm[1], idxM[1]),
aranged(idxm[2], idxM[2]), xyz,
dcell, R)
# Get initial orbital
io = geometry.a2o(ia)
if has_k:
phase = np.exp(-1j * (dot(r_k_cell, isc)))
# TODO
# Possibly the phase should be an additional
# array for the position in the unit-cell!
# + np.exp(-1j * dot(r_k, spher2cart(r, theta, np.arccos(phi)).T) )
# Allocate a temporary array where we add the psi elements
psi = psi_init(n)
# Loop on orbitals on this atom, grouped by radius
for os in atom.iter(True):
# Get the radius of orbitals (os)
oR = os[0].R
if oR <= 0.:
warn(
"Orbital(s) '{}' does not have a wave-function, skipping orbital!"
.format(os))
# Skip these orbitals
io += len(os)
continue
# Downsize to the correct indices
if R - oR < 1e-6:
idx1 = idx.view()
r1 = r.view()
theta1 = theta.view()
phi1 = phi.view()
else:
idx1 = indices_le(r, oR)
# Reduce arrays
r1 = r[idx1]
theta1 = theta[idx1]
phi1 = phi[idx1]
idx1 = idx[idx1]
# Loop orbitals with the same radius
for o in os:
# Evaluate psi component of the wavefunction and add it for this atom
psi[idx1] += o.psi_spher(r1, theta1, phi1,
cos_phi=True) * (v[io] * phase)
io += 1
# Clean-up
del idx1, r1, theta1, phi1, idx, r, theta, phi
# Convert to correct shape and add the current atom contribution to the wavefunction
psi.shape = idxM - idxm
grid.grid[idxm[0]:idxM[0], idxm[1]:idxM[1], idxm[2]:idxM[2]] += psi
# Clean-up
del psi
# Step progressbar
eta.update()
eta.close()
# Reset the error code for division
np.seterr(**old_err)