def neededVectors(self,
short_length,
centers=((0,0,0),),
):
centers = np.array(centers)
max_centers = np.max(centers, axis=0)
min_centers = np.min(centers, axis=0)
extent = max_centers - min_centers
v1, v2 = self.unitCell()
l1 = vectorLength(v1)
l2 = vectorLength(v2)
size = abs(np.dot(extent + short_length, v1/l1))
n1 = int(np.ceil(size/l1))
v1t = np.array([v1[1], -v1[0], 0])
v1t /= vectorLength(v1t)
test_vector = np.dot(v2, v1t)*v1t
lt = vectorLength(test_vector)
size = abs(np.dot(extent+short_length, test_vector/lt))
n2 = int(np.ceil(size/lt))
vectors = np.array([(n1, 0), (0, n2)])
return vectors
def relaxationFactor(self):
if self.relaxation() is None:
return 1.0
lr = vectorLength(self.relaxation().get_cell()[2])
lu = vectorLength(self.__atoms.get_cell()[2])
return lr/lu
def defaultParameters(self, parameters=DEFAULT, centers=((0,0,0), )):
if parameters is DEFAULT:
parameters = self.surface().defaultParameters()
parameters = parameters.toDictionary()
parameters.pop('kpts')
parameters.pop('vectors')
parameters = SurfaceLineDefectParameters(**parameters)
vectors = parameters['vectors']
if vectors is DEFAULT:
new_centers = self.rattleAtoms().get_positions()
tmp_centers = centers
centers = np.zeros((len(tmp_centers)+len(new_centers), 3), float)
centers[:len(tmp_centers)] = tmp_centers
centers[len(tmp_centers):] = new_centers
s_parameters = self.surface().defaultParameters(
parameters=parameters,
centers=centers,
)
vectors = np.array(s_parameters['vectors'])
parameters = parameters.copy(vectors=vectors)
if len(self.periodicity()) == 1:
vp = self.periodicity()[0]
v1, v2 = parameters['vectors']
if (vectorLength(np.cross(vp, v1))==0):
v1 = vp
elif (vectorLength(np.cross(vp, v2))==0):
v2 = vp
else:
raise Exception
vectors = np.array((v1, v2))
parameters = parameters.copy(vectors=vectors)
kpts = parameters['kpts']
if kpts is DEFAULT:
s_parameters = self.surface().defaultParameters(
parameters=parameters,
)
kpts = s_parameters['kpts']
parameters = parameters.copy(kpts=kpts)
cell_size = parameters['cell_size']
if cell_size is DEFAULT:
parameters = parameters.copy(cell_size=45)
return parameters
def atoms(self, constrained=True, parameters=DEFAULT):
if parameters is DEFAULT:
parameters = self.parameters()
parameters = self.defaultParameters(parameters)
vectors = np.array(parameters['vectors'])
lengths = vectorLength(vectors, 1)
assert lengths.all()
atoms = self.__atoms.copy()
pos = atoms.get_positions()
size = np.array([pos[:, i].max() - pos[:,i].min() for i in range(3)])
size = size + parameters['length_scales']['correlation_length']
repeats = (1, 1, vectors[0][0])
vectors = atoms.cell[2] * vectors[0][0]
atoms = atoms.repeat(repeats)
atoms.set_cell(size)
atoms.cell[2] = vectors
atoms = removeCopies(atoms)
atoms = orderAtoms(atoms)
atoms = self.makeAtomsRelaxed(atoms, self.relaxation())
return atoms
def write(self):
method = self.method()
images = self.getOriginalImages()
new_images = []
for i in range(len(images)-1):
initial, final = images[i:i+2]
diff = final.positions - initial.positions
diff = vectorLength(diff, 1)
n_images = int(np.ceil(diff.max()/0.3)) - 1
print 'n_images=%d' % n_images
t_images = [initial]
for j in range(n_images):
temp = t_images[0].copy()
t_images.append(temp)
t_images.append(final)
neb = NEB(t_images)
neb.interpolate()
new_images.extend(neb.images[:-1])
new_images.append(images[-1])
neb = NEB(new_images)
kpts = self.baseTask().parameters().kpts()
self.method().writeNEB(
runfile=self.runFile(),
neb=neb,
kpts=kpts,
)
def __init__(self, system, step, end, direction=(0,0,1)):
self.__step = step
self.__end = end
self.__relaxed_value = None
self.__system = system
direction = np.array(direction, float)
self.__diretion = direction/vectorLength(direction)
API.HasInputs.__init__(self, inputs=system.tasks())
def determineWaveFunctionRange(
rho,
r,
point_density=4,
density_range=(-3.5, -2.5),
):
min_value = 10**(density_range[0])
max_value = 10**(density_range[1])
r = np.array(r)
dh_cell = gridSpacingCell(r)
cell = np.array([r[:, -1, 0, 0], r[:, 0, -1, 0], r[:, 0, 0, -1]]) - r[:, 0, 0, 0]
assert max_value > min_value
sh = rho.shape
t_density = np.reshape(rho, (sh[0]*sh[1], sh[2]))
d_min = t_density.min(axis=0)
d_max = t_density.max(axis=0)
z_values = r[2][0,0,:]
sh = len(z_values)
z_values = (z_values + cell[2, 2]/2.0) % cell[2, 2] - cell[2, 2]/2.0
z_values = np.roll(z_values, sh/2)
d_min = np.roll(d_min, sh/2)
d_max = np.roll(d_max, sh/2)
take = z_values > - 5
take = np.logical_and(take, d_min < max_value)
take = np.logical_and(take, d_max > min_value)
z_values = z_values[take]
d_min = d_min[take]
d_max = d_max[take]
padding = dh_cell[2, 2]
z_span = (z_values.min() - padding, z_values.max() + padding)
shape = np.zeros(3, int)
shape[0] = np.ceil(vectorLength(cell[0])*point_density)
shape[1] = np.ceil(vectorLength(cell[1])*point_density)
shape[2] = np.ceil((z_span[1] - z_span[0])*point_density + 1)
X, Y, Z = xy_z(shape=shape, cell=cell, z_span=z_span)
X -= (X.max() - X.min())/2
Y -= (Y.max() - Y.min())/2
return np.array((X, Y, Z))
def getBeyondRangeMask(atoms, position, radius):
atoms = atoms.copy()
atoms.translate(-position)
middle = np.sum(atoms.get_cell(), axis=0)/2.
atoms.translate(middle)
atoms = wrap(atoms)
atoms.translate(-middle)
beyond_range = vectorLength(atoms.get_positions(), 1) > radius
return beyond_range
def makeSample(crystal, vectors):
radius = numpy.max(vectorLength(vectors))
repeats = findNeededRepetitions(crystal.unitCell(), radius)
atoms = crystal.toAseAtoms()
atoms = atoms.repeat(repeats)
atoms.set_cell(vectors)
atoms = wrap(atoms)
atoms = removeCopies(atoms)
return atoms
def findIndices(find_atoms, atoms, tolerance=1e-5):
indices = []
for pos in find_atoms.positions:
diff = vectorLength(atoms.positions - pos, 1)
argmin = np.argmin(diff)
if diff[argmin] > tolerance:
indices.append(None)
else:
indices.append(argmin)
return indices
def setCellAndPBC(atoms, periodicity):
dim = len(periodicity)
if dim == 0:
pass
elif dim == 1:
v0 = np.dot(periodicity, atoms.cell[:2])[0]
pro = [vectorLength(np.cross(v0, v)) for v in atoms.cell[:2]]
v1 = atoms.cell[np.argmax(pro)]
cell = np.array([v0, v1, atoms.cell[2]])
atoms.set_cell(cell)
atoms.set_pbc([True]*dim + [False]*(3-dim))
def makeAtomsRelaxed(atoms, relaxed_atoms, tolerance=1.0, cell=None, change=None, correct_drift=False):
atoms = atoms.copy()
if relaxed_atoms is None:
return atoms
if change is None:
change = np.ones(len(atoms), np.bool)
if cell is None:
cell = atoms.get_cell()
cell[relaxed_atoms.pbc] = relaxed_atoms.cell[relaxed_atoms.pbc]
drift = np.zeros(3, np.float)
used = np.zeros(len(relaxed_atoms), np.bool)
changed = []
if relaxed_atoms is not None:
# Find relaxed atoms closest to originals.
for i, atom in enumerate(atoms):
if not change[i]:
continue
mask = np.array([r_atom.symbol == atom.symbol for r_atom in relaxed_atoms])
mask = np.logical_and(mask, np.logical_not(used))
if mask.sum() == 0:
continue
diff = relaxed_atoms.positions[mask] - atom.position
diff = minimalDistance(diff, cell[relaxed_atoms.pbc])
index = vectorLength(diff, 1).argmin()
adjustment = diff[index]
if vectorLength(adjustment) < tolerance:
drift += adjustment
real_index = np.arange(len(relaxed_atoms))[mask][index]
used[real_index] = False
changed.append(i)
atom.position += adjustment
if correct_drift:
changed = np.array(changed)
drift /= len(changed)
atoms.positions[changed] -= drift
return atoms
def notestSaveReadWaveFunctionsTest(self):
band = 21
kn = 4
ws = 2
potential = Topographic(voltage=-2)
rho, r, dh_cell = readCubeDensity(label=test_label)
dh = np.array(map(vectorLength, dh_cell))
rho = rho.sum(axis=0)
c, variables, domain = surfaceIntegrator(rho=rho, variables=r, rho0=1e-3, DS=1)
thick_surface = vectorLength(c, axis=0) > 1e-9
take_z = thick_surface.sum(axis=0)
take_z = take_z.sum(axis=0) > 0
wf, r, dh_cell = readCubeWavefunction(label=test_label, band=band, kn=kn)
EF, eigs= readEigenvalues(label=test_label)
kpts = readKpoints(label=test_label)
energy = eigs[kn-1, band-1, 0]
we = STMWeighting(energies=[energy], potential=potential, EF=EF)
we = we[0]
kpt, wk = kpts[kn-1]
kappa = getVacuumDecayRate(energy)
eikr = phaseFactor(kpt, r)
u = wf/eikr
grad_u = np.array(np.gradient(u, *dh))
A = (c*grad_u).sum(axis=0)
B = u*c
A=A[:,:,take_z]
B=B[:,:,:,take_z]
r=r[:,:,:,take_z]
u, variables = propagateWaveFunction(
A=A,
B=B,
kpt=kpt,
r=r,
kappa=kappa,
height=10,
)
weight = we*ws*wk
Itest = weight*abs(u)**2
self.assertFalse(os.path.exists(testfile))
saveWavefunctionsToPlane(filename=testfile, label=test_label)
self.assertTrue(os.path.exists(testfile))
f = netcdf.netcdf_file(testfile, 'r')
self.assertTrue(len(f.variables.keys()) >0)
f.close()
I, r = STMFromFile(
label=join(test_folder, 'test'),
potentials=[potential],
cells=None,
)
self.assertArraysEqual(np.log(Itest[0,0]), np.log(I[0,0,0]), 5)
def modifyAtoms(self, atoms, indices):
direction = self.direction()
diff = atoms.positions[indices].mean(axis=0)
diff = np.dot(diff, direction)
move = (self.difference() - diff)*direction
atoms.positions[indices] += move
w_to = 1
mode = np.zeros(3*len(atoms))
for index1 in indices:
mode[3*index1: 3*(index1+1)] = w_to*direction
mode /= vectorLength(mode)
constraint = FixedMode(mode)
atoms.constraints.append(constraint)
return atoms
def findPeriodicallyEqualAtoms(atoms, other_atoms):
center = atoms.positions.mean(axis=0)
center, remain = convertToBasis(center, other_atoms.cell)
center = (np.array([.5, .5, .5]) - center)[0]
other_atoms = wrap(other_atoms, center=center)
cell = other_atoms.get_cell()
pbc = atoms.get_pbc()
cell = atoms.cell[pbc]
group = -np.ones(len(other_atoms), dtype=np.int)
for i, atom in enumerate(atoms):
diff = other_atoms.get_positions() - atom.position
pos = minimalDistance(diff, cell)
mask = vectorLength(pos, 1) < 1e-5
indices = np.arange(len(other_atoms))[mask]
group[indices] = i
return group
def __init__(self,
probe_symbol,
surface_symbol,
):
self.__probe_symbol = probe_symbol
surface = BodyCenteredCubic111(surface_symbol)
l = vectorLength(surface.cell()[1])/3
x, y = self.probePlacement(l)
positions = [(x,y,2.210),
(x, y + l, 0.92),
(x + l*np.cos(np.pi/6), y-l*np.sin(np.pi/6), 0.92),
(x - l*np.cos(np.pi/6),y-l*np.sin(np.pi/6), 0.92),
]
added_atoms = Atoms(probe_symbol*len(positions), positions)
SurfacePointDefect.__init__(
self,
surface=surface,
added_atoms=added_atoms,
)
def defaultParameters(
self,
parameters=DEFAULT,
centers=((0,0,0),),
):
if parameters is DEFAULT:
parameters = SurfaceParameters1D()
scales = parameters['length_scales']
short_length = scales['short_correlation_length']
depth = scales.depth()
in_equal_layers = self.inequivalentLayers()
electrode_layers = parameters['electrode_layers']
bound_layers = parameters['bound_layers']
free_layers = parameters['free_layers']
if bound_layers is DEFAULT:
bound_layers = 2
if electrode_layers is DEFAULT:
electrode_layers = 0
size = vectorLength(self.cell('orth_surface')[0])
if free_layers is DEFAULT:
n_layers = int(np.ceil(in_equal_layers*depth/size))
free_layers = n_layers - bound_layers - electrode_layers
cell_size = parameters['cell_size']
if cell_size is DEFAULT:
c_length = parameters['length_scales']['correlation_length']
cell_size = (c_length, c_length, c_length)
parameters = parameters.copy(
free_layers=free_layers,
bound_layers=bound_layers,
electrode_layers=electrode_layers,
cell_size=cell_size,
)
return parameters
def passivateLowerSurface(atoms, direction, length=1, angle=90):
s_direc = np.sign(direction)
a_direc = abs(direction) - 1
max_or_min = {-1: min, 1: max}[s_direc]
atoms = atoms.copy()
angle = angle * (math.pi / 180)
positions = atoms.get_positions()
z_m = max_or_min(positions[:, a_direc])
lower_positions = positions[s_direc * positions[:, a_direc] > s_direc * (z_m - s_direc * 0.5)]
lower_positions[:, 2] = lower_positions[:, 2].min()
upper_positions = positions[s_direc * positions[:, a_direc] < s_direc * (z_m - s_direc * 0.5)]
diff = upper_positions - lower_positions[0]
l = vectorLength(diff, 1)
not_direction = np.array([i for i in range(3) if i != a_direc], int)
closest = abs(diff[np.argmin(l)][not_direction])
if abs(closest[0]) > abs(closest[1]):
h_positions = [
position + [0, -length * math.cos(angle), s_direc * length * math.sin(angle)]
for position in lower_positions
]
h_positions += [
position + [0, length * math.cos(angle), s_direc * length * math.sin(angle)] for position in lower_positions
]
else:
h_positions = [
position + [-length * math.cos(angle), 0, s_direc * length * math.sin(angle)]
for position in lower_positions
]
h_positions += [
position + [length * math.cos(angle), 0, s_direc * length * math.sin(angle)] for position in lower_positions
]
new_atoms = Atoms("H%d" % len(h_positions), h_positions, cell=atoms.get_cell(), pbc=atoms.get_pbc())
new_atoms += atoms
return new_atoms
def make_electrodes(self, atoms):
unique_electrodes = uniqueElectrodes(atoms.electrodes())
electodes = []
for electrode, names in unique_electrodes:
electrode_atoms = makeElectrodeConform(electrode)
s_dir = electrode.semiInfiniteDirection()
parameters = self.parameters.copy()
label = '_'.join(names)
label = 'EL_%s' % label
parameters['label'] = label
kpts = np.array(parameters['kpts'] )
l = vectorLength(electrode.cell()[s_dir])
k = int(np.ceil(400/l))
kpts[s_dir] = k
parameters['kpts'] = tuple(kpts)
electrode_calculator = self.__class__(**parameters)
electrode_atoms.set_calculator(electrode_calculator)
electodes.append(electrode_atoms)
return electodes
def substitutionalDopingOfMiddleLayer(atoms, n_dopants=1, dopant_element='P', centers=None):
assert isinstance(n_dopants, int)
assert n_dopants > 0
atoms = atoms.copy()
middle_layer = list(findMiddleLayer(atoms))
symbols = np.array(atoms.get_chemical_symbols())
make_dopants = []
for i in range(n_dopants):
if centers is None:
middle_layer_index = 0
centers = []
else:
pos = atoms.positions[np.array(middle_layer, int)]
for center in centers:
middle_layer_index = vectorLength(minimalDistance(pos - center, atoms.cell), 1).argmax()
index = middle_layer.pop(middle_layer_index)
make_dopants.append(index)
centers.append(atoms[index].position)
symbols[np.array(make_dopants, int)] = dopant_element
atoms.set_chemical_symbols(symbols)
return atoms
def modifyAtoms(self, atoms, indices):
index2 = indices[-1]
other_indices = indices[:-1]
direction = np.array([0, 0, 1.0])
diff = atoms.positions[index2] - atoms.positions[other_indices].mean(axis=0)
diff = np.dot(diff, direction)
move = self.difference()*direction
move -= diff*direction
w_other = 1.0/len(indices)
w2 = 1.0 - w_other
atoms.positions[index2] += move*w2
atoms.positions[other_indices] -= move*w_other
mode = np.zeros(3*len(atoms))
for index1 in other_indices:
mode[3*index1: 3*(index1+1)] = w_other*direction
mode[3*index2: 3*(index2+1)] = -w2*direction
mode /= vectorLength(mode)
constraint = FixedMode(mode)
atoms.constraints.append(constraint)
return atoms
def atoms(self, constrained=True, parameters=DEFAULT):
parameters = self.defaultParameters(parameters)
vectors = np.array(parameters['vectors'])
lengths = vectorLength(vectors, 1)
assert lengths.all()
atoms = self.__atoms.copy()
vectors = convertFromBasis(vectors, atoms.cell)
repeats = findNeededRepetitions(atoms.cell, 1.5*lengths.max())
atoms = atoms.repeat(repeats)
atoms.cell[atoms.pbc] = vectors
atoms.wrap()
atoms = removeCopies(atoms)
atoms.setTag('Reference', picker=None)
padding = np.logical_not(atoms.pbc)
assert padding.sum() == 0
atoms = self.makeAtomsRelaxed(atoms, self.relaxation())
return atoms
def saveWavefunctionsToPlane(filename, label='./siesta', density_range=(-3.5, -2.5)):
rho, r, dh_cell = readCubeDensity(label=label)
x, y, z = r
dh = np.array([dh_cell[0,0], dh_cell[1,1], dh_cell[2,2]])
eigs, kpts, EF = readInfoForSTMSimulation(label=label)
eigs, rho, w_s = handleSpinPolarization(eigs, rho)
is_spin_polarized = w_s == 1
if is_spin_polarized:
rho = rho.sum(axis=0)
energies = np.array(eigs)[:,0]
i_o = (energies < EF).sum() - 1
i_u = i_o + 1
i_t = i_o - 2
rho0 = 10**(np.array(density_range).mean())
DS = density_range[1] - density_range[0]
c, c_r, domain = surfaceIntegrator(rho=rho, variables=r, rho0=rho0, DS=DS)
thick_surface = vectorLength(c, axis=0) > 1e-9
take_z = thick_surface.sum(axis=0)
take_z = take_z.sum(axis=0) > 0
thick_surface = thick_surface[:,:,take_z]
x, y, z = c_r
wfs = []
EF, energies = readEigenvalues(label=label)
folder = os.path.dirname(label)
for wf_filename in os.listdir(folder):
wf_filename = wf_filename.split('.')
if wf_filename[0] == 'siesta' and wf_filename[-2] == 'REAL' and wf_filename[-1] == 'cube':
kn = int(wf_filename[1][1:])
band = int(wf_filename[2][2:])
spin = wf_filename[3]
if is_spin_polarized:
spin = {'UP':0, 'DOWN':1}[spin]
elif spin=='DOWN':
continue
else:
spin = 0
wfs.append((energies[kn-1, band-1, spin], kn-1, band-1, spin))
wfs.sort()
nc_defined = False
f = netcdf.netcdf_file(filename, 'w')
for i, info in enumerate(wfs):
energy, kn, band, spin = info
kpt, w_k = kpts[kn]
if energy > 0:
continue
kappa = getVacuumDecayRate(energy)
wf, r, dh_cell = readCubeWavefunction(band + 1, kn=kn+1, spin=spin+1, folder=folder)
eikr = phaseFactor(kpt, r)
u = wf/eikr
grad_u = np.array(np.gradient(u, *dh))
A = (c*grad_u).sum(axis=0)
r = r[:,:,:, take_z]
u = u[:,:,take_z]
A = A[:,:,take_z]
ct = c[:, :, :, take_z]
if not nc_defined:
nwf = f.createDimension('nwf', len(wfs))
xd = f.createDimension('x', u.shape[0])
yd = f.createDimension('y', u.shape[1])
zd = f.createDimension('z', u.shape[2])
ran = f.createDimension('range', 2)
points = f.createDimension('points', thick_surface.sum())
vector3d = f.createDimension('vector3d', 3)
comp = f.createDimension('complex', 2)
d_var = f.createVariable('thick_surface', dimensions=('x', 'y', 'z'), type=np.dtype('b'))
ran_var = f.createVariable('grid_cell', dimensions=('vector3d', 'vector3d'), type=np.dtype('f'))
ran_var[:] = dh_cell
origin_var = f.createVariable('origin', dimensions=('vector3d', ), type=np.dtype('f'))
origin_var[:] = np.array([r[0].min(), r[1].min(), r[2].min()])
d_var[:] = thick_surface
c_var = f.createVariable('c', dimensions=('vector3d', 'points'), type=np.dtype('f4'))
for ci in range(3):
c_var[ci,:] = ct[ci, thick_surface]
spin_weight = f.createVariable('spin_weight', dimensions=tuple(), type=np.dtype('i'))
spin_weight.assignValue(w_s)
fermi_energy = f.createVariable('EF', dimensions=tuple(), type=np.dtype('f'))
fermi_energy.assignValue(EF)
kpts_var = f.createVariable('kpts', type=np.dtype(float), dimensions=('nwf', 'vector3d'))
wk_var = f.createVariable('wk', type=np.dtype(float), dimensions=('nwf',))
energy_var = f.createVariable('energy', type=np.dtype(float), dimensions=('nwf',))
spin_var = f.createVariable('spin', type=np.dtype('i'), dimensions=('nwf',))
u_var = f.createVariable('u', type=np.dtype('f4'), dimensions=('nwf', 'points', 'complex'))
A_var = f.createVariable('A', type=np.dtype('f4'), dimensions=('nwf', 'points', 'complex'))
nc_defined = True
wk_var[i] = w_k
kpts_var[i] = kpt
energy_var[i] = energy
spin_var[i] = spin
u_var[i,:, 0] = u[thick_surface].real
u_var[i,:, 1] = u[thick_surface].imag
A_var[i,:, 0] = A[thick_surface].real
A_var[i,:, 1] = A[thick_surface].imag
f.close()
return True
def __init__(self, difference, direction=(0, 0, 1)):
self.__difference = difference
direction = np.array(direction, float)
self.__direction = direction/vectorLength(direction)