def lindemann_index(trajectory_dir="./"):
"""
Calculates the Lindemann index
\delta = \frac{2}{N(N-1)} \sum_{i<j} \frac{\sqrt{\langle r_{ij}^2\rangle_t - \langle r_{ij} \rangle^2_t }}{ \langle r_{ij} \rangle_t }
"""
# Import vasprun.xml:
traj = read_trajectory(dir=trajectory_dir, unwrap_pbcs=False)
pos = traj.get_all_trajectories(coords="direct")
nsteps = pos.shape[0]
natoms = pos.shape[1]
# Get all atom pairs:
pairs = get_pairs(natoms)
npairs = pairs.shape[0]
print "%d steps, %d atoms, %d pairs" % (nsteps, natoms, npairs)
stepsize = 50
samplesteps = np.arange(0, nsteps, stepsize)
r = np.zeros((samplesteps.size, npairs)) # increase stepsize if we run out of memory
r2 = np.zeros((samplesteps.size, npairs)) # increase stepsize if we run out of memory
print "Allocated %.3f MB" % ((r.nbytes + r2.nbytes) / (1024.0 ** 2))
pbar = ProgressBar(widgets=["At step...", SimpleProgress()], maxval=samplesteps.size).start()
for idx, s in enumerate(samplesteps):
pbar.update(idx)
x = pos[s, pairs[:, 0]] - pos[s, pairs[:, 1]]
x = x - (2 * x).astype("int") # minimum image convention
r2[idx] = lensq(x)
r[idx] = np.sqrt(r2[idx])
pbar.finish()
meanr2 = np.mean(r2, axis=0)
meanr = np.mean(r, axis=0)
return np.sum(np.sqrt((meanr2 - meanr ** 2)) / meanr) * 2 / (npairs * 2)
def lindemann_index(trajectory_dir='./'):
"""
Calculates the Lindemann index
\delta = \frac{2}{N(N-1)} \sum_{i<j} \frac{\sqrt{\langle r_{ij}^2\rangle_t - \langle r_{ij} \rangle^2_t }}{ \langle r_{ij} \rangle_t }
"""
# Import vasprun.xml:
traj = read_trajectory( dir = trajectory_dir, unwrap_pbcs = False )
pos = traj.get_all_trajectories( coords = 'direct' )
nsteps = pos.shape[0]
natoms = pos.shape[1]
# Get all atom pairs:
pairs = get_pairs(natoms)
npairs = pairs.shape[0]
print "%d steps, %d atoms, %d pairs" % (nsteps, natoms, npairs)
stepsize = 50
samplesteps = np.arange(0,nsteps,stepsize)
r = np.zeros((samplesteps.size, npairs)) # increase stepsize if we run out of memory
r2 = np.zeros((samplesteps.size, npairs)) # increase stepsize if we run out of memory
print "Allocated %.3f MB" % ((r.nbytes+r2.nbytes)/(1024.**2))
pbar = ProgressBar(widgets=['At step...',SimpleProgress()], maxval = samplesteps.size).start()
for idx,s in enumerate(samplesteps):
pbar.update(idx)
x = pos[s,pairs[:,0]] - pos[s,pairs[:,1]]
x = x - (2*x).astype('int') # minimum image convention
r2[idx] = lensq(x)
r[idx] = np.sqrt(r2[idx])
pbar.finish()
meanr2 = np.mean(r2,axis=0)
meanr = np.mean(r,axis=0)
return np.sum(np.sqrt((meanr2 - meanr**2))/meanr)*2/(npairs*2)
parser.add_argument('--abs_diff', '-a', action='store_true',
help='Print abs(displacements) for all atoms' )
parser.add_argument('--rad_diff', '-r', action='store_true',
help='Print radial displacements (displacement vector norms) for all atoms' )
parser.add_argument('--no_unwrap', '-n', action='store_true',
help='Don\'t try to unwrap motion over periodic boundaries.' )
parser.add_argument('infile', nargs='?', default='POSCAR', type=argparse.FileType('r'), help='POSCAR filename')
args = parser.parse_args()
# Read atoms from POSCAR:
poscar1 = PoscarParser(args.infile).get_structure()
pos = poscar1.get_positions( coords = 'direct' )
natoms = pos.shape[0]
# Build array of pair indices:
pairs = get_pairs(natoms)
npairs = pairs.shape[0]
print "%d atoms, %d pairs" % (natoms, npairs)
# Find displacement vectors for all atoms:
x = pos[pairs[:,0]] - pos[pairs[:,1]]
# Use minimum image convention to threat bonds over PBCs
# Note: This will not work with *very* tilted unit cells
x = x - (2*x).astype('int')
X = direct_to_cartesian(x, poscar1.get_cell())
r2 = (X**2).sum(axis=1)
r = np.sqrt(r2)
action='store_true',
help='Don\'t try to unwrap motion over periodic boundaries.')
parser.add_argument('infile',
nargs='?',
default='POSCAR',
type=argparse.FileType('r'),
help='POSCAR filename')
args = parser.parse_args()
# Read atoms from POSCAR:
poscar1 = PoscarParser(args.infile).get_structure()
pos = poscar1.get_positions(coords='direct')
natoms = pos.shape[0]
# Build array of pair indices:
pairs = get_pairs(natoms)
npairs = pairs.shape[0]
print "%d atoms, %d pairs" % (natoms, npairs)
# Find displacement vectors for all atoms:
x = pos[pairs[:, 0]] - pos[pairs[:, 1]]
# Use minimum image convention to threat bonds over PBCs
# Note: This will not work with *very* tilted unit cells
x = x - (2 * x).astype('int')
X = direct_to_cartesian(x, poscar1.get_cell())
r2 = (X**2).sum(axis=1)
r = np.sqrt(r2)
def main():
import ase
#from connectivities import connectivities, partition, plot
atoms = ase.io.read('CONTCAR', format='vasp')
#dists, idx, bonds = connectivities(atoms, maxdist=2.5)
#groups = partition(atoms, dists, idx, mincount=50, maxwidth=2.0)
#cats = categorize(atoms, dists, idx)
#cats[0]
pos = atoms.positions
# Get all atom pairs:
n = len(atoms)
pairs = get_pairs(n)
# Filter pairs based on atom types:
bond = (14, 14)
pnum = atoms.numbers[pairs]
# numbers == (bond[0],bond[1]) or numbers == (bond[1],bond[0]) :
mask = np.any(np.column_stack(
(np.all(pnum == bond, axis=1), np.all(pnum == reversed(bond),
axis=1))),
axis=1)
del pnum
# Calculate distancess:
neighbours = [(-1, 2), (-1, 2), (-1, 2)]
vectors = atoms.positions[pairs[:, 0]] - atoms.positions[pairs[:, 1]]
tmp = np.zeros((len(vectors), 2))
tmp[:, 0] = lensq(vectors)
for d0 in range(*neighbours[0]):
for d1 in range(*neighbours[1]):
for d2 in range(*neighbours[2]):
if d0 == d1 == d2 == 0:
continue
tmp[:, 1] = lensq(vectors +
np.dot(np.array([d0, d1, d2]), atoms.cell))
tmp.min(axis=1, out=tmp[:, 0])
#
# vectors må korrigeres for PBC. Sjekk om vi kan få pair list rett ut fra ASE
#
dists = np.sqrt(tmp[:, 0])
del tmp
# Filter pairs based on bond lengths:
maxdist = 2.8
if maxdist is not None:
# add to mask
mask = np.all(np.column_stack((mask, dists <= maxdist)), axis=1)
dists = dists[mask]
pairs = pairs[mask, :]
vectors = vectors[mask, :]
import matplotlib.pyplot as plt
vec2d = np.zeros((vectors.shape[0], 2))
x = np.array([1, 0, 0])
y = np.array([0, 1, 0])
vec2d = vectors[:, ::2]
pos2d = pos[pairs[:, 0], ::2]
print vec2d.shape
print pos2d.shape
plt.quiver(pos[:, 0], pos[:, 1], vec2d[:, 0], vec2d[:, 1])
plt.show()
def get_shortest_bond(self, include_self = False, safe_mode = True, rmax = 3.0):
"""
Returns a tupple containing the shortest bond length in Angstrom,
followed by the indices of the two atoms making up the bond
Parameters:
include_self : bool (default False)
Whether to check for bonds between an atom and its _own_ periodic image.
This is only needed for very small unit cells, typically with a single atom.
safe_mode : bool (default True)
Much slower, but safer for non-cubic cells
rmax : float (default 3.0)
Maximum bond length (in Angstrom) to check for
(only used in safe_mode)
"""
a = self._cell[0]
b = self._cell[1]
c = self._cell[2]
pos = self._positions
natoms = pos.shape[0]
if natoms == 1:
print "Note from get_shortest_bond(): include_self is enabled since only a single atom was found!"
include_self = True
# Limit to sphere of radius Rc
if safe_mode:
#if include_self:
# print "include_self and safe_mode are not currently compatible. sorry"
# return
natoms = self.get_num_atoms()
a = self._cell[0]
b = self._cell[1]
c = self._cell[2]
# Find distance between opposing faces of the cell:
wa = abs(np.dot(a,np.cross(b,c))) / np.linalg.norm(np.cross(b,c))
wb = abs(np.dot(b,np.cross(c,a))) / np.linalg.norm(np.cross(c,a))
wc = abs(np.dot(c,np.cross(a,b))) / np.linalg.norm(np.cross(a,b))
# If half the max radius exceeds one of the face-to-face distances (wa, wb or wc),
# we add more atoms in the given direction(s) as necessary.
la = 1 + int(2*rmax/wa)
lb = 1 + int(2*rmax/wb)
lc = 1 + int(2*rmax/wc)
print "dim:",la,lb,lc
#p2 = self.get_supercell_positions(la,lb,lc, coords='d')
pos = np.zeros((natoms*la*lb*lc,3))
#offsets = np.zeros((natoms*la*lb*lc,3), dtype=np.int)
#c = np.diag((1,1,1)) # since we use direct coordinates
for i in range(la):
for j in range(lb):
for k in range(lc):
m = i*lb*lc + j*lc + k
pos[m*natoms:(m+1)*natoms] = self._positions + np.array((i, j, k))
#offsets[m*natoms:(m+1)*natoms] = [i, j, k]
indices = np.tile(np.arange(natoms), la*lb*lc)
paired = np.zeros(natoms, dtype=np.int)
minr = np.zeros(natoms)
for j in np.arange(natoms):
# Center at atom <index>:
pos -= pos[j]
# Minimum image convention with coordinates in range lb*[-0.5,0.5>
pos[:,0] -= la*(pos[:,0]*2/la).astype('int')
pos[:,1] -= lb*(pos[:,1]*2/lb).astype('int')
pos[:,2] -= lc*(pos[:,2]*2/lc).astype('int')
cart = direct_to_cartesian(pos,self._cell)
dr = np.sqrt(np.sum(cart**2,1))
cond = np.logical_and(dr < rmax, dr > 0.0)
dr = dr[cond]
if dr.shape[0] == 0:
print "[Warning]: No neighbours found within %.2f Angstrom of atom %d" % (rmax,j)
minr[j] = 1001.0
continue
so = np.argsort(dr)
#pos = pos[cond]
#offsets = (2*pos).astype('int')
##indices = indices[cond]
## sort:
#dr = dr[so]
#pos = pos[so]
#offsets = offsets[so]
#indices = indices[so]
#indices, dr, offsets, pos = self.get_neighbours(j)
paired[j] = indices[cond][so][0]
minr[j] = dr[so][0]
#pairs[j,nearest] =
#minpair = pairs[j,nearest]
#minr = dr[0]
#print nearest,shortest
minidx = np.argmin(minr)
minr = minr[minidx]
if minr > 1000.0:
print "[Error]: No bonds shorter than %.2f Angstrom found. Please increase rmax" % rmax
return (minr,minidx,paired[minidx])
else:
# Build array of pair indices:
pairs = get_pairs(natoms, include_self=include_self)
npairs = pairs.shape[0]
# Find displacement vectors for all pairs:
x = pos[pairs[:,0]] - pos[pairs[:,1]]
# Use minimum image convention to threat bonds over PBCs
# Note: use safe_mode with tilted unit cells in which the
# shortest bond is close to half of one of the cell dimensions
x = x - (2*x).astype('int')
X = direct_to_cartesian(x, self._cell)
r2 = (X**2).sum(axis=1)
r = np.sqrt(r2)
meanr2 = np.mean(r2,axis=0)
meanr = np.mean(r,axis=0)
minidx = np.argmin(r)
minpair = pairs[minidx]
minr = r[minidx]
return (minr,minpair[0],minpair[1])
def main():
import ase
#from connectivities import connectivities, partition, plot
atoms = ase.io.read('CONTCAR', format='vasp')
#dists, idx, bonds = connectivities(atoms, maxdist=2.5)
#groups = partition(atoms, dists, idx, mincount=50, maxwidth=2.0)
#cats = categorize(atoms, dists, idx)
#cats[0]
pos = atoms.positions
# Get all atom pairs:
n = len(atoms)
pairs = get_pairs(n)
# Filter pairs based on atom types:
bond = (14,14)
pnum = atoms.numbers[pairs]
# numbers == (bond[0],bond[1]) or numbers == (bond[1],bond[0]) :
mask = np.any(np.column_stack((np.all(pnum == bond, axis=1), np.all(pnum == reversed(bond), axis = 1))),axis=1)
del pnum
# Calculate distancess:
neighbours = [(-1, 2), (-1, 2), (-1, 2)]
vectors = atoms.positions[pairs[:,0]] - atoms.positions[pairs[:,1]]
tmp = np.zeros((len(vectors), 2))
tmp[:,0] = lensq(vectors)
for d0 in range(*neighbours[0]):
for d1 in range(*neighbours[1]):
for d2 in range(*neighbours[2]):
if d0 == d1 == d2 == 0:
continue
tmp[:,1] = lensq(vectors + np.dot(np.array([d0, d1, d2]),
atoms.cell))
tmp.min(axis=1, out=tmp[:,0])
#
# vectors må korrigeres for PBC. Sjekk om vi kan få pair list rett ut fra ASE
#
dists = np.sqrt(tmp[:,0])
del tmp
# Filter pairs based on bond lengths:
maxdist = 2.8
if maxdist is not None:
# add to mask
mask = np.all(np.column_stack((mask, dists <= maxdist)), axis = 1)
dists = dists[mask]
pairs = pairs[mask,:]
vectors = vectors[mask,:]
import matplotlib.pyplot as plt
vec2d = np.zeros((vectors.shape[0],2))
x = np.array([1,0,0])
y = np.array([0,1,0])
vec2d = vectors[:,::2]
pos2d = pos[pairs[:,0],::2]
print vec2d.shape
print pos2d.shape
plt.quiver(pos[:,0], pos[:,1], vec2d[:,0], vec2d[:,1])
plt.show()
def get_shortest_bond(self, include_self=False, safe_mode=True, rmax=3.0):
"""
Returns a tupple containing the shortest bond length in Angstrom,
followed by the indices of the two atoms making up the bond
Parameters:
include_self : bool (default False)
Whether to check for bonds between an atom and its _own_ periodic image.
This is only needed for very small unit cells, typically with a single atom.
safe_mode : bool (default True)
Much slower, but safer for non-cubic cells
rmax : float (default 3.0)
Maximum bond length (in Angstrom) to check for
(only used in safe_mode)
"""
a = self._cell[0]
b = self._cell[1]
c = self._cell[2]
pos = self._positions
natoms = pos.shape[0]
if natoms == 1:
print "Note from get_shortest_bond(): include_self is enabled since only a single atom was found!"
include_self = True
# Limit to sphere of radius Rc
if safe_mode:
#if include_self:
# print "include_self and safe_mode are not currently compatible. sorry"
# return
natoms = self.get_num_atoms()
a = self._cell[0]
b = self._cell[1]
c = self._cell[2]
# Find distance between opposing faces of the cell:
wa = abs(np.dot(a, np.cross(b, c))) / np.linalg.norm(np.cross(
b, c))
wb = abs(np.dot(b, np.cross(c, a))) / np.linalg.norm(np.cross(
c, a))
wc = abs(np.dot(c, np.cross(a, b))) / np.linalg.norm(np.cross(
a, b))
# If half the max radius exceeds one of the face-to-face distances (wa, wb or wc),
# we add more atoms in the given direction(s) as necessary.
la = 1 + int(2 * rmax / wa)
lb = 1 + int(2 * rmax / wb)
lc = 1 + int(2 * rmax / wc)
print "dim:", la, lb, lc
#p2 = self.get_supercell_positions(la,lb,lc, coords='d')
pos = np.zeros((natoms * la * lb * lc, 3))
#offsets = np.zeros((natoms*la*lb*lc,3), dtype=np.int)
#c = np.diag((1,1,1)) # since we use direct coordinates
for i in range(la):
for j in range(lb):
for k in range(lc):
m = i * lb * lc + j * lc + k
pos[m * natoms:(m + 1) *
natoms] = self._positions + np.array((i, j, k))
#offsets[m*natoms:(m+1)*natoms] = [i, j, k]
indices = np.tile(np.arange(natoms), la * lb * lc)
paired = np.zeros(natoms, dtype=np.int)
minr = np.zeros(natoms)
for j in np.arange(natoms):
# Center at atom <index>:
pos -= pos[j]
# Minimum image convention with coordinates in range lb*[-0.5,0.5>
pos[:, 0] -= la * (pos[:, 0] * 2 / la).astype('int')
pos[:, 1] -= lb * (pos[:, 1] * 2 / lb).astype('int')
pos[:, 2] -= lc * (pos[:, 2] * 2 / lc).astype('int')
cart = direct_to_cartesian(pos, self._cell)
dr = np.sqrt(np.sum(cart**2, 1))
cond = np.logical_and(dr < rmax, dr > 0.0)
dr = dr[cond]
if dr.shape[0] == 0:
print "[Warning]: No neighbours found within %.2f Angstrom of atom %d" % (
rmax, j)
minr[j] = 1001.0
continue
so = np.argsort(dr)
#pos = pos[cond]
#offsets = (2*pos).astype('int')
##indices = indices[cond]
## sort:
#dr = dr[so]
#pos = pos[so]
#offsets = offsets[so]
#indices = indices[so]
#indices, dr, offsets, pos = self.get_neighbours(j)
paired[j] = indices[cond][so][0]
minr[j] = dr[so][0]
#pairs[j,nearest] =
#minpair = pairs[j,nearest]
#minr = dr[0]
#print nearest,shortest
minidx = np.argmin(minr)
minr = minr[minidx]
if minr > 1000.0:
print "[Error]: No bonds shorter than %.2f Angstrom found. Please increase rmax" % rmax
return (minr, minidx, paired[minidx])
else:
# Build array of pair indices:
pairs = get_pairs(natoms, include_self=include_self)
npairs = pairs.shape[0]
# Find displacement vectors for all pairs:
x = pos[pairs[:, 0]] - pos[pairs[:, 1]]
# Use minimum image convention to threat bonds over PBCs
# Note: use safe_mode with tilted unit cells in which the
# shortest bond is close to half of one of the cell dimensions
x = x - (2 * x).astype('int')
X = direct_to_cartesian(x, self._cell)
r2 = (X**2).sum(axis=1)
r = np.sqrt(r2)
meanr2 = np.mean(r2, axis=0)
meanr = np.mean(r, axis=0)
minidx = np.argmin(r)
minpair = pairs[minidx]
minr = r[minidx]
return (minr, minpair[0], minpair[1])