def distance2(self, x1, x2, option='reduced', radius=20, limits=None):
# Compute the vector from x1 to x2
dv = np.array(x2) - np.array(x1)
# If we are not in reduced coordinates,
# Convert into them
if option != 'reduced':
dred = self.cartesian2reduced(dv)
else:
dred = dv
dwrap = wrap2_pmhalf(dred)
if limits is None:
limits = np.zeros(3, dtype=int)
corners = self.get_wigner_seitz_container()
limits[0] = min(int(ceil(max(1e-14 + abs(np.array([corners[x][0] for x in corners]))))), 5)
limits[1] = min(int(ceil(max(1e-14 + abs(np.array([corners[x][1] for x in corners]))))), 5)
limits[2] = min(int(ceil(max(1e-14 + abs(np.array([corners[x][2] for x in corners]))))), 5)
ret = {}
for i0 in np.arange(-limits[0], limits[0] + 1):
for i1 in np.arange(-limits[1], limits[1] + 1):
for i2 in np.arange(-limits[2], limits[2] + 1):
dtot = dwrap + np.array([i0, i1, i2])
norm2 = np.dot(np.dot(dtot, self.metric), dtot)
if norm2 < radius * radius:
ret[(i0, i1, i2)] = {'distance': sqrt(norm2), 'image': dtot}
return ret
def distance2(self, x1, x2, option='reduced', radius=20, limits=None):
# Compute the vector from x1 to x2
dv = np.array(x2) - np.array(x1)
# If we are not in reduced coordinates,
# Convert into them
if option != 'reduced':
dred = self.cartesian2reduced(dv)
else:
dred = dv
dwrap = wrap2_pmhalf(dred)
if limits is None:
limits = np.zeros(3, dtype=int)
corners = self.get_wigner_seitz_container()
limits[0] = min(int(ceil(max(1e-14 + abs(np.array([corners[x][0] for x in corners]))))), 5)
limits[1] = min(int(ceil(max(1e-14 + abs(np.array([corners[x][1] for x in corners]))))), 5)
limits[2] = min(int(ceil(max(1e-14 + abs(np.array([corners[x][2] for x in corners]))))), 5)
ret = {}
for i0 in np.arange(-limits[0], limits[0] + 1):
for i1 in np.arange(-limits[1], limits[1] + 1):
for i2 in np.arange(-limits[2], limits[2] + 1):
dtot = dwrap + np.array([i0, i1, i2])
norm2 = np.dot(np.dot(dtot, self.metric), dtot)
if norm2 < radius * radius:
ret[(i0, i1, i2)] = {'distance': sqrt(norm2), 'image': dtot}
return ret
def distance2(self, x1, x2, option='reduced'):
# Compute the vector from x1 to x2
dv = _np.array(x2)-_np.array(x1)
# If we are not in reduced coordinates,
# Convert into them
if option != 'reduced':
dred = self.cartesian2reduced(dv)
else:
dred = dv
dwrap = wrap2_pmhalf(dred)
limits = _np.zeros(3)
corners = self.get_wigner_seitz_container()
#for key, value in corners.iteritems():
# print key, value
limits[0] = int(math.ceil(max(1e-14+abs(_np.array([corners[x][0] for x in corners])))))
limits[1] = int(math.ceil(max(1e-14+abs(_np.array([corners[x][1] for x in corners])))))
limits[2] = int(math.ceil(max(1e-14+abs(_np.array([corners[x][2] for x in corners])))))
#print limits
ret = {}
for i0 in _np.arange(-limits[0], limits[0]+1):
for i1 in _np.arange(-limits[1], limits[1]+1):
for i2 in _np.arange(-limits[2], limits[2]+1):
dtot = dwrap+_np.array([i0, i1, i2])
norm2 = _np.dot(_np.dot(dtot, self.metric), dtot)
ret[(i0, i1, i2)] = {'distance': math.sqrt(norm2), 'image': dtot}
return ret
def distances_in_sphere(self, x1, x2, radius, option='reduced', exclude_out_sphere=True, sort_by_distance=True):
"""
Returns all the distances between two positions x1 and x2
taking into account the periodicity of the cell
:param sort_by_distance:
:param exclude_out_sphere:
:param x1:
:param x2:
:param radius:
:param option:
:return:
"""
# Compute the vector from x1 to x2
dv = np.array(x2) - np.array(x1)
# If the positions are not in reduced coordinates,convert into them
if option != 'reduced':
dred = self.cartesian2reduced(dv)
else:
dred = dv
dwrap = wrap2_pmhalf(dred)
# log.debug('The wrap vector is: %7.3f %7.3f %7.3f' % tuple(dwrap))
# We need to compute the distances between equivalent faces
# For that we to compute the perpendicular distance between
# two faces, the reciprocal lattice produces the inverse of
# those distances
recp_len = np.array(self.reciprocal().lengths)
# The reciprocal (2*pi) is not necessary
limits = np.ceil(radius * recp_len).astype(int)
# log.debug('The limits are: %d %d %d' % tuple(limits))
ret = {}
# The total size is the product of the number in the 3 directions
# that is double the limits plus 1 to include the zero
total_size = np.prod(2 * limits + 1)
# log.debug('The total size is: %d' % total_size)
ret['distance'] = np.zeros(total_size)
ret['image'] = np.zeros((total_size, 3), dtype=int)
ret['dwrap'] = dwrap
ret['limits'] = limits
index = 0
for i0 in np.arange(-limits[0], limits[0] + 1):
for i1 in np.arange(-limits[1], limits[1] + 1):
for i2 in np.arange(-limits[2], limits[2] + 1):
dtot = dwrap + np.array([i0, i1, i2])
norm2 = np.dot(np.dot(dtot, self.metric), dtot)
ret['distance'][index] = sqrt(norm2)
ret['image'][index] = np.array([i0, i1, i2])
index += 1
# Exclude distances out of sphere
if exclude_out_sphere:
inside_sphere = ret['distance'] <= radius
if sum(inside_sphere) > 0:
ret['distance'] = ret['distance'][inside_sphere]
ret['image'] = ret['image'][inside_sphere]
if sort_by_distance:
sorted_indices = np.argsort(ret['distance'])
ret['distance'] = ret['distance'][sorted_indices]
ret['image'] = ret['image'][sorted_indices]
return ret
def distances_in_sphere(self, x1, x2, radius, option='reduced', exclude_out_sphere=True, sort_by_distance=True):
"""
Returns all the distances between two positions x1 and x2
taking into account the periodicity of the cell
:param sort_by_distance:
:param exclude_out_sphere:
:param x1:
:param x2:
:param radius:
:param option:
:return:
"""
# Compute the vector from x1 to x2
dv = np.array(x2) - np.array(x1)
# If the positions are not in reduced coordinates,convert into them
if option != 'reduced':
dred = self.cartesian2reduced(dv)
else:
dred = dv
dwrap = wrap2_pmhalf(dred)
# log.debug('The wrap vector is: %7.3f %7.3f %7.3f' % tuple(dwrap))
# We need to compute the distances between equivalent faces
# For that we to compute the perpendicular distance between
# two faces, the reciprocal lattice produces the inverse of
# those distances
recp_len = np.array(self.reciprocal().lengths)
# The reciprocal (2*pi) is not necessary
limits = np.ceil(radius * recp_len).astype(int)
# log.debug('The limits are: %d %d %d' % tuple(limits))
ret = {}
# The total size is the product of the number in the 3 directions
# that is double the limits plus 1 to include the zero
total_size = np.prod(2 * limits + 1)
# log.debug('The total size is: %d' % total_size)
ret['distance'] = np.zeros(total_size)
ret['image'] = np.zeros((total_size, 3), dtype=int)
ret['dwrap'] = dwrap
ret['limits'] = limits
index = 0
for i0 in np.arange(-limits[0], limits[0] + 1):
for i1 in np.arange(-limits[1], limits[1] + 1):
for i2 in np.arange(-limits[2], limits[2] + 1):
dtot = dwrap + np.array([i0, i1, i2])
norm2 = np.dot(np.dot(dtot, self.metric), dtot)
ret['distance'][index] = sqrt(norm2)
ret['image'][index] = np.array([i0, i1, i2])
index += 1
# Exclude distances out of sphere
if exclude_out_sphere:
inside_sphere = ret['distance'] <= radius
if sum(inside_sphere) > 0:
ret['distance'] = ret['distance'][inside_sphere]
ret['image'] = ret['image'][inside_sphere]
if sort_by_distance:
sorted_indices = np.argsort(ret['distance'])
ret['distance'] = ret['distance'][sorted_indices]
ret['image'] = ret['image'][sorted_indices]
return ret