from __future__ import division
import numpy as np
from ase.neighborlist import NeighborList, PrimitiveNeighborList
from optparse import OptionParser
from scipy.special import sph_harm, spherical_in
from ase import Atoms
[docs]class SO3:
'''
A class to generate the SO3 power spectrum components
based off of the Gaussian atomic neighbor density function
defined in "On Representing Atomic Environments".
args:
nmax: int, degree of radial expansion
lmax: int, degree of spherical harmonic expansion
rcut: float, cutoff radius for neighbor calculation
alpha: float, gaussian width parameter
derivative: bool, whether to calculate the gradient of not
weight_on: bool, if True, the neighbors with different type will be counted as negative
primitive: bool, use the asePrimitiveNeighborList
'''
def __init__(self, nmax=3, lmax=3, rcut=3.5, alpha=2.0, derivative=True, stress=False, cutoff_function='cosine', weight_on=False, primitive=False):
# populate attributes
self.nmax = nmax
self.lmax = lmax
self.rcut = rcut
self.alpha = alpha
self.derivative = derivative
self.stress = stress
self._type = "SO3"
self.cutoff_function = cutoff_function
self.weight_on = weight_on
self.primitive = primitive
#return
def __str__(self):
s = "SO3 descriptor with Cutoff: {:6.3f}".format(self.rcut)
s += " lmax: {:d}, nmax: {:d}, alpha: {:.3f}\n".format(self.lmax, self.nmax, self.alpha)
return s
def __repr__(self):
return str(self)
[docs] def load_from_dict(self, dict0):
self.nmax = dict0["nmax"]
self.lmax = dict0["lmax"]
self.rcut = dict0["rcut"]
self.alpha = dict0["alpha"]
self.derivative = dict0["derivative"]
self.stress = dict0["stress"]
[docs] def save_dict(self):
"""
save the model as a dictionary in json
"""
dict = {"nmax": self.nmax,
"lmax": self.lmax,
"rcut": self.rcut,
"alpha": self.alpha,
"derivative": self.derivative,
"stress": self.stress,
"_type": "SO3",
}
return dict
@property
def nmax(self):
return self._nmax
@nmax.setter
def nmax(self, nmax):
if isinstance(nmax, int) is True:
if nmax < 1:
raise ValueError('nmax must be greater than or equal to 1')
if nmax > 11:
raise ValueError('nmax > 11 yields complex eigenvalues which will mess up the calculation')
self._nmax = nmax
else:
raise ValueError('nmax must be an integer')
@property
def lmax(self):
return self._lmax
@lmax.setter
def lmax(self, lmax):
if isinstance(lmax, int) is True:
if lmax < 0:
raise ValueError('lmax must be greater than or equal to zero')
elif lmax > 32:
raise NotImplementedError('''Currently we only support Wigner-D matrices and spherical harmonics
for arguments up to l=32. If you need higher functionality, raise an issue
in our Github and we will expand the set of supported functions''')
self._lmax = lmax
else:
raise ValueError('lmax must be an integer')
@property
def rcut(self):
return self._rcut
@rcut.setter
def rcut(self, rcut):
if isinstance(rcut, float) is True or isinstance(rcut, int) is True:
if rcut <= 0:
raise ValueError('rcut must be greater than zero')
self._rcut = rcut
else:
raise ValueError('rcut must be a float')
@property
def alpha(self):
return self._alpha
@alpha.setter
def alpha(self, alpha):
if isinstance(alpha, float) is True or isinstance(alpha, int) is True:
if alpha <= 0:
raise ValueError('alpha must be greater than zero')
self._alpha = alpha
else:
raise ValueError('alpha must be a float')
@property
def derivative(self):
return self._derivative
@derivative.setter
def derivative(self, derivative):
if isinstance(derivative, bool) is True:
self._derivative = derivative
else:
raise ValueError('derivative must be a boolean value')
@property
def stress(self):
return self._stress
@stress.setter
def stress(self, stress):
if isinstance(stress, bool) is True:
self._stress = stress
else:
raise ValueError('stress must be a boolean value')
@property
def cutoff_function(self):
return self._cutoff_function
@cutoff_function.setter
def cutoff_function(self, cutoff_function):
if isinstance(cutoff_function, str) is True:
# more conditions
if cutoff_function == 'cosine':
self._cutoff_function = Cosine
elif cutoff_function == 'tanh':
self._cutoff_function = Tanh
elif cutoff_function == 'poly1':
self._cutoff_function = Poly1
elif cutoff_function == 'poly2':
self._cutoff_function = Poly2
elif cutoff_function == 'poly3':
self._cutoff_function = Poly3
elif cutoff_function == 'poly4':
self._cutoff_function = Poly4
elif cutoff_function == 'exp':
self._cutoff_function = Exponent
elif cutoff_function == 'unity':
self._cutoff_function = Unity
else:
raise NotImplementedError('The requested cutoff function has not been implemented')
else:
raise ValueError('You must specify the cutoff function as a string')
[docs] def clear_memory(self):
'''
Clears all memory that isn't an essential attribute for the calculator
'''
attrs = list(vars(self).keys())
for attr in attrs:
if attr not in {'_nmax', '_lmax', '_rcut', '_alpha', '_derivative', '_stress', '_cutoff_function', 'weight_on', 'primitive'}:
delattr(self, attr)
return
[docs] def calculate(self, atoms, atom_ids=None):
'''
Calculates the SO(3) power spectrum components of the
smoothened atomic neighbor density function
for given nmax, lmax, rcut, and alpha.
Args:
atoms: an ASE atoms object corresponding to the desired
atomic arrangement
backend: string, specifies the method to compute the neighborlist
elements, either ASE or pymatgen
'''
self._atoms = atoms
self.build_neighbor_list(atom_ids)
self.initialize_arrays()
ncoefs = self.nmax*(self.nmax+1)//2*(self.lmax+1)
tril_indices = np.tril_indices(self.nmax, k=0)
ls = np.arange(self.lmax+1)
norm = np.sqrt(2*np.sqrt(2)*np.pi/np.sqrt(2*ls+1))
if self.derivative:
# get expansion coefficients and derivatives
cs, dcs = compute_dcs(self.neighborlist, self.nmax, self.lmax, self.rcut, self.alpha, self._cutoff_function)
# weight cs and dcs
cs *= self.atomic_weights[:,np.newaxis,np.newaxis,np.newaxis]
dcs *= self.atomic_weights[:,np.newaxis,np.newaxis,np.newaxis,np.newaxis]
cs = np.einsum('inlm,l->inlm', cs, norm)
dcs = np.einsum('inlmj,l->inlmj', dcs, norm)
Ris = self.center_atoms
Rjs = self.neighborlist + Ris
for i in np.unique(self.seq[:,0]):
# find atoms for which i is the center
centers = self.neighbor_indices[:,0] == i
# find neighbors for which i is not the index
neighs = self.neighbor_indices[:,1] != i
# get the indices for both conditions
inds = centers*neighs
# total up the c array for the center atom
ctot = cs[centers].sum(axis=0)
#ctot = np.einsum('nlm,l->nlm', ctot,norm)
# get dc weights
# compute the power spectrum
P = np.einsum('ijk,ljk->ilj', ctot, np.conj(ctot)).real
# compute the gradient of the power spectrum for each neighbor
dP = np.einsum('wijkn,ljk->wiljn', dcs[centers], np.conj(ctot))
dP += np.conj(np.transpose(dP, axes=[0,2,1,3,4]))
dP = dP.real
rdPi = np.einsum('wn,wijkm->wijknm', Ris[centers], dP)
rdPj = np.einsum('wn,wijkm->wijknm', Rjs[centers], dP)
# get ij pairs for center atom
ijs = self.neighbor_indices[centers]
# loop over unique neighbor indices
for j in np.unique(ijs[:,1]):
# get the location of ij pairs in the NL
# and therefore dP
ijlocs = self.neighbor_indices[centers,1] == j
# get the location of the dplist element
temp = self.seq == np.array([i,j])
seqloc = temp[:,0]*temp[:,1]
# sum over ij pairs
dPsum = np.sum(dP[ijlocs], axis=0)
rdPjsum = np.sum(rdPj[ijlocs], axis=0)
# flatten into dplist and rdplist
self._dplist[seqloc] += (dPsum[tril_indices].flatten()).reshape(ncoefs,3)
self._pstress[seqloc] -= (rdPjsum[tril_indices].flatten()).reshape(ncoefs,3,3)
# get unique elements and store in feature vector
self._plist[i] = P[tril_indices].flatten()
# get location if ii pair in seq
temp = self.seq == np.array([i,i])
iiloc = temp[:,0]*temp[:,1]
# get location of all ijs in seq
ilocs = self.seq[:,0] == i
self._dplist[iiloc] -= np.sum(self._dplist[ilocs],axis=0)
rdPisum = np.sum(rdPi, axis=0)
self._pstress[iiloc] += (rdPisum[tril_indices].flatten()).reshape(ncoefs,3,3)
x = {'x':self._plist, 'dxdr':self._dplist,
'elements':list(atoms.symbols), 'seq':self.seq}
if self._stress:
vol = atoms.get_volume()
x['rdxdr'] = -self._pstress/vol
else:
x['rdxdr'] = None
else:
cs = compute_cs(self.neighborlist, self.nmax, self.lmax, self.rcut, self.alpha, self._cutoff_function)
cs *= self.atomic_weights[:,np.newaxis,np.newaxis,np.newaxis]
cs = np.einsum('inlm,l->inlm', cs, norm)
# everything good up to here
for i in np.unique(self.seq[:,0]):
centers = self.neighbor_indices[:,0] == i
ctot = cs[centers].sum(axis=0)
P = np.einsum('ijk,ljk->ilj', ctot, np.conj(ctot)).real
self._plist[i] = P[tril_indices].flatten()
x = {'x':self._plist, 'dxdr': None, 'rdxdr': None, 'elements':list(atoms.symbols)}
self.clear_memory()
return x
[docs] def initialize_arrays(self):
# number of atoms in periodic arrangement
# for a crystal this will be the number of
# atoms in the unit cell
# for a cluster/molecule(s) this will be the total number
# of atoms
ncell = len(self._atoms) #self._atoms)
# degree of spherical harmonic expansion
lmax = self.lmax
# degree of radial expansion
nmax = self.nmax
# number of unique power spectrum components
# this is given by the triangular elements of
# the radial expansion multiplied by the degree
# of spherical harmonic expansion (including 0)
ncoefs = nmax*(nmax+1)//2*(lmax+1)
self._plist = np.zeros((ncell, ncoefs), dtype=np.float64)
self._dplist = np.zeros((len(self.seq), ncoefs, 3), dtype=np.float64)
self._pstress = np.zeros((len(self.seq), ncoefs, 3, 3), dtype=np.float64)
return
[docs] def build_neighbor_list(self, atom_ids=None):
'''
Builds a neighborlist for the calculation of bispectrum components for
a given ASE atoms object given in the calculate method.
'''
atoms = self._atoms
if atom_ids is None:
atom_ids = range(len(atoms))
cutoffs = [self.rcut/2]*len(atoms)
if self.primitive:
nl = PrimitiveNeighborList(cutoffs, self_interaction=False, bothways=True, skin=0.0)
nl.build(atoms.pbc, atoms.cell, atoms.get_scaled_positions())
else:
nl = NeighborList(cutoffs, self_interaction=False, bothways=True, skin=0.0)
nl.update(atoms)
center_atoms = []
neighbors = []
neighbor_indices = []
atomic_weights = []
temp_indices = []
for i in atom_ids:
# get center atom position vector
center_atom = atoms.positions[i]
# get indices and cell offsets for each neighbor
indices, offsets = nl.get_neighbors(i)
temp_indices.append(indices)
for j, offset in zip(indices, offsets):
pos = atoms.positions[j] + np.dot(offset,atoms.get_cell()) - center_atom
center_atoms.append(center_atom)
neighbors.append(pos)
if self.weight_on and atoms[j].number != atoms[i].number:
factor = -1
else:
factor = 1
atomic_weights.append(factor*atoms[j].number)
neighbor_indices.append([i,j])
neighbor_indices = np.array(neighbor_indices, dtype=np.int64)
Seq = []
for i in atom_ids:
ineighs = neighbor_indices[:,0] == i
unique_atoms = np.unique(neighbor_indices[ineighs])
if i not in unique_atoms:
at = list(unique_atoms)
at.append(i)
at.sort()
unique_atoms = np.array(at)
for j in unique_atoms:
Seq.append([i,j])
Seq = np.array(Seq, dtype=np.int64)
self.center_atoms = np.array(center_atoms, dtype=np.float64)
self.neighborlist = np.array(neighbors, dtype=np.float64)
self.seq = Seq
self.atomic_weights = np.array(atomic_weights, dtype=np.int64)
self.neighbor_indices = neighbor_indices
return
[docs]def Cosine(Rij, Rc, derivative=False):
# Rij is the norm
if derivative is False:
result = 0.5 * (np.cos(np.pi * Rij / Rc) + 1.)
else:
result = -0.5 * np.pi / Rc * np.sin(np.pi * Rij / Rc)
return result
[docs]def Tanh(Rij, Rc, derivative=False):
if derivative is False:
result = np.tanh(1-Rij/Rc)**3
else:
tanh_square = np.tanh(1-Rij/Rc)**2
result = - (3/Rc) * tanh_square * (1-tanh_square)
return result
[docs]def Poly1(Rij, Rc, derivative=False):
if derivative is False:
x = Rij/Rc
x_square = x**2
result = x_square * (2*x-3) + 1
else:
term1 = (6 / Rc**2) * Rij
term2 = Rij/Rc - 1
result = term1*term2
return result
[docs]def Poly2(Rij, Rc, derivative=False):
if derivative is False:
x = Rij/Rc
result = x**3 * (x*(15-6*x)-10) + 1
else:
x = Rij/Rc
result = (-30/Rc) * (x**2 * (x-1)**2)
return result
[docs]def Poly3(Rij, Rc, derivative=False):
if derivative is False:
x = Rij/Rc
result = x**4*(x*(x*(20*x-70)+84)-35)+1
else:
x = Rij/Rc
result = (140/Rc) * (x**3 * (x-1)**3)
return result
[docs]def Poly4(Rij, Rc, derivative=False):
if derivative is False:
x = Rij/Rc
result = x**5*(x*(x*(x*(315-70*x)-540)+420)-126)+1
else:
x = Rij/Rc
result = (-630/Rc) * (x**4 * (x-1)**4)
return result
[docs]def Exponent(Rij, Rc, derivative=False):
if derivative is False:
x = Rij/Rc
try:
result = np.exp(1 - 1/(1-x**2))
except:
result = 0
else:
x = Rij/Rc
try:
result = 2*x * np.exp(1 - 1/(1-x**2)) / (1+x**2)**2
except:
result = 0
return result
[docs]def Unity(Rij, Rc, derivative=False):
if derivative is False:
return np.ones(len(Rij))
else:
return np.ones(len(Rij))
[docs]def W(nmax):
arr = np.zeros((nmax,nmax), np.float64)
for alpha in range(1, nmax+1, 1):
temp1 = (2*alpha+5)*(2*alpha+6)*(2*alpha+7)
for beta in range(1, alpha+1, 1):
temp2 = (2*beta+5)*(2*beta+6)*(2*beta+7)
arr[alpha-1, beta-1] = np.sqrt(temp1*temp2)/(5+alpha+beta)/(6+alpha+beta)/(7+alpha+beta)
arr[beta-1, alpha-1] = arr[alpha-1, beta-1]
sinv = np.linalg.inv(arr)
eigvals, V = np.linalg.eig(sinv)
sqrtD = np.diag(np.sqrt(eigvals))
arr[:,:] = np.dot(np.dot(V, sqrtD), np.linalg.inv(V))
return arr
[docs]def phi(r, alpha, rcut):
'''
See g below
'''
return (rcut-r)**(alpha+2)/np.sqrt(2*rcut**(2*alpha+7)/(2*alpha+5)/(2*alpha+6)/(2*alpha+7))
[docs]def g(r, n, nmax, rcut, w):
Sum = 0.0
for alpha in range(1, nmax+1):
Sum += w[n-1, alpha-1]*phi(r, alpha, rcut)
return Sum
[docs]def GaussChebyshevQuadrature(nmax,lmax):
NQuad = (nmax+lmax+1)*10
quad_array = np.zeros(NQuad, dtype=np.float64)
for i in range(1,NQuad+1,1):
# roots of Chebyshev polynomial of degree N
x = np.cos((2*i-1)*np.pi/2/NQuad)
quad_array[i-1] = x
return quad_array, np.pi/NQuad
[docs]def compute_cs(pos, nmax, lmax, rcut, alpha, cutoff):
# compute the overlap matrix
w = W(nmax)
# get the norm of the position vectors
Ris = np.linalg.norm(pos, axis=1) # (Nneighbors)
# initialize Gauss Chebyshev Quadrature
GCQuadrature, weight = GaussChebyshevQuadrature(nmax,lmax) #(Nquad)
weight *= rcut/2
# transform the quadrature from (-1,1) to (0, rcut)
Quadrature = rcut/2*(GCQuadrature+1)
# compute the arguments for the bessel functions
BesselArgs = 2*alpha*np.outer(Ris,Quadrature)#(Nneighbors x Nquad)
# initalize the arrays for the bessel function values
# and the G function values
Bessels = np.zeros((len(Ris), len(Quadrature), lmax+1), dtype=np.float64) #(Nneighbors x Nquad x lmax+1)
Gs = np.zeros((nmax, len(Quadrature)), dtype=np.float64) # (nmax, nquad)
# compute the g values
for n in range(1,nmax+1,1):
Gs[n-1,:] = g(Quadrature, n, nmax, rcut, w)
# compute the bessel values
for l in range(lmax+1):
Bessels[:,:,l] = spherical_in(l, BesselArgs)
# mutliply the terms in the integral separate from the Bessels
Quad_Squared = Quadrature**2
Gs *= Quad_Squared * np.exp(-alpha*Quad_Squared) * np.sqrt(1-GCQuadrature**2) * weight
# perform the integration with the Bessels
integral_array = np.einsum('ij,kjl->kil', Gs, Bessels) # (Nneighbors x nmax x lmax+1)
# compute the gaussian for each atom and multiply with 4*pi
# to minimize floating point operations
# weight can also go here since the Chebyshev gauss quadrature weights are uniform
exparray = 4*np.pi*np.exp(-alpha*Ris**2) # (Nneighbors)
cutoff_array = cutoff(Ris, rcut)
exparray *= cutoff_array
# get the spherical coordinates of each atom
thetas = np.arccos(pos[:,2]/Ris[:])
phis = np.arctan2(pos[:,1], pos[:,0])
# determine the size of the m axis
msize = 2*lmax+1
# initialize an array for the spherical harmonics
ylms = np.zeros((len(Ris), lmax+1, msize), dtype=np.complex128)
# compute the spherical harmonics
for l in range(lmax+1):
for m in range(-l,l+1,1):
midx = msize//2 + m
ylms[:,l,midx] = sph_harm(m, l, phis, thetas)
# multiply the spherical harmonics and the radial inner product
Y_mul_innerprod = np.einsum('ijk,ilj->iljk', ylms, integral_array)
# multiply the gaussians into the expression
C = np.einsum('i,ijkl->ijkl', exparray, Y_mul_innerprod)
return C
[docs]def compute_dcs(pos, nmax, lmax, rcut, alpha, cutoff):
# compute the overlap matrix
w = W(nmax)
# get the norm of the position vectors
Ris = np.linalg.norm(pos, axis=1) # (Nneighbors)
# get unit vectors
upos = pos/Ris[:,np.newaxis]
# initialize Gauss Chebyshev Quadrature
GCQuadrature, weight = GaussChebyshevQuadrature(nmax,lmax) #(Nquad)
weight *= rcut/2
# transform from (-1,1) to (0, rcut)
Quadrature = rcut/2*(GCQuadrature+1)
# compute the arguments for the bessel functions
BesselArgs = 2*alpha*np.outer(Ris,Quadrature)#(Nneighbors x Nquad)
# initalize the arrays for the bessel function values
# and the G function values
Bessels = np.zeros((len(Ris), len(Quadrature), lmax+1), dtype=np.float64) #(Nneighbors x Nquad x lmax+1)
Gs = np.zeros((nmax, len(Quadrature)), dtype=np.float64) # (nmax, nquad)
dBessels = np.zeros((len(Ris), len(Quadrature), lmax+1), dtype=np.float64) #(Nneighbors x Nquad x lmax+1)
# compute the g values
for n in range(1,nmax+1,1):
Gs[n-1,:] = g(Quadrature, n, nmax, rcut,w)*weight
# compute the bessel values
for l in range(lmax+1):
Bessels[:,:,l] = spherical_in(l, BesselArgs)
dBessels[:,:,l] = spherical_in(l, BesselArgs, derivative=True)
#(Nneighbors x Nquad x lmax+1) unit vector here
gradBessels = np.einsum('ijk,in->ijkn',dBessels,upos)
gradBessels *= 2*alpha
# multiply with r for the integral
gradBessels = np.einsum('ijkn,j->ijkn',gradBessels,Quadrature)
# mutliply the terms in the integral separate from the Bessels
Quad_Squared = Quadrature**2
Gs *= Quad_Squared * np.exp(-alpha*Quad_Squared) * np.sqrt(1-GCQuadrature**2)
# perform the integration with the Bessels
integral_array = np.einsum('ij,kjl->kil', Gs, Bessels) # (Nneighbors x nmax x lmax+1)
grad_integral_array = np.einsum('ij,kjlm->kilm', Gs, gradBessels)# (Nneighbors x nmax x lmax+1, 3)
# compute the gaussian for each atom
exparray = 4*np.pi*np.exp(-alpha*Ris**2) # (Nneighbors)
gradexparray = (-2*alpha*Ris*exparray)[:,np.newaxis]*upos
cutoff_array = cutoff(Ris, rcut)
grad_cutoff_array = np.einsum('i,in->in',cutoff(Ris, rcut, True), upos)
# get the spherical coordinates of each atom
thetas = np.arccos(pos[:,2]/Ris[:])
phis = np.arctan2(pos[:,1], pos[:,0])
# the size changes temporarily for the derivative
# determine the size of the m axis
Msize = 2*(lmax+1)+1
msize = 2*lmax + 1
# initialize an array for the spherical harmonics and gradients
#(Nneighbors, l, m, *3*)
ylms = np.zeros((len(Ris), lmax+1+1, Msize), dtype=np.complex128)
gradylms = np.zeros((len(Ris), lmax+1, msize, 3), dtype=np.complex128)
# compute the spherical harmonics
for l in range(lmax+1+1):
for m in range(-l,l+1,1):
midx = Msize//2 + m
ylms[:,l,midx] = sph_harm(m, l, phis, thetas)
for l in range(1, lmax+1):
for m in range(-l, l+1, 1):
midx = msize//2 + m
Midx = Msize//2 + m
# get gradient with recpect to spherical covariant components
xcov0 = -np.sqrt(((l+1)**2-m**2)/(2*l+1)/(2*l+3))*l*ylms[:,l+1,Midx]/Ris
if abs(m) <= l-1:
xcov0 += np.sqrt((l**2-m**2)/(2*l-1)/(2*l+1))*(l+1)*ylms[:,l-1,Midx]/Ris
xcovpl1 = -np.sqrt((l+m+1)*(l+m+2)/2/(2*l+1)/(2*l+3))*l*ylms[:,l+1,Midx+1]/Ris
if abs(m+1) <= l-1:
xcovpl1 -= np.sqrt((l-m-1)*(l-m)/2/(2*l-1)/(2*l+1))*(l+1)*ylms[:,l-1,Midx+1]/Ris
xcovm1 = -np.sqrt((l-m+1)*(l-m+2)/2/(2*l+1)/(2*l+3))*l*ylms[:,l+1,Midx-1]/Ris
if abs(m-1) <= l-1:
xcovm1 -= np.sqrt((l+m-1)*(l+m)/2/(2*l-1)/(2*l+1))*(l+1)*ylms[:,l-1,Midx-1]/Ris
#transform the gradient to cartesian
gradylms[:,l,midx,0] = 1/np.sqrt(2)*(xcovm1-xcovpl1)
gradylms[:,l,midx,1] = 1j/np.sqrt(2)*(xcovm1+xcovpl1)
gradylms[:,l,midx,2] = xcov0
# index ylms to get rid of extra terms for derivative
ylms = ylms[:,0:lmax+1,1:1+2*lmax+1]
# multiply the spherical harmonics and the radial inner product
Y_mul_innerprod = np.einsum('ijk,ilj->iljk', ylms, integral_array)
# multiply the gradient of the spherical harmonics with the radial inner get_radial_inner_product
dY_mul_innerprod = np.einsum('ijkn,ilj->iljkn', gradylms, integral_array)
# multiply the spherical harmonics with the gradient of the radial inner get_radial_inner_product
Y_mul_dinnerprod = np.einsum('ijk,iljn->iljkn', ylms, grad_integral_array)
# multiply the gaussians into the expression with 4pi
C = np.einsum('i,ijkl->ijkl', exparray, Y_mul_innerprod)
# multiply the gradient of the gaussian with the other terms
gradexp_mul_y_inner = np.einsum('in,ijkl->ijkln', gradexparray, Y_mul_innerprod)
# add gradient of inner product and spherical harmonic terms
gradHarmonics_mul_gaussian = np.einsum('ijkln,i->ijkln', dY_mul_innerprod+Y_mul_dinnerprod, exparray)
dC = gradexp_mul_y_inner + gradHarmonics_mul_gaussian
dC *= cutoff_array[:,np.newaxis,np.newaxis,np.newaxis,np.newaxis]
dC += np.einsum('in,ijkl->ijkln', grad_cutoff_array, C)
C *= cutoff_array[:,np.newaxis,np.newaxis,np.newaxis]
return C, dC
if __name__ == "__main__":
from ase.io import read
import time
# ---------------------- Options ------------------------
parser = OptionParser()
parser.add_option("-c", "--crystal", dest="structure",
help="crystal from file, cif or poscar, REQUIRED",
metavar="crystal")
parser.add_option("-r", "--rcut", dest="rcut", default=3.0, type=float,
help="cutoff for neighbor calcs, default: 3.0"
)
parser.add_option("-l", "--lmax", dest="lmax", default=2, type=int,
help="lmax, default: 1"
)
parser.add_option("-n", "--nmax", dest="nmax", default=1, type=int,
help="nmax, default: 1"
)
parser.add_option("-a", "--alpha", dest="alpha", default=2.0, type=float,
help="cutoff for neighbor calcs, default: 2.0"
)
parser.add_option("-s", dest="stress", default=True,
action='store_true',help='derivative flag')
parser.add_option("-f", dest="der", default=True,
action='store_false',help='derivative flag')
(options, args) = parser.parse_args()
if options.structure is None:
from ase.build import bulk
test = bulk('Si', 'diamond', a=5.459, cubic=True)
cell = test.get_cell()
cell[0,1] += 0.5
test.set_cell(cell)
else:
test = read(options.structure, format='vasp')
lmax = options.lmax
nmax = options.nmax
rcut = options.rcut
alpha = options.alpha
der = options.der
stress = options.stress
start1 = time.time()
f = SO3(nmax=nmax, lmax=lmax, rcut=rcut, alpha=alpha, derivative=True, stress=False, cutoff_function='cosine')
x = f.calculate(test)
start2 = time.time()
print('x', x['x'])
#print('dxdr', x['dxdr'])
print('calculation time {}'.format(start2-start1))