import numpy as np
from numpy import sqrt
from ase.data import atomic_numbers
from ase.calculators.calculator import Parameters
from scipy.special import sph_harm
from ..utilities import Data, Logger, importer
from .cutoffs import Cosine, Polynomial, dict2cutoff
NeighborList = importer('NeighborList')
try:
from .. import fmodules
except ImportError:
fmodules = None
[docs]class Zernike(object):
"""Class that calculates Zernike fingerprints.
Parameters
----------
cutoff : object or float
Cutoff function, typically from amp.descriptor.cutoffs. Can be also
fed as a float representing the radius above which neighbor
interactions are ignored; in this case a cosine cutoff function will be
employed. Default is a 6.5-Angstrom cosine cutoff.
Gs : dict
Dictionary of symbols and dictionaries for making symmetry functions.
Either auto-genetrated, or given in the following form, for example:
>>> Gs = {"Au": {"Au": 3., "O": 2.}, "O": {"Au": 5., "O": 10.}}
nmax : integer or dict
Maximum degree of Zernike polynomials that will be included in the
fingerprint vector. Can be different values for different species fed
as a dictionary with chemical elements as keys.
dblabel : str
Optional separate prefix/location for database files, including
fingerprints, fingerprint derivatives, and neighborlists. This file
location can be shared between calculator instances to avoid
re-calculating redundant information. If not supplied, just uses the
value from label.
elements : list
List of allowed elements present in the system. If not provided, will
be found automatically.
version : str
Version of fingerprints.
mode : str
Can be either 'atom-centered' or 'image-centered'.
fortran : bool
If True, will use fortran modules, if False, will not.
Raises
------
RuntimeError, TypeError
"""
def __init__(self, cutoff=Cosine(6.5), Gs=None, nmax=5, dblabel=None,
elements=None, version='2016.02', mode='atom-centered',
fortran=True):
# Check of the version of descriptor, particularly if restarting.
compatibleversions = ['2016.02', ]
if (version is not None) and version not in compatibleversions:
raise RuntimeError('Error: Trying to use Zernike fingerprints'
' version %s, but this module only supports'
' versions %s. You may need an older or '
' newer version of Amp.' %
(version, compatibleversions))
else:
version = compatibleversions[-1]
# Check that the mode is atom-centered.
if mode != 'atom-centered':
raise RuntimeError('Zernike scheme only works '
'in atom-centered mode. %s '
'specified.' % mode)
# If the cutoff is provided as a number, Cosine function will be used
# by default.
if isinstance(cutoff, int) or isinstance(cutoff, float):
cutoff = Cosine(cutoff)
# If the cutoff is provided as a dictionary, assume we need to load it
# with dict2cutoff.
if type(cutoff) is dict:
cutoff = dict2cutoff(cutoff)
# The parameters dictionary contains the minimum information
# to produce a compatible descriptor; that is, one that gives
# an identical fingerprint when fed an ASE image.
p = self.parameters = Parameters(
{'importname': '.descriptor.zernike.Zernike',
'mode': 'atom-centered'})
p.version = version
p.cutoff = cutoff.todict()
if p.cutoff['name'] == 'Polynomial':
self.gamma = cutoff.gamma
p.Gs = Gs
p.nmax = nmax
p.elements = elements
self.dblabel = dblabel
self.fortran = fortran
self.parent = None # Can hold a reference to main Amp instance.
[docs] def tostring(self):
"""Returns an evaluatable representation of the calculator that can
be used to restart the calculator."""
return self.parameters.tostring()
[docs] def calculate_fingerprints(self, images, parallel=None, log=None,
calculate_derivatives=False):
"""Calculates the fingerpints of the images, for the ones not already
done.
Parameters
----------
images : list or str
List of ASE atoms objects with positions, symbols, energies, and
forces in ASE format. This is the training set of data. This can
also be the path to an ASE trajectory (.traj) or database (.db)
file. Energies can be obtained from any reference, e.g. DFT
calculations.
parallel : dict
Configuration for parallelization. Should be in same form as in
amp.Amp.
log : Logger object
Write function at which to log data. Note this must be a callable
function.
calculate_derivatives : bool
Decides whether or not fingerprintprimes should also be calculated.
"""
if parallel is None:
parallel = {'cores': 1}
log = Logger(file=None) if log is None else log
if (self.dblabel is None) and hasattr(self.parent, 'dblabel'):
self.dblabel = self.parent.dblabel
self.dblabel = 'amp-data' if self.dblabel is None else self.dblabel
p = self.parameters
if p.cutoff['name'] == 'Cosine':
log('Cutoff radius: %.2f ' % p.cutoff['kwargs']['Rc'])
else:
log('Cutoff radius: %.2f and gamma=%i ' % (p.cutoff['kwargs']['Rc'], self.gamma))
log('Cutoff function: %s' % repr(dict2cutoff(p.cutoff)))
if p.elements is None:
log('Finding unique set of elements in training data.')
p.elements = set([atom.symbol for atoms in images.values()
for atom in atoms])
p.elements = sorted(p.elements)
log('%i unique elements included: ' % len(p.elements) +
', '.join(p.elements))
log('Maximum degree of Zernike polynomials:')
if isinstance(p.nmax, dict):
for _ in p.nmax.keys():
log(' %2s: %d' % (_, p.nmax[_]))
else:
log('nmax: %d' % p.nmax)
if p.Gs is None:
log('No coefficient for atomic density function supplied; '
'creating defaults.')
p.Gs = generate_coefficients(p.elements)
log('Coefficients of atomic density function for each element:')
for _ in p.Gs.keys():
log(' %2s: %s' % (_, str(p.Gs[_])))
# Counts the number of descriptors for each element.
no_of_descriptors = {}
for element in p.elements:
count = 0
if isinstance(p.nmax, dict):
for n in xrange(p.nmax[element] + 1):
for l in xrange(n + 1):
if (n - l) % 2 == 0:
count += 1
else:
for n in xrange(p.nmax + 1):
for l in xrange(n + 1):
if (n - l) % 2 == 0:
count += 1
no_of_descriptors[element] = count
log('Number of descriptors for each element:')
for element in p.elements:
log(' %2s: %d' % (element, no_of_descriptors.pop(element)))
log('Calculating neighborlists...', tic='nl')
if not hasattr(self, 'neighborlist'):
calc = NeighborlistCalculator(cutoff=p.cutoff['kwargs']['Rc'])
self.neighborlist = Data(filename='%s-neighborlists'
% self.dblabel,
calculator=calc)
self.neighborlist.calculate_items(images, parallel=parallel, log=log)
log('...neighborlists calculated.', toc='nl')
log('Fingerprinting images...', tic='fp')
if not hasattr(self, 'fingerprints'):
calc = FingerprintCalculator(neighborlist=self.neighborlist,
Gs=p.Gs,
nmax=p.nmax,
cutoff=p.cutoff,
fortran=self.fortran)
self.fingerprints = Data(filename='%s-fingerprints'
% self.dblabel,
calculator=calc)
self.fingerprints.calculate_items(images, parallel=parallel, log=log)
log('...fingerprints calculated.', toc='fp')
if calculate_derivatives:
log('Calculating fingerprint derivatives of images...',
tic='derfp')
if not hasattr(self, 'fingerprintprimes'):
calc = \
FingerprintPrimeCalculator(neighborlist=self.neighborlist,
Gs=p.Gs,
nmax=p.nmax,
cutoff=p.cutoff,
fortran=self.fortran)
self.fingerprintprimes = \
Data(filename='%s-fingerprint-primes'
% self.dblabel,
calculator=calc)
self.fingerprintprimes.calculate_items(
images, parallel=parallel, log=log)
log('...fingerprint derivatives calculated.', toc='derfp')
# Calculators #################################################################
# Neighborlist Calculator
[docs]class NeighborlistCalculator:
"""For integration with .utilities.Data
For each image fed to calculate, a list of neighbors with offset
distances is returned.
Parameters
----------
cutoff : object or float
Cutoff function, typically from amp.descriptor.cutoffs. Can be also
fed as a float representing the radius above which neighbor
interactions are ignored; in this case a cosine cutoff function will be
employed. Default is a 6.5-Angstrom cosine cutoff.
"""
def __init__(self, cutoff):
self.globals = Parameters({'cutoff': cutoff})
self.keyed = Parameters()
self.parallel_command = 'calculate_neighborlists'
[docs] def calculate(self, image, key):
"""For integration with .utilities.Data
For each image fed to calculate, a list of neighbors with offset
distances is returned.
Parameters
----------
image : object
ASE atoms object.
key : str
Key of the image after being hashed.
"""
cutoff = self.globals.cutoff
n = NeighborList(cutoffs=[cutoff / 2.] * len(image),
self_interaction=False,
bothways=True,
skin=0.)
n.update(image)
return [n.get_neighbors(index) for index in xrange(len(image))]
[docs]class FingerprintCalculator:
"""For integration with .utilities.Data"""
def __init__(self, neighborlist, Gs, nmax, cutoff, fortran):
self.globals = Parameters({ 'cutoff': cutoff,
'Gs': Gs,
'nmax': nmax})
self.keyed = Parameters({'neighborlist': neighborlist})
self.parallel_command = 'calculate_fingerprints'
self.fortran = fortran
self.cutoff = cutoff
try: # for scipy v <= 0.90
from scipy import factorial as fac
except ImportError:
try: # for scipy v >= 0.10
from scipy.misc import factorial as fac
except ImportError: # for newer version of scipy
from scipy.special import factorial as fac
self.factorial = [fac(0.5 * _) for _ in xrange(4 * nmax + 3)]
[docs] def calculate(self, image, key):
"""Makes a list of fingerprints, one per atom, for the fed image.
Parameters
----------
image : object
ASE atoms object.
key : str
Key of the image after being hashed.
"""
nl = self.keyed.neighborlist[key]
fingerprints = []
for atom in image:
symbol = atom.symbol
index = atom.index
neighbors, offsets = nl[index]
neighborsymbols = [image[_].symbol for _ in neighbors]
Rs = [image.positions[neighbor] + np.dot(offset, image.cell)
for (neighbor, offset) in zip(neighbors, offsets)]
self.atoms = image
indexfp = self.get_fingerprint(index, symbol, neighborsymbols, Rs)
fingerprints.append(indexfp)
return fingerprints
[docs] def get_fingerprint(self, index, symbol, n_symbols, Rs):
"""Returns the fingerprint of symmetry function values for atom
specified by its index and symbol.
n_symbols and Rs are lists of neighbors' symbols and Cartesian
positions, respectively.
Parameters
----------
index : int
Index of the center atom.
symbol : str
Symbol of the center atom.
n_symbols : list of str
List of neighbors' symbols.
Rs : list of list of float
List of Cartesian atomic positions of neighbors.
Returns
-------
symbols, fingerprints : list of float
Fingerprints for atom specified by its index and symbol.
"""
home = self.atoms[index].position
cutoff = self.cutoff
Rc = cutoff['kwargs']['Rc']
if cutoff['name'] == 'Cosine':
cutoff_fxn = Cosine(Rc)
elif cutoff['name'] == 'Polynomial':
p_gamma = cutoff['kwargs']['gamma']
cutoff_fxn = Polynomial(Rc, gamma=p_gamma)
fingerprint = []
for n in xrange(self.globals.nmax + 1):
for l in xrange(n + 1):
if (n - l) % 2 == 0:
norm = 0.
for m in xrange(l + 1):
c_nlm = 0.
for n_symbol, neighbor in zip(n_symbols, Rs):
x = (neighbor[0] - home[0]) / Rc
y = (neighbor[1] - home[1]) / Rc
z = (neighbor[2] - home[2]) / Rc
rho = np.linalg.norm([x, y, z])
if self.fortran:
c_args = [Rc * rho]
if cutoff['name'] == 'Polynomial':
c_args.append(p_gamma)
Z_nlm = fmodules.calculate_z(n=n, l=l, m=m,
x=x, y=y, z=z,
factorial=self.factorial,
length=len(self.factorial))
Z_nlm = self.globals.Gs[symbol][n_symbol] * \
Z_nlm * cutoff_fxn(*c_args)
else:
# Alternative ways to calculate Z_nlm
# Z_nlm = self.globals.Gs[symbol][n_symbol] * \
# calculate_Z(n, l, m, x, y, z,
# self.factorial) * \
# cutoff_fxn(rho * Rc)
# Z_nlm = self.globals.Gs[symbol][n_symbol] * \
# calculate_Z2(n, l, m, x, y, z) * \
# cutoff_fxn(rho * Rc)
if rho > 0.:
theta = np.arccos(z / rho)
else:
theta = 0.
if x < 0.:
phi = np.pi + np.arctan(y / x)
elif 0. < x and y < 0.:
phi = 2 * np.pi + np.arctan(y / x)
elif 0. < x and 0. <= y:
phi = np.arctan(y / x)
elif x == 0. and 0. < y:
phi = 0.5 * np.pi
elif x == 0. and y < 0.:
phi = 1.5 * np.pi
else:
phi = 0.
c_args = [Rc * rho]
if cutoff['name'] == 'Polynomial':
c_args.append(p_gamma)
Z_nlm = self.globals.Gs[symbol][n_symbol] * \
calculate_R(n, l, rho, self.factorial) * \
sph_harm(m, l, phi, theta) * \
cutoff_fxn(*c_args)
# sum over neighbors
c_nlm += np.conjugate(Z_nlm)
# sum over m values
if m == 0:
norm += c_nlm * np.conjugate(c_nlm)
else:
norm += 2. * c_nlm * np.conjugate(c_nlm)
fingerprint.append(norm.real)
return symbol, fingerprint
[docs]class FingerprintPrimeCalculator:
"""For integration with .utilities.Data"""
def __init__(self, neighborlist, Gs, nmax, cutoff, fortran):
self.globals = Parameters({'cutoff': cutoff,
'Gs': Gs,
'nmax': nmax})
self.keyed = Parameters({'neighborlist': neighborlist})
self.parallel_command = 'calculate_fingerprint_primes'
self.fortran = fortran
try: # for scipy v <= 0.90
from scipy import factorial as fac
except ImportError:
try: # for scipy v >= 0.10
from scipy.misc import factorial as fac
except ImportError: # for newer version of scipy
from scipy.special import factorial as fac
self.factorial = [fac(0.5 * _) for _ in xrange(4 * nmax + 3)]
[docs] def calculate(self, image, key):
"""Makes a list of fingerprint derivatives, one per atom, for the fed
image.
Parameters
---------
image : object
ASE atoms object.
key : str
Key of the image after being hashed.
"""
self.atoms = image
nl = self.keyed.neighborlist[key]
fingerprintprimes = {}
for atom in image:
selfsymbol = atom.symbol
selfindex = atom.index
selfneighborindices, selfneighboroffsets = nl[selfindex]
selfneighborsymbols = [
image[_].symbol for _ in selfneighborindices]
for i in xrange(3):
# Calculating derivative of self atom fingerprints w.r.t.
# coordinates of itself.
nneighborindices, nneighboroffsets = nl[selfindex]
nneighborsymbols = [image[_].symbol for _ in nneighborindices]
Rs = [image.positions[_index] +
np.dot(_offset, image.get_cell())
for _index, _offset
in zip(nneighborindices,
nneighboroffsets)]
der_indexfp = self.get_fingerprintprime(
selfindex, selfsymbol,
nneighborindices,
nneighborsymbols,
Rs, selfindex, i)
fingerprintprimes[
(selfindex, selfsymbol, selfindex, selfsymbol, i)] = \
der_indexfp
# Calculating derivative of neighbor atom fingerprints w.r.t.
# coordinates of self atom.
for nindex, nsymbol, noffset in \
zip(selfneighborindices,
selfneighborsymbols,
selfneighboroffsets):
# for calculating forces, summation runs over neighbor
# atoms of type II (within the main cell only)
if noffset.all() == 0:
nneighborindices, nneighboroffsets = nl[nindex]
nneighborsymbols = \
[image[_].symbol for _ in nneighborindices]
Rs = [image.positions[_index] +
np.dot(_offset, image.get_cell())
for _index, _offset
in zip(nneighborindices,
nneighboroffsets)]
# for calculating derivatives of fingerprints,
# summation runs over neighboring atoms of type
# I (either inside or outside the main cell)
der_indexfp = self.get_fingerprintprime(
nindex, nsymbol,
nneighborindices,
nneighborsymbols,
Rs, selfindex, i)
fingerprintprimes[
(selfindex, selfsymbol, nindex, nsymbol, i)] = \
der_indexfp
return fingerprintprimes
[docs] def get_fingerprintprime(self, index, symbol, n_indices, n_symbols, Rs,
p, q):
"""Returns the value of the derivative of G for atom with index and
symbol with respect to coordinate x_{i} of atom index m. n_indices,
n_symbols and Rs are lists of neighbors' indices, symbols and Cartesian
positions, respectively.
Parameters
----------
index : int
Index of the center atom.
symbol : str
Symbol of the center atom.
n_indices : list of int
List of neighbors' indices.
n_symbols : list of str
List of neighbors' symbols.
Rs : list of list of float
List of Cartesian atomic positions.
p : int
Index of the pair atom.
q : int
Direction of the derivative; is an integer from 0 to 2.
Returns
-------
fingerprint_prime : list of float
The value of the derivative of the fingerprints for atom with index
and symbol with respect to coordinate x_{i} of atom index m.
"""
home = self.atoms[index].position
cutoff = self.globals.cutoff
Rc = cutoff['kwargs']['Rc']
if cutoff['name'] is 'Cosine':
cutoff_fxn = Cosine(Rc)
elif cutoff['name'] is 'Polynomial':
p_gamma = cutoff['kwargs']['gamma']
cutoff_fxn = Polynomial(Rc, gamma=p_gamma)
fingerprint_prime = []
for n in xrange(self.globals.nmax + 1):
for l in xrange(n + 1):
if (n - l) % 2 == 0:
if self.fortran: # fortran version; faster
G_numbers = [self.globals.Gs[symbol][elm]
for elm in n_symbols]
numbers = [atomic_numbers[elm] for elm in n_symbols]
if len(Rs) == 0:
norm_prime = 0.
else:
args_calculate_zernike_prime = dict(
n=n,
l=l,
n_length=len(n_indices),
n_indices=list(n_indices),
numbers=numbers,
rs=Rs,
g_numbers=G_numbers,
cutoff=Rc,
cutofffn=cutoff['name'],
indexx=index,
home=home,
p=p,
q=q,
fac_length=len(self.factorial),
factorial=self.factorial)
if cutoff['name'] == 'Polynomial':
args_calculate_zernike_prime['p_gamma'] = cutoff['kwargs']['gamma']
norm_prime = \
fmodules.calculate_zernike_prime(**args_calculate_zernike_prime)
else:
norm_prime = 0.
for m in xrange(l + 1):
c_nlm = 0.
c_nlm_prime = 0.
for n_index, n_symbol, neighbor in zip(n_indices,
n_symbols,
Rs):
x = (neighbor[0] - home[0]) / Rc
y = (neighbor[1] - home[1]) / Rc
z = (neighbor[2] - home[2]) / Rc
rho = np.linalg.norm([x, y, z])
c_args = [rho * Rc]
if cutoff['name'] == 'Polynomial':
c_args.append(p_gamma)
_Z_nlm = calculate_Z(n, l, m,
x, y, z,
self.factorial)
# Calculates Z_nlm
Z_nlm = _Z_nlm * \
cutoff_fxn(*c_args)
# Calculates Z_nlm_prime
Z_nlm_prime = _Z_nlm * \
cutoff_fxn.prime(*c_args) * \
der_position(
index, n_index, home, neighbor, p, q)
_Z_nlm_prime = calculate_Z_prime(n, l, m,
x, y, z, q,
self.factorial)
if (Kronecker(n_index, p) -
Kronecker(index, p)) == 1:
Z_nlm_prime += \
cutoff_fxn(*c_args) * \
_Z_nlm_prime / Rc
elif (Kronecker(n_index, p) -
Kronecker(index, p)) == -1:
Z_nlm_prime -= \
cutoff_fxn(*c_args) * \
_Z_nlm_prime / Rc
# sum over neighbors
c_nlm += self.globals.Gs[symbol][
n_symbol] * np.conjugate(Z_nlm)
c_nlm_prime += self.globals.Gs[symbol][
n_symbol] * np.conjugate(Z_nlm_prime)
# sum over m values
if m == 0:
norm_prime += 2. * c_nlm * \
np.conjugate(c_nlm_prime)
else:
norm_prime += 4. * c_nlm * \
np.conjugate(c_nlm_prime)
fingerprint_prime.append(norm_prime.real)
return fingerprint_prime
# Auxiliary functions #########################################################
[docs]def binomial(n, k, factorial):
""" Returns C(n,k) = n!/(k!(n-k)!).
"""
assert n >= 0 and k >= 0 and n >= k, \
'n and k should be non-negative integers with n >= k.'
c = factorial[int(2 * n)] / \
(factorial[int(2 * k)] * factorial[int(2 * (n - k))])
return c
[docs]def calculate_R(n, l, rho, factorial):
"""Calculates R_{n}^{l}(rho) according to the last equation of wikipedia.
"""
if (n - l) % 2 != 0:
return 0
else:
value = 0.
k = (n - l) / 2
term1 = np.sqrt(2. * n + 3.)
for s in xrange(k + 1):
b1 = binomial(k, s, factorial)
b2 = binomial(n - s - 1 + 1.5, k, factorial)
value += ((-1) ** s) * b1 * b2 * (rho ** (n - 2. * s))
value *= term1
return value
[docs]def generate_coefficients(elements):
"""Automatically generates coefficients if not given by the user.
Parameters
----------
elements : list of str
List of symbols of all atoms.
Returns
-------
G : dict of dicts
"""
_G = {}
for element in elements:
_G[element] = atomic_numbers[element]
G = {}
for element in elements:
G[element] = _G
return G
[docs]def Kronecker(i, j):
"""Kronecker delta function.
i : int
First index of Kronecker delta.
j : int
Second index of Kronecker delta.
Returns
-------
Kronecker delta : int
"""
if i == j:
return 1
else:
return 0
[docs]def der_position(m, n, Rm, Rn, l, i):
"""Returns the derivative of the norm of position vector R_{mn} with
respect to x_{i} of atomic index l.
Parameters
----------
m : int
Index of the first atom.
n : int
Index of the second atom.
Rm : float
Position of the first atom.
Rn : float
Position of the second atom.
l : int
Index of the atom force is acting on.
i : int
Direction of force.
Returns
-------
der_position : list of float
The derivative of the norm of position vector R_{mn} with respect to
x_{i} of atomic index l.
"""
Rmn = np.linalg.norm(Rm - Rn)
# mm != nn is necessary for periodic systems
if l == m and m != n:
der_position = (Rm[i] - Rn[i]) / Rmn
elif l == n and m != n:
der_position = -(Rm[i] - Rn[i]) / Rmn
else:
der_position = 0.
return der_position
[docs]def calculate_q(nu, k, l, factorial):
"""Calculates q_{kl}^{nu} according to the unnumbered equation afer Eq. (7)
of "3D Zernike Descriptors for Content Based Shape Retrieval",
Computer-Aided Design 36 (2004) 1047-1062.
"""
result = ((-1) ** (k + nu)) * sqrt((2. * l + 4. * k + 3.) / 3.) * \
binomial(k, nu, factorial) * \
binomial(2. * k, k, factorial) * \
binomial(2. * (k + l + nu) + 1., 2. * k, factorial) / \
binomial(k + l + nu, k, factorial) / (2. ** (2. * k))
return result
[docs]def calculate_Z(n, l, m, x, y, z, factorial):
"""Calculates Z_{nl}^{m}(x, y, z) according to the unnumbered equation afer
Eq. (11) of "3D Zernike Descriptors for Content Based Shape Retrieval",
Computer-Aided Design 36 (2004) 1047-1062.
"""
value = 0.
term1 = sqrt((2. * l + 1.) * factorial[int(2 * (l + m))] *
factorial[int(2 * (l - m))]) / factorial[int(2 * l)]
term2 = 2. ** (-m)
k = int((n - l) / 2.)
for nu in xrange(k + 1):
q = calculate_q(nu, k, l, factorial)
for alpha in xrange(nu + 1):
b1 = binomial(nu, alpha, factorial)
for beta in xrange(nu - alpha + 1):
b2 = binomial(nu - alpha, beta, factorial)
term3 = q * b1 * b2
for u in xrange(m + 1):
b5 = binomial(m, u, factorial)
term4 = ((-1.)**(m - u)) * b5 * (1j**u)
for mu in xrange(int((l - m) / 2.) + 1):
b6 = binomial(l, mu, factorial)
b7 = binomial(l - mu, m + mu, factorial)
term5 = ((-1.)**mu) * (2.**(-2. * mu)) * b6 * b7
for eta in xrange(mu + 1):
r = 2. * (eta + alpha) + u
s = 2. * (mu - eta + beta) + m - u
t = 2. * (nu - alpha - beta - mu) + l - m
value += term3 * term4 * term5 * \
binomial(mu, eta, factorial) * \
(x ** r) * (y ** s) * (z ** t)
term6 = (1j) ** m
value = term1 * term2 * term6 * value
value = value / sqrt(4. * np.pi / 3.)
return value
[docs]def calculate_Z_prime(n, l, m, x, y, z, p, factorial):
"""Calculates dZ_{nl}^{m}(x, y, z)/dR_{p} according to the unnumbered
equation afer Eq. (11) of "3D Zernike Descriptors for Content Based Shape
Retrieval", Computer-Aided Design 36 (2004) 1047-1062.
"""
value = 0.
term1 = sqrt((2. * l + 1.) * factorial[int(2 * (l + m))] *
factorial[int(2 * (l - m))]) / factorial[int(2 * l)]
term2 = 2. ** (-m)
k = int((n - l) / 2.)
for nu in xrange(k + 1):
q = calculate_q(nu, k, l, factorial)
for alpha in xrange(nu + 1):
b1 = binomial(nu, alpha, factorial)
for beta in xrange(nu - alpha + 1):
b2 = binomial(nu - alpha, beta, factorial)
term3 = q * b1 * b2
for u in xrange(m + 1):
term4 = ((-1.)**(m - u)) * binomial(
m, u, factorial) * (1j**u)
for mu in xrange(int((l - m) / 2.) + 1):
term5 = ((-1.)**mu) * (2.**(-2. * mu)) * \
binomial(l, mu, factorial) * \
binomial(l - mu, m + mu, factorial)
for eta in xrange(mu + 1):
r = 2 * (eta + alpha) + u
s = 2 * (mu - eta + beta) + m - u
t = 2 * (nu - alpha - beta - mu) + l - m
coefficient = term3 * term4 * \
term5 * binomial(mu, eta, factorial)
if p == 0:
if r != 0:
value += coefficient * r * \
(x ** (r - 1)) * (y ** s) * (z ** t)
elif p == 1:
if s != 0:
value += coefficient * s * \
(x ** r) * (y ** (s - 1)) * (z ** t)
elif p == 2:
if t != 0:
value += coefficient * t * \
(x ** r) * (y ** s) * (z ** (t - 1))
term6 = (1j) ** m
value = term1 * term2 * term6 * value
value = value / sqrt(4. * np.pi / 3.)
return value
if __name__ == "__main__":
"""Directly calling this module; apparently from another node.
Calls should come as
python -m amp.descriptor.example id hostname:port
This session will then start a zmq session with that socket, labeling
itself with id. Instructions on what to do will come from the socket.
"""
import sys
import tempfile
import zmq
from ..utilities import MessageDictionary
fortran = False if fmodules is None else True
hostsocket = sys.argv[-1]
proc_id = sys.argv[-2]
msg = MessageDictionary(proc_id)
# Send standard lines to stdout signaling process started and where
# error is directed. This should be caught by pxssh. (This could
# alternatively be done by zmq, but this works.)
print('<amp-connect>') # Signal that program started.
sys.stderr = tempfile.NamedTemporaryFile(mode='w', delete=False,
suffix='.stderr')
print('Log and error written to %s<stderr>' % sys.stderr.name)
# Establish client session via zmq; find purpose.
context = zmq.Context()
socket = context.socket(zmq.REQ)
socket.connect('tcp://%s' % hostsocket)
socket.send_pyobj(msg('<purpose>'))
purpose = socket.recv_pyobj()
if purpose == 'calculate_neighborlists':
# Request variables.
socket.send_pyobj(msg('<request>', 'cutoff'))
cutoff = socket.recv_pyobj()
socket.send_pyobj(msg('<request>', 'images'))
images = socket.recv_pyobj()
# sys.stderr.write(str(images)) # Just to see if they are there.
# Perform the calculations.
calc = NeighborlistCalculator(cutoff=cutoff)
neighborlist = {}
# for key in images.iterkeys():
while len(images) > 0:
key, image = images.popitem() # Reduce memory.
neighborlist[key] = calc.calculate(image, key)
# Send the results.
socket.send_pyobj(msg('<result>', neighborlist))
socket.recv_string() # Needed to complete REQ/REP.
elif purpose == 'calculate_fingerprints':
# Request variables.
socket.send_pyobj(msg('<request>', 'cutoff'))
cutoff = socket.recv_pyobj()
socket.send_pyobj(msg('<request>', 'Gs'))
Gs = socket.recv_pyobj()
socket.send_pyobj(msg('<request>', 'nmax'))
nmax = socket.recv_pyobj()
socket.send_pyobj(msg('<request>', 'neighborlist'))
neighborlist = socket.recv_pyobj()
socket.send_pyobj(msg('<request>', 'images'))
images = socket.recv_pyobj()
calc = FingerprintCalculator(neighborlist, Gs, nmax,
cutoff, fortran)
result = {}
while len(images) > 0:
key, image = images.popitem() # Reduce memory.
result[key] = calc.calculate(image, key)
if len(images) % 100 == 0:
socket.send_pyobj(msg('<info>', len(images)))
socket.recv_string() # Needed to complete REQ/REP.
# Send the results.
socket.send_pyobj(msg('<result>', result))
socket.recv_string() # Needed to complete REQ/REP.
elif purpose == 'calculate_fingerprint_primes':
# Request variables.
socket.send_pyobj(msg('<request>', 'cutoff'))
cutoff = socket.recv_pyobj()
socket.send_pyobj(msg('<request>', 'Gs'))
Gs = socket.recv_pyobj()
socket.send_pyobj(msg('<request>', 'nmax'))
nmax = socket.recv_pyobj()
socket.send_pyobj(msg('<request>', 'neighborlist'))
neighborlist = socket.recv_pyobj()
socket.send_pyobj(msg('<request>', 'images'))
images = socket.recv_pyobj()
calc = FingerprintPrimeCalculator(neighborlist, Gs, nmax,
cutoff, fortran)
result = {}
while len(images) > 0:
key, image = images.popitem() # Reduce memory.
result[key] = calc.calculate(image, key)
if len(images) % 100 == 0:
socket.send_pyobj(msg('<info>', len(images)))
socket.recv_string() # Needed to complete REQ/REP.
# Send the results.
socket.send_pyobj(msg('<result>', result))
socket.recv_string() # Needed to complete REQ/REP.
else:
raise NotImplementedError('purpose %s unknown.' % purpose)
