def binomial2(n, k):
"""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.'
c = float(fac(n)) / (float(fac(k)) * float(fac(n - k)))
return c
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 range(4 * nmax + 3)]
def calculate_Z2(n, l, m, x, y, z):
"""
The second implementation of Z_{nl}^{m}(x, y, z).
"""
value1 = 0.
k1 = (n - l) / 2
for nu in range(k1 + 1):
value1 += (x**2. + y**2. + z**2.)**(nu + 0.5 * l) * calculate_q(
nu, k1, l)
term1 = sqrt((2. * l + 1.) * float(fac(l + m)) * float(fac(l - m))) / \
float(fac(l))
term2 = 2.**(-m)
term3 = (1j * x - y)**m
term4 = z**(l - m)
k2 = int((l - m) / 2.)
value2 = 0.
for mu in range(k2 + 1):
term5 = binomial2(l, mu)
term6 = binomial2(l - mu, m + mu)
term7 = ((-1.) ** mu) * \
((x ** 2. + y ** 2.) ** mu) / ((4 * (z ** 2.)) ** mu)
value2 += term5 * term6 * term7
value2 *= term1 * term2 * term3 * term4
value2 *= (1j)**m
value = value1 * value2
value = value / (x**2. + y**2. + z**2.)**(0.5 * l)
value *= sqrt(3. / (4. * np.pi))
return value
def __init__(self, neighborlist, Gs, nmax, cutoff, cutofffn, fortran):
self.globals = Parameters({'cutoff': cutoff,
'cutofffn': cutofffn,
'Gs': Gs,
'nmax': nmax})
self.keyed = Parameters({'neighborlist': neighborlist})
self.parallel_command = 'calculate_fingerprint_prime'
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)]
def __init__(
self,
cutoff=6.5,
Gs=None,
nmax=1,
fingerprints_tag=1,
):
self.cutoff = cutoff
self.Gs = Gs
self.nmax = nmax
self.fingerprints_tag = fingerprints_tag
self.no_of_element_fingerprints = {}
if Gs is not None:
for element in Gs.keys():
no_of_element_fps = 0
if isinstance(nmax, dict):
for n in range(nmax[element] + 1):
for l in range(n + 1):
if (n - l) % 2 == 0:
no_of_element_fps += 1
else:
for n in range(nmax + 1):
for l in range(n + 1):
if (n - l) % 2 == 0:
no_of_element_fps += 1
self.no_of_element_fingerprints[element] = no_of_element_fps
self.factorial = []
for _ in range(4 * nmax + 3):
self.factorial += [float(fac(0.5 * _))]
# Checking if the functional forms of fingerprints in the train set
# is the same as those of the current version of the code:
if self.fingerprints_tag != 1:
raise FingerprintsError('Functional form of fingerprints has been '
'changed. Re-train you train images set, '
'and use the new variables.')