def I_lu(nballs, nboxes, labels):
if nballs == 0:
yield (tuple(), ) * nboxes
else:
for idxs in labeled_balls_in_unlabeled_boxes(nballs,
[nballs] * nboxes):
yield tuple(tuple(labels[i] for i in subset) for subset in idxs)
def I_lubar(nballs, nboxes, labels):
if nballs != 0:
for idxs in labeled_balls_in_unlabeled_boxes(nballs, [nballs]*nboxes):
if not all(len(i) > 0 for i in idxs):
continue
else:
yield tuple(tuple(labels[i] for i in subset) for subset in idxs)
def I_lubar(nballs, nboxes, labels):
if nballs != 0:
for idxs in labeled_balls_in_unlabeled_boxes(nballs,
[nballs] * nboxes):
if not all(len(i) > 0 for i in idxs):
continue
else:
yield tuple(
tuple(labels[i] for i in subset) for subset in idxs)
def brace_notation_iter(sequence_of_sequences):
"""
This iterates over the brace notation combinations from Allen, et al. Mol. Phys. 89 (1996), 1213-1221
See the explanation of its funtion therein. This is needed for the arbitrary order B
tensor formulae.
:Examples:
>>> [tuple(''.join(part) for part in parts) for parts in brace_notation_iter(['AB', 'C', 'D'])]
[('AB', 'C', 'D'), ('AC', 'B', 'D'), ('AD', 'B', 'C'), ('BC', 'A', 'D'), ('BD', 'A', 'C'), ('CD', 'A', 'B')]
"""
seq = [p for p in sequence_of_sequences]
joined = [item for item in chain(*seq)]
for indices in labeled_balls_in_unlabeled_boxes(len(joined), [len(s) for s in seq]):
yield tuple(tuple(joined[idx] for idx in subset) for subset in indices)
def brace_notation_iter(sequence_of_sequences):
"""
This iterates over the brace notation combinations from Allen, et al. Mol. Phys. 89 (1996), 1213-1221
See the explanation of its funtion therein. This is needed for the arbitrary order B
tensor formulae.
:Examples:
>>> [tuple(''.join(part) for part in parts) for parts in brace_notation_iter(['AB', 'C', 'D'])]
[('AB', 'C', 'D'), ('AC', 'B', 'D'), ('AD', 'B', 'C'), ('BC', 'A', 'D'), ('BD', 'A', 'C'), ('CD', 'A', 'B')]
"""
seq = [p for p in sequence_of_sequences]
joined = [item for item in chain(*seq)]
for indices in labeled_balls_in_unlabeled_boxes(len(joined),
[len(s) for s in seq]):
yield tuple(tuple(joined[idx] for idx in subset) for subset in indices)
def Bcscphi(phi, *b_alphas):
phi_val = phi.value * phi.units.to(Radians)
sinphi = sin(phi_val)
cscphi = 1.0 / sinphi
if len(b_alphas) == 0:
return cscphi
cotphi = cos(phi_val) / sinphi
#------------------------------------#
def dcsc_n(n):
def t(n_t, k):
if k == 0:
return 1
elif k <= n_t//2:
return (2*k + 1) * t(n_t-1, k) + (n_t - 2*k + 1) * t(n_t-1, k-1)
else:
return 0
#--------------------------------#
ret_val = 0.0
for kk in xrange(n//2 + 1):
ret_val += t(n, kk) * cotphi**(n - 2*kk) * cscphi**(2*kk + 1)
if n % 2 == 1:
return -ret_val
else:
return ret_val
#------------------------------------#
outer_sum = 0.0
for k in xrange(1, len(b_alphas) + 1):
inner_sum = 0.0
for idx_sets in labeled_balls_in_unlabeled_boxes(len(b_alphas), [len(b_alphas)]*k):
if any(len(st) == 0 for st in idx_sets):
continue
b_idx_sets = tuple(tuple(b_alphas[i] for i in idxset) for idxset in idx_sets)
product = 1.0
for b_idxs in b_idx_sets:
product *= B(phi, *b_idxs)
inner_sum += product
outer_sum += dcsc_n(k) * inner_sum
return outer_sum
def I_lu(nballs, nboxes, labels):
if nballs == 0:
yield (tuple(),) * nboxes
else:
for idxs in labeled_balls_in_unlabeled_boxes(nballs, [nballs]*nboxes):
yield tuple(tuple(labels[i] for i in subset) for subset in idxs)
