def bigFloat_nCr(n, r):
'''
Outputs:
- ret_val: bigFloat, n choose r
'''
ret_val = bf.factorial(n) / (bf.factorial(r) * bf.factorial(n - r))
return ret_val
def factorial(n, approx_threshold=100):
# start_time = time.time()
if approx_threshold < 0 or n < approx_threshold:
result = bf.factorial(n)
else:
result = math.sqrt(2 * math.pi * n) * bf.pow(n / math.e, n)
# end_time = time.time()
# print(end_time - start_time)
return result
def degdist_bigfloat(self, maxdeg, n, mindeg=0):
"""Returns the degree distribution from 0 to maxdeg degree.
It should be use with the (iterated) link probability measure.
Parameters:
maxdeg: the maximal degree for we calculate the degree distribution
n: the size of the network (the number of vertices)
Returns:
rho: the degree distribution as a list with length of maxdeg+1.
The index k gives the probability of having degree k.
"""
assert isinstance(n, int) and isinstance(maxdeg, int) and n > maxdeg
import bigfloat
context = bigfloat.Context(precision=10)
divs = self.divs
n_intervals = len(divs)
lengths = [divs[i] - divs[i - 1] for i in xrange(1, n_intervals)]
lengths.insert(0, divs[0])
log_lengths = numpy.log(lengths)
# Eq. 5, where ...
avgdeg = [
bigfloat.BigFloat(n * sum(
[self.probs[i][j] * lengths[j] for j in xrange(n_intervals)]),
context=context) for i in xrange(n_intervals)
]
#log_factorial = [ 0.5*bigfloat.log(2*math.pi, context=context) + (d+.5)*bigfloat.log(d, context=context) - d
# for d in xrange(1,maxdeg+1) ]
log_factorial = [
bigfloat.log(bigfloat.factorial(k), context=context)
for k in xrange(1, maxdeg + 1)
]
log_factorial.insert(0, 0)
rho = [bigfloat.BigFloat(0, context=context)] * (maxdeg + 1)
# Eq. 4
for i in xrange(n_intervals):
# Eq. 5
log_rho_i = [
(bigfloat.mul(k, bigfloat.log(avgdeg[i]), context=context) -
log_factorial[k] - avgdeg[i])
for k in xrange(mindeg, maxdeg + 1)
]
log_rho_i_length = [
log_rho_i[k] + log_lengths[i]
for k in xrange(mindeg, maxdeg + 1)
]
for k in xrange(mindeg, maxdeg + 1):
rho[k] += bigfloat.exp(log_rho_i_length[k], context=context)
return rho
def degdist_bigfloat(self, maxdeg, n, mindeg=0):
"""Returns the degree distribution from 0 to maxdeg degree.
It should be use with the (iterated) link probability measure.
Parameters:
maxdeg: the maximal degree for we calculate the degree distribution
n: the size of the network (the number of vertices)
Returns:
rho: the degree distribution as a list with length of maxdeg+1.
The index k gives the probability of having degree k.
"""
assert isinstance(n, int) and isinstance(maxdeg, int) and n > maxdeg
import bigfloat
context = bigfloat.Context(precision=10)
divs = self.divs
n_intervals = len(divs)
lengths = [divs[i] - divs[i-1] for i in xrange(1, n_intervals)]
lengths.insert(0, divs[0])
log_lengths = numpy.log(lengths)
# Eq. 5, where ...
avgdeg = [bigfloat.BigFloat(n*sum([self.probs[i][j]*lengths[j]
for j in xrange(n_intervals)]), context=context) for i in xrange(n_intervals)]
#log_factorial = [ 0.5*bigfloat.log(2*math.pi, context=context) + (d+.5)*bigfloat.log(d, context=context) - d
# for d in xrange(1,maxdeg+1) ]
log_factorial = [bigfloat.log(bigfloat.factorial(k), context=context)
for k in xrange(1, maxdeg+1)]
log_factorial.insert(0, 0)
rho = [bigfloat.BigFloat(0, context=context)] * (maxdeg+1)
# Eq. 4
for i in xrange(n_intervals):
# Eq. 5
log_rho_i = [(bigfloat.mul(k, bigfloat.log(avgdeg[i]), context=context) - log_factorial[k] - avgdeg[i])
for k in xrange(mindeg, maxdeg+1)]
log_rho_i_length = [log_rho_i[k] + log_lengths[i]
for k in xrange(mindeg, maxdeg+1)]
for k in xrange(mindeg, maxdeg+1):
rho[k] += bigfloat.exp(log_rho_i_length[k], context=context)
return rho
def c(n, k):
with precision(bigFloatPrecision):
return factorial(n) / factorial(n - k) / factorial(k)
def lasum(self, x):
return 1 + sum(bigfloat.pow(x, f) / bigfloat.factorial(f) for f in range(1, self.f))