def _self_info_rate(source):
"""
returns 'rate of self-information' --
i.e. average (per-symbol) entropy of the sequence **source**,
where probability of a given symbol occurring is calculated based on
the number of occurrences within the sequence itself.
if all elements of the source are unique, this should equal ``log(len(source), 2)``.
:arg source:
iterable containing 0+ symbols
(e.g. list of strings or ints, string of characters, etc).
:returns:
float bits of entropy
"""
try:
size = len(source)
except TypeError:
# if len() doesn't work, calculate size by summing counts later
size = None
counts = defaultdict(int)
for char in source:
counts[char] += 1
if size is None:
values = counts.values()
size = sum(values)
else:
values = itervalues(counts)
if not size:
return 0
# NOTE: the following performs ``- sum(value / size * logf(value / size, 2) for value in values)``,
# it just does so with as much pulled out of the sum() loop as possible...
return logf(size, 2) - sum(value * logf(value, 2)
for value in values) / size
def _self_info_rate(source):
"""
returns 'rate of self-information' --
i.e. average (per-symbol) entropy of the sequence **source**,
where probability of a given symbol occurring is calculated based on
the number of occurrences within the sequence itself.
if all elements of the source are unique, this should equal ``log(len(source), 2)``.
:arg source:
iterable containing 0+ symbols
(e.g. list of strings or ints, string of characters, etc).
:returns:
float bits of entropy
"""
try:
size = len(source)
except TypeError:
# if len() doesn't work, calculate size by summing counts later
size = None
counts = defaultdict(int)
for char in source:
counts[char] += 1
if size is None:
values = counts.values()
size = sum(values)
else:
values = itervalues(counts)
if not size:
return 0
# NOTE: the following performs ``- sum(value / size * logf(value / size, 2) for value in values)``,
# it just does so with as much pulled out of the sum() loop as possible...
return logf(size, 2) - sum(value * logf(value, 2) for value in values) / size
def _average_entropy(source, total=False):
"""returns the rate of self-information in a sequence of symbols,
(or total self-information if total=True).
this is eqvuialent to the average entropy of a given symbol,
using the sequence itself as the symbol probability distribution.
if all elements of the source are unique, this should equal
``log(len(source), 2)``.
:arg source:
iterable containing 0+ symbols
:param total:
instead of returning average entropy rate,
return total self-information
:returns:
float bits
"""
try:
size = len(source)
except TypeError:
# if len() doesn't work, calculate size by summing counts later
size = None
counts = defaultdict(int)
for char in source:
counts[char] += 1
if size is None:
values = counts.values()
size = sum(values)
else:
values = itervalues(counts)
if not size:
return 0
### NOTE: below code performs the calculation
### ``- sum(value / size * logf(value / size, 2) for value in values)``,
### and then multplies by ``size`` if total is True,
### it just does it with fewer operations.
tmp = sum(value * logf(value, 2) for value in values)
if total:
return size * logf(size, 2) - tmp
else:
return logf(size, 2) - tmp / size