import collections
+from math import log10
def normalise(frequencies):
"""Scale a set of frequencies so they sum to one
return collections.defaultdict(int, ((k, v / length)
for (k, v) in frequencies.items()))
-
-def scale(frequencies):
- """Scale a set of frequencies so the largest is 1
-
- >>> sorted(scale({1: 1, 2: 0}).items())
- [(1, 1.0), (2, 0.0)]
- >>> sorted(scale({1: 1, 2: 1}).items())
- [(1, 1.0), (2, 1.0)]
- >>> sorted(scale({1: 1, 2: 1, 3: 1}).items())
- [(1, 1.0), (2, 1.0), (3, 1.0)]
- >>> sorted(scale({1: 1, 2: 2, 3: 1}).items())
- [(1, 0.5), (2, 1.0), (3, 0.5)]
- """
- largest = max(frequencies.values())
- return collections.defaultdict(int, ((k, v / largest)
- for (k, v) in frequencies.items()))
-
+def identity_scale(frequencies):
+ return frequencies
+
def l2(frequencies1, frequencies2):
"""Finds the distances between two frequency profiles, expressed as dictionaries.
1.0
"""
total = 0
- for k in frequencies1.keys():
+ for k in frequencies1:
total += (frequencies1[k] - frequencies2[k]) ** 2
return total ** 0.5
euclidean_distance = l2
1
"""
total = 0
- for k in frequencies1.keys():
+ for k in frequencies1:
total += abs(frequencies1[k] - frequencies2[k])
return total
0.6299605249...
"""
total = 0
- for k in frequencies1.keys():
+ for k in frequencies1:
total += abs(frequencies1[k] - frequencies2[k]) ** 3
return total ** (1/3)
0.009259259...
"""
total = 1
- for k in frequencies1.keys():
+ for k in frequencies1:
total *= abs(frequencies1[k] - frequencies2[k])
return total
0.2
"""
total = 0
- for k in frequencies1.keys():
+ for k in frequencies1:
if abs(frequencies1[k] - frequencies2[k]) == 0:
return 0
total += 1 / abs(frequencies1[k] - frequencies2[k])
numerator = 0
length1 = 0
length2 = 0
- for k in frequencies1.keys():
+ for k in frequencies1:
numerator += frequencies1[k] * frequencies2[k]
length1 += frequencies1[k]**2
for k in frequencies2.keys():
return 1 - (numerator / (length1 ** 0.5 * length2 ** 0.5))
+def log_pl(frequencies1, frequencies2):
+ return sum([frequencies2[l] * log10(frequencies1[l]) for l in frequencies1])
+
+def inverse_log_pl(frequencies1, frequencies2):
+ return -log_pl(frequencies1, frequencies2)
+
def index_of_coincidence(frequencies):
"""Finds the (expected) index of coincidence given a set of frequencies
"""