+++ /dev/null
-import collections
-from math import log10
-
-def normalise(frequencies):
- """Scale a set of frequencies so they sum to one
-
- >>> sorted(normalise({1: 1, 2: 0}).items())
- [(1, 1.0), (2, 0.0)]
- >>> sorted(normalise({1: 1, 2: 1}).items())
- [(1, 0.5), (2, 0.5)]
- >>> sorted(normalise({1: 1, 2: 1, 3: 1}).items()) # doctest: +ELLIPSIS
- [(1, 0.333...), (2, 0.333...), (3, 0.333...)]
- >>> sorted(normalise({1: 1, 2: 2, 3: 1}).items())
- [(1, 0.25), (2, 0.5), (3, 0.25)]
- """
- length = sum(f for f in frequencies.values())
- return collections.defaultdict(int, ((k, v / length)
- for (k, v) in frequencies.items()))
-
-def euclidean_scale(frequencies):
- """Scale a set of frequencies so they have a unit euclidean length
-
- >>> sorted(euclidean_scale({1: 1, 2: 0}).items())
- [(1, 1.0), (2, 0.0)]
- >>> sorted(euclidean_scale({1: 1, 2: 1}).items()) # doctest: +ELLIPSIS
- [(1, 0.7071067...), (2, 0.7071067...)]
- >>> sorted(euclidean_scale({1: 1, 2: 1, 3: 1}).items()) # doctest: +ELLIPSIS
- [(1, 0.577350...), (2, 0.577350...), (3, 0.577350...)]
- >>> sorted(euclidean_scale({1: 1, 2: 2, 3: 1}).items()) # doctest: +ELLIPSIS
- [(1, 0.408248...), (2, 0.81649658...), (3, 0.408248...)]
- """
- length = sum([f ** 2 for f in frequencies.values()]) ** 0.5
- return collections.defaultdict(int, ((k, v / length)
- 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.
- Assumes every key in frequencies1 is also in frequencies2
-
- >>> l2({'a':1, 'b':1, 'c':1}, {'a':1, 'b':1, 'c':1})
- 0.0
- >>> l2({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
- 1.73205080...
- >>> l2(normalise({'a':2, 'b':2, 'c':2}), normalise({'a':1, 'b':1, 'c':1}))
- 0.0
- >>> l2({'a':0, 'b':2, 'c':0}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
- 1.732050807...
- >>> l2(normalise({'a':0, 'b':2, 'c':0}), \
- normalise({'a':1, 'b':1, 'c':1})) # doctest: +ELLIPSIS
- 0.81649658...
- >>> l2({'a':0, 'b':1}, {'a':1, 'b':1})
- 1.0
- """
- total = 0
- for k in frequencies1:
- total += (frequencies1[k] - frequencies2[k]) ** 2
- return total ** 0.5
-euclidean_distance = l2
-
-def l1(frequencies1, frequencies2):
- """Finds the distances between two frequency profiles, expressed as
- dictionaries. Assumes every key in frequencies1 is also in frequencies2
-
- >>> l1({'a':1, 'b':1, 'c':1}, {'a':1, 'b':1, 'c':1})
- 0
- >>> l1({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1})
- 3
- >>> l1(normalise({'a':2, 'b':2, 'c':2}), normalise({'a':1, 'b':1, 'c':1}))
- 0.0
- >>> l1({'a':0, 'b':2, 'c':0}, {'a':1, 'b':1, 'c':1})
- 3
- >>> l1({'a':0, 'b':1}, {'a':1, 'b':1})
- 1
- """
- total = 0
- for k in frequencies1:
- total += abs(frequencies1[k] - frequencies2[k])
- return total
-
-def l3(frequencies1, frequencies2):
- """Finds the distances between two frequency profiles, expressed as
- dictionaries. Assumes every key in frequencies1 is also in frequencies2
-
- >>> l3({'a':1, 'b':1, 'c':1}, {'a':1, 'b':1, 'c':1})
- 0.0
- >>> l3({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
- 1.44224957...
- >>> l3({'a':0, 'b':2, 'c':0}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
- 1.4422495703...
- >>> l3(normalise({'a':0, 'b':2, 'c':0}), \
- normalise({'a':1, 'b':1, 'c':1})) # doctest: +ELLIPSIS
- 0.718144896...
- >>> l3({'a':0, 'b':1}, {'a':1, 'b':1})
- 1.0
- >>> l3(normalise({'a':0, 'b':1}), normalise({'a':1, 'b':1})) # doctest: +ELLIPSIS
- 0.6299605249...
- """
- total = 0
- for k in frequencies1:
- total += abs(frequencies1[k] - frequencies2[k]) ** 3
- return total ** (1/3)
-
-def geometric_mean(frequencies1, frequencies2):
- """Finds the geometric mean of the absolute differences between two frequency profiles,
- expressed as dictionaries.
- Assumes every key in frequencies1 is also in frequencies2
-
- >>> geometric_mean({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1})
- 1
- >>> geometric_mean({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1})
- 1
- >>> geometric_mean({'a':2, 'b':2, 'c':2}, {'a':1, 'b':5, 'c':1})
- 3
- >>> geometric_mean(normalise({'a':2, 'b':2, 'c':2}), \
- normalise({'a':1, 'b':5, 'c':1})) # doctest: +ELLIPSIS
- 0.01382140...
- >>> geometric_mean(normalise({'a':2, 'b':2, 'c':2}), \
- normalise({'a':1, 'b':1, 'c':1})) # doctest: +ELLIPSIS
- 0.0
- >>> geometric_mean(normalise({'a':2, 'b':2, 'c':2}), \
- normalise({'a':1, 'b':1, 'c':0})) # doctest: +ELLIPSIS
- 0.009259259...
- """
- total = 1
- for k in frequencies1:
- total *= abs(frequencies1[k] - frequencies2[k])
- return total
-
-def harmonic_mean(frequencies1, frequencies2):
- """Finds the harmonic mean of the absolute differences between two frequency profiles,
- expressed as dictionaries.
- Assumes every key in frequencies1 is also in frequencies2
-
- >>> harmonic_mean({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1})
- 1.0
- >>> harmonic_mean({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1})
- 1.0
- >>> harmonic_mean({'a':2, 'b':2, 'c':2}, {'a':1, 'b':5, 'c':1}) # doctest: +ELLIPSIS
- 1.285714285...
- >>> harmonic_mean(normalise({'a':2, 'b':2, 'c':2}), \
- normalise({'a':1, 'b':5, 'c':1})) # doctest: +ELLIPSIS
- 0.228571428571...
- >>> harmonic_mean(normalise({'a':2, 'b':2, 'c':2}), \
- normalise({'a':1, 'b':1, 'c':1})) # doctest: +ELLIPSIS
- 0
- >>> harmonic_mean(normalise({'a':2, 'b':2, 'c':2}), \
- normalise({'a':1, 'b':1, 'c':0})) # doctest: +ELLIPSIS
- 0.2
- """
- total = 0
- for k in frequencies1:
- if abs(frequencies1[k] - frequencies2[k]) == 0:
- return 0
- total += 1 / abs(frequencies1[k] - frequencies2[k])
- return len(frequencies1) / total
-
-
-def cosine_similarity(frequencies1, frequencies2):
- """Finds the distances between two frequency profiles, expressed as dictionaries.
- Assumes every key in frequencies1 is also in frequencies2
-
- >>> cosine_similarity({'a':1, 'b':1, 'c':1}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
- 1.0000000000...
- >>> cosine_similarity({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
- 1.0000000000...
- >>> cosine_similarity({'a':0, 'b':2, 'c':0}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
- 0.5773502691...
- >>> cosine_similarity({'a':0, 'b':1}, {'a':1, 'b':1}) # doctest: +ELLIPSIS
- 0.7071067811...
- """
- numerator = 0
- length1 = 0
- length2 = 0
- for k in frequencies1:
- numerator += frequencies1[k] * frequencies2[k]
- length1 += frequencies1[k]**2
- for k in frequencies2.keys():
- length2 += frequencies2[k]**2
- return numerator / (length1 ** 0.5 * length2 ** 0.5)
-
-
-
-if __name__ == "__main__":
- import doctest
- doctest.testmod()
projects / cipher-training.git / blobdiff