X-Git-Url: https://git.njae.me.uk/?a=blobdiff_plain;f=norms.py;h=c9cafc4f718b05b697a20e4f8b5f55085336bc88;hb=1635c5915dc678efd90fffc5cb01c8f4bede9f47;hp=08cff74b82541f2e2331f2ce85775db68ea44399;hpb=ac47ee478ba8e785037c9f25367c111f630eea54;p=cipher-tools.git diff --git a/norms.py b/norms.py index 08cff74..c9cafc4 100644 --- a/norms.py +++ b/norms.py @@ -1,19 +1,37 @@ import collections def normalise(frequencies): - """Scale a set of frequenies so they have a unit euclidean length + """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, 0.7071067811865475), (2, 0.7071067811865475)] - >>> sorted(normalise({1: 1, 2: 1, 3: 1}).items()) - [(1, 0.5773502691896258), (2, 0.5773502691896258), (3, 0.5773502691896258)] + [(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, 0.4082482904638631), (2, 0.8164965809277261), (3, 0.4082482904638631)] - """ + [(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())) + 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 @@ -28,7 +46,8 @@ def scale(frequencies): [(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())) + return collections.defaultdict(int, ((k, v / largest) + for (k, v) in frequencies.items())) def l2(frequencies1, frequencies2): @@ -37,14 +56,15 @@ def l2(frequencies1, 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}) - 1.7320508075688772 + >>> 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}) - 1.7320508075688772 - >>> l2(normalise({'a':0, 'b':2, 'c':0}), normalise({'a':1, 'b':1, 'c':1})) - 0.9194016867619662 + >>> 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 """ @@ -55,8 +75,8 @@ def l2(frequencies1, frequencies2): 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 + """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 @@ -75,21 +95,22 @@ def l1(frequencies1, frequencies2): 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 + """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}) - 1.4422495703074083 - >>> l3({'a':0, 'b':2, 'c':0}, {'a':1, 'b':1, 'c':1}) - 1.4422495703074083 - >>> l3(normalise({'a':0, 'b':2, 'c':0}), normalise({'a':1, 'b':1, 'c':1})) - 0.7721675487598008 + >>> 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})) - 0.7234757712960591 + >>> l3(normalise({'a':0, 'b':1}), normalise({'a':1, 'b':1})) # doctest: +ELLIPSIS + 0.6299605249... """ total = 0 for k in frequencies1.keys(): @@ -107,12 +128,15 @@ def geometric_mean(frequencies1, frequencies2): 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})) - 0.057022248808851934 - >>> geometric_mean(normalise({'a':2, 'b':2, 'c':2}), normalise({'a':1, 'b':1, 'c':1})) + >>> 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})) - 0.009720703533656434 + >>> 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.keys(): @@ -128,14 +152,17 @@ def harmonic_mean(frequencies1, frequencies2): 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}) - 1.2857142857142858 - >>> harmonic_mean(normalise({'a':2, 'b':2, 'c':2}), normalise({'a':1, 'b':5, 'c':1})) - 0.3849001794597505 - >>> harmonic_mean(normalise({'a':2, 'b':2, 'c':2}), normalise({'a':1, 'b':1, 'c':1})) + >>> 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})) - 0.17497266360581604 + >>> 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.keys(): @@ -149,14 +176,14 @@ def cosine_distance(frequencies1, frequencies2): """Finds the distances between two frequency profiles, expressed as dictionaries. Assumes every key in frequencies1 is also in frequencies2 - >>> cosine_distance({'a':1, 'b':1, 'c':1}, {'a':1, 'b':1, 'c':1}) - -2.220446049250313e-16 - >>> cosine_distance({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1}) - -2.220446049250313e-16 - >>> cosine_distance({'a':0, 'b':2, 'c':0}, {'a':1, 'b':1, 'c':1}) - 0.42264973081037416 - >>> cosine_distance({'a':0, 'b':1}, {'a':1, 'b':1}) - 0.29289321881345254 + >>> cosine_distance({'a':1, 'b':1, 'c':1}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS + -2.22044604...e-16 + >>> cosine_distance({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS + -2.22044604...e-16 + >>> cosine_distance({'a':0, 'b':2, 'c':0}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS + 0.4226497308... + >>> cosine_distance({'a':0, 'b':1}, {'a':1, 'b':1}) # doctest: +ELLIPSIS + 0.29289321881... """ numerator = 0 length1 = 0 @@ -169,6 +196,12 @@ def cosine_distance(frequencies1, frequencies2): return 1 - (numerator / (length1 ** 0.5 * length2 ** 0.5)) +def index_of_coincidence(frequencies): + """Finds the (expected) index of coincidence given a set of frequencies + """ + return sum([f ** 2 for f in frequencies.values()]) * len(frequencies.keys()) + + if __name__ == "__main__": import doctest doctest.testmod()