+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.keys():
+ 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.keys():
+ if abs(frequencies1[k] - frequencies2[k]) == 0:
+ return 0
+ total += 1 / abs(frequencies1[k] - frequencies2[k])
+ return len(frequencies1) / total
+
+