Added spreadsheet for solving caesar ciphers

[cipher-tools.git] / norms.py

diff --git a/norms.py b/norms.py
index c9cafc4f718b05b697a20e4f8b5f55085336bc88..eb436c3b8163141a3ada1f1f02f8be741d6f47fb 100644 (file)
--- a/norms.py
+++ b/norms.py
@@ -1,4 +1,5 @@
 import collections
+from math import log10
 
 def normalise(frequencies):
     """Scale a set of frequencies so they sum to one
@@ -12,7 +13,7 @@ def normalise(frequencies):
     >>> 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()])
+    length = sum(f for f in frequencies.values())
     return collections.defaultdict(int, ((k, v / length) 
         for (k, v) in frequencies.items()))
 
@@ -32,23 +33,9 @@ def euclidean_scale(frequencies):
     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.
@@ -69,7 +56,7 @@ def l2(frequencies1, frequencies2):
     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
@@ -90,7 +77,7 @@ def l1(frequencies1, frequencies2):
     1
     """
     total = 0
-    for k in frequencies1.keys():
+    for k in frequencies1:
         total += abs(frequencies1[k] - frequencies2[k])
     return total
 
@@ -113,7 +100,7 @@ def l3(frequencies1, frequencies2):
     0.6299605249...
     """
     total = 0
-    for k in frequencies1.keys():
+    for k in frequencies1:
         total += abs(frequencies1[k] - frequencies2[k]) ** 3
     return total ** (1/3)
 
@@ -139,7 +126,7 @@ def geometric_mean(frequencies1, frequencies2):
     0.009259259...
     """
     total = 1
-    for k in frequencies1.keys():
+    for k in frequencies1:
         total *= abs(frequencies1[k] - frequencies2[k])
     return total
 
@@ -165,42 +152,37 @@ def harmonic_mean(frequencies1, frequencies2):
     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])
     return len(frequencies1) / total
 
 
-def cosine_distance(frequencies1, frequencies2):
+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_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...
+    >>> 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.keys():
+    for k in frequencies1:
         numerator += frequencies1[k] * frequencies2[k]
         length1 += frequencies1[k]**2
-    for k in frequencies2.keys():
-        length2 += frequencies2[k]
-    return 1 - (numerator / (length1 ** 0.5 * length2 ** 0.5))
+    for k in frequencies2:
+        length2 += frequencies2[k]**2
+    return 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