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    <p>I don't suppose performance matters much here, but I can't resist. The zip() function completely recopies both vectors (more of a matrix transpose, actually) just to get the data in "Pythonic" order. It would be interesting to time the nuts-and-bolts implementation:</p> <pre><code>import math def cosine_similarity(v1,v2): "compute cosine similarity of v1 to v2: (v1 dot v2)/{||v1||*||v2||)" sumxx, sumxy, sumyy = 0, 0, 0 for i in range(len(v1)): x = v1[i]; y = v2[i] sumxx += x*x sumyy += y*y sumxy += x*y return sumxy/math.sqrt(sumxx*sumyy) v1,v2 = [3, 45, 7, 2], [2, 54, 13, 15] print(v1, v2, cosine_similarity(v1,v2)) Output: [3, 45, 7, 2] [2, 54, 13, 15] 0.972284251712 </code></pre> <p>That goes through the C-like noise of extracting elements one-at-a-time, but does no bulk array copying and gets everything important done in a single for loop, and uses a single square root.</p> <p>ETA: Updated print call to be a function. (The original was Python 2.7, not 3.3. The current runs under Python 2.7 with a <code>from __future__ import print_function</code> statement.) The output is the same, either way.</p> <p>CPYthon 2.7.3 on 3.0GHz Core 2 Duo:</p> <pre><code>&gt;&gt;&gt; timeit.timeit("cosine_similarity(v1,v2)",setup="from __main__ import cosine_similarity, v1, v2") 2.4261788514654654 &gt;&gt;&gt; timeit.timeit("cosine_measure(v1,v2)",setup="from __main__ import cosine_measure, v1, v2") 8.794677709375264 </code></pre> <p>So, the unpythonic way is about 3.6 times faster in this case.</p>
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