title: Grouping continguous values in a numpy array with their length
body: <p>In numpy / scipy (or pure python if you prefer), what would be a good way to group contiguous regions in a numpy array and count the length of these regions?</p>
  
  <p>Something like this:</p>
  
  <pre><code>x = np.array([1,1,1,2,2,3,0,0,0,0,0,1,2,3,1,1,0,0,0])
  y = contiguousGroup(x)
  print y
  
  &gt;&gt; [[1,3], [2,2], [3,1], [0,5], [1,1], [2,1], [3,1], [1,2], [0,3]]
  </code></pre>
  
  <p>I have tried to do this just with loops however it takes a longer time than I would like (6 seconds) to do a list with about 30 million samples and 20000 contiguous regions. </p>
  
  <p>Edit:</p>
  
  <p>And now for some speed comparisons (just using time.clock() and a few hundred iterations, or less if it is in seconds). </p>
  
  <p>Firstly my python loop code tested on 5 samples. </p>
  
  <pre><code>Number of elements  33718251
  Number of regions  135137
  Time taken = 8.644007 seconds...
  
  Number of elements  42503100
  Number of regions  6985
  Time taken = 10.533305 seconds...
  
  Number of elements  21841302
  Number of regions  7619335
  Time taken = 7.671015 seconds...
  
  Number of elements  19723928
  Number of regions  10799
  Time taken = 5.014807 seconds...
  
  Number of elements  16619539
  Number of regions  19293
  Time taken = 4.207359 seconds...
  </code></pre>
  
  <p>And now with Divakar's vectorized solution.</p>
  
  <pre><code>Number of elements  33718251
  Number of regions  135137
  Time taken = 0.063470 seconds...
  
  Number of elements  42503100
  Number of regions  6985
  Time taken = 0.046293 seconds...
  
  Number of elements  21841302
  Number of regions  7619335
  Time taken = 1.654288 seconds...
  
  Number of elements  19723928
  Number of regions  10799
  Time taken = 0.022651 seconds...
  
  Number of elements  16619539
  Number of regions  19293
  Time taken = 0.021189 seconds...
  </code></pre>
  
  <p>Modified approach gives roughly same times (maybe 5% slower at worst)</p>
  
  <p>And now with with the generator approach from Kasramvd.</p>
  
  <pre><code>Number of elements  33718251
  Number of regions  135137
  Time taken = 3.834922 seconds...
  
  Number of elements  42503100
  Number of regions  6985
  Time taken = 4.785480 seconds...
  
  Number of elements  21841302
  Number of regions  7619335
  Time taken = 6.806867 seconds...
  
  Number of elements  19723928
  Number of regions  10799
  Time taken = 2.264413 seconds...
  
  Number of elements  16619539
  Number of regions  19293
  Time taken = 1.778873 seconds...
  </code></pre>
  
  <p>And now his numpythonic version.</p>
  
  <pre><code>Number of elements  33718251
  Number of regions  135137
  Time taken = 0.286336 seconds...
  
  Number of elements  42503100
  Number of regions  6985
  Time taken = 0.174769 seconds...
  
  Memory error sample 3 (too many regions)
  
  Number of elements  19723928
  Number of regions  10799
  Time taken = 0.087028 seconds...
  
  Number of elements  16619539
  Number of regions  19293
  Time taken = 0.084963 seconds...
  </code></pre>
  
  <p>Anyway I think the moral of the story is that numpy is very good. </p>