title: Distance calculation between rows in Pandas Dataframe using a distance matrix
body: <p>I have the following Pandas DataFrame:</p>
  
  <pre><code>In [31]:
  import pandas as pd
  sample = pd.DataFrame({'Sym1': ['a','a','a','d'],'Sym2':['a','c','b','b'],'Sym3':['a','c','b','d'],'Sym4':['b','b','b','a']},index=['Item1','Item2','Item3','Item4'])
  In [32]: print(sample)
  Out [32]:
        Sym1 Sym2 Sym3 Sym4
  Item1    a    a    a    b
  Item2    a    c    c    b
  Item3    a    b    b    b
  Item4    d    b    d    a
  </code></pre>
  
  <p>and I want to find the elegant way to get the distance between each <code>Item</code> according to this distance matrix:</p>
  
  <pre><code>In [34]:
  DistMatrix = pd.DataFrame({'a': [0,0,0.67,1.34],'b':[0,0,0,0.67],'c':[0.67,0,0,0],'d':[1.34,0.67,0,0]},index=['a','b','c','d'])
  print(DistMatrix)
  Out[34]:
        a     b     c     d
  a  0.00  0.00  0.67  1.34
  b  0.00  0.00  0.00  0.67
  c  0.67  0.00  0.00  0.00
  d  1.34  0.67  0.00  0.00 
  </code></pre>
  
  <p>For example comparing <code>Item1</code> to <code>Item2</code> would compare <code>aaab</code> -> <code>accb</code> -- using the distance matrix this would be <code>0+0.67+0.67+0=1.34</code> </p>
  
  <p>Ideal output:</p>
  
  <pre><code>       Item1   Item2  Item3  Item4
  Item1      0    1.34     0    2.68
  Item2     1.34    0      0    1.34
  Item3      0      0      0    2.01
  Item4     2.68  1.34   2.01    0
  </code></pre>