title: Interpolating multi index a pandas dataframe
body: <p>I need to interpolate multi index dataframe:</p>
  
  <p>for example:</p>
  
  <p>this is the main dataframe:</p>
  
  <pre><code>a    b    c    result
  1    1    1    6
  1    1    2    9
  1    2    1    8
  1    2    2    11
  2    1    1    7
  2    1    2    10
  2    2    1    9
  2    2    2    12
  </code></pre>
  
  <p>I need to find the result for:</p>
  
  <pre><code>1.3    1.7    1.55    
  </code></pre>
  
  <p>What I've been doing so far is appending a pd.Series inside with NaN
  for each index individually.</p>
  
  <p>As you can see. this seems like a VERY inefficient way.</p>
  
  <p>I would be happy if someone can enrich me.</p>
  
  <p>P.S.
  I spent some time looking over SO, and if the answer is in there, I missed it:</p>
  
  <p><a href="https://stackoverflow.com/questions/27640202/fill-multi-index-pandas-dataframe-with-interpolation/27657638">Fill multi-index Pandas DataFrame with interpolation</a></p>
  
  <p><a href="https://stackoverflow.com/questions/15799162/resampling-within-a-pandas-multiindex">Resampling Within a Pandas MultiIndex</a></p>
  
  <p><a href="https://stackoverflow.com/questions/29465398/pandas-multiindex-dataframe-nd-interpolation-for-missing-values">pandas multiindex dataframe, ND interpolation for missing values</a></p>
  
  <p><a href="https://stackoverflow.com/questions/27640202/fill-multi-index-pandas-dataframe-with-interpolation">Fill multi-index Pandas DataFrame with interpolation</a></p>
  
  <p>Algorithm:</p>
  
  <p>stage 1:</p>
  
  <pre><code>a    b    c    result
  1    1    1    6
  1    1    2    9
  1    2    1    8
  1    2    2    11
  1.3    1    1    6.3
  1.3    1    2    9.3
  1.3    2    1    8.3
  1.3    2    2    11.3
  2    1    1    7
  2    1    2    10
  2    2    1    9
  2    2    2    12
  </code></pre>
  
  <p>stage 2:</p>
  
  <pre><code>a    b    c    result
  1    1    1    6
  1    1    2    9
  1    2    1    8
  1    2    2    11
  1.3    1    1    6.3
  1.3    1    2    9.3
  1.3    1.7    1    7.7
  1.3    1.7    2    10.7
  1.3    2    1    8.3
  1.3    2    2    11.3
  2    1    1    7
  2    1    2    10
  2    2    1    9
  2    2    2    12
  </code></pre>
  
  <p>stage 3:</p>
  
  <pre><code>a    b    c    result
  1    1    1    6
  1    1    2    9
  1    2    1    8
  1    2    2    11
  1.3    1    1    6.3
  1.3    1    2    9.3
  1.3    1.7    1    7.7
  1.3    1.7    1.55    9.35
  1.3    1.7    2    10.7
  1.3    2    1    8.3
  1.3    2    2    11.3
  2    1    1    7
  2    1    2    10
  2    2    1    9
  2    2    2    12
  </code></pre>