title: Pandas Multi-index DataFrame: aggregate sub-groups within groups
body: <p>I have the following multi-indexed DataFrame:</p>
  <pre><code>df = pd.DataFrame({
        'cluster': [1, 1, 2, 1, 2, 2, 1, 3, 2],
        'mark': [8, 5, 10, 20, 4, 1, 6, 4, 1],
        'dt': ['2021-03-23', '2021-03-25', '2021-03-23', '2021-03-28', '2021-03-25', '2021-03-28', '2021-03-29', '2021-03-23', '2021-03-31']
  })
  df.set_index(['cluster', 'dt'], inplace=True)
  df.sort_index(inplace=True)
  df
  </code></pre>
  <pre>
  
                                  mark
  cluster     dt  
  1           2021-03-23          8
              2021-03-25          5
              2021-03-28          20
              2021-03-29          6
  2           2021-03-23          10
              2021-03-25          4
              2021-03-28          1
              2021-03-31          1
  3           2021-03-23          4
  
  </pre>
  <p>What I am looking to do is to generate the sum over the weekly subgroups within each indexed group, something like</p>
  <pre>
  
                                  total mark
  cluster     start_date_of_week  
  1           2021-03-21          13
              2021-03-28          26
  2           2021-03-21          14
              2021-03-28          2
  3           2021-03-23          4
  
  </pre>
  <p>I know how to generate groups based on frequency of a datetime index. I don't know how to do this using one level of a multi-index. Any ideas?</p>