Use Index of the Loadings (IL) method to calculate the optimal number of principal components

Question

I want to use Index of the Loadings method to calculate the optimal number of principal components using the index_of_loadings_matrix function. My dataframe was converted into a matrix before I feed it into the function. My code is raising "self._check_indexing_error(key)" error.

import pandas as pd

# Choose the optimal number of principal components using Index of the Loadings
mat = df.cov()

def index_of_loadings_matrix(cov_matrix):
    eig_val, eig_vec = np.linalg.eig(cov_matrix)
    r = np.zeros((len(eig_vec), cov_matrix.shape[0]))
    for i in range(len(eig_vec)):
        for j in range(cov_matrix.shape[0]):
            r[i][j] = (eig_vec[i][j]**2 * eig_val[i])**2 / np.sqrt(cov_matrix[j][j])
    return r

index_of_loadings_matrix(mat)

Traceback:

---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
File ~/env/lib/python3.8/site-packages/pandas/core/indexes/base.py:3621, in Index.get_loc(self, key, method, tolerance)
   3620 try:
-> 3621     return self._engine.get_loc(casted_key)
   3622 except KeyError as err:

File ~/env/lib/python3.8/site-packages/pandas/_libs/index.pyx:136, in pandas._libs.index.IndexEngine.get_loc()

File ~/env/lib/python3.8/site-packages/pandas/_libs/index.pyx:163, in pandas._libs.index.IndexEngine.get_loc()

File pandas/_libs/hashtable_class_helper.pxi:5198, in pandas._libs.hashtable.PyObjectHashTable.get_item()

File pandas/_libs/hashtable_class_helper.pxi:5206, in pandas._libs.hashtable.PyObjectHashTable.get_item()

KeyError: 0

The above exception was the direct cause of the following exception:

KeyError                                  Traceback (most recent call last)
Input In [555], in <cell line: 12>()
      9             r[i][j] = (eig_vec[i][j]**2 * eig_val[i])**2 / np.sqrt(cov_matrix[j][j])
     10     return r
---> 12 index_of_loadings_matrix(mat)

Input In [555], in index_of_loadings_matrix(cov_matrix)
      7 for i in range(len(eig_vec)):
      8     for j in range(cov_matrix.shape[0]):
----> 9         r[i][j] = (eig_vec[i][j]**2 * eig_val[i])**2 / np.sqrt(cov_matrix[j][j])
     10 return r

File ~/env/lib/python3.8/site-packages/pandas/core/frame.py:3505, in DataFrame.__getitem__(self, key)
   3503 if self.columns.nlevels > 1:
   3504     return self._getitem_multilevel(key)
-> 3505 indexer = self.columns.get_loc(key)
   3506 if is_integer(indexer):
   3507     indexer = [indexer]

File ~/env/lib/python3.8/site-packages/pandas/core/indexes/base.py:3623, in Index.get_loc(self, key, method, tolerance)
   3621     return self._engine.get_loc(casted_key)
   3622 except KeyError as err:
-> 3623     raise KeyError(key) from err
   3624 except TypeError:
   3625     # If we have a listlike key, _check_indexing_error will raise
   3626     #  InvalidIndexError. Otherwise we fall through and re-raise
   3627     #  the TypeError.
   3628     self._check_indexing_error(key)

KeyError: 0