`PolynomialFeatures(2)` with out `sklearn`

gistfile1.txt

new_M = np.apply_along_axis(lambda x: np.array([x[k1]*x[k2] for k2 in range(len(x)) for k1 in range(len(x)) if k1>=k2]), axis=1, arr=M)

N.B.: ^ could be simpler and more efficient

Is _roughly_ equivalent to:

[pseudocode]

new_M = empty array
Foreach row in M:
  row_length = len(row)
  new_row = empty row
  for k1 in range(row_length):
    for k2 in range(k1, row_length);
      append row[k1]*row[k2] to new_row
  append new_row to new_M