code: def irls_one_step(
      pdf: pd.DataFrame, alpha_value: Float, n_cov: Int
  ) -> NDArray[Float]:
      """
      Performs one step of the IRLS algorithm using the components found in pdf and a value of alpha.
      Returns the resulting coefficient values.  If n_cov > 0, then the first n_cov columns from the design matrix X
      are assumed to be fixed effects and the corresponding parameter estimates are not updated during the step.
  
      Args:
           pdf : Pandas DataFrame for the group.  Contains one set of IRLS equation components (beta, xtgx, xty)
           corresponding to the value of alpha provided
           alpha_value : regularization parameter alpha
           n_cov : number of columns in X (starting from the left) to consider fixed, and freeze at the initial guess
              prior to taking the step.
  
      Returns:
          vector of coefficients of size [number of columns in X]
  
      """
      xtgx = np.stack(pdf["xtgx"])[n_cov:, n_cov:]
      xty = pdf["xty"].to_numpy()[n_cov:]
      beta0 = pdf["beta"].to_numpy()
      alpha_arr = np.ones(xtgx.shape[1]) * alpha_value
      dbeta = np.zeros(beta0.size)
      dbeta[n_cov:] = np.linalg.inv(xtgx + np.diag(alpha_arr)) @ (
          xty + beta0[n_cov:] * alpha_arr
      )
      return beta0 - dbeta
  
imports: import itertools
  import math
  import re
  import warnings
  from typing import Any, Dict, Iterable, List, Tuple
  import numpy
  import pandas
  import pyspark.sql.functions
  import scipy.optimize
  from nptyping import Float, Int, NDArray
  from pyspark.sql import DataFrame, Row
  from pyspark.sql.window import Window
  from typeguard import typechecked
label_desc: Use image node_id 9 for calling a global function with example usage: irls_one_step(pdf, alpha_value, n_cov) and returns: unknown