code: def get_irls_pieces(
      X: NDArray[Float],
      y: NDArray[Float],
      alpha_value: Float,
      beta_cov: NDArray[Float],
  ) -> (NDArray[Float], NDArray[Float], NDArray[Float]):
      """
      Fits a logistic regression model logit(p(y|X)) ~ X*beta with L2 shrinkage C = 1/alpha, using scikit-learn.  Returns
      the vector beta, the matrix transpose(X)*diag(p(1-p))*X, and the vector transpose(X)*(y - p), which are the pieces
      needed to perform one step of the IRLS algorithm.
  
      Args:
           X : Matrix of n samples m features.  Matrix X is expected to include a constant intercept = 1 term as the first
            column.
           y : Binary response vector of  length n
           alpha_value : Shrinkage parameter to be used in the fit
           beta_cov : array of fixed covariate parameter estimates to use in the fitting.
  
      Returns:
          beta : m length array representing coefficients found from the fit, including the intercept term as the first
          element.
          XtGX : m by m matrix representing transpose(X)*diag(p(1-p))*X.
          XtY : m length array representing transpose(X)*(y - p)
  
      """
      n_cov = beta_cov.size
      # If we have no observations in this block (i.e, y.sum() == 0), then we should not try to fit a model and instead
      # just return a parameterless model based on the population frequency of observations p0
      if y.sum() > 0:
          alpha_arr = np.zeros(X.shape[1])
          alpha_arr[n_cov:] = alpha_value
          guess = np.zeros(X.shape[1])
          guess[:n_cov] = beta_cov
          ridge_fit = constrained_logistic_fit(
              X, y, alpha_arr, guess, n_cov
          )
          beta = ridge_fit.x
      else:
          beta = np.zeros(X.shape[1])
          if n_cov > 0:
              beta[:n_cov] = beta_cov
  
      z = X @ beta
      p = sigmoid(z)
      XtGX = (X.T * (p * (1 - p))) @ X
      XtY = X.T @ (p - y)
      return beta, XtGX, XtY
  
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 6 for calling a global function with example usage: get_irls_pieces(X, y, alpha_value, beta_cov) and returns: beta,  XtGX,  XtY