code: def _fit(self, X):
      if sklearn_check_version("1.4"):
          xp, is_array_api_compliant = get_namespace(X)
  
          if issparse(X) and self.svd_solver != "arpack":
              raise TypeError(
                  'PCA only support sparse inputs with the "arpack" solver, while '
                  f'"{self.svd_solver}" was passed. See TruncatedSVD for a possible'
                  " alternative."
              )
          # Raise an error for non-Numpy input and arpack solver.
          if self.svd_solver == "arpack" and is_array_api_compliant:
              raise ValueError(
                  "PCA with svd_solver='arpack' is not supported for Array API inputs."
              )
  
          X = self._validate_data(
              X,
              dtype=[xp.float64, xp.float32],
              accept_sparse=("csr", "csc"),
              ensure_2d=True,
              copy=self.copy,
          )
  
      else:
          if issparse(X):
              raise TypeError(
                  "PCA does not support sparse input. See "
                  "TruncatedSVD for a possible alternative."
              )
  
          if sklearn_check_version("0.23"):
              X = self._validate_data(
                  X,
                  dtype=[np.float64, np.float32],
                  ensure_2d=True,
                  copy=False,
              )
          else:
              X = check_array(
                  X,
                  dtype=[np.float64, np.float32],
                  ensure_2d=True,
                  copy=False,
              )
  
      if self.n_components is None:
          if self.svd_solver != "arpack":
              n_components = min(X.shape)
          else:
              n_components = min(X.shape) - 1
      else:
          n_components = self.n_components
  
      self._fit_svd_solver = self.svd_solver
      shape_good_for_daal = X.shape[1] / X.shape[0] < 2
  
      if self._fit_svd_solver == "auto":
          if sklearn_check_version("1.1"):
              # Small problem or n_components == 'mle', just call full PCA
              if max(X.shape) <= 500 or n_components == "mle":
                  self._fit_svd_solver = "full"
              elif 1 <= n_components < 0.8 * min(X.shape):
                  self._fit_svd_solver = "randomized"
              # This is also the case of n_components in (0,1)
              else:
                  self._fit_svd_solver = "full"
          else:
              if n_components == "mle":
                  self._fit_svd_solver = "full"
              else:
                  n, p, k = X.shape[0], X.shape[1], n_components
                  # These coefficients are result of training of Logistic Regression
                  # (max_iter=10000, solver="liblinear", fit_intercept=False)
                  # on different datasets and number of components.
                  # X is a dataset with npk, np^2, and n^2 columns.
                  # And y is speedup of patched scikit-learn's
                  # full PCA against stock scikit-learn's randomized PCA.
                  regression_coefs = np.array(
                      [
                          [9.779873e-11, n * p * k],
                          [-1.122062e-11, n * p * p],
                          [1.127905e-09, n**2],
                      ]
                  )
  
                  if (
                      n_components >= 1
                      and np.dot(
                          regression_coefs[:, 0], regression_coefs[:, 1]
                      )
                      <= 0
                  ):
                      self._fit_svd_solver = "randomized"
                  else:
                      self._fit_svd_solver = "full"
  
      if not shape_good_for_daal or self._fit_svd_solver != "full":
          if sklearn_check_version("1.4"):
              X = self._validate_data(
                  X, copy=self.copy, accept_sparse=("csr", "csc")
              )
          elif sklearn_check_version("0.23"):
              X = self._validate_data(X, copy=self.copy)
          else:
              X = check_array(X, copy=self.copy)
  
      _patching_status = PatchingConditionsChain(
          "sklearn.decomposition.PCA.fit"
      )
      _dal_ready = _patching_status.and_conditions(
          [
              (
                  self._fit_svd_solver == "full",
                  f"'{self._fit_svd_solver}' SVD solver is not supported. "
                  "Only 'full' solver is supported.",
              )
          ]
      )
  
      if _dal_ready:
          _dal_ready = _patching_status.and_conditions(
              [
                  (
                      shape_good_for_daal,
                      "The shape of X does not satisfy oneDAL requirements: "
                      "number of features / number of samples >= 2",
                  ),
              ]
          )
          if _dal_ready:
              result = self._fit_full(X, n_components)
          else:
              result = PCA_original._fit_full(self, X, n_components)
      elif self._fit_svd_solver in ["arpack", "randomized"]:
          result = self._fit_truncated(
              X, n_components, self._fit_svd_solver
          )
      else:
          raise ValueError(
              "Unrecognized svd_solver='{0}'"
              "".format(self._fit_svd_solver)
          )
  
      _patching_status.write_log()
      return result
  
file_path: scikit-learn-intelex/daal4py/sklearn/decomposition/_pca.py
imports: import numbers
  from math import sqrt
  import numpy
  from scipy.sparse import issparse
  from sklearn.utils import check_array
  from sklearn.utils.extmath import stable_cumsum
  from sklearn.utils.validation import check_is_fitted
  import daal4py
  from .._device_offload import support_usm_ndarray
  from .._utils import PatchingConditionsChain, control_n_jobs, getFPType, run_with_n_jobs, sklearn_check_version
label_desc: Use image node_id 5 for calling the PCA obj's underlying member method code with example usage: obj._fit(X) and returns: result