class_docstr: Principal component analysis (PCA)
  
  Linear dimensionality reduction using Singular Value Decomposition of the
  data to project it to a lower dimensional space.
  
  It uses the LAPACK implementation of the full SVD or a randomized truncated
  SVD by the method of Halko et al. 2009, depending on the shape of the input
  data and the number of components to extract.
  
  It can also use the scipy.sparse.linalg ARPACK implementation of the
  truncated SVD.
  
  Notice that this class does not support sparse input. See
  :class:`TruncatedSVD` for an alternative with sparse data.
  
  Read more in the :ref:`User Guide <PCA>`.
  
  Parameters
  ----------
  n_components : int, float, None or string
      Number of components to keep.
      if n_components is not set all components are kept::
  
          n_components == min(n_samples, n_features)
  
      if n_components == 'mle' and svd_solver == 'full', Minka's MLE is used
      to guess the dimension
      if ``0 < n_components < 1`` and svd_solver == 'full', select the number
      of components such that the amount of variance that needs to be
      explained is greater than the percentage specified by n_components
      n_components cannot be equal to n_features for svd_solver == 'arpack'.
  
  copy : bool (default True)
      If False, data passed to fit are overwritten and running
      fit(X).transform(X) will not yield the expected results,
      use fit_transform(X) instead.
  
  whiten : bool, optional (default False)
      When True (False by default) the `components_` vectors are multiplied
      by the square root of n_samples and then divided by the singular values
      to ensure uncorrelated outputs with unit component-wise variances.
  
      Whitening will remove some information from the transformed signal
      (the relative variance scales of the components) but can sometime
      improve the predictive accuracy of the downstream estimators by
      making their data respect some hard-wired assumptions.
  
  svd_solver : string {'auto', 'full', 'arpack', 'randomized'}
      auto :
          the solver is selected by a default policy based on `X.shape` and
          `n_components`: if the input data is larger than 500x500 and the
          number of components to extract is lower than 80% of the smallest
          dimension of the data, then the more efficient 'randomized'
          method is enabled. Otherwise the exact full SVD is computed and
          optionally truncated afterwards.
      full :
          run exact full SVD calling the standard LAPACK solver via
          `scipy.linalg.svd` and select the components by postprocessing
      arpack :
          run SVD truncated to n_components calling ARPACK solver via
          `scipy.sparse.linalg.svds`. It requires strictly
          0 < n_components < X.shape[1]
      randomized :
          run randomized SVD by the method of Halko et al.
  
      .. versionadded:: 0.18.0
  
  tol : float >= 0, optional (default .0)
      Tolerance for singular values computed by svd_solver == 'arpack'.
  
      .. versionadded:: 0.18.0
  
  iterated_power : int >= 0, or 'auto', (default 'auto')
      Number of iterations for the power method computed by
      svd_solver == 'randomized'.
  
      .. versionadded:: 0.18.0
  
  random_state : int or RandomState instance or None (default None)
      Pseudo Random Number generator seed control. If None, use the
      numpy.random singleton. Used by svd_solver == 'arpack' or 'randomized'.
  
      .. versionadded:: 0.18.0
  
  Attributes
  ----------
  components_ : array, [n_components, n_features]
      Principal axes in feature space, representing the directions of
      maximum variance in the data. The components are sorted by
      ``explained_variance_``.
  
  explained_variance_ : array, [n_components]
      The amount of variance explained by each of the selected components.
  
      .. versionadded:: 0.18
  
  explained_variance_ratio_ : array, [n_components]
      Percentage of variance explained by each of the selected components.
  
      If ``n_components`` is not set then all components are stored and the
      sum of explained variances is equal to 1.0.
  
  mean_ : array, [n_features]
      Per-feature empirical mean, estimated from the training set.
  
      Equal to `X.mean(axis=1)`.
  
  n_components_ : int
      The estimated number of components. When n_components is set
      to 'mle' or a number between 0 and 1 (with svd_solver == 'full') this
      number is estimated from input data. Otherwise it equals the parameter
      n_components, or n_features if n_components is None.
  
  noise_variance_ : float
      The estimated noise covariance following the Probabilistic PCA model
      from Tipping and Bishop 1999. See "Pattern Recognition and
      Machine Learning" by C. Bishop, 12.2.1 p. 574 or
      http://www.miketipping.com/papers/met-mppca.pdf. It is required to
      computed the estimated data covariance and score samples.
  
  References
  ----------
  For n_components == 'mle', this class uses the method of `Thomas P. Minka:
  Automatic Choice of Dimensionality for PCA. NIPS 2000: 598-604`
  
  Implements the probabilistic PCA model from:
  M. Tipping and C. Bishop, Probabilistic Principal Component Analysis,
  Journal of the Royal Statistical Society, Series B, 61, Part 3, pp. 611-622
  via the score and score_samples methods.
  See http://www.miketipping.com/papers/met-mppca.pdf
  
  For svd_solver == 'arpack', refer to `scipy.sparse.linalg.svds`.
  
  For svd_solver == 'randomized', see:
  `Finding structure with randomness: Stochastic algorithms
  for constructing approximate matrix decompositions Halko, et al., 2009
  (arXiv:909)`
  `A randomized algorithm for the decomposition of matrices
  Per-Gunnar Martinsson, Vladimir Rokhlin and Mark Tygert`
  
  
  Examples
  --------
  >>> import numpy as np
  >>> from sklearn.decomposition import PCA
  >>> X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
  >>> pca = PCA(n_components=2)
  >>> pca.fit(X)
  PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,
    svd_solver='auto', tol=0.0, whiten=False)
  >>> print(pca.explained_variance_ratio_) # doctest: +ELLIPSIS
  [ 0.99244...  0.00755...]
  
  >>> pca = PCA(n_components=2, svd_solver='full')
  >>> pca.fit(X)                 # doctest: +ELLIPSIS +NORMALIZE_WHITESPACE
  PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,
    svd_solver='full', tol=0.0, whiten=False)
  >>> print(pca.explained_variance_ratio_) # doctest: +ELLIPSIS
  [ 0.99244...  0.00755...]
  
  >>> pca = PCA(n_components=1, svd_solver='arpack')
  >>> pca.fit(X)
  PCA(copy=True, iterated_power='auto', n_components=1, random_state=None,
    svd_solver='arpack', tol=0.0, whiten=False)
  >>> print(pca.explained_variance_ratio_) # doctest: +ELLIPSIS
  [ 0.99244...]
  
  See also
  --------
  KernelPCA
  SparsePCA
  TruncatedSVD
  IncrementalPCA
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docstr: Fit the model with X.
  
  Parameters
  ----------
  X: array-like, shape (n_samples, n_features)
      Training data, where n_samples in the number of samples
      and n_features is the number of features.
  
  Returns
  -------
  self : object
      Returns the instance itself.
docstr_tok: ["Fit","the","model","with","X.","Parameters","--","--","--","--","--","X",":","array-like",",","shape","(","n_samples",",","n_features",")","Training","data",",","where","n_samples","in","the","number","of","samples","and","n_features","is","the","number","of","features",".","Returns","--","--","--","-","self",":","object","Returns","the","instance","itself","."]
code: def fit(self, X, y=None):
      """Fit the model with X.
  
      Parameters
      ----------
      X: array-like, shape (n_samples, n_features)
          Training data, where n_samples in the number of samples
          and n_features is the number of features.
  
      Returns
      -------
      self : object
          Returns the instance itself.
      """
      self._fit(X)
      return self
  
imports: from math import log, sqrt
  import numpy
  from scipy import linalg
  from scipy.special import gammaln
  from scipy.sparse import issparse
  from ..externals import six
  from .base import _BasePCA
  from ..base import BaseEstimator, TransformerMixin
  from ..utils import deprecated
  from ..utils import check_random_state, as_float_array
  from ..utils import check_array
  from ..utils.extmath import fast_dot, fast_logdet, randomized_svd, svd_flip
  from ..utils.validation import check_is_fitted
  from ..utils.arpack import svds
label_desc: Use image node_id 2 for calling the PCA obj's underlying member method code with example usage: obj.fit(X, y) and returns: self