






"""simple docstring"""





import logging

import numpy as np
import pytest
from scipy.linalg import eigh

logging.basicConfig(level=logging.INFO, format='%(message)s')


def       lowerCamelCase_       (   UpperCAmelCase_  )						->np.ndarray:





  """simple docstring"""


  return input_array.reshape((input_array.size, 1)  )


def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  )						->np.ndarray:





  """simple docstring"""


  __UpperCAmelCase    :						Tuple       =						np.nan
  for i in range(_A  ):
    __UpperCAmelCase    :						Dict       =						features[:, labels == i]
    __UpperCAmelCase    :						Dict       =						data.mean(1  )
    # Centralize the data of class i
    __UpperCAmelCase    :						Union[str, Any]       =						data - column_reshape(_A  )
    if i > 0:
      # If covariance_sum is not None
      covariance_sum += np.dot(_A  ,			centered_data.T  )
    else:
      # If covariance_sum is np.nan (i.e. first loop)
      __UpperCAmelCase    :						str       =						np.dot(_A  ,			centered_data.T  )

  return covariance_sum / features.shape[1]


def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  )						->np.ndarray:





  """simple docstring"""


  __UpperCAmelCase    :						str       =						features.mean(1  )
  __UpperCAmelCase    :						List[str]       =						np.nan
  for i in range(_A  ):
    __UpperCAmelCase    :						List[str]       =						features[:, labels == i]
    __UpperCAmelCase    :						List[str]       =						data.shape[1]
    __UpperCAmelCase    :						List[str]       =						data.mean(1  )
    if i > 0:
      # If covariance_sum is not None
      covariance_sum += device_data * np.dot(
          column_reshape(_A  ) - column_reshape(_A  )  ,			(column_reshape(_A  ) - column_reshape(_A  )).T  ,			)
    else:
      # If covariance_sum is np.nan (i.e. first loop)
      __UpperCAmelCase    :						int       =						device_data * np.dot(
          column_reshape(_A  ) - column_reshape(_A  )  ,			(column_reshape(_A  ) - column_reshape(_A  )).T  ,			)

  return covariance_sum / features.shape[1]


def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  )						->np.ndarray:





  """simple docstring"""


  if features.any():
    __UpperCAmelCase    :						str       =						features.mean(1  )
    # Center the dataset
    __UpperCAmelCase    :						List[str]       =						features - np.reshape(_A  ,			(data_mean.size, 1)  )
    __UpperCAmelCase    :						Tuple       =						np.dot(_A  ,			centered_data.T  ) / features.shape[1]
    __UpperCAmelCase       ,     __UpperCAmelCase    :						Optional[int]       =						np.linalg.eigh(_A  )
    # Take all the columns in the reverse order (-1), and then takes only the first
    __UpperCAmelCase    :						Dict       =						eigenvectors[:, ::-1][:, 0:dimensions]
    # Project the database on the new space
    __UpperCAmelCase    :						int       =						np.dot(filtered_eigenvectors.T  ,			_A  )
    logging.info('''Principal Component Analysis computed'''  )

    return projected_data
  else:
    logging.basicConfig(level=logging.ERROR  ,			format='''%(message)s'''  ,			force=_A  )
    logging.error('''Dataset empty'''  )
    raise AssertionError


def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  )						->np.ndarray:





  """simple docstring"""


  assert classes > dimensions

  # Check if features have been already loaded
  if features.any:
    __UpperCAmelCase       ,     __UpperCAmelCase    :						Dict       =						eigh(
        covariance_between_classes(_A  ,			_A  ,			_A  )  ,			covariance_within_classes(_A  ,			_A  ,			_A  )  ,			)
    __UpperCAmelCase    :						Optional[Any]       =						eigenvectors[:, ::-1][:, :dimensions]
    __UpperCAmelCase       ,     __UpperCAmelCase       ,     __UpperCAmelCase    :						Dict       =						np.linalg.svd(_A  )
    __UpperCAmelCase    :						Union[str, Any]       =						svd_matrix[:, 0:dimensions]
    __UpperCAmelCase    :						Tuple       =						np.dot(filtered_svd_matrix.T  ,			_A  )
    logging.info('''Linear Discriminant Analysis computed'''  )

    return projected_data
  else:
    logging.basicConfig(level=logging.ERROR  ,			format='''%(message)s'''  ,			force=_A  )
    logging.error('''Dataset empty'''  )
    raise AssertionError


def       lowerCamelCase_       (   )						->None:





  """simple docstring"""


  __UpperCAmelCase    :						str       =						np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]  )
  __UpperCAmelCase    :						Optional[Any]       =						np.array([0, 0, 0, 1, 1]  )
  __UpperCAmelCase    :						Tuple       =						2
  __UpperCAmelCase    :						Tuple       =						2

  # Assert that the function raises an AssertionError if dimensions > classes
  with pytest.raises(_A  ) as error_info:
    __UpperCAmelCase    :						Any       =						linear_discriminant_analysis(
        _A  ,			_A  ,			_A  ,			_A  )
    if isinstance(_A  ,			np.ndarray  ):
      raise AssertionError(
          '''Did not raise AssertionError for dimensions > classes'''  )
    assert error_info.type is AssertionError


def       lowerCamelCase_       (   )						->None:





  """simple docstring"""


  __UpperCAmelCase    :						Optional[Any]       =						np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]  )
  __UpperCAmelCase    :						Dict       =						2
  __UpperCAmelCase    :						Optional[int]       =						np.array([[6.92_820_323, 8.66_025_404, 10.39_23_04_85], [3.0, 3.0, 3.0]]  )

  with pytest.raises(_A  ) as error_info:
    __UpperCAmelCase    :						List[str]       =						principal_component_analysis(_A  ,			_A  )
    if not np.allclose(_A  ,			_A  ):
      raise AssertionError
    assert error_info.type is AssertionError


if __name__ == "__main__":
  import doctest

  doctest.testmod()






"""simple docstring"""





# flake8: noqa
# Lint as: python3
lowercase__				:Tuple				   =       [
    'VerificationMode',
    'Version',
    'disable_progress_bar',
    'enable_progress_bar',
    'is_progress_bar_enabled',
    'experimental',
]

from .info_utils import VerificationMode
from .logging import disable_progress_bar, enable_progress_bar, is_progress_bar_enabled
from .version import Version
from .experimental import experimental