





import logging

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

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



def 				lowerCAmelCase_ (							A_):
    return input_array.reshape((input_array.size, 1))



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

    return covariance_sum / features.shape[1]



def 				lowerCAmelCase_ (							A_    ,A_    ,A_):
    UpperCamelCase__:	str					=     features.mean(1)
    UpperCamelCase__:	Optional[int]					=     np.nan
    for i in range(UpperCAmelCase__):
        UpperCamelCase__:	Union[str, Any]					=     features[:, labels == i]
        UpperCamelCase__:	Optional[Any]					=     data.shape[1]
        UpperCamelCase__:	Tuple					=     data.mean(1)
        if i > 0:
            # If covariance_sum is not None
            covariance_sum += device_data * np.dot(
                column_reshape(UpperCAmelCase__) - column_reshape(UpperCAmelCase__)    ,(column_reshape(UpperCAmelCase__) - column_reshape(UpperCAmelCase__)).T    ,)
        else:
            # If covariance_sum is np.nan (i.e. first loop)
            UpperCamelCase__:	Tuple					=     device_data * np.dot(
                column_reshape(UpperCAmelCase__) - column_reshape(UpperCAmelCase__)    ,(column_reshape(UpperCAmelCase__) - column_reshape(UpperCAmelCase__)).T    ,)

    return covariance_sum / features.shape[1]



def 				lowerCAmelCase_ (							A_    ,A_):

    # Check if the features have been loaded
    if features.any():
        UpperCamelCase__:	Dict					=     features.mean(1)
        # Center the dataset
        UpperCamelCase__:	str					=     features - np.reshape(UpperCAmelCase__    ,(data_mean.size, 1))
        UpperCamelCase__:	Tuple					=     np.dot(UpperCAmelCase__    ,centered_data.T) / features.shape[1]
        UpperCamelCase__				, UpperCamelCase__:	Optional[int]					=     np.linalg.eigh(UpperCAmelCase__)
        # Take all the columns in the reverse order (-1), and then takes only the first
        UpperCamelCase__:	List[str]					=     eigenvectors[:, ::-1][:, 0:dimensions]
        # Project the database on the new space
        UpperCamelCase__:	Optional[Any]					=     np.dot(filtered_eigenvectors.T    ,UpperCAmelCase__)
        logging.info("Principal Component Analysis computed")

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



def 				lowerCAmelCase_ (							A_    ,A_    ,A_    ,A_):
    assert classes > dimensions

    # Check if features have been already loaded
    if features.any:
        UpperCamelCase__				, UpperCamelCase__:	Dict					=     eigh(
            covariance_between_classes(UpperCAmelCase__    ,UpperCAmelCase__    ,UpperCAmelCase__)    ,covariance_within_classes(UpperCAmelCase__    ,UpperCAmelCase__    ,UpperCAmelCase__)    ,)
        UpperCamelCase__:	List[Any]					=     eigenvectors[:, ::-1][:, :dimensions]
        UpperCamelCase__				, UpperCamelCase__				, UpperCamelCase__:	Union[str, Any]					=     np.linalg.svd(UpperCAmelCase__)
        UpperCamelCase__:	Optional[int]					=     svd_matrix[:, 0:dimensions]
        UpperCamelCase__:	Tuple					=     np.dot(filtered_svd_matrix.T    ,UpperCAmelCase__)
        logging.info("Linear Discriminant Analysis computed")

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



def 				lowerCAmelCase_ (							):
    # Create dummy dataset with 2 classes and 3 features
    UpperCamelCase__:	List[str]					=     np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]])
    UpperCamelCase__:	List[str]					=     np.array([0, 0, 0, 1, 1])
    UpperCamelCase__:	List[Any]					=     2
    UpperCamelCase__:	str					=     2

    # Assert that the function raises an AssertionError if dimensions > classes
    with pytest.raises(UpperCAmelCase__) as error_info:
        UpperCamelCase__:	Union[str, Any]					=     linear_discriminant_analysis(
            UpperCAmelCase__    ,UpperCAmelCase__    ,UpperCAmelCase__    ,UpperCAmelCase__)
        if isinstance(UpperCAmelCase__    ,np.ndarray):
            raise AssertionError(
                "Did not raise AssertionError for dimensions > classes")
        assert error_info.type is AssertionError



def 				lowerCAmelCase_ (							):
    UpperCamelCase__:	Dict					=     np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
    UpperCamelCase__:	Tuple					=     2
    UpperCamelCase__:	str					=     np.array([[6.9282_0323, 8.6602_5404, 10.3923_0485], [3.0, 3.0, 3.0]])

    with pytest.raises(UpperCAmelCase__) as error_info:
        UpperCamelCase__:	Any					=     principal_component_analysis(UpperCAmelCase__    ,UpperCAmelCase__)
        if not np.allclose(UpperCAmelCase__    ,UpperCAmelCase__):
            raise AssertionError
        assert error_info.type is AssertionError


if __name__ == "__main__":
   import doctest

   doctest.testmod()




'''simple docstring'''







from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tensorflow_text_available, is_torch_available


__lowerCamelCase									=     {
    '''configuration_ernie''': ['''ERNIE_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''ErnieConfig''', '''ErnieOnnxConfig'''],
}

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      __lowerCamelCase									=     [
          '''ERNIE_PRETRAINED_MODEL_ARCHIVE_LIST''',
          '''ErnieForCausalLM''',
          '''ErnieForMaskedLM''',
          '''ErnieForMultipleChoice''',
          '''ErnieForNextSentencePrediction''',
          '''ErnieForPreTraining''',
          '''ErnieForQuestionAnswering''',
          '''ErnieForSequenceClassification''',
          '''ErnieForTokenClassification''',
          '''ErnieModel''',
          '''ErniePreTrainedModel''',
      ]

if TYPE_CHECKING:
      from .configuration_ernie import ERNIE_PRETRAINED_CONFIG_ARCHIVE_MAP, ErnieConfig, ErnieOnnxConfig

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_ernie import (
                ERNIE_PRETRAINED_MODEL_ARCHIVE_LIST,
                ErnieForCausalLM,
                ErnieForMaskedLM,
                ErnieForMultipleChoice,
                ErnieForNextSentencePrediction,
                ErnieForPreTraining,
                ErnieForQuestionAnswering,
                ErnieForSequenceClassification,
                ErnieForTokenClassification,
                ErnieModel,
                ErniePreTrainedModel,
            )

else:
      import sys

      __lowerCamelCase									=     _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)
