

import logging

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

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

def 	snake_case__			(    SCREAMING_SNAKE_CASE_		:    np.ndarray			):



     '''simple docstring'''





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

def 	snake_case__			(    SCREAMING_SNAKE_CASE_		:    np.ndarray	,     SCREAMING_SNAKE_CASE_		:    np.ndarray	,     SCREAMING_SNAKE_CASE_		:    int			):



     '''simple docstring'''





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

     return covariance_sum / features.shape[1]

def 	snake_case__			(    SCREAMING_SNAKE_CASE_		:    np.ndarray	,     SCREAMING_SNAKE_CASE_		:    np.ndarray	,     SCREAMING_SNAKE_CASE_		:    int			):



     '''simple docstring'''





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

     return covariance_sum / features.shape[1]

def 	snake_case__			(    SCREAMING_SNAKE_CASE_		:    np.ndarray	,     SCREAMING_SNAKE_CASE_		:    int			):



     '''simple docstring'''





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

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

def 	snake_case__			(    SCREAMING_SNAKE_CASE_		:    np.ndarray	,     SCREAMING_SNAKE_CASE_		:    np.ndarray	,     SCREAMING_SNAKE_CASE_		:    int	,     SCREAMING_SNAKE_CASE_		:    int			):



     '''simple docstring'''





     assert classes > dimensions

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

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

def 	snake_case__			(    ):



     '''simple docstring'''





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

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

def 	snake_case__			(    ):



     '''simple docstring'''





     lowercase__    :   Union[str, Any]      =       np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]			)
     lowercase__    :   Optional[int]      =       2
     lowercase__    :   Union[str, Any]      =       np.array([[6.9282_0323, 8.6602_5404, 10.3923_0485], [3.0, 3.0, 3.0]]			)

     with pytest.raises(SCREAMING_SNAKE_CASE_			) as error_info:
          lowercase__    :   Dict      =       principal_component_analysis(SCREAMING_SNAKE_CASE_	,     SCREAMING_SNAKE_CASE_			)
          if not np.allclose(SCREAMING_SNAKE_CASE_	,     SCREAMING_SNAKE_CASE_			):
               raise AssertionError
          assert error_info.type is AssertionError


if __name__ == "__main__":
       import doctest

       doctest.testmod()




# flake8: noqa
# Lint as: python3

from typing import Dict, List, Optional, Type

from .. import config
from ..utils import logging
from .formatting import (
    ArrowFormatter,
    CustomFormatter,
    Formatter,
    PandasFormatter,
    PythonFormatter,
    TensorFormatter,
    format_table,
    query_table,
)
from .np_formatter import NumpyFormatter


snake_case_			  = logging.get_logger(__name__)

snake_case_			  = {}
snake_case_			  = {}
snake_case_			  = {}

def 	snake_case__			(    SCREAMING_SNAKE_CASE_		:    type	,     SCREAMING_SNAKE_CASE_		:    Optional[str]	,     SCREAMING_SNAKE_CASE_		:    Optional[List[str]] = None	,     ):



     '''simple docstring'''





     lowercase__    :   Union[str, Any]      =       aliases if aliases is not None else []
     if format_type in _FORMAT_TYPES:
          logger.warning(
              f"""Overwriting format type '{format_type}' ({_FORMAT_TYPES[format_type].__name__} -> {formatter_cls.__name__})"""			)
     lowercase__    :   Any      =       formatter_cls
     for alias in set(aliases + [format_type]			):
          if alias in _FORMAT_TYPES_ALIASES:
               logger.warning(
                   f"""Overwriting format type alias '{alias}' ({_FORMAT_TYPES_ALIASES[alias]} -> {format_type})"""			)
          lowercase__    :   int      =       format_type

def 	snake_case__			(    SCREAMING_SNAKE_CASE_		:    Exception	,     SCREAMING_SNAKE_CASE_		:    Optional[str]	,     SCREAMING_SNAKE_CASE_		:    Optional[List[str]] = None			):



     '''simple docstring'''





     lowercase__    :   Optional[Any]      =       aliases if aliases is not None else []
     for alias in set(aliases + [format_type]			):
          lowercase__    :   Any      =       unavailable_error


# Here we define all the available formatting functions that can be used by `Dataset.set_format`
_register_formatter(PythonFormatter, None, aliases=['''python'''])
_register_formatter(ArrowFormatter, '''arrow''', aliases=['''pa''', '''pyarrow'''])
_register_formatter(NumpyFormatter, '''numpy''', aliases=['''np'''])
_register_formatter(PandasFormatter, '''pandas''', aliases=['''pd'''])
_register_formatter(CustomFormatter, '''custom''')

if config.TORCH_AVAILABLE:
       from .torch_formatter import TorchFormatter

       _register_formatter(TorchFormatter, '''torch''', aliases=['''pt''', '''pytorch'''])
else:
       snake_case_			  = ValueError('''PyTorch needs to be installed to be able to return PyTorch tensors.''')
       _register_unavailable_formatter(_torch_error, '''torch''', aliases=['''pt''', '''pytorch'''])

if config.TF_AVAILABLE:
       from .tf_formatter import TFFormatter

       _register_formatter(TFFormatter, '''tensorflow''', aliases=['''tf'''])
else:
       snake_case_			  = ValueError('''Tensorflow needs to be installed to be able to return Tensorflow tensors.''')
       _register_unavailable_formatter(_tf_error, '''tensorflow''', aliases=['''tf'''])

if config.JAX_AVAILABLE:
       from .jax_formatter import JaxFormatter

       _register_formatter(JaxFormatter, '''jax''', aliases=[])
else:
       snake_case_			  = ValueError('''JAX needs to be installed to be able to return JAX arrays.''')
       _register_unavailable_formatter(_jax_error, '''jax''', aliases=[])

def 	snake_case__			(    SCREAMING_SNAKE_CASE_		:    Optional[str]			):



     '''simple docstring'''





     if format_type in _FORMAT_TYPES_ALIASES:
          return _FORMAT_TYPES_ALIASES[format_type]
     else:
          return format_type

def 	snake_case__			(    SCREAMING_SNAKE_CASE_		:    Optional[str]	,     **SCREAMING_SNAKE_CASE_		:    Any			):



     '''simple docstring'''





     lowercase__    :   Tuple      =       get_format_type_from_alias(SCREAMING_SNAKE_CASE_			)
     if format_type in _FORMAT_TYPES:
          return _FORMAT_TYPES[format_type](**SCREAMING_SNAKE_CASE_			)
     if format_type in _FORMAT_TYPES_ALIASES_UNAVAILABLE:
          raise _FORMAT_TYPES_ALIASES_UNAVAILABLE[format_type]
     else:
          raise ValueError(
              f"""Return type should be None or selected in {list(type for type in _FORMAT_TYPES.keys() if type != None			)}, but got '{format_type}'"""			)

