






'''simple docstring'''

from typing import Any



def 				snake_case       (  a_				:			int     , a_				:			Dict     , a_				:			Tuple     , a_				:			int     , a_				:			Optional[int]     , )							->					int:





      """simple docstring"""

      _validation(
          __a     , __a     , __a     , __a     , __a     , )
      # Creates data structures and fill initial step
      UpperCamelCase_					: Dict            =				{}
      UpperCamelCase_					: Any            =				{}
      for state in states_space:
            UpperCamelCase_					: List[Any]            =				observations_space[0]
            UpperCamelCase_					: Dict            =				(
                initial_probabilities[state] * emission_probabilities[state][observation]
            )
            UpperCamelCase_					: Dict            =				None

      # Fills the data structure with the probabilities of
      # different transitions and pointers to previous states
      for o in range(1     , len(__a						)						):
            UpperCamelCase_					: Optional[int]            =				observations_space[o]
            UpperCamelCase_					: Dict            =				observations_space[o - 1]
            for state in states_space:
                  # Calculates the argmax for probability function
                  UpperCamelCase_					: Any            =				""""""
                  UpperCamelCase_					: List[str]            =				-1
                  for k_state in states_space:
                        UpperCamelCase_					: Union[str, Any]            =				(
                            probabilities[(k_state, prior_observation)]
                            * transition_probabilities[k_state][state]
                            * emission_probabilities[state][observation]
                        )
                        if probability > max_probability:
                              UpperCamelCase_					: Tuple            =				probability
                              UpperCamelCase_					: int            =				k_state

            # Update probabilities and pointers dicts
                  UpperCamelCase_					: List[str]            =				(
                      probabilities[(arg_max, prior_observation)]
                      * transition_probabilities[arg_max][state]
                      * emission_probabilities[state][observation]
                  )

                  UpperCamelCase_					: List[Any]            =				arg_max

    # The final observation
      UpperCamelCase_					: Optional[int]            =				observations_space[len(__a						) - 1]

      # argmax for given final observation
      UpperCamelCase_					: Optional[Any]            =				""""""
      UpperCamelCase_					: Dict            =				-1
      for k_state in states_space:
            UpperCamelCase_					: Dict            =				probabilities[(k_state, final_observation)]
            if probability > max_probability:
                  UpperCamelCase_					: str            =				probability
                  UpperCamelCase_					: Dict            =				k_state
      UpperCamelCase_					: Tuple            =				arg_max

      # Process pointers backwards
      UpperCamelCase_					: Any            =				last_state
      UpperCamelCase_					: str            =				[]
      for o in range(len(__a						) - 1     , -1     , -1						):
            result.append(__a						)
            UpperCamelCase_					: List[Any]            =				pointers[previous, observations_space[o]]
      result.reverse()

      return result



def 				snake_case       (  a_				:			Union[str, Any]     , a_				:			Optional[int]     , a_				:			Dict     , a_				:			Any     , a_				:			List[str]     , )							->					Dict:





      """simple docstring"""

      _validate_not_empty(
          __a     , __a     , __a     , __a     , __a     , )
      _validate_lists(__a     , __a						)
      _validate_dicts(
          __a     , __a     , __a						)



def 				snake_case       (  a_				:			Optional[int]     , a_				:			List[Any]     , a_				:			Tuple     , a_				:			Optional[Any]     , a_				:			str     , )							->					str:





      """simple docstring"""

      if not all(
          [
              observations_space,
              states_space,
              initial_probabilities,
              transition_probabilities,
              emission_probabilities,
          ]						):
            raise ValueError("""There\'s an empty parameter"""						)



def 				snake_case       (  a_				:			Union[str, Any]     , a_				:			List[str]						)							->					Dict:





      """simple docstring"""

      _validate_list(__a     , """observations_space"""						)
      _validate_list(__a     , """states_space"""						)



def 				snake_case       (  a_				:			str     , a_				:			List[Any]						)							->					List[Any]:





      """simple docstring"""

      if not isinstance(_object     , __a						):
            UpperCamelCase_					: Optional[int]            =				f"{var_name} must be a list"
            raise ValueError(__a						)
      else:
            for x in _object:
                  if not isinstance(__a     , __a						):
                        UpperCamelCase_					: List[str]            =				f"{var_name} must be a list of strings"
                        raise ValueError(__a						)



def 				snake_case       (  a_				:			List[str]     , a_				:			Optional[int]     , a_				:			int     , )							->					str:





      """simple docstring"""

      _validate_dict(__a     , """initial_probabilities"""     , __a						)
      _validate_nested_dict(__a     , """transition_probabilities"""						)
      _validate_nested_dict(__a     , """emission_probabilities"""						)



def 				snake_case       (  a_				:			Tuple     , a_				:			List[Any]						)							->					str:





      """simple docstring"""

      _validate_dict(_object     , __a     , __a						)
      for x in _object.values():
            _validate_dict(__a     , __a     , __a     , __a						)



def 				snake_case       (  a_				:			Optional[int]     , a_				:			Optional[int]     , a_				:			Union[str, Any]     , a_				:			List[Any] = False						)							->					Any:





      """simple docstring"""

      if not isinstance(_object     , __a						):
            UpperCamelCase_					: int            =				f"{var_name} must be a dict"
            raise ValueError(__a						)
      if not all(isinstance(__a     , __a						) for x in _object						):
            UpperCamelCase_					: Tuple            =				f"{var_name} all keys must be strings"
            raise ValueError(__a						)
      if not all(isinstance(__a     , __a						) for x in _object.values()						):
            UpperCamelCase_					: Optional[int]            =				"""nested dictionary """ if nested else """"""
            UpperCamelCase_					: List[Any]            =				f"{var_name} {nested_text}all values must be {value_type.__name__}"
            raise ValueError(__a						)


if __name__ == "__main__":
      from doctest import testmod

      testmod()








"""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			(			__a     ):
		return input_array.reshape((input_array.size, 1)     )



def 							_lowerCamelCase			(			__a,				__a,				__a     ):
		SCREAMING_SNAKE_CASE_    			=			np.nan
		for i in range(__a     ):
				SCREAMING_SNAKE_CASE_    			=			features[:, labels == i]
				SCREAMING_SNAKE_CASE_    			=			data.mean(1     )
				# Centralize the data of class i
				SCREAMING_SNAKE_CASE_    			=			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)
						SCREAMING_SNAKE_CASE_    			=			np.dot(__a,				centered_data.T     )

		return covariance_sum / features.shape[1]



def 							_lowerCamelCase			(			__a,				__a,				__a     ):
		SCREAMING_SNAKE_CASE_    			=			features.mean(1     )
		SCREAMING_SNAKE_CASE_    			=			np.nan
		for i in range(__a     ):
				SCREAMING_SNAKE_CASE_    			=			features[:, labels == i]
				SCREAMING_SNAKE_CASE_    			=			data.shape[1]
				SCREAMING_SNAKE_CASE_    			=			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)
						SCREAMING_SNAKE_CASE_    			=			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			(			__a,				__a     ):

		# Check if the features have been loaded
		if features.any():
				SCREAMING_SNAKE_CASE_    			=			features.mean(1     )
				# Center the dataset
				SCREAMING_SNAKE_CASE_    			=			features - np.reshape(__a,				(data_mean.size, 1)     )
				SCREAMING_SNAKE_CASE_    			=			np.dot(__a,				centered_data.T     ) / features.shape[1]
				SCREAMING_SNAKE_CASE_			,SCREAMING_SNAKE_CASE_    			=			np.linalg.eigh(__a     )
				# Take all the columns in the reverse order (-1), and then takes only the first
				SCREAMING_SNAKE_CASE_    			=			eigenvectors[:, ::-1][:, 0:dimensions]
				# Project the database on the new space
				SCREAMING_SNAKE_CASE_    			=			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			(			__a,				__a,				__a,				__a     ):
		assert classes > dimensions

		# Check if features have been already loaded
		if features.any:
				SCREAMING_SNAKE_CASE_			,SCREAMING_SNAKE_CASE_    			=			eigh(
				    covariance_between_classes(__a,				__a,				__a     ),				covariance_within_classes(__a,				__a,				__a     ),				)
				SCREAMING_SNAKE_CASE_    			=			eigenvectors[:, ::-1][:, :dimensions]
				SCREAMING_SNAKE_CASE_			,SCREAMING_SNAKE_CASE_			,SCREAMING_SNAKE_CASE_    			=			np.linalg.svd(__a     )
				SCREAMING_SNAKE_CASE_    			=			svd_matrix[:, 0:dimensions]
				SCREAMING_SNAKE_CASE_    			=			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			(			):
		# Create dummy dataset with 2 classes and 3 features
		SCREAMING_SNAKE_CASE_    			=			np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]     )
		SCREAMING_SNAKE_CASE_    			=			np.array([0, 0, 0, 1, 1]     )
		SCREAMING_SNAKE_CASE_    			=			2
		SCREAMING_SNAKE_CASE_    			=			2

		# Assert that the function raises an AssertionError if dimensions > classes
		with pytest.raises(__a     ) as error_info:
				SCREAMING_SNAKE_CASE_    			=			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			(			):
		SCREAMING_SNAKE_CASE_    			=			np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]     )
		SCREAMING_SNAKE_CASE_    			=			2
		SCREAMING_SNAKE_CASE_    			=			np.array([[6.9_2_8_2_0_3_2_3, 8.6_6_0_2_5_4_0_4, 1_0.3_9_2_3_0_4_8_5], [3.0, 3.0, 3.0]]     )

		with pytest.raises(__a     ) as error_info:
				SCREAMING_SNAKE_CASE_    			=			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()