"""simple docstring"""






import logging

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

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



def   a_						(					lowerCamelCase       ):
				return input_array.reshape((input_array.size, 1)       )



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

				return covariance_sum / features.shape[1]



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

				return covariance_sum / features.shape[1]



def   a_						(					lowerCamelCase					,			lowerCamelCase       ):

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

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



def   a_						(					lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase       ):
				assert classes > dimensions

				# Check if features have been already loaded
				if features.any:
								UpperCAmelCase__      ,	UpperCAmelCase__             =							eigh(
								    covariance_between_classes(lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase       )					,			covariance_within_classes(lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase       )					,			)
								UpperCAmelCase__             =							eigenvectors[:, ::-1][:, :dimensions]
								UpperCAmelCase__      ,	UpperCAmelCase__      ,	UpperCAmelCase__             =							np.linalg.svd(lowerCamelCase       )
								UpperCAmelCase__             =							svd_matrix[:, 0:dimensions]
								UpperCAmelCase__             =							np.dot(filtered_svd_matrix.T					,			lowerCamelCase       )
								logging.info('Linear Discriminant Analysis computed'       )

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



def   a_						(					):
				# Create dummy dataset with 2 classes and 3 features
				UpperCAmelCase__             =							np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]       )
				UpperCAmelCase__             =							np.array([0, 0, 0, 1, 1]       )
				UpperCAmelCase__             =							2
				UpperCAmelCase__             =							2

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



def   a_						(					):
				UpperCAmelCase__             =							np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]       )
				UpperCAmelCase__             =							2
				UpperCAmelCase__             =							np.array([[6.92820323, 8.66025404, 10.39230485], [3.0, 3.0, 3.0]]       )

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


if __name__ == "__main__":
						import doctest

						doctest.testmod()









"""simple docstring"""


from __future__ import annotations

from collections.abc import Sequence
from typing import Literal


def 					UpperCAmelCase__       (snake_case__							:					str		,   snake_case__							:					str    ):
  """simple docstring"""

  _snake_case							:		Optional[Any]								=  list(snake_case__    )
  _snake_case							:		List[Any]								=  list(snake_case__    )
  _snake_case							:		List[Any]								=  0
  for i in range(len(snake_case__    )    ):
    if lista[i] != lista[i]:
      count += 1
      _snake_case							:		Any								=  """_"""
  if count > 1:
    return False
  else:
    return "".join(snake_case__    )


def 					UpperCAmelCase__       (snake_case__							:					list[str]    ):
  """simple docstring"""

  _snake_case							:		int								=  []
  while True:
    _snake_case							:		Union[str, Any]								=  ["""$"""] * len(snake_case__    )
    _snake_case							:		int								=  []
    for i in range(len(snake_case__    )    ):
      for j in range(i + 1		,   len(snake_case__    )    ):
        _snake_case							:		List[Any]								=  compare_string(binary[i]		,   binary[j]    )
        if k is False:
          _snake_case							:		Dict								=  """*"""
          _snake_case							:		List[Any]								=  """*"""
          temp.append("""X"""    )
    for i in range(len(snake_case__    )    ):
      if checka[i] == "$":
        pi.append(binary[i]    )
    if len(snake_case__    ) == 0:
      return pi
    _snake_case							:		Optional[int]								=  list(set(snake_case__    )    )


def 					UpperCAmelCase__       (snake_case__							:					int		,   snake_case__							:					Sequence[float]    ):
  """simple docstring"""

  _snake_case							:		Optional[int]								=  []
  for minterm in minterms:
    _snake_case							:		Any								=  """"""
    for _ in range(snake_case__    ):
      _snake_case							:		Optional[Any]								=  str(minterm % 2    ) + string
      minterm //= 2
    temp.append(snake_case__    )
  return temp


def 					UpperCAmelCase__       (snake_case__							:					str		,   snake_case__							:					str		,   snake_case__							:					int    ):
  """simple docstring"""

  _snake_case							:		Dict								=  list(snake_case__    )
  _snake_case							:		List[str]								=  list(snake_case__    )
  _snake_case							:		Tuple								=  0
  for i in range(len(snake_case__    )    ):
    if lista[i] != lista[i]:
      count_n += 1
  return count_n == count


def 					UpperCAmelCase__       (snake_case__							:					list[list[int]]		,   snake_case__							:					list[str]    ):
  """simple docstring"""

  _snake_case							:		Any								=  []
  _snake_case							:		Union[str, Any]								=  [0] * len(snake_case__    )
  for i in range(len(chart[0]    )    ):
    _snake_case							:		Tuple								=  0
    _snake_case							:		str								=  -1
    for j in range(len(snake_case__    )    ):
      if chart[j][i] == 1:
        count += 1
        _snake_case							:		Union[str, Any]								=  j
    if count == 1:
      _snake_case							:		Union[str, Any]								=  1
  for i in range(len(snake_case__    )    ):
    if select[i] == 1:
      for j in range(len(chart[0]    )    ):
        if chart[i][j] == 1:
          for k in range(len(snake_case__    )    ):
            _snake_case							:		List[Any]								=  0
      temp.append(prime_implicants[i]    )
  while True:
    _snake_case							:		Optional[int]								=  0
    _snake_case							:		str								=  -1
    _snake_case							:		Any								=  0
    for i in range(len(snake_case__    )    ):
      _snake_case							:		Union[str, Any]								=  chart[i].count(1    )
      if count_n > max_n:
        _snake_case							:		Dict								=  count_n
        _snake_case							:		Dict								=  i

    if max_n == 0:
      return temp

    temp.append(prime_implicants[rem]    )

    for i in range(len(chart[0]    )    ):
      if chart[rem][i] == 1:
        for j in range(len(snake_case__    )    ):
          _snake_case							:		Optional[Any]								=  0


def 					UpperCAmelCase__       (snake_case__							:					list[str]		,   snake_case__							:					list[str]    ):
  """simple docstring"""

  _snake_case							:		int								=  [[0 for x in range(len(snake_case__    )    )] for x in range(len(snake_case__    )    )]
  for i in range(len(snake_case__    )    ):
    _snake_case							:		Any								=  prime_implicants[i].count("""_"""    )
    for j in range(len(snake_case__    )    ):
      if is_for_table(prime_implicants[i]		,   binary[j]		,   snake_case__    ):
        _snake_case							:		Tuple								=  1

  return chart


def 					UpperCAmelCase__       ():
  """simple docstring"""

  _snake_case							:		int								=  int(input("""Enter the no. of variables\n"""    )    )
  _snake_case							:		List[str]								=  [
      float(snake_case__    )
      for x in input(
          """Enter the decimal representation of Minterms 'Spaces Separated'\n"""    ).split()
  ]
  _snake_case							:		List[str]								=  decimal_to_binary(snake_case__		,   snake_case__    )

  _snake_case							:		str								=  check(snake_case__    )
  print("""Prime Implicants are:"""    )
  print(snake_case__    )
  _snake_case							:		int								=  prime_implicant_chart(snake_case__		,   snake_case__    )

  _snake_case							:		str								=  selection(snake_case__		,   snake_case__    )
  print("""Essential Prime Implicants are:"""    )
  print(snake_case__    )


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     main()


