






import logging

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

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




def      lowercase__      (     __snake_case    :							np.ndarray  ):


					'''simple docstring'''


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




def      lowercase__      (     __snake_case    :							np.ndarray     ,       __snake_case    :							np.ndarray     ,       __snake_case    :							int  ):


					'''simple docstring'''


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

					return covariance_sum / features.shape[1]




def      lowercase__      (     __snake_case    :							np.ndarray     ,       __snake_case    :							np.ndarray     ,       __snake_case    :							int  ):


					'''simple docstring'''


					UpperCAmelCase_    :      List[str]            =						features.mean(1  )
					UpperCAmelCase_    :      Tuple            =						np.nan
					for i in range(__snake_case  ):
										UpperCAmelCase_    :      Tuple            =						features[:, labels == i]
										UpperCAmelCase_    :      Union[str, Any]            =						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(__snake_case  ) - column_reshape(__snake_case  )     ,       (column_reshape(__snake_case  ) - column_reshape(__snake_case  )).T     ,       )
										else:
															# If covariance_sum is np.nan (i.e. first loop)
															UpperCAmelCase_    :      Any            =						device_data * np.dot(
															    column_reshape(__snake_case  ) - column_reshape(__snake_case  )     ,       (column_reshape(__snake_case  ) - column_reshape(__snake_case  )).T     ,       )

					return covariance_sum / features.shape[1]




def      lowercase__      (     __snake_case    :							np.ndarray     ,       __snake_case    :							int  ):


					'''simple docstring'''


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

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




def      lowercase__      (     __snake_case    :							np.ndarray     ,       __snake_case    :							np.ndarray     ,       __snake_case    :							int     ,       __snake_case    :							int  ):


					'''simple docstring'''


					assert classes > dimensions

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

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




def      lowercase__      (     ):


					'''simple docstring'''


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

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




def      lowercase__      (     ):


					'''simple docstring'''


					UpperCAmelCase_    :      str            =						np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]  )
					UpperCAmelCase_    :      Optional[Any]            =						2
					UpperCAmelCase_    :      Optional[Any]            =						np.array([[6.92820323, 8.66025404, 10.39230485], [3.0, 3.0, 3.0]]  )

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


if __name__ == "__main__":
		import doctest

		doctest.testmod()







from __future__ import annotations

from PIL import Image

# Define glider example
__lowercase							 =					[
    [0, 1, 0, 0, 0, 0, 0, 0],
    [0, 0, 1, 0, 0, 0, 0, 0],
    [1, 1, 1, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
]

# Define blinker example
__lowercase							 =					[[0, 1, 0], [0, 1, 0], [0, 1, 0]]



def lowerCamelCase  (   SCREAMING_SNAKE_CASE	):
    '''simple docstring'''







    __UpperCamelCase     :int			  =		[]
    for i in range(len(SCREAMING_SNAKE_CASE	)	):
        __UpperCamelCase     :Dict			  =		[]
        for j in range(len(cells[i]	)	):
            # Get the number of live neighbours
            __UpperCamelCase     :List[str]			  =		0
            if i > 0 and j > 0:
                neighbour_count += cells[i - 1][j - 1]
            if i > 0:
                neighbour_count += cells[i - 1][j]
            if i > 0 and j < len(cells[i]	) - 1:
                neighbour_count += cells[i - 1][j + 1]
            if j > 0:
                neighbour_count += cells[i][j - 1]
            if j < len(cells[i]	) - 1:
                neighbour_count += cells[i][j + 1]
            if i < len(SCREAMING_SNAKE_CASE	) - 1 and j > 0:
                neighbour_count += cells[i + 1][j - 1]
            if i < len(SCREAMING_SNAKE_CASE	) - 1:
                neighbour_count += cells[i + 1][j]
            if i < len(SCREAMING_SNAKE_CASE	) - 1 and j < len(cells[i]	) - 1:
                neighbour_count += cells[i + 1][j + 1]

            # Rules of the game of life (excerpt from Wikipedia):
            # 1. Any live cell with two or three live neighbours survives.
            # 2. Any dead cell with three live neighbours becomes a live cell.
            # 3. All other live cells die in the next generation.
            #    Similarly, all other dead cells stay dead.
            __UpperCamelCase     :List[str]			  =		cells[i][j] == 1
            if (
                (alive and 2 <= neighbour_count <= 3)
                or not alive
                and neighbour_count == 3
            ):
                next_generation_row.append(1	)
            else:
                next_generation_row.append(0	)

        next_generation.append(SCREAMING_SNAKE_CASE	)
    return next_generation



def lowerCamelCase  (   SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE	):
    '''simple docstring'''







    __UpperCamelCase     :Optional[Any]			  =		[]
    for _ in range(SCREAMING_SNAKE_CASE	):
        # Create output image
        __UpperCamelCase     :Dict			  =		Image.new('''RGB'''  ,			(len(cells[0]	), len(SCREAMING_SNAKE_CASE	))	)
        __UpperCamelCase     :Any			  =		img.load()

        # Save cells to image
        for x in range(len(SCREAMING_SNAKE_CASE	)	):
            for y in range(len(cells[0]	)	):
                __UpperCamelCase     :Optional[Any]			  =		255 - cells[y][x] * 255
                __UpperCamelCase     :int			  =		(colour, colour, colour)

        # Save image
        images.append(SCREAMING_SNAKE_CASE	)
        __UpperCamelCase     :Optional[int]			  =		new_generation(SCREAMING_SNAKE_CASE	)
    return images


if __name__ == "__main__":
    __lowercase							 =					generate_images(GLIDER, 16)
    images[0].save('''out.gif''', save_all=True, append_images=images[1:])





