
'''simple docstring'''
import logging

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

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




def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__			)  ->							np.ndarray:


		'''simple docstring'''


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




def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__			)  ->							np.ndarray:


		'''simple docstring'''


		snake_case  :       Any     			=						np.nan
		for i in range(SCREAMING_SNAKE_CASE__			):
				snake_case  :       Optional[Any]     			=						features[:, labels == i]
				snake_case  :       Tuple     			=						data.mean(1			)
				# Centralize the data of class i
				snake_case  :       Tuple     			=						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)
						snake_case  :       Tuple     			=						np.dot(SCREAMING_SNAKE_CASE__ ,       centered_data.T			)

		return covariance_sum / features.shape[1]




def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__			)  ->							np.ndarray:


		'''simple docstring'''


		snake_case  :       Union[str, Any]     			=						features.mean(1			)
		snake_case  :       Tuple     			=						np.nan
		for i in range(SCREAMING_SNAKE_CASE__			):
				snake_case  :       List[str]     			=						features[:, labels == i]
				snake_case  :       str     			=						data.shape[1]
				snake_case  :       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)
						snake_case  :       Optional[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    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__			)  ->							np.ndarray:


		'''simple docstring'''


		if features.any():
				snake_case  :       Tuple     			=						features.mean(1			)
				# Center the dataset
				snake_case  :       Tuple     			=						features - np.reshape(SCREAMING_SNAKE_CASE__ ,       (data_mean.size, 1)			)
				snake_case  :       Optional[Any]     			=						np.dot(SCREAMING_SNAKE_CASE__ ,       centered_data.T			) / features.shape[1]
				snake_case			,snake_case  :       Union[str, Any]     			=						np.linalg.eigh(SCREAMING_SNAKE_CASE__			)
				# Take all the columns in the reverse order (-1), and then takes only the first
				snake_case  :       Dict     			=						eigenvectors[:, ::-1][:, 0:dimensions]
				# Project the database on the new space
				snake_case  :       Tuple     			=						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    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__			)  ->							np.ndarray:


		'''simple docstring'''


		assert classes > dimensions

		# Check if features have been already loaded
		if features.any:
				snake_case			,snake_case  :       Optional[Any]     			=						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__			) ,       )
				snake_case  :       str     			=						eigenvectors[:, ::-1][:, :dimensions]
				snake_case			,snake_case			,snake_case  :       int     			=						np.linalg.svd(SCREAMING_SNAKE_CASE__			)
				snake_case  :       List[str]     			=						svd_matrix[:, 0:dimensions]
				snake_case  :       List[str]     			=						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    _UpperCamelCase						(       )  ->							None:


		'''simple docstring'''


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

		# Assert that the function raises an AssertionError if dimensions > classes
		with pytest.raises(SCREAMING_SNAKE_CASE__			) as error_info:
				snake_case  :       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    _UpperCamelCase						(       )  ->							None:


		'''simple docstring'''


		snake_case  :       Any     			=						np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]			)
		snake_case  :       str     			=						2
		snake_case  :       int     			=						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:
				snake_case  :       List[str]     			=						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()




'''simple docstring'''
import os
from collections.abc import Iterator




def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__ = "."			)  ->							Iterator[str]:


		'''simple docstring'''


		for dir_path, dir_names, filenames in os.walk(SCREAMING_SNAKE_CASE__			):
				snake_case  :       Optional[Any]     			=						[d for d in dir_names if d != '''scripts''' and d[0] not in '''._''']
				for filename in filenames:
						if filename == "__init__.py":
								continue
						if os.path.splitext(SCREAMING_SNAKE_CASE__			)[1] in (".py", ".ipynb"):
								yield os.path.join(SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__			).lstrip('''./'''			)




def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__			)  ->							List[str]:


		'''simple docstring'''


		return F'{i * "  "}*' if i else "\n##"




def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__			)  ->							str:


		'''simple docstring'''


		snake_case  :       Union[str, Any]     			=						old_path.split(os.sep			)
		for i, new_part in enumerate(new_path.split(os.sep			)			):
				if (i + 1 > len(SCREAMING_SNAKE_CASE__			) or old_parts[i] != new_part) and new_part:
						print(F'{md_prefix(SCREAMING_SNAKE_CASE__			)} {new_part.replace("_" ,       " "			).title()}'			)
		return new_path




def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__ = "."			)  ->							None:


		'''simple docstring'''


		snake_case  :       List[Any]     			=						''''''
		for filepath in sorted(good_file_paths(SCREAMING_SNAKE_CASE__			)			):
				snake_case			,snake_case  :       Optional[Any]     			=						os.path.split(SCREAMING_SNAKE_CASE__			)
				if filepath != old_path:
						snake_case  :       Dict     			=						print_path(SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__			)
				snake_case  :       int     			=						(filepath.count(os.sep			) + 1) if filepath else 0
				snake_case  :       int     			=						F'{filepath}/{filename}'.replace(''' ''' ,       '''%20'''			)
				snake_case  :       int     			=						os.path.splitext(filename.replace('''_''' ,       ''' '''			).title()			)[0]
				print(F'{md_prefix(SCREAMING_SNAKE_CASE__			)} [{filename}]({url})'			)


if __name__ == "__main__":
						print_directory_md(".")


