
from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
lowercase__	:Optional[int]										=					2_9979_2458

# Symbols
lowercase__						,  lowercase__						,  lowercase__						,  lowercase__	:Dict										=					symbols("ct x y z")



def  UpperCamelCase					(							lowerCAmelCase__	):
					'''simple docstring'''
					if velocity > c:
										raise ValueError('''Speed must not exceed light speed 299,792,458 [m/s]!'''	)
					elif velocity < 1:
										# Usually the speed should be much higher than 1 (c order of magnitude)
										raise ValueError('''Speed must be greater than or equal to 1!'''	)

					return velocity / c



def  UpperCamelCase					(							lowerCAmelCase__	):
					'''simple docstring'''
					return 1 / sqrt(1 - beta(lowerCAmelCase__	) ** 2	)



def  UpperCamelCase					(							lowerCAmelCase__	):
					'''simple docstring'''
					return np.array(
					    [
					        [gamma(lowerCAmelCase__	), -gamma(lowerCAmelCase__	) * beta(lowerCAmelCase__	), 0, 0],
					        [-gamma(lowerCAmelCase__	) * beta(lowerCAmelCase__	), gamma(lowerCAmelCase__	), 0, 0],
					        [0, 0, 1, 0],
					        [0, 0, 0, 1],
					    ]	)



def  UpperCamelCase					(							lowerCAmelCase__				,    lowerCAmelCase__ = None	):
					'''simple docstring'''
					# Ensure event is not empty
					if event is None:
										lowercase					=		np.array([ct, x, y, z]	)  # Symbolic four vector
					else:
										event[0] *= c  # x0 is ct (speed of light * time)

					return transformation_matrix(lowerCAmelCase__	) @ event


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							# Example of symbolic vector:
							lowercase__	:Dict										=					transform(2997_9245)
							print("Example of four vector: ")
							print(F'ct\' = {four_vector[0]}')
							print(F'x\' = {four_vector[1]}')
							print(F'y\' = {four_vector[2]}')
							print(F'z\' = {four_vector[3]}')

							# Substitute symbols with numerical values
							lowercase__	:Any										=					{ct: c, x: 1, y: 1, z: 1}
							lowercase__	:List[str]										=					[four_vector[i].subs(sub_dict) for i in range(4)]

							print(F'\n{numerical_vector}')






import argparse
from collections import defaultdict

import yaml


lowercase__	:Optional[int]										=					"docs/source/en/_toctree.yml"



def  UpperCamelCase					(							lowerCAmelCase__	):
					'''simple docstring'''
					lowercase					=		defaultdict(lowerCAmelCase__	)
					for doc in model_doc:
										counts[doc["local"]] += 1
					lowercase					=		[key for key, value in counts.items() if value > 1]

					lowercase					=		[]
					for duplicate_key in duplicates:
										lowercase					=		list({doc['''title'''] for doc in model_doc if doc['''local'''] == duplicate_key}	)
										if len(lowerCAmelCase__	) > 1:
															raise ValueError(
															    f'{duplicate_key} is present several times in the documentation table of content at '
															    '''`docs/source/en/_toctree.yml` with different *Title* values. Choose one of those and remove the '''
															    '''others.'''	)
										# Only add this once
										new_doc.append({'''local''': duplicate_key, '''title''': titles[0]}	)

					# Add none duplicate-keys
					new_doc.extend([doc for doc in model_doc if counts[doc['''local''']] == 1]	)

					# Sort
					return sorted(lowerCAmelCase__				,    key=lambda lowerCAmelCase__	: s["title"].lower()	)



def  UpperCamelCase					(							lowerCAmelCase__=False	):
					'''simple docstring'''
					with open(lowerCAmelCase__				,    encoding='''utf-8'''	) as f:
										lowercase					=		yaml.safe_load(f.read()	)

					# Get to the API doc
					lowercase					=		0
					while content[api_idx]["title"] != "API":
										api_idx += 1
					lowercase					=		content[api_idx]['''sections''']

					# Then to the model doc
					lowercase					=		0
					while api_doc[model_idx]["title"] != "Models":
										model_idx += 1

					lowercase					=		api_doc[model_idx]['''sections''']

					lowercase					=		[(idx, section) for idx, section in enumerate(lowerCAmelCase__	) if '''sections''' in section]
					lowercase					=		False
					for idx, modality_doc in modalities_docs:
										lowercase					=		modality_doc['''sections''']
										lowercase					=		clean_model_doc_toc(lowerCAmelCase__	)

										if old_modality_doc != new_modality_doc:
															lowercase					=		True
															if overwrite:
																				lowercase					=		new_modality_doc

					if diff:
										if overwrite:
															lowercase					=		model_doc
															lowercase					=		api_doc
															with open(lowerCAmelCase__				,    '''w'''				,    encoding='''utf-8'''	) as f:
																				f.write(yaml.dump(lowerCAmelCase__				,    allow_unicode=lowerCAmelCase__	)	)
										else:
															raise ValueError(
															    '''The model doc part of the table of content is not properly sorted, run `make style` to fix this.'''	)


if __name__ == "__main__":
							lowercase__	:Any										=					argparse.ArgumentParser()
							parser.add_argument("--fix_and_overwrite", action="store_true", help="Whether to fix inconsistencies.")
							lowercase__	:int										=					parser.parse_args()

							check_model_doc(args.fix_and_overwrite)




