


from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
_lowercase							:   str						=						2_9979_2458

# Symbols
_lowercase						,				_lowercase						,				_lowercase						,				_lowercase							:   str						=						symbols("ct x y z")





def 	_lowerCAmelCase					( UpperCamelCase__:  float    )			-> float:





	"""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 	_lowerCAmelCase					( UpperCamelCase__:  float    )			-> float:





	"""simple docstring"""







	return 1 / sqrt(1 - beta(UpperCamelCase__    ) ** 2    )





def 	_lowerCAmelCase					( UpperCamelCase__:  float    )			-> np.ndarray:





	"""simple docstring"""







	return np.array(
	    [
	        [gamma(UpperCamelCase__    ), -gamma(UpperCamelCase__    ) * beta(UpperCamelCase__    ), 0, 0],
	        [-gamma(UpperCamelCase__    ) * beta(UpperCamelCase__    ), gamma(UpperCamelCase__    ), 0, 0],
	        [0, 0, 1, 0],
	        [0, 0, 0, 1],
	    ]    )





def 	_lowerCAmelCase					( UpperCamelCase__:  float				,       UpperCamelCase__:  np.ndarray | None = None    )			-> np.ndarray:





	"""simple docstring"""







	if event is None:
		A             =					np.array([ct, x, y, z]    )  # Symbolic four vector
	else:
		event[0] *= c  # x0 is ct (speed of light * time)

	return transformation_matrix(UpperCamelCase__    ) @ event


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				# Example of symbolic vector:
				_lowercase							:   List[Any]						=						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							:   str						=						{ct: c, x: 1, y: 1, z: 1}
				_lowercase							:   Union[str, Any]						=						[four_vector[i].subs(sub_dict) for i in range(4)]

				print(f'''\n{numerical_vector}''')







from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_torch_available,
)


_lowercase							:   int						=						{
    "configuration_roberta_prelayernorm": [
        "ROBERTA_PRELAYERNORM_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "RobertaPreLayerNormConfig",
        "RobertaPreLayerNormOnnxConfig",
    ],
}

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				_lowercase							:   List[Any]						=						[
				    "ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST",
				    "RobertaPreLayerNormForCausalLM",
				    "RobertaPreLayerNormForMaskedLM",
				    "RobertaPreLayerNormForMultipleChoice",
				    "RobertaPreLayerNormForQuestionAnswering",
				    "RobertaPreLayerNormForSequenceClassification",
				    "RobertaPreLayerNormForTokenClassification",
				    "RobertaPreLayerNormModel",
				    "RobertaPreLayerNormPreTrainedModel",
				]

try:
				if not is_tf_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				_lowercase							:   Optional[int]						=						[
				    "TF_ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST",
				    "TFRobertaPreLayerNormForCausalLM",
				    "TFRobertaPreLayerNormForMaskedLM",
				    "TFRobertaPreLayerNormForMultipleChoice",
				    "TFRobertaPreLayerNormForQuestionAnswering",
				    "TFRobertaPreLayerNormForSequenceClassification",
				    "TFRobertaPreLayerNormForTokenClassification",
				    "TFRobertaPreLayerNormMainLayer",
				    "TFRobertaPreLayerNormModel",
				    "TFRobertaPreLayerNormPreTrainedModel",
				]

try:
				if not is_flax_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				_lowercase							:   str						=						[
				    "FlaxRobertaPreLayerNormForCausalLM",
				    "FlaxRobertaPreLayerNormForMaskedLM",
				    "FlaxRobertaPreLayerNormForMultipleChoice",
				    "FlaxRobertaPreLayerNormForQuestionAnswering",
				    "FlaxRobertaPreLayerNormForSequenceClassification",
				    "FlaxRobertaPreLayerNormForTokenClassification",
				    "FlaxRobertaPreLayerNormModel",
				    "FlaxRobertaPreLayerNormPreTrainedModel",
				]


if TYPE_CHECKING:
				from .configuration_roberta_prelayernorm import (
				    ROBERTA_PRELAYERNORM_PRETRAINED_CONFIG_ARCHIVE_MAP,
				    RobertaPreLayerNormConfig,
				    RobertaPreLayerNormOnnxConfig,
				)

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_roberta_prelayernorm import (
								    ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST,
								    RobertaPreLayerNormForCausalLM,
								    RobertaPreLayerNormForMaskedLM,
								    RobertaPreLayerNormForMultipleChoice,
								    RobertaPreLayerNormForQuestionAnswering,
								    RobertaPreLayerNormForSequenceClassification,
								    RobertaPreLayerNormForTokenClassification,
								    RobertaPreLayerNormModel,
								    RobertaPreLayerNormPreTrainedModel,
								)

				try:
								if not is_tf_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_tf_roberta_prelayernorm import (
								    TF_ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST,
								    TFRobertaPreLayerNormForCausalLM,
								    TFRobertaPreLayerNormForMaskedLM,
								    TFRobertaPreLayerNormForMultipleChoice,
								    TFRobertaPreLayerNormForQuestionAnswering,
								    TFRobertaPreLayerNormForSequenceClassification,
								    TFRobertaPreLayerNormForTokenClassification,
								    TFRobertaPreLayerNormMainLayer,
								    TFRobertaPreLayerNormModel,
								    TFRobertaPreLayerNormPreTrainedModel,
								)

				try:
								if not is_flax_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_flax_roberta_prelayernorm import (
								    FlaxRobertaPreLayerNormForCausalLM,
								    FlaxRobertaPreLayerNormForMaskedLM,
								    FlaxRobertaPreLayerNormForMultipleChoice,
								    FlaxRobertaPreLayerNormForQuestionAnswering,
								    FlaxRobertaPreLayerNormForSequenceClassification,
								    FlaxRobertaPreLayerNormForTokenClassification,
								    FlaxRobertaPreLayerNormModel,
								    FlaxRobertaPreLayerNormPreTrainedModel,
								)

else:
				import sys

				_lowercase							:   List[Any]						=						_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)



