



'''simple docstring'''




from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
UpperCamelCase_       :  str					=  299_792_458

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






def 		_lowerCAmelCase				(_lowercase			):

       """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				(_lowercase			):

       """simple docstring"""

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






def 		_lowerCAmelCase				(_lowercase			):

       """simple docstring"""

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






def 		_lowerCAmelCase				(_lowercase   ,					_lowercase = None			):

       """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(_snake_case			) @ event


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    # Example of symbolic vector:
    UpperCamelCase_       :  str					=  transform(29_979_245)
    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
    UpperCamelCase_       :  Dict					=  {ct: c, x: 1, y: 1, z: 1}
    UpperCamelCase_       :  str					=  [four_vector[i].subs(sub_dict) for i in range(4)]

    print(F"\n{numerical_vector}")








# Copyright 2023 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_SCREAMING_SNAKE_CASE   =  {
    "configuration_xmod": [
        "XMOD_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "XmodConfig",
        "XmodOnnxConfig",
    ],
}

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    _SCREAMING_SNAKE_CASE   =  [
        "XMOD_PRETRAINED_MODEL_ARCHIVE_LIST",
        "XmodForCausalLM",
        "XmodForMaskedLM",
        "XmodForMultipleChoice",
        "XmodForQuestionAnswering",
        "XmodForSequenceClassification",
        "XmodForTokenClassification",
        "XmodModel",
        "XmodPreTrainedModel",
    ]

if TYPE_CHECKING:
    from .configuration_xmod import XMOD_PRETRAINED_CONFIG_ARCHIVE_MAP, XmodConfig, XmodOnnxConfig

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_xmod import (
            XMOD_PRETRAINED_MODEL_ARCHIVE_LIST,
            XmodForCausalLM,
            XmodForMaskedLM,
            XmodForMultipleChoice,
            XmodForQuestionAnswering,
            XmodForSequenceClassification,
            XmodForTokenClassification,
            XmodModel,
            XmodPreTrainedModel,
        )

else:
    import sys

    _SCREAMING_SNAKE_CASE   =  _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)


