






"""simple docstring"""






from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
UpperCAmelCase_     :				Tuple         =				299792458

# Symbols
UpperCAmelCase_    ,						UpperCAmelCase_    ,						UpperCAmelCase_    ,						UpperCAmelCase_     :				Optional[Any]         =				symbols("""ct x y z""")



def       _A    (__a							)				-> 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       _A    (__a							)				-> float:
    """simple docstring"""






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



def       _A    (__a							)				-> np.ndarray:
    """simple docstring"""






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



def       _A    (__a					,       __a = None							)				-> np.ndarray:
    """simple docstring"""






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

    return transformation_matrix(__a							) @ event


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  # Example of symbolic vector:
  UpperCAmelCase_     :				List[str]         =				transform(29979245)
  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_     :				Union[str, Any]         =				{ct: c, x: 1, y: 1, z: 1}
  UpperCAmelCase_     :				Dict         =				[four_vector[i].subs(sub_dict) for i in range(4)]

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










"""simple docstring"""






import unittest

import numpy as np

from transformers.testing_utils import require_flax, require_tf, require_torch
from transformers.utils import (
    expand_dims,
    flatten_dict,
    is_flax_available,
    is_tf_available,
    is_torch_available,
    reshape,
    squeeze,
    transpose,
)


if is_flax_available():
  import jax.numpy as jnp

if is_tf_available():
  import tensorflow as tf

if is_torch_available():
  import torch




class 							lowerCAmelCase__       (    unittest.TestCase				):






      '''simple docstring'''

      def _SCREAMING_SNAKE_CASE				(		self  :						str):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_   :						str							=	{
              '''task_specific_params''': {
                  '''summarization''': {'''length_penalty''': 1.0, '''max_length''': 128, '''min_length''': 12, '''num_beams''': 4},
                  '''summarization_cnn''': {'''length_penalty''': 2.0, '''max_length''': 142, '''min_length''': 56, '''num_beams''': 4},
                  '''summarization_xsum''': {'''length_penalty''': 1.0, '''max_length''': 62, '''min_length''': 11, '''num_beams''': 6},
              }
          }
          SCREAMING_SNAKE_CASE_   :						List[str]							=	{
              '''task_specific_params.summarization.length_penalty''': 1.0,
              '''task_specific_params.summarization.max_length''': 128,
              '''task_specific_params.summarization.min_length''': 12,
              '''task_specific_params.summarization.num_beams''': 4,
              '''task_specific_params.summarization_cnn.length_penalty''': 2.0,
              '''task_specific_params.summarization_cnn.max_length''': 142,
              '''task_specific_params.summarization_cnn.min_length''': 56,
              '''task_specific_params.summarization_cnn.num_beams''': 4,
              '''task_specific_params.summarization_xsum.length_penalty''': 1.0,
              '''task_specific_params.summarization_xsum.max_length''': 62,
              '''task_specific_params.summarization_xsum.min_length''': 11,
              '''task_specific_params.summarization_xsum.num_beams''': 6,
          }

          self.assertEqual(flatten_dict(lowercase_)		,			lowercase_)
      def _SCREAMING_SNAKE_CASE				(		self  :						List[Any]):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_   :						Optional[int]							=	np.random.randn(3		,			4)
          self.assertTrue(np.allclose(transpose(lowercase_)		,			x.transpose()))

          SCREAMING_SNAKE_CASE_   :						Optional[Any]							=	np.random.randn(3		,			4		,			5)
          self.assertTrue(np.allclose(transpose(lowercase_		,			axes=(1, 2, 0))		,			x.transpose((1, 2, 0))))
      @require_torch
      def _SCREAMING_SNAKE_CASE				(		self  :						Dict):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_   :						str							=	np.random.randn(3		,			4)
          SCREAMING_SNAKE_CASE_   :						str							=	torch.tensor(lowercase_)
          self.assertTrue(np.allclose(transpose(lowercase_)		,			transpose(lowercase_).numpy()))

          SCREAMING_SNAKE_CASE_   :						List[Any]							=	np.random.randn(3		,			4		,			5)
          SCREAMING_SNAKE_CASE_   :						Dict							=	torch.tensor(lowercase_)
          self.assertTrue(np.allclose(transpose(lowercase_		,			axes=(1, 2, 0))		,			transpose(lowercase_		,			axes=(1, 2, 0)).numpy()))
      @require_tf
      def _SCREAMING_SNAKE_CASE				(		self  :						Tuple):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_   :						Union[str, Any]							=	np.random.randn(3		,			4)
          SCREAMING_SNAKE_CASE_   :						str							=	tf.constant(lowercase_)
          self.assertTrue(np.allclose(transpose(lowercase_)		,			transpose(lowercase_).numpy()))

          SCREAMING_SNAKE_CASE_   :						Optional[int]							=	np.random.randn(3		,			4		,			5)
          SCREAMING_SNAKE_CASE_   :						int							=	tf.constant(lowercase_)
          self.assertTrue(np.allclose(transpose(lowercase_		,			axes=(1, 2, 0))		,			transpose(lowercase_		,			axes=(1, 2, 0)).numpy()))
      @require_flax
      def _SCREAMING_SNAKE_CASE				(		self  :						Optional[Any]):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_   :						Tuple							=	np.random.randn(3		,			4)
          SCREAMING_SNAKE_CASE_   :						Any							=	jnp.array(lowercase_)
          self.assertTrue(np.allclose(transpose(lowercase_)		,			np.asarray(transpose(lowercase_))))

          SCREAMING_SNAKE_CASE_   :						Dict							=	np.random.randn(3		,			4		,			5)
          SCREAMING_SNAKE_CASE_   :						Any							=	jnp.array(lowercase_)
          self.assertTrue(np.allclose(transpose(lowercase_		,			axes=(1, 2, 0))		,			np.asarray(transpose(lowercase_		,			axes=(1, 2, 0)))))
      def _SCREAMING_SNAKE_CASE				(		self  :						Optional[int]):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_   :						Dict							=	np.random.randn(3		,			4)
          self.assertTrue(np.allclose(reshape(lowercase_		,			(4, 3))		,			np.reshape(lowercase_		,			(4, 3))))

          SCREAMING_SNAKE_CASE_   :						Dict							=	np.random.randn(3		,			4		,			5)
          self.assertTrue(np.allclose(reshape(lowercase_		,			(12, 5))		,			np.reshape(lowercase_		,			(12, 5))))
      @require_torch
      def _SCREAMING_SNAKE_CASE				(		self  :						Union[str, Any]):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_   :						Union[str, Any]							=	np.random.randn(3		,			4)
          SCREAMING_SNAKE_CASE_   :						List[str]							=	torch.tensor(lowercase_)
          self.assertTrue(np.allclose(reshape(lowercase_		,			(4, 3))		,			reshape(lowercase_		,			(4, 3)).numpy()))

          SCREAMING_SNAKE_CASE_   :						int							=	np.random.randn(3		,			4		,			5)
          SCREAMING_SNAKE_CASE_   :						int							=	torch.tensor(lowercase_)
          self.assertTrue(np.allclose(reshape(lowercase_		,			(12, 5))		,			reshape(lowercase_		,			(12, 5)).numpy()))
      @require_tf
      def _SCREAMING_SNAKE_CASE				(		self  :						Dict):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_   :						Optional[Any]							=	np.random.randn(3		,			4)
          SCREAMING_SNAKE_CASE_   :						int							=	tf.constant(lowercase_)
          self.assertTrue(np.allclose(reshape(lowercase_		,			(4, 3))		,			reshape(lowercase_		,			(4, 3)).numpy()))

          SCREAMING_SNAKE_CASE_   :						List[Any]							=	np.random.randn(3		,			4		,			5)
          SCREAMING_SNAKE_CASE_   :						Union[str, Any]							=	tf.constant(lowercase_)
          self.assertTrue(np.allclose(reshape(lowercase_		,			(12, 5))		,			reshape(lowercase_		,			(12, 5)).numpy()))
      @require_flax
      def _SCREAMING_SNAKE_CASE				(		self  :						Any):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_   :						Any							=	np.random.randn(3		,			4)
          SCREAMING_SNAKE_CASE_   :						List[Any]							=	jnp.array(lowercase_)
          self.assertTrue(np.allclose(reshape(lowercase_		,			(4, 3))		,			np.asarray(reshape(lowercase_		,			(4, 3)))))

          SCREAMING_SNAKE_CASE_   :						Optional[Any]							=	np.random.randn(3		,			4		,			5)
          SCREAMING_SNAKE_CASE_   :						List[Any]							=	jnp.array(lowercase_)
          self.assertTrue(np.allclose(reshape(lowercase_		,			(12, 5))		,			np.asarray(reshape(lowercase_		,			(12, 5)))))
      def _SCREAMING_SNAKE_CASE				(		self  :						List[Any]):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_   :						List[Any]							=	np.random.randn(1		,			3		,			4)
          self.assertTrue(np.allclose(squeeze(lowercase_)		,			np.squeeze(lowercase_)))

          SCREAMING_SNAKE_CASE_   :						str							=	np.random.randn(1		,			4		,			1		,			5)
          self.assertTrue(np.allclose(squeeze(lowercase_		,			axis=2)		,			np.squeeze(lowercase_		,			axis=2)))
      @require_torch
      def _SCREAMING_SNAKE_CASE				(		self  :						Any):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_   :						Union[str, Any]							=	np.random.randn(1		,			3		,			4)
          SCREAMING_SNAKE_CASE_   :						int							=	torch.tensor(lowercase_)
          self.assertTrue(np.allclose(squeeze(lowercase_)		,			squeeze(lowercase_).numpy()))

          SCREAMING_SNAKE_CASE_   :						Optional[Any]							=	np.random.randn(1		,			4		,			1		,			5)
          SCREAMING_SNAKE_CASE_   :						str							=	torch.tensor(lowercase_)
          self.assertTrue(np.allclose(squeeze(lowercase_		,			axis=2)		,			squeeze(lowercase_		,			axis=2).numpy()))
      @require_tf
      def _SCREAMING_SNAKE_CASE				(		self  :						List[str]):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_   :						int							=	np.random.randn(1		,			3		,			4)
          SCREAMING_SNAKE_CASE_   :						Dict							=	tf.constant(lowercase_)
          self.assertTrue(np.allclose(squeeze(lowercase_)		,			squeeze(lowercase_).numpy()))

          SCREAMING_SNAKE_CASE_   :						List[Any]							=	np.random.randn(1		,			4		,			1		,			5)
          SCREAMING_SNAKE_CASE_   :						Any							=	tf.constant(lowercase_)
          self.assertTrue(np.allclose(squeeze(lowercase_		,			axis=2)		,			squeeze(lowercase_		,			axis=2).numpy()))
      @require_flax
      def _SCREAMING_SNAKE_CASE				(		self  :						int):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_   :						Union[str, Any]							=	np.random.randn(1		,			3		,			4)
          SCREAMING_SNAKE_CASE_   :						Optional[Any]							=	jnp.array(lowercase_)
          self.assertTrue(np.allclose(squeeze(lowercase_)		,			np.asarray(squeeze(lowercase_))))

          SCREAMING_SNAKE_CASE_   :						Union[str, Any]							=	np.random.randn(1		,			4		,			1		,			5)
          SCREAMING_SNAKE_CASE_   :						str							=	jnp.array(lowercase_)
          self.assertTrue(np.allclose(squeeze(lowercase_		,			axis=2)		,			np.asarray(squeeze(lowercase_		,			axis=2))))
      def _SCREAMING_SNAKE_CASE				(		self  :						Tuple):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_   :						int							=	np.random.randn(3		,			4)
          self.assertTrue(np.allclose(expand_dims(lowercase_		,			axis=1)		,			np.expand_dims(lowercase_		,			axis=1)))
      @require_torch
      def _SCREAMING_SNAKE_CASE				(		self  :						Dict):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_   :						int							=	np.random.randn(3		,			4)
          SCREAMING_SNAKE_CASE_   :						int							=	torch.tensor(lowercase_)
          self.assertTrue(np.allclose(expand_dims(lowercase_		,			axis=1)		,			expand_dims(lowercase_		,			axis=1).numpy()))
      @require_tf
      def _SCREAMING_SNAKE_CASE				(		self  :						str):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_   :						List[str]							=	np.random.randn(3		,			4)
          SCREAMING_SNAKE_CASE_   :						Any							=	tf.constant(lowercase_)
          self.assertTrue(np.allclose(expand_dims(lowercase_		,			axis=1)		,			expand_dims(lowercase_		,			axis=1).numpy()))



      @require_flax
      def _SCREAMING_SNAKE_CASE				(		self  :						Optional[Any]):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_   :						Tuple							=	np.random.randn(3		,			4)
          SCREAMING_SNAKE_CASE_   :						int							=	jnp.array(lowercase_)
          self.assertTrue(np.allclose(expand_dims(lowercase_		,			axis=1)		,			np.asarray(expand_dims(lowercase_		,			axis=1))))


