



"""simple docstring"""







from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
lowercase__		:				Tuple          =	2_9_9_7_9_2_4_5_8

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

def 				UpperCamelCase_    (    lowerCAmelCase__      :				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 				UpperCamelCase_    (    lowerCAmelCase__      :				float						)						->   float:

  """simple docstring"""




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

def 				UpperCamelCase_    (    lowerCAmelCase__      :				float						)						->   np.ndarray:

  """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__      :				float    ,   lowerCAmelCase__      :				np.ndarray | None = None						)						->   np.ndarray:

  """simple docstring"""




  if event is None:
    lowerCAmelCase_   :				int								= 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__		:				List[str]          =	transform(2_9_9_7_9_2_4_5)
     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__		:				Dict          =	{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}')










"""simple docstring"""







import unittest

from transformers import is_tf_available
from transformers.testing_utils import require_tf


if is_tf_available():
     import tensorflow as tf
     from tensorflow.python.eager import context
     from tensorflow.python.framework import ops

     from transformers import GradientAccumulator, create_optimizer







@require_tf
class       UpperCamelCase__   (	unittest.TestCase  ):




      """simple docstring"""




      def      SCREAMING_SNAKE_CASE__ (      self				:      List[str]    ,			SCREAMING_SNAKE_CASE_				:      str    ,			SCREAMING_SNAKE_CASE_				:      List[Any]    ,			SCREAMING_SNAKE_CASE_				:      List[str]       ):
        self.assertEqual(len(SCREAMING_SNAKE_CASE_       )    ,			len(SCREAMING_SNAKE_CASE_       )       )
        for a, b in zip(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_       ):
          self.assertAlmostEqual(SCREAMING_SNAKE_CASE_    ,			SCREAMING_SNAKE_CASE_    ,			delta=SCREAMING_SNAKE_CASE_       )



      def      SCREAMING_SNAKE_CASE__ (      self				:      int       ):
        lowerCAmelCase_   :				int								= GradientAccumulator()
        accumulator([tf.constant([1.0, 2.0]       )]       )
        accumulator([tf.constant([-2.0, 1.0]       )]       )
        accumulator([tf.constant([-1.0, 2.0]       )]       )
        with self.assertRaises(SCREAMING_SNAKE_CASE_       ):
          accumulator([tf.constant([1.0, 1.0]       ), tf.constant([2.0, 2.0]       )]       )
        self.assertEqual(accumulator.step    ,			3       )
        self.assertEqual(len(accumulator.gradients       )    ,			1       )
        self.assertListAlmostEqual(accumulator.gradients[0].numpy().tolist()    ,			[-2.0, 5.0]    ,			tol=1E-2       )
        accumulator.reset()
        self.assertEqual(accumulator.step    ,			0       )
        self.assertListAlmostEqual(accumulator.gradients[0].numpy().tolist()    ,			[0.0, 0.0]    ,			tol=1E-2       )





      def      SCREAMING_SNAKE_CASE__ (      self				:      str       ):
        lowerCAmelCase_   :				Optional[int]								= None
        ops.enable_eager_execution_internal()
        lowerCAmelCase_   :				str								= tf.config.list_physical_devices('CPU'       )
        if len(SCREAMING_SNAKE_CASE_       ) == 1:
          tf.config.set_logical_device_configuration(
              physical_devices[0]    ,			[tf.config.LogicalDeviceConfiguration(), tf.config.LogicalDeviceConfiguration()]       )
        lowerCAmelCase_   :				Dict								= tf.config.list_logical_devices(device_type='CPU'       )
        lowerCAmelCase_   :				Optional[int]								= tf.distribute.MirroredStrategy(devices=devices[:2]       )

        with strategy.scope():
          lowerCAmelCase_   :				Union[str, Any]								= GradientAccumulator()
          lowerCAmelCase_   :				int								= tf.Variable([4.0, 3.0]       )
          lowerCAmelCase_						,lowerCAmelCase_   :				Optional[int]								= create_optimizer(5E-5    ,			1_0    ,			5       )
          lowerCAmelCase_   :				Union[str, Any]								= tf.Variable([0.0, 0.0]    ,			trainable=SCREAMING_SNAKE_CASE_       )

        def accumulate_on_replica(SCREAMING_SNAKE_CASE_				:      Optional[int]       ):
          accumulator([gradient]       )

        def apply_on_replica():
          optimizer.apply_gradients(list(zip(accumulator.gradients    ,			[variable]       )       )       )

        @tf.function
        def accumulate(SCREAMING_SNAKE_CASE_				:      Optional[int]    ,			SCREAMING_SNAKE_CASE_				:      Union[str, Any]       ):
          with strategy.scope():
            lowerCAmelCase_   :				Tuple								= strategy.experimental_local_results(SCREAMING_SNAKE_CASE_       )
            local_variables[0].assign(SCREAMING_SNAKE_CASE_       )
            local_variables[1].assign(SCREAMING_SNAKE_CASE_       )
            strategy.run(SCREAMING_SNAKE_CASE_    ,			args=(gradient_placeholder,)       )

        @tf.function
        def apply_grad():
          with strategy.scope():
            strategy.run(SCREAMING_SNAKE_CASE_       )

        def _check_local_values(SCREAMING_SNAKE_CASE_				:      Union[str, Any]    ,			SCREAMING_SNAKE_CASE_				:      Optional[int]       ):
          lowerCAmelCase_   :				List[Any]								= strategy.experimental_local_results(accumulator._gradients[0]       )
          self.assertListAlmostEqual(values[0].value()    ,			SCREAMING_SNAKE_CASE_    ,			tol=1E-2       )
          self.assertListAlmostEqual(values[1].value()    ,			SCREAMING_SNAKE_CASE_    ,			tol=1E-2       )

        accumulate([1.0, 2.0]    ,			[-1.0, 1.0]       )
        accumulate([3.0, -1.0]    ,			[-1.0, -1.0]       )
        accumulate([-2.0, 2.0]    ,			[3.0, -2.0]       )
        self.assertEqual(accumulator.step    ,			3       )
        _check_local_values([2.0, 3.0]    ,			[1.0, -2.0]       )
        apply_grad()
        self.assertListAlmostEqual(variable.value()    ,			[4.0, 3.0]    ,			tol=1E-2       )
        accumulator.reset()
        self.assertEqual(accumulator.step    ,			0       )
        _check_local_values([0.0, 0.0]    ,			[0.0, 0.0]       )





