






"""simple docstring"""



from math import sqrt

import numpy as np
from sympy import symbols

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

# Symbols
__A		:       Union[str, Any]  				=		symbols('''ct x y z''')



def 						lowercase    (				__snake_case				: float	):
		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 						lowercase    (				__snake_case				: float	):
		return 1 / sqrt(1 - beta(__lowerCamelCase	) ** 2	)



def 						lowercase    (				__snake_case				: float	):
		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 						lowercase    (				__snake_case				: float		,					__snake_case				: np.ndarray | None = None	):
		# Ensure event is not empty
		if event is None:
				lowercase_ : Dict							       =   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:
						__A		:       List[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
						__A		:       int  				=		{ct: c, x: 1, y: 1, z: 1}
						__A		:       Dict  				=		[four_vector[i].subs(sub_dict) for i in range(4)]

						print(F"""\n{numerical_vector}""")











from typing import Mapping

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxSeqaSeqConfigWithPast
from ...utils import logging


a		:       Tuple			     = logging.get_logger(__name__)

a		:       Dict			     = {
    "t5-small": "https://huggingface.co/t5-small/resolve/main/config.json",
    "t5-base": "https://huggingface.co/t5-base/resolve/main/config.json",
    "t5-large": "https://huggingface.co/t5-large/resolve/main/config.json",
    "t5-3b": "https://huggingface.co/t5-3b/resolve/main/config.json",
    "t5-11b": "https://huggingface.co/t5-11b/resolve/main/config.json",
}
class     a    ( lowercase__   ):



      """simple docstring"""


      a  : int							       =	't5'
      a  : Dict							       =	['past_key_values']
      a  : Tuple							       =	{'hidden_size': 'd_model', 'num_attention_heads': 'num_heads', 'num_hidden_layers': 'num_layers'}
      def __init__(      self					:			str		,      __lowercase					:			Optional[int]=32128		,      __lowercase					:			Optional[int]=512		,      __lowercase					:			int=64		,      __lowercase					:			Any=2048		,      __lowercase					:			Tuple=6		,      __lowercase					:			Tuple=None		,      __lowercase					:			int=8		,      __lowercase					:			List[Any]=32		,      __lowercase					:			Dict=128		,      __lowercase					:			Optional[int]=0.1		,      __lowercase					:			int=1e-6		,      __lowercase					:			List[str]=1.0		,      __lowercase					:			List[str]="relu"		,      __lowercase					:			Dict=True		,      __lowercase					:			Optional[Any]=True		,      __lowercase					:			Tuple=0		,      __lowercase					:			List[str]=1		,      **__lowercase					:			Any		,      )							->      str:
        __UpperCAmelCase							:	Tuple           =  vocab_size
        __UpperCAmelCase							:	Optional[int]           =  d_model
        __UpperCAmelCase							:	Union[str, Any]           =  d_kv
        __UpperCAmelCase							:	Union[str, Any]           =  d_ff
        __UpperCAmelCase							:	int           =  num_layers
        __UpperCAmelCase							:	Any           =  (
            num_decoder_layers if num_decoder_layers is not None else self.num_layers
        )  # default = symmetry
        __UpperCAmelCase							:	Dict           =  num_heads
        __UpperCAmelCase							:	List[Any]           =  relative_attention_num_buckets
        __UpperCAmelCase							:	List[str]           =  relative_attention_max_distance
        __UpperCAmelCase							:	Union[str, Any]           =  dropout_rate
        __UpperCAmelCase							:	List[str]           =  layer_norm_epsilon
        __UpperCAmelCase							:	str           =  initializer_factor
        __UpperCAmelCase							:	Dict           =  feed_forward_proj
        __UpperCAmelCase							:	Optional[int]           =  use_cache

        __UpperCAmelCase							:	List[Any]           =  self.feed_forward_proj.split("""-"""					)
        __UpperCAmelCase							:	Tuple           =  act_info[-1]
        __UpperCAmelCase							:	int           =  act_info[0] == """gated"""

        if len(__lowercase					) > 1 and act_info[0] != "gated" or len(__lowercase					) > 2:
          raise ValueError(
              f"""`feed_forward_proj`: {feed_forward_proj} is not a valid activation function of the dense layer."""
              """Please make sure `feed_forward_proj` is of the format `gated-{ACT_FN}` or `{ACT_FN}`, e.g. """
              """'gated-gelu' or 'relu'"""					)

        # for backwards compatibility
        if feed_forward_proj == "gated-gelu":
          __UpperCAmelCase							:	Dict           =  """gelu_new"""

        super().__init__(
            pad_token_id=__lowercase		,      eos_token_id=__lowercase		,      is_encoder_decoder=__lowercase		,      **__lowercase		,      )


class     a    ( lowercase__   ):



      """simple docstring"""


      @property
      def 	UpperCAmelCase      (      self					:			str					)							->      Mapping[str, Mapping[int, str]]:
        __UpperCAmelCase							:	Union[str, Any]           =  {
            """input_ids""": {0: """batch""", 1: """encoder_sequence"""},
            """attention_mask""": {0: """batch""", 1: """encoder_sequence"""},
        }
        if self.use_past:
          __UpperCAmelCase							:	List[Any]           =  """past_encoder_sequence + sequence"""
          __UpperCAmelCase							:	Optional[int]           =  {0: """batch"""}
          __UpperCAmelCase							:	Union[str, Any]           =  {0: """batch""", 1: """past_decoder_sequence + sequence"""}
        else:
          __UpperCAmelCase							:	str           =  {0: """batch""", 1: """decoder_sequence"""}
          __UpperCAmelCase							:	str           =  {0: """batch""", 1: """decoder_sequence"""}

        if self.use_past:
          self.fill_with_past_key_values_(__lowercase		,      direction="""inputs"""					)

        return common_inputs




      @property
      def 	UpperCAmelCase      (      self					:			int					)							->      int:
        return 13


