

"""simple docstring"""




from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
__A  :					Dict												=	20

# Time between time steps in seconds
__A  :					Tuple												=	INTERVAL / 10_00





class     __UpperCamelCase				:


		def __init__(self				:	Tuple  ,  __SCREAMING_SNAKE_CASE				:	float  ,  __SCREAMING_SNAKE_CASE				:	float  ,  __SCREAMING_SNAKE_CASE				:	float  ,  __SCREAMING_SNAKE_CASE				:	float  ,  __SCREAMING_SNAKE_CASE				:	float = 1.0  ,  __SCREAMING_SNAKE_CASE				:	float = 1.0  ,  __SCREAMING_SNAKE_CASE				:	str = "blue"  ,  ):
							A    =      position_x
							A    =      position_y
							A    =      velocity_x
							A    =      velocity_y
							A    =      mass
							A    =      size
							A    =      color


		@property
		def       SCREAMING_SNAKE_CASE__     (self				:	Tuple):
							return self.position_x, self.position_y


		@property
		def       SCREAMING_SNAKE_CASE__     (self				:	Union[str, Any]):
							return self.velocity_x, self.velocity_y


		def       SCREAMING_SNAKE_CASE__     (self				:	str  ,  __SCREAMING_SNAKE_CASE				:	float  ,  __SCREAMING_SNAKE_CASE				:	float  ,  __SCREAMING_SNAKE_CASE				:	float):
							self.velocity_x += force_x * delta_time
							self.velocity_y += force_y * delta_time


		def       SCREAMING_SNAKE_CASE__     (self				:	Any  ,  __SCREAMING_SNAKE_CASE				:	float):
							self.position_x += self.velocity_x * delta_time
							self.position_y += self.velocity_y * delta_time





class     __UpperCamelCase				:


		def __init__(self				:	Tuple  ,  __SCREAMING_SNAKE_CASE				:	list[Body]  ,  __SCREAMING_SNAKE_CASE				:	float = 1.0  ,  __SCREAMING_SNAKE_CASE				:	float = 1.0  ,  __SCREAMING_SNAKE_CASE				:	float = 0.0  ,  ):
							A    =      bodies
							A    =      gravitation_constant
							A    =      time_factor
							A    =      softening_factor


		def __len__(self				:	Optional[Any]):
							return len(self.bodies)


		def       SCREAMING_SNAKE_CASE__     (self				:	str  ,  __SCREAMING_SNAKE_CASE				:	float):
							for bodya in self.bodies:
												A    =      0.0
												A    =      0.0
												for bodya in self.bodies:
																	if bodya != bodya:
																						A    =      bodya.position_x - bodya.position_x
																						A    =      bodya.position_y - bodya.position_y

																						# Calculation of the distance using Pythagoras's theorem
																						# Extra factor due to the softening technique
																						A    =      (dif_x**2 + dif_y**2 + self.softening_factor) ** (
																						    1 / 2
																						)

																						# Newton's law of universal gravitation.
																						force_x += (
																						    self.gravitation_constant * bodya.mass * dif_x / distance**3
																						)
																						force_y += (
																						    self.gravitation_constant * bodya.mass * dif_y / distance**3
																						)

            # Update the body's velocity once all the force components have been added
												bodya.update_velocity(__SCREAMING_SNAKE_CASE  ,  __SCREAMING_SNAKE_CASE  ,  delta_time * self.time_factor)

							# Update the positions only after all the velocities have been updated
							for body in self.bodies:
												body.update_position(delta_time * self.time_factor)

def      __SCREAMING_SNAKE_CASE		(		lowercase__    ,							lowercase__    ,							lowercase__   ):
					"""simple docstring"""
					body_system.update_system(lowercase__   )

					# Update the positions of the patches
					for patch, body in zip(lowercase__    ,							body_system.bodies   ):
										A    =      (body.position_x, body.position_y)
def      __SCREAMING_SNAKE_CASE		(		lowercase__    ,							lowercase__    ,							lowercase__ = -1    ,							lowercase__ = 1    ,							lowercase__ = -1    ,							lowercase__ = 1    ,							):
					"""simple docstring"""
					A    =      plt.figure()
					fig.canvas.set_window_title(lowercase__   )
					A    =      plt.axes(
					    xlim=(x_start, x_end)    ,							ylim=(y_start, y_end)   )  # Set section to be plotted
					plt.gca().set_aspect("equal"   )  # Fix aspect ratio

					# Each body is drawn as a patch by the plt-function
					A    =      [
					    plt.Circle((body.position_x, body.position_y)    ,							body.size    ,							fc=body.color   )
					    for body in body_system.bodies
					]

					for patch in patches:
										ax.add_patch(lowercase__   )

					# Function called at each step of the animation
					def update(lowercase__   ) -> list[plt.Circle]:
										update_step(lowercase__    ,							lowercase__    ,							lowercase__   )
										return patches

					A    =      animation.FuncAnimation(  # noqa: F841
					    lowercase__    ,							lowercase__    ,							interval=lowercase__    ,							blit=lowercase__   )

					plt.show()
def      __SCREAMING_SNAKE_CASE		(		):
					"""simple docstring"""
					A    =      0.9_70_04_36
					A    =      -0.24_30_87_53
					A    =      0.4_66_20_36_85
					A    =      0.43_23_65_73

					A    =      [
					    Body(lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__    ,							size=0.2    ,							color="red"   ),
					    Body(-position_x    ,							-position_y    ,							lowercase__    ,							lowercase__    ,							size=0.2    ,							color="green"   ),
					    Body(0    ,							0    ,							-2 * velocity_x    ,							-2 * velocity_y    ,							size=0.2    ,							color="blue"   ),
					]
					return BodySystem(lowercase__    ,							time_factor=3   )
def      __SCREAMING_SNAKE_CASE		(		):
					"""simple docstring"""
					A    =      7.3476e22
					A    =      5.972e24
					A    =      1_022
					A    =      384_399_000
					A    =      6.674e-11

					# Calculation of the respective velocities so that total impulse is zero,
					# i.e. the two bodies together don't move
					A    =      earth_mass * velocity_dif / (earth_mass + moon_mass)
					A    =      moon_velocity - velocity_dif

					A    =      Body(-earth_moon_distance    ,							0    ,							0    ,							lowercase__    ,							lowercase__    ,							10_000_000    ,							"grey"   )
					A    =      Body(0    ,							0    ,							0    ,							lowercase__    ,							lowercase__    ,							50_000_000    ,							"blue"   )
					return BodySystem([earth, moon]    ,							lowercase__    ,							time_factor=1_000_000   )
def      __SCREAMING_SNAKE_CASE		(		):
					"""simple docstring"""
					A    =      []
					for _ in range(10   ):
										A    =      random.uniform(-0.5    ,							0.5   )
										A    =      random.uniform(-0.5    ,							0.5   )

										# Bodies are created pairwise with opposite velocities so that the
										# total impulse remains zero
										bodies.append(
										    Body(
										        random.uniform(-0.5    ,							0.5   )    ,							random.uniform(-0.5    ,							0.5   )    ,							lowercase__    ,							lowercase__    ,							size=0.05    ,							)   )
										bodies.append(
										    Body(
										        random.uniform(-0.5    ,							0.5   )    ,							random.uniform(-0.5    ,							0.5   )    ,							-velocity_x    ,							-velocity_y    ,							size=0.05    ,							)   )
					return BodySystem(lowercase__    ,							0.01    ,							10    ,							0.1   )


if __name__ == "__main__":
	plot('Figure-8 solution to the 3-body-problem', example_a(), -2, 2, -2, 2)
	plot(
	    'Moon\'s orbit around the earth',
	    example_a(),
	    -4_30_00_00_00,
	    4_30_00_00_00,
	    -4_30_00_00_00,
	    4_30_00_00_00,
	)
	plot('Random system with many bodies', example_a(), -1.5, 1.5, -1.5, 1.5)








"""simple docstring"""




from typing import Mapping

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


__A  :					List[str]												=	logging.get_logger(__name__)





class     __UpperCamelCase				(     _A		):
		SCREAMING_SNAKE_CASE              =					"mt5"
		SCREAMING_SNAKE_CASE              =					["past_key_values"]


		def __init__(self				:	Optional[Any]  ,  __SCREAMING_SNAKE_CASE				:	Union[str, Any]=2_5_0_1_1_2  ,  __SCREAMING_SNAKE_CASE				:	int=5_1_2  ,  __SCREAMING_SNAKE_CASE				:	Tuple=6_4  ,  __SCREAMING_SNAKE_CASE				:	Union[str, Any]=1_0_2_4  ,  __SCREAMING_SNAKE_CASE				:	Optional[int]=8  ,  __SCREAMING_SNAKE_CASE				:	Any=None  ,  __SCREAMING_SNAKE_CASE				:	Tuple=6  ,  __SCREAMING_SNAKE_CASE				:	int=3_2  ,  __SCREAMING_SNAKE_CASE				:	List[Any]=1_2_8  ,  __SCREAMING_SNAKE_CASE				:	Tuple=0.1  ,  __SCREAMING_SNAKE_CASE				:	Tuple=1E-6  ,  __SCREAMING_SNAKE_CASE				:	List[Any]=1.0  ,  __SCREAMING_SNAKE_CASE				:	Optional[int]="gated-gelu"  ,  __SCREAMING_SNAKE_CASE				:	List[str]=True  ,  __SCREAMING_SNAKE_CASE				:	str=True  ,  __SCREAMING_SNAKE_CASE				:	int="T5Tokenizer"  ,  __SCREAMING_SNAKE_CASE				:	Optional[int]=False  ,  __SCREAMING_SNAKE_CASE				:	Optional[Any]=0  ,  __SCREAMING_SNAKE_CASE				:	Tuple=1  ,  __SCREAMING_SNAKE_CASE				:	List[str]=0  ,  **__SCREAMING_SNAKE_CASE				:	str  ,  ):
							super().__init__(
							    is_encoder_decoder=__SCREAMING_SNAKE_CASE  ,  tokenizer_class=__SCREAMING_SNAKE_CASE  ,  tie_word_embeddings=__SCREAMING_SNAKE_CASE  ,  pad_token_id=__SCREAMING_SNAKE_CASE  ,  eos_token_id=__SCREAMING_SNAKE_CASE  ,  decoder_start_token_id=__SCREAMING_SNAKE_CASE  ,  **__SCREAMING_SNAKE_CASE  ,  )
							A    =      vocab_size
							A    =      d_model
							A    =      d_kv
							A    =      d_ff
							A    =      num_layers
							A    =      (
							    num_decoder_layers if num_decoder_layers is not None else self.num_layers
							)  # default = symmetry
							A    =      num_heads
							A    =      relative_attention_num_buckets
							A    =      relative_attention_max_distance
							A    =      dropout_rate
							A    =      layer_norm_epsilon
							A    =      initializer_factor
							A    =      feed_forward_proj
							A    =      use_cache

							A    =      self.feed_forward_proj.split("-")
							A    =      act_info[-1]
							A    =      act_info[0] == "gated"

							if len(__SCREAMING_SNAKE_CASE) > 1 and act_info[0] != "gated" or len(__SCREAMING_SNAKE_CASE) > 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":
												A    =      "gelu_new"


		@property
		def       SCREAMING_SNAKE_CASE__     (self				:	List[Any]):
							return self.d_model


		@property
		def       SCREAMING_SNAKE_CASE__     (self				:	Optional[int]):
							return self.num_heads


		@property
		def       SCREAMING_SNAKE_CASE__     (self				:	Optional[int]):
							return self.num_layers





class     __UpperCamelCase				(     _A		):


		@property
		# Copied from transformers.models.t5.configuration_t5.T5OnnxConfig.inputs
		def       SCREAMING_SNAKE_CASE__     (self				:	int):
							A    =      {
							    "input_ids": {0: "batch", 1: "encoder_sequence"},
							    "attention_mask": {0: "batch", 1: "encoder_sequence"},
							}
							if self.use_past:
												A    =      "past_encoder_sequence + sequence"
												A    =      {0: "batch"}
												A    =      {0: "batch", 1: "past_decoder_sequence + sequence"}
							else:
												A    =      {0: "batch", 1: "decoder_sequence"}
												A    =      {0: "batch", 1: "decoder_sequence"}

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

							return common_inputs


		@property
		# Copied from transformers.models.t5.configuration_t5.T5OnnxConfig.default_onnx_opset
		def       SCREAMING_SNAKE_CASE__     (self				:	Union[str, Any]):
							return 1_3


		@property
		def       SCREAMING_SNAKE_CASE__     (self				:	int):
							return 5E-4





