




from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
lowercase__      :			Optional[int]           =					20

# Time between time steps in seconds
lowercase__      :			List[str]           =					INTERVAL / 1_000




class 			a__       :







     def __init__(	self  ,		A  ,		A  ,		A  ,		A  ,		A = 1.0  ,		A = 1.0  ,		A = "blue"  ,		)  ->    None:



          '''simple docstring'''



          a      =      position_x
          a      =      position_y
          a      =      velocity_x
          a      =      velocity_y
          a      =      mass
          a      =      size
          a      =      color







     @property
     def 			lowerCAmelCase_				(	self )  ->    tuple[float, float]:



          '''simple docstring'''



          return self.position_x, self.position_y







     @property
     def 			lowerCAmelCase_				(	self )  ->    tuple[float, float]:



          '''simple docstring'''



          return self.velocity_x, self.velocity_y







     def 			lowerCAmelCase_				(	self  ,		A  ,		A  ,		A )  ->    None:



          '''simple docstring'''



          self.velocity_x += force_x * delta_time
          self.velocity_y += force_y * delta_time







     def 			lowerCAmelCase_				(	self  ,		A )  ->    None:



          '''simple docstring'''



          self.position_x += self.velocity_x * delta_time
          self.position_y += self.velocity_y * delta_time







class 			a__       :







     def __init__(	self  ,		A  ,		A = 1.0  ,		A = 1.0  ,		A = 0.0  ,		)  ->    None:



          '''simple docstring'''



          a      =      bodies
          a      =      gravitation_constant
          a      =      time_factor
          a      =      softening_factor







     def __len__(	self )  ->    int:



          '''simple docstring'''



          return len(self.bodies )







     def 			lowerCAmelCase_				(	self  ,		A )  ->    None:



          '''simple docstring'''



          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(A  ,		A  ,		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							(   __UpperCamelCase		,					__UpperCamelCase		,					__UpperCamelCase)			->     None:
     body_system.update_system(__UpperCamelCase)

     # Update the positions of the patches
     for patch, body in zip(__UpperCamelCase		,					body_system.bodies):
          a      =      (body.position_x, body.position_y)

def 					SCREAMING_SNAKE_CASE							(   __UpperCamelCase		,					__UpperCamelCase		,					__UpperCamelCase = -1		,					__UpperCamelCase = 1		,					__UpperCamelCase = -1		,					__UpperCamelCase = 1		,					)			->     None:
     a      =      plt.figure()
     fig.canvas.set_window_title(__UpperCamelCase)
     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(__UpperCamelCase)

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

     a      =      animation.FuncAnimation(  # noqa: F841
         __UpperCamelCase		,					__UpperCamelCase		,					interval=__UpperCamelCase		,					blit=__UpperCamelCase)

     plt.show()

def 					SCREAMING_SNAKE_CASE							(   )			->     BodySystem:
     a      =      0.9_700_436
     a      =      -0.24_308_753
     a      =      0.466_203_685
     a      =      0.43_236_573

     a      =      [
         Body(__UpperCamelCase		,					__UpperCamelCase		,					__UpperCamelCase		,					__UpperCamelCase		,					size=0.2		,					color="red"),
         Body(-position_x		,					-position_y		,					__UpperCamelCase		,					__UpperCamelCase		,					size=0.2		,					color="green"),
         Body(0		,					0		,					-2 * velocity_x		,					-2 * velocity_y		,					size=0.2		,					color="blue"),
     ]
     return BodySystem(__UpperCamelCase		,					time_factor=3)

def 					SCREAMING_SNAKE_CASE							(   )			->     BodySystem:
     a      =      7.3476e22
     a      =      5.972e24
     a      =      10_22
     a      =      3_84_39_90_00
     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		,					__UpperCamelCase		,					__UpperCamelCase		,					10_00_00_00		,					"grey")
     a      =      Body(0		,					0		,					0		,					__UpperCamelCase		,					__UpperCamelCase		,					50_00_00_00		,					"blue")
     return BodySystem([earth, moon]		,					__UpperCamelCase		,					time_factor=1_00_00_00)

def 					SCREAMING_SNAKE_CASE							(   )			->     BodySystem:
     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)		,					__UpperCamelCase		,					__UpperCamelCase		,					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(__UpperCamelCase		,					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(),
       -430_000_000,
       430_000_000,
       -430_000_000,
       430_000_000,
   )
   plot("Random system with many bodies", example_a(), -1.5, 1.5, -1.5, 1.5)







import logging
from pathlib import Path

import numpy as np
import pytorch_lightning as pl
import torch
from pytorch_lightning.callbacks import EarlyStopping, ModelCheckpoint
from pytorch_lightning.utilities import rank_zero_only

from utils import save_json

def 					SCREAMING_SNAKE_CASE							(   __UpperCamelCase)			->     int:
     a      =      filter(lambda __UpperCamelCase: p.requires_grad		,					model.parameters())
     a      =      sum([np.prod(p.size()) for p in model_parameters])
     return params


lowercase__      :			Optional[int]           =					logging.getLogger(__name__)




class 			a__       (					pl.Callback      ):







     def 			lowerCAmelCase_				(	self  ,		A  ,		A )  ->    str:



          '''simple docstring'''



          a      =      {F'''lr_group_{i}''': param["lr"] for i, param in enumerate(pl_module.trainer.optimizers[0].param_groups )}
          pl_module.logger.log_metrics(A )







     @rank_zero_only
     def 			lowerCAmelCase_				(	self  ,		A  ,		A  ,		A  ,		A=True )  ->    None:



          '''simple docstring'''



          logger.info(F'''***** {type_path} results at step {trainer.global_step:05d} *****''' )
          a      =      trainer.callback_metrics
          trainer.logger.log_metrics({k: v for k, v in metrics.items() if k not in ["log", "progress_bar", "preds"]} )
          # Log results
          a      =      Path(pl_module.hparams.output_dir )
          if type_path == "test":
               a      =      od / "test_results.txt"
               a      =      od / "test_generations.txt"
          else:
               # this never gets hit. I prefer not to save intermediate generations, and results are in metrics.json
               # If people want this it will be easy enough to add back.
               a      =      od / F'''{type_path}_results/{trainer.global_step:05d}.txt'''
               a      =      od / F'''{type_path}_generations/{trainer.global_step:05d}.txt'''
               results_file.parent.mkdir(exist_ok=A )
               generations_file.parent.mkdir(exist_ok=A )
          with open(A  ,		"a+" ) as writer:
               for key in sorted(A ):
                    if key in ["log", "progress_bar", "preds"]:
                         continue
                    a      =      metrics[key]
                    if isinstance(A  ,		torch.Tensor ):
                         a      =      val.item()
                    a      =      F'''{key}: {val:.6f}\n'''
                    writer.write(A )

          if not save_generations:
               return

          if "preds" in metrics:
               a      =      "\n".join(metrics["preds"] )
               generations_file.open("w+" ).write(A )







     @rank_zero_only
     def 			lowerCAmelCase_				(	self  ,		A  ,		A )  ->    Any:



          '''simple docstring'''



          try:
               a      =      pl_module.model.model.num_parameters()
          except AttributeError:
               a      =      pl_module.model.num_parameters()

          a      =      count_trainable_parameters(A )
          # mp stands for million parameters
          trainer.logger.log_metrics({"n_params": npars, "mp": npars / 1e6, "grad_mp": n_trainable_pars / 1e6} )







     @rank_zero_only
     def 			lowerCAmelCase_				(	self  ,		A  ,		A )  ->    Optional[int]:



          '''simple docstring'''



          save_json(pl_module.metrics  ,		pl_module.metrics_save_path )
          return self._write_logs(A  ,		A  ,		"test" )







     @rank_zero_only
     def 			lowerCAmelCase_				(	self  ,		A  ,		A )  ->    Dict:



          '''simple docstring'''



          save_json(pl_module.metrics  ,		pl_module.metrics_save_path )
          # Uncommenting this will save val generations
          # return self._write_logs(trainer, pl_module, "valid")







def 					SCREAMING_SNAKE_CASE							(   __UpperCamelCase		,					__UpperCamelCase		,					__UpperCamelCase=1		,					__UpperCamelCase=False)			->     Optional[int]:
     if metric == "rouge2":
          a      =      "{val_avg_rouge2:.4f}-{step_count}"
     elif metric == "bleu":
          a      =      "{val_avg_bleu:.4f}-{step_count}"
     elif metric == "loss":
          a      =      "{val_avg_loss:.4f}-{step_count}"
     else:
          raise NotImplementedError(
              f'''seq2seq callbacks only support rouge2, bleu and loss, got {metric}, You can make your own by adding to'''
              " this function.")

     a      =      ModelCheckpoint(
         dirpath=__UpperCamelCase		,					filename=__UpperCamelCase		,					monitor=f'''val_{metric}'''		,					mode="min" if "loss" in metric else "max"		,					save_top_k=__UpperCamelCase		,					)
     return checkpoint_callback





def 					SCREAMING_SNAKE_CASE							(   __UpperCamelCase		,					__UpperCamelCase)			->     Union[str, Any]:
     return EarlyStopping(
         monitor=f'''val_{metric}'''		,					mode="min" if "loss" in metric else "max"		,					patience=__UpperCamelCase		,					verbose=__UpperCamelCase		,					)

