



"""simple docstring"""





# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

from dataclasses import dataclass
from typing import Optional, Tuple, Union

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import FlaxSchedulerMixin, FlaxSchedulerOutput, broadcast_to_shape_from_left


@flax.struct.dataclass
class       __lowerCamelCase	:
   # setable values
   __UpperCamelCase									=   None
   __UpperCamelCase									=   None
   __UpperCamelCase									=   None







   @classmethod
   def 							A__						(cls				):




      '''simple docstring'''




      return cls()





@dataclass
class       __lowerCamelCase	(   __lowercase    ):
   __UpperCamelCase									=   42
   __UpperCamelCase									=   42
   __UpperCamelCase									=   None





class       __lowerCamelCase	(   __lowercase   ,							__lowercase    ):







   @property
   def 							A__						(self				):




      '''simple docstring'''




      return True







   @register_to_config
   def __init__(self       ,	lowerCamelCase = 2_000       ,	lowerCamelCase = 0.15       ,	lowerCamelCase = 0.01       ,	lowerCamelCase = 1348.0       ,	lowerCamelCase = 1e-5       ,	lowerCamelCase = 1       ,	):




      '''simple docstring'''




      pass







   def 							A__						(self				):




      '''simple docstring'''




      _lowerCAmelCase					     =		ScoreSdeVeSchedulerState.create()
      return self.set_sigmas(
          lowerCamelCase       ,	self.config.num_train_timesteps       ,	self.config.sigma_min       ,	self.config.sigma_max       ,	self.config.sampling_eps       ,	)







   def 							A__						(self       ,	lowerCamelCase       ,	lowerCamelCase       ,	lowerCamelCase = ()       ,	lowerCamelCase = None				):




      '''simple docstring'''




      _lowerCAmelCase					     =		sampling_eps if sampling_eps is not None else self.config.sampling_eps

      _lowerCAmelCase					     =		jnp.linspace(1       ,	lowerCamelCase       ,	lowerCamelCase				)
      return state.replace(timesteps=lowerCamelCase				)







   def 							A__						(self       ,	lowerCamelCase       ,	lowerCamelCase       ,	lowerCamelCase = None       ,	lowerCamelCase = None       ,	lowerCamelCase = None       ,	):




      '''simple docstring'''




      _lowerCAmelCase					     =		sigma_min if sigma_min is not None else self.config.sigma_min
      _lowerCAmelCase					     =		sigma_max if sigma_max is not None else self.config.sigma_max
      _lowerCAmelCase					     =		sampling_eps if sampling_eps is not None else self.config.sampling_eps
      if state.timesteps is None:
         _lowerCAmelCase					     =		self.set_timesteps(lowerCamelCase       ,	lowerCamelCase       ,	lowerCamelCase				)

      _lowerCAmelCase					     =		jnp.exp(jnp.linspace(jnp.log(lowerCamelCase				)       ,	jnp.log(lowerCamelCase				)       ,	lowerCamelCase				)				)
      _lowerCAmelCase					     =		jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]				)

      return state.replace(discrete_sigmas=lowerCamelCase       ,	sigmas=lowerCamelCase				)







   def 							A__						(self       ,	lowerCamelCase       ,	lowerCamelCase       ,	lowerCamelCase				):




      '''simple docstring'''




      return jnp.where(timesteps == 0       ,	jnp.zeros_like(lowerCamelCase				)       ,	state.discrete_sigmas[timesteps - 1]				)







   def 							A__						(self       ,	lowerCamelCase       ,	lowerCamelCase       ,	lowerCamelCase       ,	lowerCamelCase       ,	lowerCamelCase       ,	lowerCamelCase = True       ,	):




      '''simple docstring'''




      if state.timesteps is None:
         raise ValueError(
             """`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""				)

      _lowerCAmelCase					     =		timestep * jnp.ones(
          sample.shape[0]       ,	)
      _lowerCAmelCase					     =		(timestep * (len(state.timesteps				) - 1)).long()

      _lowerCAmelCase					     =		state.discrete_sigmas[timesteps]
      _lowerCAmelCase					     =		self.get_adjacent_sigma(lowerCamelCase       ,	lowerCamelCase       ,	lowerCamelCase				)
      _lowerCAmelCase					     =		jnp.zeros_like(lowerCamelCase				)
      _lowerCAmelCase					     =		(sigma**2 - adjacent_sigma**2) ** 0.5

      # equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
      # also equation 47 shows the analog from SDE models to ancestral sampling methods
      _lowerCAmelCase					     =		diffusion.flatten()
      _lowerCAmelCase					     =		broadcast_to_shape_from_left(lowerCamelCase       ,	sample.shape				)
      _lowerCAmelCase					     =		drift - diffusion**2 * model_output

      #  equation 6: sample noise for the diffusion term of
      _lowerCAmelCase					     =		random.split(lowerCamelCase       ,	num=1				)
      _lowerCAmelCase					     =		random.normal(key=lowerCamelCase       ,	shape=sample.shape				)
      _lowerCAmelCase					     =		sample - drift  # subtract because `dt` is a small negative timestep
      # TODO is the variable diffusion the correct scaling term for the noise?
      _lowerCAmelCase					     =		prev_sample_mean + diffusion * noise  # add impact of diffusion field g

      if not return_dict:
         return (prev_sample, prev_sample_mean, state)

      return FlaxSdeVeOutput(prev_sample=lowerCamelCase       ,	prev_sample_mean=lowerCamelCase       ,	state=lowerCamelCase				)







   def 							A__						(self       ,	lowerCamelCase       ,	lowerCamelCase       ,	lowerCamelCase       ,	lowerCamelCase       ,	lowerCamelCase = True       ,	):




      '''simple docstring'''




      if state.timesteps is None:
         raise ValueError(
             """`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""				)

      # For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
      # sample noise for correction
      _lowerCAmelCase					     =		random.split(lowerCamelCase       ,	num=1				)
      _lowerCAmelCase					     =		random.normal(key=lowerCamelCase       ,	shape=sample.shape				)

      # compute step size from the model_output, the noise, and the snr
      _lowerCAmelCase					     =		jnp.linalg.norm(lowerCamelCase				)
      _lowerCAmelCase					     =		jnp.linalg.norm(lowerCamelCase				)
      _lowerCAmelCase					     =		(self.config.snr * noise_norm / grad_norm) ** 2 * 2
      _lowerCAmelCase					     =		step_size * jnp.ones(sample.shape[0]				)

      # compute corrected sample: model_output term and noise term
      _lowerCAmelCase					     =		step_size.flatten()
      _lowerCAmelCase					     =		broadcast_to_shape_from_left(lowerCamelCase       ,	sample.shape				)
      _lowerCAmelCase					     =		sample + step_size * model_output
      _lowerCAmelCase					     =		prev_sample_mean + ((step_size * 2) ** 0.5) * noise

      if not return_dict:
         return (prev_sample, state)

      return FlaxSdeVeOutput(prev_sample=lowerCamelCase       ,	state=lowerCamelCase				)







   def __len__(self				):




      '''simple docstring'''




      return self.config.num_train_timesteps




"""simple docstring"""





from itertools import combinations_with_replacement






def 	__UpperCAmelCase					(       snake_case_  :  int = 100   )							->	int:






   """simple docstring"""


   _lowerCAmelCase					     =		[*list(range(1   ,	21   )   ), 25]
   _lowerCAmelCase					     =		[2 * x for x in range(1   ,	21   )] + [50]
   _lowerCAmelCase					     =		[3 * x for x in range(1   ,	21   )]
   _lowerCAmelCase					     =		singles + doubles + triples + [0]

   _lowerCAmelCase					     =		0
   _lowerCAmelCase					     =		42
   _lowerCAmelCase					     =		42
   _lowerCAmelCase					     =		42
   _lowerCAmelCase					     =		42

   for double in doubles:
      for throwa, throwa in combinations_with_replacement(snake_case_   ,	2   ):
         _lowerCAmelCase					     =		double + throwa + throwa
         if checkout_total < limit:
            num_checkouts += 1

   return num_checkouts


if __name__ == "__main__":
  print(F'{solution() = }')