


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 							lowercase__:






      '''simple docstring'''







      snake_case__       =					None
      snake_case__       =					None
      snake_case__       =					None




      @classmethod
      def    UpperCAmelCase							(		cls)					->						Any:







         """simple docstring"""







         return cls()




@dataclass
class 							lowercase__(						__A			):






      '''simple docstring'''







      snake_case__       =					42
      snake_case__       =					42
      snake_case__       =					None




class 							lowercase__(						__A			,							__A			):






      '''simple docstring'''







      @property
      def    UpperCAmelCase							(		self)					->						int:







         """simple docstring"""







         return True




      @register_to_config
      def __init__(		self   ,			__SCREAMING_SNAKE_CASE = 20_00   ,			__SCREAMING_SNAKE_CASE = 0.15   ,			__SCREAMING_SNAKE_CASE = 0.01   ,			__SCREAMING_SNAKE_CASE = 13_48.0   ,			__SCREAMING_SNAKE_CASE = 1E-5   ,			__SCREAMING_SNAKE_CASE = 1   ,			)					->						str:







         """simple docstring"""







         pass




      def    UpperCAmelCase							(		self)					->						Dict:







         """simple docstring"""







         UpperCamelCase__ :			List[Any] 						=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    UpperCAmelCase							(		self   ,			__SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE = ()   ,			__SCREAMING_SNAKE_CASE = None)					->						ScoreSdeVeSchedulerState:







         """simple docstring"""







         UpperCamelCase__ :			List[str] 						=sampling_eps if sampling_eps is not None else self.config.sampling_eps

         UpperCamelCase__ :			Any 						=jnp.linspace(1   ,			lowerCamelCase__   ,			lowerCamelCase__)
         return state.replace(timesteps=lowerCamelCase__)




      def    UpperCAmelCase							(		self   ,			__SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE = None   ,			__SCREAMING_SNAKE_CASE = None   ,			__SCREAMING_SNAKE_CASE = None   ,			)					->						ScoreSdeVeSchedulerState:







         """simple docstring"""







         UpperCamelCase__ :			str 						=sigma_min if sigma_min is not None else self.config.sigma_min
         UpperCamelCase__ :			str 						=sigma_max if sigma_max is not None else self.config.sigma_max
         UpperCamelCase__ :			str 						=sampling_eps if sampling_eps is not None else self.config.sampling_eps
         if state.timesteps is None:
            UpperCamelCase__ :			Optional[Any] 						=self.set_timesteps(lowerCamelCase__   ,			lowerCamelCase__   ,			lowerCamelCase__)

         UpperCamelCase__ :			List[str] 						=jnp.exp(jnp.linspace(jnp.log(lowerCamelCase__)   ,			jnp.log(lowerCamelCase__)   ,			lowerCamelCase__))
         UpperCamelCase__ :			str 						=jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps])

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




      def    UpperCAmelCase							(		self   ,			__SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE)					->						Tuple:







         """simple docstring"""







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




      def    UpperCAmelCase							(		self   ,			__SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE = True   ,			)					->						Union[FlaxSdeVeOutput, Tuple]:







         """simple docstring"""







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

         UpperCamelCase__ :			Any 						=timestep * jnp.ones(
             sample.shape[0]   ,			)
         UpperCamelCase__ :			Union[str, Any] 						=(timestep * (len(state.timesteps) - 1)).long()

         UpperCamelCase__ :			Dict 						=state.discrete_sigmas[timesteps]
         UpperCamelCase__ :			List[str] 						=self.get_adjacent_sigma(lowerCamelCase__   ,			lowerCamelCase__   ,			lowerCamelCase__)
         UpperCamelCase__ :			int 						=jnp.zeros_like(lowerCamelCase__)
         UpperCamelCase__ :			Dict 						=(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
         UpperCamelCase__ :			Union[str, Any] 						=diffusion.flatten()
         UpperCamelCase__ :			Tuple 						=broadcast_to_shape_from_left(lowerCamelCase__   ,			sample.shape)
         UpperCamelCase__ :			str 						=drift - diffusion**2 * model_output

         #  equation 6: sample noise for the diffusion term of
         UpperCamelCase__ :			List[str] 						=random.split(lowerCamelCase__   ,			num=1)
         UpperCamelCase__ :			Any 						=random.normal(key=lowerCamelCase__   ,			shape=sample.shape)
         UpperCamelCase__ :			Union[str, Any] 						=sample - drift  # subtract because `dt` is a small negative timestep
         # TODO is the variable diffusion the correct scaling term for the noise?
         UpperCamelCase__ :			Tuple 						=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    UpperCAmelCase							(		self   ,			__SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE = True   ,			)					->						Union[FlaxSdeVeOutput, Tuple]:







         """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
         UpperCamelCase__ :			List[Any] 						=random.split(lowerCamelCase__   ,			num=1)
         UpperCamelCase__ :			int 						=random.normal(key=lowerCamelCase__   ,			shape=sample.shape)

         # compute step size from the model_output, the noise, and the snr
         UpperCamelCase__ :			Any 						=jnp.linalg.norm(lowerCamelCase__)
         UpperCamelCase__ :			List[str] 						=jnp.linalg.norm(lowerCamelCase__)
         UpperCamelCase__ :			Tuple 						=(self.config.snr * noise_norm / grad_norm) ** 2 * 2
         UpperCamelCase__ :			Optional[Any] 						=step_size * jnp.ones(sample.shape[0])

         # compute corrected sample: model_output term and noise term
         UpperCamelCase__ :			List[Any] 						=step_size.flatten()
         UpperCamelCase__ :			Optional[int] 						=broadcast_to_shape_from_left(lowerCamelCase__   ,			sample.shape)
         UpperCamelCase__ :			Optional[int] 						=sample + step_size * model_output
         UpperCamelCase__ :			Dict 						=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)					->						Union[str, Any]:







         """simple docstring"""







         return self.config.num_train_timesteps







'''simple docstring'''
def 							snake_case_    (  a__						:      int     ):



    """simple docstring"""




    __lowercase     							=		1
    __lowercase     							=		0
    __lowercase     							=		1
    __lowercase     							=		1
    __lowercase     							=		3
    __lowercase     							=		3
    __lowercase     							=		limit
    __lowercase     							=		0

    __lowercase     							=		""""""
    while counter != decimal + 1:
        if 4 * q + r - t < n * t:
            result += str(a__     )
            if counter == 0:
                result += "."

            if decimal == counter:
                break

            counter += 1
            __lowercase     							=		10 * (r - n * t)
            __lowercase     							=		((10 * (3 * q + r)) // t) - 10 * n
            q *= 10
            __lowercase     							=		nr
        else:
            __lowercase     							=		(2 * q + r) * l
            __lowercase     							=		(q * (7 * k) + 2 + (r * l)) // (t * l)
            q *= k
            t *= l
            l += 2
            k += 1
            __lowercase     							=		nn
            __lowercase     							=		nr
    return result
def 							snake_case_    (  ):



    """simple docstring"""




    print(f'{calculate_pi(50     ) = }'     )
    import doctest

    doctest.testmod()


if __name__ == "__main__":
  main()




