






"""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 						_a  :





   '''simple docstring'''






   UpperCamelCase__     	=							None
   UpperCamelCase__     	=							None
   UpperCamelCase__     	=							None





   @classmethod
   def __lowercase							(       cls)			->   Union[str, Any]:




          '''simple docstring'''




          return cls()







@dataclass
class 						_a  (		lowercase_       ):





   '''simple docstring'''






   UpperCamelCase__     	=							42
   UpperCamelCase__     	=							42
   UpperCamelCase__     	=							None







class 						_a  (		lowercase_							,	lowercase_       ):





   '''simple docstring'''






   @property
   def __lowercase							(       self)			->   List[str]:




          '''simple docstring'''




          return True





   @register_to_config
   def __init__(       self					, UpperCAmelCase_ = 2_000					, UpperCAmelCase_ = 0.15					, UpperCAmelCase_ = 0.01					, UpperCAmelCase_ = 13_48.0					, UpperCAmelCase_ = 1E-5					, UpperCAmelCase_ = 1					, )			->   Dict:




          '''simple docstring'''




          pass





   def __lowercase							(       self)			->   str:




          '''simple docstring'''




          lowercase__:							List[Any]         =     ScoreSdeVeSchedulerState.create()
          return self.set_sigmas(
              UpperCAmelCase_					, self.config.num_train_timesteps					, self.config.sigma_min					, self.config.sigma_max					, self.config.sampling_eps					, )





   def __lowercase							(       self					, UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_ = ()					, UpperCAmelCase_ = None)			->   ScoreSdeVeSchedulerState:




          '''simple docstring'''




          lowercase__:							Union[str, Any]         =     sampling_eps if sampling_eps is not None else self.config.sampling_eps

          lowercase__:							Union[str, Any]         =     jnp.linspace(1					, UpperCAmelCase_					, UpperCAmelCase_)
          return state.replace(timesteps=UpperCAmelCase_)





   def __lowercase							(       self					, UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_ = None					, UpperCAmelCase_ = None					, UpperCAmelCase_ = None					, )			->   ScoreSdeVeSchedulerState:




          '''simple docstring'''




          lowercase__:							Optional[int]         =     sigma_min if sigma_min is not None else self.config.sigma_min
          lowercase__:							Any         =     sigma_max if sigma_max is not None else self.config.sigma_max
          lowercase__:							Dict         =     sampling_eps if sampling_eps is not None else self.config.sampling_eps
          if state.timesteps is None:
                 lowercase__:							int         =     self.set_timesteps(UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_)

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

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





   def __lowercase							(       self					, UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_)			->   Tuple:




          '''simple docstring'''




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





   def __lowercase							(       self					, UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_ = 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")

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

          lowercase__:							List[str]         =     state.discrete_sigmas[timesteps]
          lowercase__:							Optional[int]         =     self.get_adjacent_sigma(UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_)
          lowercase__:							List[Any]         =     jnp.zeros_like(UpperCAmelCase_)
          lowercase__:							str         =     (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
          lowercase__:							Optional[int]         =     diffusion.flatten()
          lowercase__:							List[Any]         =     broadcast_to_shape_from_left(UpperCAmelCase_					, sample.shape)
          lowercase__:							List[Any]         =     drift - diffusion**2 * model_output

          #  equation 6: sample noise for the diffusion term of
          lowercase__:							Dict         =     random.split(UpperCAmelCase_					, num=1)
          lowercase__:							Tuple         =     random.normal(key=UpperCAmelCase_					, shape=sample.shape)
          lowercase__:							str         =     sample - drift  # subtract because `dt` is a small negative timestep
          # TODO is the variable diffusion the correct scaling term for the noise?
          lowercase__:							List[Any]         =     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=UpperCAmelCase_					, prev_sample_mean=UpperCAmelCase_					, state=UpperCAmelCase_)





   def __lowercase							(       self					, UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_ = 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
          lowercase__:							Optional[int]         =     random.split(UpperCAmelCase_					, num=1)
          lowercase__:							Optional[Any]         =     random.normal(key=UpperCAmelCase_					, shape=sample.shape)

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

          # compute corrected sample: model_output term and noise term
          lowercase__:							List[Any]         =     step_size.flatten()
          lowercase__:							Dict         =     broadcast_to_shape_from_left(UpperCAmelCase_					, sample.shape)
          lowercase__:							Optional[int]         =     sample + step_size * model_output
          lowercase__:							Optional[Any]         =     prev_sample_mean + ((step_size * 2) ** 0.5) * noise

          if not return_dict:
                 return (prev_sample, state)

          return FlaxSdeVeOutput(prev_sample=UpperCAmelCase_					, state=UpperCAmelCase_)





   def __len__(       self)			->   Tuple:




          '''simple docstring'''




          return self.config.num_train_timesteps








from __future__ import annotations




def 		A						(  SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE     ,						):




			"""simple docstring"""


			if not all((nth_term, start_term_a, common_ratio_r)							):
						return []
			UpperCAmelCase__		:list[float | int] 		=    []
			UpperCAmelCase__		:str 		=    1
			UpperCAmelCase__		:Any 		=    common_ratio_r
			for _ in range(int(SCREAMING_SNAKE_CASE							)							):
						if not series:
									series.append(SCREAMING_SNAKE_CASE							)
						else:
									power += 1
									series.append(float(start_term_a * multiple							)							)
									UpperCAmelCase__		:str 		=    pow(float(SCREAMING_SNAKE_CASE							)     ,						SCREAMING_SNAKE_CASE							)
			return series


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						__snake_case					:							Optional[int]           =							float(input('Enter the last number (n term) of the Geometric Series'))
						__snake_case					:							List[str]           =							float(input('Enter the starting term (a) of the Geometric Series'))
						__snake_case					:							Optional[int]           =							float(
						    input('Enter the common ratio between two terms (r) of the Geometric Series')
						)
						print('Formula of Geometric Series => a + ar + ar^2 ... +ar^n')
						print(geometric_series(nth_term, start_term_a, common_ratio_r))





