


'''simple docstring'''

# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion

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

import flax
import jax.numpy as jnp

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    add_noise_common,
    get_velocity_common,
)





@flax.struct.dataclass
class     __SCREAMING_SNAKE_CASE       :
     UpperCAmelCase			       =					42
     UpperCAmelCase			       =					42

     # setable values
     UpperCAmelCase			       =					42
     UpperCAmelCase			       =					42
     UpperCAmelCase			       =					None






     @classmethod
     def 			a_       (      cls  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				)							->     Optional[int]:
          return cls(
              common=__UpperCamelCase  ,				final_alpha_cumprod=__UpperCamelCase  ,				init_noise_sigma=__UpperCamelCase  ,				timesteps=__UpperCamelCase  ,				)







@dataclass
class     __SCREAMING_SNAKE_CASE       (   lowerCamelCase__			):
     UpperCAmelCase			       =					42







class     __SCREAMING_SNAKE_CASE       (   lowerCamelCase__			,      lowerCamelCase__			):
     UpperCAmelCase			       =					[e.name for e in FlaxKarrasDiffusionSchedulers]

     UpperCAmelCase			       =					42






     @property
     def 			a_       (      self		)							->     Any:
          return True






     @register_to_config
     def __init__(      self  ,				__UpperCamelCase = 1_000  ,				__UpperCamelCase = 0.00_01  ,				__UpperCamelCase = 0.02  ,				__UpperCamelCase = "linear"  ,				__UpperCamelCase = None  ,				__UpperCamelCase = True  ,				__UpperCamelCase = 0  ,				__UpperCamelCase = "epsilon"  ,				__UpperCamelCase = jnp.floataa  ,				)							->     Dict:
          _a            =		dtype






     def 			a_       (      self  ,				__UpperCamelCase = None		)							->     DDIMSchedulerState:
          if common is None:
               _a            =		CommonSchedulerState.create(self		)

          # At every step in ddim, we are looking into the previous alphas_cumprod
          # For the final step, there is no previous alphas_cumprod because we are already at 0
          # `set_alpha_to_one` decides whether we set this parameter simply to one or
          # whether we use the final alpha of the "non-previous" one.
          _a            =		(
              jnp.array(1.0  ,				dtype=self.dtype		) if self.config.set_alpha_to_one else common.alphas_cumprod[0]
          )

          # standard deviation of the initial noise distribution
          _a            =		jnp.array(1.0  ,				dtype=self.dtype		)

          _a            =		jnp.arange(0  ,				self.config.num_train_timesteps		).round()[::-1]

          return DDIMSchedulerState.create(
              common=__UpperCamelCase  ,				final_alpha_cumprod=__UpperCamelCase  ,				init_noise_sigma=__UpperCamelCase  ,				timesteps=__UpperCamelCase  ,				)






     def 			a_       (      self  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase = None		)							->     jnp.ndarray:
          return sample






     def 			a_       (      self  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase = ()		)							->     DDIMSchedulerState:
          _a            =		self.config.num_train_timesteps // num_inference_steps
          # creates integer timesteps by multiplying by ratio
          # rounding to avoid issues when num_inference_step is power of 3
          _a            =		(jnp.arange(0  ,				__UpperCamelCase		) * step_ratio).round()[::-1] + self.config.steps_offset

          return state.replace(
              num_inference_steps=__UpperCamelCase  ,				timesteps=__UpperCamelCase  ,				)






     def 			a_       (      self  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase		)							->     Optional[int]:
          _a            =		state.common.alphas_cumprod[timestep]
          _a            =		jnp.where(
              prev_timestep >= 0  ,				state.common.alphas_cumprod[prev_timestep]  ,				state.final_alpha_cumprod		)
          _a            =		1 - alpha_prod_t
          _a            =		1 - alpha_prod_t_prev

          _a            =		(beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

          return variance






     def 			a_       (      self  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase = 0.0  ,				__UpperCamelCase = True  ,				)							->     Union[FlaxDDIMSchedulerOutput, Tuple]:
          if state.num_inference_steps is None:
               raise ValueError(
                   "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"		)

          # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
          # Ideally, read DDIM paper in-detail understanding

          # Notation (<variable name> -> <name in paper>
          # - pred_noise_t -> e_theta(x_t, t)
          # - pred_original_sample -> f_theta(x_t, t) or x_0
          # - std_dev_t -> sigma_t
          # - eta -> η
          # - pred_sample_direction -> "direction pointing to x_t"
          # - pred_prev_sample -> "x_t-1"

          # 1. get previous step value (=t-1)
          _a            =		timestep - self.config.num_train_timesteps // state.num_inference_steps

          _a            =		state.common.alphas_cumprod
          _a            =		state.final_alpha_cumprod

          # 2. compute alphas, betas
          _a            =		alphas_cumprod[timestep]
          _a            =		jnp.where(prev_timestep >= 0  ,				alphas_cumprod[prev_timestep]  ,				__UpperCamelCase		)

          _a            =		1 - alpha_prod_t

          # 3. compute predicted original sample from predicted noise also called
          # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
          if self.config.prediction_type == "epsilon":
               _a            =		(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
               _a            =		model_output
          elif self.config.prediction_type == "sample":
               _a            =		model_output
               _a            =		(sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
          elif self.config.prediction_type == "v_prediction":
               _a            =		(alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
               _a            =		(alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
          else:
               raise ValueError(
                   f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
                   " `v_prediction`"		)

          # 4. compute variance: "sigma_t(η)" -> see formula (16)
          # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
          _a            =		self._get_variance(__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase		)
          _a            =		eta * variance ** 0.5

          # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
          _a            =		(1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * pred_epsilon

          # 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
          _a            =		alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

          if not return_dict:
               return (prev_sample, state)

          return FlaxDDIMSchedulerOutput(prev_sample=__UpperCamelCase  ,				state=__UpperCamelCase		)






     def 			a_       (      self  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				)							->     jnp.ndarray:
          return add_noise_common(state.common  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase		)






     def 			a_       (      self  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				)							->     jnp.ndarray:
          return get_velocity_common(state.common  ,				__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase		)






     def __len__(      self		)							->     List[Any]:
          return self.config.num_train_timesteps





'''simple docstring'''

from __future__ import annotations






def __UpperCamelCase (      __lowerCamelCase		:			float | int   ,	__lowerCamelCase		:			float | int   ,	__lowerCamelCase		:			float | int   ,	)   ->  list[float | int]:







     '''simple docstring'''






     if not all((nth_term, start_term_a, common_ratio_r)					):
          return []
     _a            =		[]
     _a            =		1
     _a            =		common_ratio_r
     for _ in range(int(__lowerCamelCase					)					):
          if not series:
               series.append(__lowerCamelCase					)
          else:
               power += 1
               series.append(float(start_term_a * multiple					)					)
               _a            =		pow(float(__lowerCamelCase					)   ,	__lowerCamelCase					)
     return series


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   lowercase__					  =		float(input("Enter the last number (n term) of the Geometric Series"))
   lowercase__					  =		float(input("Enter the starting term (a) of the Geometric Series"))
   lowercase__					  =		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))

