





"""simple docstring"""





# DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim

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

import flax
import jax
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    _lowerCAmelCase  :
       """simple docstring"""




       __magic_name__	:CommonSchedulerState

       # setable values
       __magic_name__	:jnp.ndarray
       __magic_name__	:jnp.ndarray
       __magic_name__	:Optional[int]						    =   None






       @classmethod
       def 	snake_case		(       cls       ,					__UpperCAmelCase       ,					__UpperCAmelCase       ,					__UpperCAmelCase ):



         '''simple docstring'''

         return cls(common=__UpperCAmelCase       ,					init_noise_sigma=__UpperCAmelCase       ,					timesteps=__UpperCAmelCase )






@dataclass
class    _lowerCAmelCase  (	a			):
       """simple docstring"""




       __magic_name__	:DDPMSchedulerState






class    _lowerCAmelCase  (	a    ,  a			):
       """simple docstring"""




       __magic_name__	:Union[str, Any]						    =   [e.name for e in FlaxKarrasDiffusionSchedulers]

       __magic_name__	:jnp.dtype






       @property
       def 	snake_case		(       self ):



         '''simple docstring'''

         return True






       @register_to_config
       def __init__(       self       ,					__UpperCAmelCase = 1_0_0_0       ,					__UpperCAmelCase = 0.00_01       ,					__UpperCAmelCase = 0.02       ,					__UpperCAmelCase = "linear"       ,					__UpperCAmelCase = None       ,					__UpperCAmelCase = "fixed_small"       ,					__UpperCAmelCase = True       ,					__UpperCAmelCase = "epsilon"       ,					__UpperCAmelCase = jnp.floataa       ,					):



         '''simple docstring'''

         lowerCAmelCase__     :int											=				dtype






       def 	snake_case		(       self       ,					__UpperCAmelCase = None ):



         '''simple docstring'''

         if common is None:
           lowerCAmelCase__     :Tuple											=				CommonSchedulerState.create(self )

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

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

         return DDPMSchedulerState.create(
             common=__UpperCAmelCase       ,					init_noise_sigma=__UpperCAmelCase       ,					timesteps=__UpperCAmelCase       ,					)






       def 	snake_case		(       self       ,					__UpperCAmelCase       ,					__UpperCAmelCase       ,					__UpperCAmelCase = None ):



         '''simple docstring'''

         return sample






       def 	snake_case		(       self       ,					__UpperCAmelCase       ,					__UpperCAmelCase       ,					__UpperCAmelCase = () ):



         '''simple docstring'''

         lowerCAmelCase__     :Any											=				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
         lowerCAmelCase__     :Any											=				(jnp.arange(0       ,					__UpperCAmelCase ) * step_ratio).round()[::-1]

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






       def 	snake_case		(       self       ,					__UpperCAmelCase       ,					__UpperCAmelCase       ,					__UpperCAmelCase=None       ,					__UpperCAmelCase=None ):



         '''simple docstring'''

         lowerCAmelCase__     :Union[str, Any]											=				state.common.alphas_cumprod[t]
         lowerCAmelCase__     :List[Any]											=				jnp.where(t > 0       ,					state.common.alphas_cumprod[t - 1]       ,					jnp.array(1.0       ,					dtype=self.dtype ) )

         # For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
         # and sample from it to get previous sample
         # x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
         lowerCAmelCase__     :List[str]											=				(1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

         if variance_type is None:
           lowerCAmelCase__     :Tuple											=				self.config.variance_type

         # hacks - were probably added for training stability
         if variance_type == "fixed_small":
           lowerCAmelCase__     :Optional[Any]											=				jnp.clip(__UpperCAmelCase       ,					a_min=1E-20 )
         # for rl-diffuser https://arxiv.org/abs/2205.09991
         elif variance_type == "fixed_small_log":
           lowerCAmelCase__     :Optional[int]											=				jnp.log(jnp.clip(__UpperCAmelCase       ,					a_min=1E-20 ) )
         elif variance_type == "fixed_large":
           lowerCAmelCase__     :Any											=				state.common.betas[t]
         elif variance_type == "fixed_large_log":
           # Glide max_log
           lowerCAmelCase__     :str											=				jnp.log(state.common.betas[t] )
         elif variance_type == "learned":
           return predicted_variance
         elif variance_type == "learned_range":
           lowerCAmelCase__     :int											=				variance
           lowerCAmelCase__     :str											=				state.common.betas[t]
           lowerCAmelCase__     :Union[str, Any]											=				(predicted_variance + 1) / 2
           lowerCAmelCase__     :Dict											=				frac * max_log + (1 - frac) * min_log

         return variance






       def 	snake_case		(       self       ,					__UpperCAmelCase       ,					__UpperCAmelCase       ,					__UpperCAmelCase       ,					__UpperCAmelCase       ,					__UpperCAmelCase = None       ,					__UpperCAmelCase = True       ,					):



         '''simple docstring'''

         lowerCAmelCase__     :Dict											=				timestep

         if key is None:
           lowerCAmelCase__     :Any											=				jax.random.PRNGKey(0 )

         if model_output.shape[1] == sample.shape[1] * 2 and self.config.variance_type in ["learned", "learned_range"]:
           lowerCAmelCase__				,							lowerCAmelCase__     :Optional[Any]											=				jnp.split(__UpperCAmelCase       ,					sample.shape[1]       ,					axis=1 )
         else:
           lowerCAmelCase__     :Optional[int]											=				None

         # 1. compute alphas, betas
         lowerCAmelCase__     :Tuple											=				state.common.alphas_cumprod[t]
         lowerCAmelCase__     :List[str]											=				jnp.where(t > 0       ,					state.common.alphas_cumprod[t - 1]       ,					jnp.array(1.0       ,					dtype=self.dtype ) )
         lowerCAmelCase__     :str											=				1 - alpha_prod_t
         lowerCAmelCase__     :int											=				1 - alpha_prod_t_prev

         # 2. compute predicted original sample from predicted noise also called
         # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
         if self.config.prediction_type == "epsilon":
           lowerCAmelCase__     :Union[str, Any]											=				(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
         elif self.config.prediction_type == "sample":
           lowerCAmelCase__     :str											=				model_output
         elif self.config.prediction_type == "v_prediction":
           lowerCAmelCase__     :Any											=				(alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
         else:
           raise ValueError(
               F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` "
               ' for the FlaxDDPMScheduler.' )

         # 3. Clip "predicted x_0"
         if self.config.clip_sample:
           lowerCAmelCase__     :Optional[int]											=				jnp.clip(__UpperCAmelCase       ,					-1       ,					1 )

         # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
         # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
         lowerCAmelCase__     :Union[str, Any]											=				(alpha_prod_t_prev ** 0.5 * state.common.betas[t]) / beta_prod_t
         lowerCAmelCase__     :Union[str, Any]											=				state.common.alphas[t] ** 0.5 * beta_prod_t_prev / beta_prod_t

         # 5. Compute predicted previous sample µ_t
         # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
         lowerCAmelCase__     :Optional[int]											=				pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

         # 6. Add noise
         def random_variance():
           lowerCAmelCase__     :List[Any]											=				jax.random.split(__UpperCAmelCase       ,					num=1 )
           lowerCAmelCase__     :Union[str, Any]											=				jax.random.normal(__UpperCAmelCase       ,					shape=model_output.shape       ,					dtype=self.dtype )
           return (self._get_variance(__UpperCAmelCase       ,					__UpperCAmelCase       ,					predicted_variance=__UpperCAmelCase ) ** 0.5) * noise

         lowerCAmelCase__     :Optional[int]											=				jnp.where(t > 0       ,					random_variance()       ,					jnp.zeros(model_output.shape       ,					dtype=self.dtype ) )

         lowerCAmelCase__     :str											=				pred_prev_sample + variance

         if not return_dict:
           return (pred_prev_sample, state)

         return FlaxDDPMSchedulerOutput(prev_sample=__UpperCAmelCase       ,					state=__UpperCAmelCase )






       def 	snake_case		(       self       ,					__UpperCAmelCase       ,					__UpperCAmelCase       ,					__UpperCAmelCase       ,					__UpperCAmelCase       ,					):



         '''simple docstring'''

         return add_noise_common(state.common       ,					__UpperCAmelCase       ,					__UpperCAmelCase       ,					__UpperCAmelCase )






       def 	snake_case		(       self       ,					__UpperCAmelCase       ,					__UpperCAmelCase       ,					__UpperCAmelCase       ,					__UpperCAmelCase       ,					):



         '''simple docstring'''

         return get_velocity_common(state.common       ,					__UpperCAmelCase       ,					__UpperCAmelCase       ,					__UpperCAmelCase )






       def __len__(       self ):



         '''simple docstring'''

         return self.config.num_train_timesteps





'''simple docstring'''

def 	__lowerCamelCase	( )     -> Union[str, Any]:
		_a	: Optional[Any]								=				[]
		_a	: List[str]								=				1

		while len(lowerCAmelCase_    ) < 1E6:
				constant.append(str(lowerCAmelCase_    )    )
				i += 1

		_a	: Optional[Any]								=				''.join(lowerCAmelCase_    )

		return (
		    int(constant[0]    )
		    * int(constant[9]    )
		    * int(constant[99]    )
		    * int(constant[999]    )
		    * int(constant[9999]    )
		    * int(constant[99999]    )
		    * int(constant[999999]    )
		)


if __name__ == "__main__":
							print(solution())




