





# 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 A_					:
   lowerCAmelCase__        = 42

   # setable values
   lowerCAmelCase__        = 42
   lowerCAmelCase__        = 42
   lowerCAmelCase__        = None




   @classmethod
   def _lowerCAmelCase      (cls	:Union[str, Any]    ,   _UpperCamelCase	:CommonSchedulerState    ,   _UpperCamelCase	:jnp.ndarray    ,   _UpperCamelCase	:jnp.ndarray )->					List[Any]:
         return cls(common=_UpperCamelCase    ,   init_noise_sigma=_UpperCamelCase    ,   timesteps=_UpperCamelCase )





@dataclass
class A_					(			_lowerCamelCase   ):
   lowerCAmelCase__        = 42





class A_					(			_lowerCamelCase ,      _lowerCamelCase   ):
   lowerCAmelCase__        = [e.name for e in FlaxKarrasDiffusionSchedulers]

   lowerCAmelCase__        = 42




   @property
   def _lowerCAmelCase      (self	:List[str] )->					Tuple:
         return True




   @register_to_config
   def __init__(self	:List[Any]    ,   _UpperCamelCase	:int = 1000    ,   _UpperCamelCase	:float = 0.0_0_0_1    ,   _UpperCamelCase	:float = 0.0_2    ,   _UpperCamelCase	:str = "linear"    ,   _UpperCamelCase	:Optional[jnp.ndarray] = None    ,   _UpperCamelCase	:str = "fixed_small"    ,   _UpperCamelCase	:bool = True    ,   _UpperCamelCase	:str = "epsilon"    ,   _UpperCamelCase	:jnp.dtype = jnp.floataa    ,   )->					List[Any]:
         __A          =				dtype




   def _lowerCAmelCase      (self	:Optional[int]    ,   _UpperCamelCase	:Optional[CommonSchedulerState] = None )->					DDPMSchedulerState:
         if common is None:
               __A          =				CommonSchedulerState.create(self )

         # 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 DDPMSchedulerState.create(
             common=_UpperCamelCase    ,   init_noise_sigma=_UpperCamelCase    ,   timesteps=_UpperCamelCase    ,   )




   def _lowerCAmelCase      (self	:Any    ,   _UpperCamelCase	:DDPMSchedulerState    ,   _UpperCamelCase	:jnp.ndarray    ,   _UpperCamelCase	:Optional[int] = None )->					jnp.ndarray:
         return sample




   def _lowerCAmelCase      (self	:int    ,   _UpperCamelCase	:DDPMSchedulerState    ,   _UpperCamelCase	:int    ,   _UpperCamelCase	:Tuple = () )->					DDPMSchedulerState:
         __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]

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




   def _lowerCAmelCase      (self	:Optional[Any]    ,   _UpperCamelCase	:DDPMSchedulerState    ,   _UpperCamelCase	:Optional[int]    ,   _UpperCamelCase	:List[Any]=None    ,   _UpperCamelCase	:Any=None )->					Optional[Any]:
         __A          =				state.common.alphas_cumprod[t]
         __A          =				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
         __A          =				(1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

         if variance_type is None:
               __A          =				self.config.variance_type

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

         return variance




   def _lowerCAmelCase      (self	:Union[str, Any]    ,   _UpperCamelCase	:DDPMSchedulerState    ,   _UpperCamelCase	:jnp.ndarray    ,   _UpperCamelCase	:int    ,   _UpperCamelCase	:jnp.ndarray    ,   _UpperCamelCase	:Optional[jax.random.KeyArray] = None    ,   _UpperCamelCase	:bool = True    ,   )->					Union[FlaxDDPMSchedulerOutput, Tuple]:
         __A          =				timestep

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

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

         # 1. compute alphas, betas
         __A          =				state.common.alphas_cumprod[t]
         __A          =				jnp.where(t > 0    ,   state.common.alphas_cumprod[t - 1]    ,   jnp.array(1.0    ,   dtype=self.dtype ) )
         __A          =				1 - alpha_prod_t
         __A          =				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":
               __A          =				(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
         elif self.config.prediction_type == "sample":
               __A          =				model_output
         elif self.config.prediction_type == "v_prediction":
               __A          =				(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:
               __A          =				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
         __A          =				(alpha_prod_t_prev ** 0.5 * state.common.betas[t]) / beta_prod_t
         __A          =				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
         __A          =				pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

         # 6. Add noise
         def random_variance():
               __A          =				jax.random.split(_UpperCamelCase    ,   num=1 )
               __A          =				jax.random.normal(_UpperCamelCase    ,   shape=model_output.shape    ,   dtype=self.dtype )
               return (self._get_variance(_UpperCamelCase    ,   _UpperCamelCase    ,   predicted_variance=_UpperCamelCase ) ** 0.5) * noise

         __A          =				jnp.where(t > 0    ,   random_variance()    ,   jnp.zeros(model_output.shape    ,   dtype=self.dtype ) )

         __A          =				pred_prev_sample + variance

         if not return_dict:
               return (pred_prev_sample, state)

         return FlaxDDPMSchedulerOutput(prev_sample=_UpperCamelCase    ,   state=_UpperCamelCase )




   def _lowerCAmelCase      (self	:Optional[int]    ,   _UpperCamelCase	:DDPMSchedulerState    ,   _UpperCamelCase	:jnp.ndarray    ,   _UpperCamelCase	:jnp.ndarray    ,   _UpperCamelCase	:jnp.ndarray    ,   )->					jnp.ndarray:
         return add_noise_common(state.common    ,   _UpperCamelCase    ,   _UpperCamelCase    ,   _UpperCamelCase )




   def _lowerCAmelCase      (self	:Union[str, Any]    ,   _UpperCamelCase	:DDPMSchedulerState    ,   _UpperCamelCase	:jnp.ndarray    ,   _UpperCamelCase	:jnp.ndarray    ,   _UpperCamelCase	:jnp.ndarray    ,   )->					jnp.ndarray:
         return get_velocity_common(state.common    ,   _UpperCamelCase    ,   _UpperCamelCase    ,   _UpperCamelCase )






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












from __future__ import annotations

from collections.abc import Iterable, Iterator
from dataclasses import dataclass

snake_case__					:							Union[str, Any]													=     (3, 9, -11, 0, 7, 5, 1, -1)
snake_case__					:							int													=     (4, 6, 2, 0, 8, 10, 3, -2)





@dataclass
class A_					:
   lowerCAmelCase__        = 42
   lowerCAmelCase__        = 42





class A_					:




   def __init__(self	:Dict    ,   _UpperCamelCase	:Iterable[int] )->					None:
         __A          =				None
         for i in sorted(_UpperCamelCase    ,   reverse=_UpperCamelCase ):
               __A          =				Node(_UpperCamelCase    ,   self.head )




   def __iter__(self	:List[str] )->					Iterator[int]:
         __A          =				self.head
         while node:
               yield node.data
               __A          =				node.next_node




   def __len__(self	:Union[str, Any] )->					int:
         return sum(1 for _ in self )






   def __str__(self	:List[Any] )->					str:
         return " -> ".join([str(_UpperCamelCase ) for node in self] )





def _a				(	lowerCamelCase:   SortedLinkedList					,				lowerCamelCase:   SortedLinkedList )	->						SortedLinkedList:







      '''simple docstring'''






      return SortedLinkedList(list(lowerCamelCase ) + list(lowerCamelCase ) )


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       snake_case__					:							Any													=     SortedLinkedList
       print(merge_lists(SSL(test_data_odd), SSL(test_data_even)))





