




# 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:






    """simple docstring"""





    lowerCAmelCase        =				42

    # setable values
    lowerCAmelCase        =				42
    lowerCAmelCase        =				42
    lowerCAmelCase        =				None





    @classmethod
    def 							a__				(				cls       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  )			->		Optional[Any]:
         return cls(common=_SCREAMING_SNAKE_CASE       ,init_noise_sigma=_SCREAMING_SNAKE_CASE       ,timesteps=_SCREAMING_SNAKE_CASE  )


@dataclass
class   __a(					_a       ):






    """simple docstring"""





    lowerCAmelCase        =				42


class   __a(					_a    ,						_a       ):






    """simple docstring"""





    lowerCAmelCase        =				[e.name for e in FlaxKarrasDiffusionSchedulers]

    lowerCAmelCase        =				42





    @property
    def 							a__				(				self  )			->		Dict:
         return True





    @register_to_config
    def __init__(				self       ,_SCREAMING_SNAKE_CASE = 1_000       ,_SCREAMING_SNAKE_CASE = 0.00_01       ,_SCREAMING_SNAKE_CASE = 0.02       ,_SCREAMING_SNAKE_CASE = "linear"       ,_SCREAMING_SNAKE_CASE = None       ,_SCREAMING_SNAKE_CASE = "fixed_small"       ,_SCREAMING_SNAKE_CASE = True       ,_SCREAMING_SNAKE_CASE = "epsilon"       ,_SCREAMING_SNAKE_CASE = jnp.floataa       ,)			->		Optional[int]:
         UpperCAmelCase_      :							str       =      dtype





    def 							a__				(				self       ,_SCREAMING_SNAKE_CASE = None  )			->		DDPMSchedulerState:
         if common is None:
              UpperCAmelCase_      :							Tuple       =      CommonSchedulerState.create(self  )

         # standard deviation of the initial noise distribution
         UpperCAmelCase_      :							Optional[Any]       =      jnp.array(1.0       ,dtype=self.dtype  )

         UpperCAmelCase_      :							Union[str, Any]       =      jnp.arange(0       ,self.config.num_train_timesteps  ).round()[::-1]

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





    def 							a__				(				self       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE = None  )			->		jnp.ndarray:
         return sample





    def 							a__				(				self       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE = ()  )			->		DDPMSchedulerState:
         UpperCAmelCase_      :							str       =      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
         UpperCAmelCase_      :							Tuple       =      (jnp.arange(0       ,_SCREAMING_SNAKE_CASE  ) * step_ratio).round()[::-1]

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





    def 							a__				(				self       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE=None       ,_SCREAMING_SNAKE_CASE=None  )			->		Optional[int]:
         UpperCAmelCase_      :							Union[str, Any]       =      state.common.alphas_cumprod[t]
         UpperCAmelCase_      :							List[str]       =      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
         UpperCAmelCase_      :							Tuple       =      (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

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

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

         return variance





    def 							a__				(				self       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE = None       ,_SCREAMING_SNAKE_CASE = True       ,)			->		Union[FlaxDDPMSchedulerOutput, Tuple]:
         UpperCAmelCase_      :							int       =      timestep

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

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

         # 1. compute alphas, betas
         UpperCAmelCase_      :							int       =      state.common.alphas_cumprod[t]
         UpperCAmelCase_      :							int       =      jnp.where(t > 0       ,state.common.alphas_cumprod[t - 1]       ,jnp.array(1.0       ,dtype=self.dtype  )  )
         UpperCAmelCase_      :							Optional[Any]       =      1 - alpha_prod_t
         UpperCAmelCase_      :							Optional[Any]       =      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":
              UpperCAmelCase_      :							Any       =      (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
         elif self.config.prediction_type == "sample":
              UpperCAmelCase_      :							Union[str, Any]       =      model_output
         elif self.config.prediction_type == "v_prediction":
              UpperCAmelCase_      :							Dict       =      (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:
              UpperCAmelCase_      :							Any       =      jnp.clip(_SCREAMING_SNAKE_CASE       ,-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
         UpperCAmelCase_      :							Union[str, Any]       =      (alpha_prod_t_prev ** 0.5 * state.common.betas[t]) / beta_prod_t
         UpperCAmelCase_      :							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
         UpperCAmelCase_      :							List[str]       =      pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

         # 6. Add noise
         def random_variance():
              UpperCAmelCase_      :							Optional[int]       =      jax.random.split(_SCREAMING_SNAKE_CASE       ,num=1  )
              UpperCAmelCase_      :							Any       =      jax.random.normal(_SCREAMING_SNAKE_CASE       ,shape=model_output.shape       ,dtype=self.dtype  )
              return (self._get_variance(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,predicted_variance=_SCREAMING_SNAKE_CASE  ) ** 0.5) * noise

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

         UpperCAmelCase_      :							Optional[Any]       =      pred_prev_sample + variance

         if not return_dict:
              return (pred_prev_sample, state)

         return FlaxDDPMSchedulerOutput(prev_sample=_SCREAMING_SNAKE_CASE       ,state=_SCREAMING_SNAKE_CASE  )





    def 							a__				(				self       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,)			->		jnp.ndarray:
         return add_noise_common(state.common       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  )





    def 							a__				(				self       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,)			->		jnp.ndarray:
         return get_velocity_common(state.common       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  )





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





from math import ceil







def lowerCamelCase__       (      _lowercase = 1001				):

     '''simple docstring'''


     UpperCAmelCase_      :							Optional[Any]       =      1

     for i in range(1			,						int(ceil(n / 2.0				)				)				):
          UpperCAmelCase_      :							List[Any]       =      2 * i + 1
          UpperCAmelCase_      :							Optional[int]       =      2 * i
          UpperCAmelCase_      :							Any       =      total + 4 * odd**2 - 6 * even

     return total


if __name__ == "__main__":
     import sys

     if len(sys.argv) == 1:
          print(solution())
     else:
          try:
               __a          =			int(sys.argv[1])
               print(solution(n))
          except ValueError:
               print('Invalid entry - please enter a number')