






"""simple docstring"""
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     UpperCamelCase_ :
 __magic_name__			   =       42

 # setable values
 __magic_name__			   =       42
 __magic_name__			   =       42
 __magic_name__			   =       None





 @classmethod
 def   _SCREAMING_SNAKE_CASE   (   cls      :				str			,			lowerCAmelCase_      :				CommonSchedulerState			,			lowerCAmelCase_      :				jnp.ndarray			,			lowerCAmelCase_      :				jnp.ndarray		)		->    List[str]:
    return cls(common=lowerCAmelCase_			,			init_noise_sigma=lowerCAmelCase_			,			timesteps=lowerCAmelCase_		)







@dataclass
class     UpperCamelCase_ (__A  ):
 __magic_name__			   =       42







class     UpperCamelCase_ (__A       ,		__A  ):
 __magic_name__			   =       [e.name for e in FlaxKarrasDiffusionSchedulers]

 __magic_name__			   =       42





 @property
 def   _SCREAMING_SNAKE_CASE   (   self      :				str		)		->    str:
    return True





 @register_to_config
 def __init__(   self      :				List[Any]			,			lowerCAmelCase_      :				int = 1_000			,			lowerCAmelCase_      :				float = 0.0_0_0_1			,			lowerCAmelCase_      :				float = 0.0_2			,			lowerCAmelCase_      :				str = "linear"			,			lowerCAmelCase_      :				Optional[jnp.ndarray] = None			,			lowerCAmelCase_      :				str = "fixed_small"			,			lowerCAmelCase_      :				bool = True			,			lowerCAmelCase_      :				str = "epsilon"			,			lowerCAmelCase_      :				jnp.dtype = jnp.floataa			,			)		->    Tuple:
    UpperCAmelCase_  :				int      =      dtype





 def   _SCREAMING_SNAKE_CASE   (   self      :				Union[str, Any]			,			lowerCAmelCase_      :				Optional[CommonSchedulerState] = None		)		->    DDPMSchedulerState:




    if common is None:
       UpperCAmelCase_  :				Optional[Any]      =      CommonSchedulerState.create(self		)

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

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

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





 def   _SCREAMING_SNAKE_CASE   (   self      :				Union[str, Any]			,			lowerCAmelCase_      :				DDPMSchedulerState			,			lowerCAmelCase_      :				jnp.ndarray			,			lowerCAmelCase_      :				Optional[int] = None		)		->    jnp.ndarray:
    return sample





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

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





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

    if variance_type is None:
       UpperCAmelCase_  :				Union[str, Any]      =      self.config.variance_type

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

    return variance





 def   _SCREAMING_SNAKE_CASE   (   self      :				List[str]			,			lowerCAmelCase_      :				DDPMSchedulerState			,			lowerCAmelCase_      :				jnp.ndarray			,			lowerCAmelCase_      :				int			,			lowerCAmelCase_      :				jnp.ndarray			,			lowerCAmelCase_      :				Optional[jax.random.KeyArray] = None			,			lowerCAmelCase_      :				bool = True			,			)		->    Union[FlaxDDPMSchedulerOutput, Tuple]:
    UpperCAmelCase_  :				List[str]      =      timestep

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

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

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

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

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

    UpperCAmelCase_  :				Union[str, Any]      =      pred_prev_sample + variance

    if not return_dict:
       return (pred_prev_sample, state)

    return FlaxDDPMSchedulerOutput(prev_sample=lowerCAmelCase_			,			state=lowerCAmelCase_		)





 def   _SCREAMING_SNAKE_CASE   (   self      :				List[Any]			,			lowerCAmelCase_      :				DDPMSchedulerState			,			lowerCAmelCase_      :				jnp.ndarray			,			lowerCAmelCase_      :				jnp.ndarray			,			lowerCAmelCase_      :				jnp.ndarray			,			)		->    jnp.ndarray:
    return add_noise_common(state.common			,			lowerCAmelCase_			,			lowerCAmelCase_			,			lowerCAmelCase_		)





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





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











"""simple docstring"""
from itertools import count

def        snake_case   (     A__ = 50		):
			UpperCAmelCase_  :				Any      =      [1] * min_block_length

			for n in count(A__		):
						fill_count_functions.append(1		)

						for block_length in range(A__			,n + 1		):
									for block_start in range(n - block_length		):
												fill_count_functions[n] += fill_count_functions[
												    n - block_start - block_length - 1
												]

									fill_count_functions[n] += 1

						if fill_count_functions[n] > 1_00_00_00:
									break

			return n


if __name__ == "__main__":
			print(f'{solution() = }')



