






"""simple docstring"""





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

import flax
import jax.numpy as jnp
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    broadcast_to_shape_from_left,
)
@flax.struct.dataclass
class  __lowerCamelCase     :
   a   :					List[str]			    =4_2

   # setable values
   a   :					Union[str, Any]			    =4_2
   a   :					Optional[int]			    =4_2
   a   :					Union[str, Any]			    =4_2
   a   :					Tuple			    =None

   # running values
   a   :					List[Any]			    =None

   @classmethod
   def     SCREAMING_SNAKE_CASE__			(       cls			,					snake_case_			,					snake_case_			,					snake_case_			,					snake_case_   )		->							Optional[Any]:
       return cls(common=snake_case_			,					init_noise_sigma=snake_case_			,					timesteps=snake_case_			,					sigmas=snake_case_   )







@dataclass
class  __lowerCamelCase     (	lowerCamelCase_	):
   a   :					Optional[Any]			    =4_2







class  __lowerCamelCase     (	lowerCamelCase_				,						lowerCamelCase_	):
   a   :					List[Any]			    =[e.name for e in FlaxKarrasDiffusionSchedulers]

   a   :					Dict			    =4_2

   @property
   def     SCREAMING_SNAKE_CASE__			(       self   )		->							int:
       return True

   @register_to_config
   def __init__(       self			,					snake_case_ = 1000			,					snake_case_ = 0.0_001			,					snake_case_ = 0.02			,					snake_case_ = "linear"			,					snake_case_ = None			,					snake_case_ = "epsilon"			,					snake_case_ = jnp.floataa			,					)		->							Union[str, Any]:
       UpperCamelCase__								=     dtype

   def     SCREAMING_SNAKE_CASE__			(       self			,					snake_case_ = None   )		->							Any:
       if common is None:
           UpperCamelCase__								=     CommonSchedulerState.create(self   )

       UpperCamelCase__								=     jnp.arange(0			,					self.config.num_train_timesteps   ).round()[::-1]
       UpperCamelCase__								=     ((1 - common.alphas_cumprod) / common.alphas_cumprod) ** 0.5

       # standard deviation of the initial noise distribution
       UpperCamelCase__								=     sigmas.max()

       return LMSDiscreteSchedulerState.create(
           common=snake_case_			,					init_noise_sigma=snake_case_			,					timesteps=snake_case_			,					sigmas=snake_case_			,					)

   def     SCREAMING_SNAKE_CASE__			(       self			,					snake_case_			,					snake_case_			,					snake_case_   )		->							List[str]:
       ((UpperCamelCase__    )							,        )								=     jnp.where(state.timesteps == timestep			,					size=1   )
       UpperCamelCase__								=     step_index[0]

       UpperCamelCase__								=     state.sigmas[step_index]
       UpperCamelCase__								=     sample / ((sigma**2 + 1) ** 0.5)
       return sample

   def     SCREAMING_SNAKE_CASE__			(       self			,					snake_case_			,					snake_case_			,					snake_case_			,					snake_case_   )		->							Optional[Any]:

       def lms_derivative(snake_case_   ):
           UpperCamelCase__								=     1.0
           for k in range(snake_case_   ):
               if current_order == k:
                   continue
               prod *= (tau - state.sigmas[t - k]) / (state.sigmas[t - current_order] - state.sigmas[t - k])
           return prod

       UpperCamelCase__								=     integrate.quad(snake_case_			,					state.sigmas[t]			,					state.sigmas[t + 1]			,					epsrel=1E-4   )[0]

       return integrated_coeff

   def     SCREAMING_SNAKE_CASE__			(       self			,					snake_case_			,					snake_case_			,					snake_case_ = ()   )		->							str:
       UpperCamelCase__								=     jnp.linspace(self.config.num_train_timesteps - 1			,					0			,					snake_case_			,					dtype=self.dtype   )

       UpperCamelCase__								=     jnp.floor(snake_case_   ).astype(jnp.intaa   )
       UpperCamelCase__								=     jnp.ceil(snake_case_   ).astype(jnp.intaa   )

       UpperCamelCase__								=     jnp.mod(snake_case_			,					1.0   )

       UpperCamelCase__								=     ((1 - state.common.alphas_cumprod) / state.common.alphas_cumprod) ** 0.5
       UpperCamelCase__								=     (1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx]
       UpperCamelCase__								=     jnp.concatenate([sigmas, jnp.array([0.0]			,					dtype=self.dtype   )]   )

       UpperCamelCase__								=     timesteps.astype(jnp.intaa   )

       # initial running values
       UpperCamelCase__								=     jnp.zeros((0,) + shape			,					dtype=self.dtype   )

       return state.replace(
           timesteps=snake_case_			,					sigmas=snake_case_			,					num_inference_steps=snake_case_			,					derivatives=snake_case_			,					)

   def     SCREAMING_SNAKE_CASE__			(       self			,					snake_case_			,					snake_case_			,					snake_case_			,					snake_case_			,					snake_case_ = 4			,					snake_case_ = True			,					)		->							List[Any]:
       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'   )

       UpperCamelCase__								=     state.sigmas[timestep]

       # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
       if self.config.prediction_type == "epsilon":
           UpperCamelCase__								=     sample - sigma * model_output
       elif self.config.prediction_type == "v_prediction":
           # * c_out + input * c_skip
           UpperCamelCase__								=     model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
       else:
           raise ValueError(
               F'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'   )

       # 2. Convert to an ODE derivative
       UpperCamelCase__								=     (sample - pred_original_sample) / sigma
       UpperCamelCase__								=     state.replace(derivatives=jnp.append(state.derivatives			,					snake_case_   )   )
       if len(state.derivatives   ) > order:
           UpperCamelCase__								=     state.replace(derivatives=jnp.delete(state.derivatives			,					0   )   )

       # 3. Compute linear multistep coefficients
       UpperCamelCase__								=     min(timestep + 1			,					snake_case_   )
       UpperCamelCase__								=     [self.get_lms_coefficient(snake_case_			,					snake_case_			,					snake_case_			,					snake_case_   ) for curr_order in range(snake_case_   )]

       # 4. Compute previous sample based on the derivatives path
       UpperCamelCase__								=     sample + sum(
           coeff * derivative for coeff, derivative in zip(snake_case_			,					reversed(state.derivatives   )   )   )

       if not return_dict:
           return (prev_sample, state)

       return FlaxLMSSchedulerOutput(prev_sample=snake_case_			,					state=snake_case_   )

   def     SCREAMING_SNAKE_CASE__			(       self			,					snake_case_			,					snake_case_			,					snake_case_			,					snake_case_			,					)		->							List[str]:
       UpperCamelCase__								=     state.sigmas[timesteps].flatten()
       UpperCamelCase__								=     broadcast_to_shape_from_left(snake_case_			,					noise.shape   )

       UpperCamelCase__								=     original_samples + noise * sigma

       return noisy_samples







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







from math import cos, sin







def      snake_case__							(  lowerCAmelCase_     ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE 		=float(lowerCAmelCase_     )
     return [[scaling_factor * int(x == y     ) for x in range(2     )] for y in range(2     )]







def      snake_case__							(  lowerCAmelCase_     ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE		,    SCREAMING_SNAKE_CASE 		=cos(lowerCAmelCase_     ), sin(lowerCAmelCase_     )
     return [[c, -s], [s, c]]







def      snake_case__							(  lowerCAmelCase_     ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE		,    SCREAMING_SNAKE_CASE 		=cos(lowerCAmelCase_     ), sin(lowerCAmelCase_     )
     SCREAMING_SNAKE_CASE 		=c * s
     return [[c * c, cs], [cs, s * s]]







def      snake_case__							(  lowerCAmelCase_     ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE		,    SCREAMING_SNAKE_CASE 		=cos(lowerCAmelCase_     ), sin(lowerCAmelCase_     )
     SCREAMING_SNAKE_CASE 		=c * s
     return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(f'    {scaling(5) = }')
print(f'  {rotation(45) = }')
print(f'{projection(45) = }')



print(f'{reflection(45) = }')

