

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 						a_			:



      """simple docstring"""







      __UpperCAmelCase     						= 42

      # setable values
      __UpperCAmelCase     						= 42
      __UpperCAmelCase     						= 42
      __UpperCAmelCase     						= 42
      __UpperCAmelCase     						= None

      # running values
      __UpperCAmelCase     						= None
      @classmethod
      def 			_lowerCAmelCase	( cls	:				List[Any]     ,snake_case	:				CommonSchedulerState     ,snake_case	:				jnp.ndarray     ,snake_case	:				jnp.ndarray     ,snake_case	:				jnp.ndarray							):
           return cls(common=snake_case     ,init_noise_sigma=snake_case     ,timesteps=snake_case     ,sigmas=snake_case							)







@dataclass
class 						a_			(				lowerCamelCase_	):



      """simple docstring"""







      __UpperCAmelCase     						= 42







class 						a_			(				lowerCamelCase_					,     lowerCamelCase_	):



      """simple docstring"""







      __UpperCAmelCase     						= [e.name for e in FlaxKarrasDiffusionSchedulers]

      __UpperCAmelCase     						= 42
      @property
      def 			_lowerCAmelCase	( self	:				int							):
           return True
      @register_to_config
      def __init__( self	:				Optional[Any]     ,snake_case	:				int = 1000     ,snake_case	:				float = 0.0_001     ,snake_case	:				float = 0.02     ,snake_case	:				str = "linear"     ,snake_case	:				Optional[jnp.ndarray] = None     ,snake_case	:				str = "epsilon"     ,snake_case	:				jnp.dtype = jnp.floataa     ,):
           SCREAMING_SNAKE_CASE 		=dtype
      def 			_lowerCAmelCase	( self	:				Union[str, Any]     ,snake_case	:				Optional[CommonSchedulerState] = None							):
           if common is None:
                SCREAMING_SNAKE_CASE 		=CommonSchedulerState.create(self							)

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

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

           return LMSDiscreteSchedulerState.create(
               common=snake_case     ,init_noise_sigma=snake_case     ,timesteps=snake_case     ,sigmas=snake_case     ,)
      def 			_lowerCAmelCase	( self	:				List[Any]     ,snake_case	:				LMSDiscreteSchedulerState     ,snake_case	:				jnp.ndarray     ,snake_case	:				int							):
           ((SCREAMING_SNAKE_CASE)		,    ) 		=jnp.where(state.timesteps == timestep     ,size=1							)
           SCREAMING_SNAKE_CASE 		=step_index[0]

           SCREAMING_SNAKE_CASE 		=state.sigmas[step_index]
           SCREAMING_SNAKE_CASE 		=sample / ((sigma**2 + 1) ** 0.5)
           return sample
      def 			_lowerCAmelCase	( self	:				str     ,snake_case	:				LMSDiscreteSchedulerState     ,snake_case	:				int     ,snake_case	:				int     ,snake_case	:				Union[str, Any]							):

           def lms_derivative(snake_case	:				Optional[int]							):
                SCREAMING_SNAKE_CASE 		=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

           SCREAMING_SNAKE_CASE 		=integrate.quad(snake_case     ,state.sigmas[t]     ,state.sigmas[t + 1]     ,epsrel=1e-4							)[0]

           return integrated_coeff
      def 			_lowerCAmelCase	( self	:				Dict     ,snake_case	:				LMSDiscreteSchedulerState     ,snake_case	:				int     ,snake_case	:				Tuple = ()							):
           SCREAMING_SNAKE_CASE 		=jnp.linspace(self.config.num_train_timesteps - 1     ,0     ,snake_case     ,dtype=self.dtype							)

           SCREAMING_SNAKE_CASE 		=jnp.floor(snake_case							).astype(jnp.intaa							)
           SCREAMING_SNAKE_CASE 		=jnp.ceil(snake_case							).astype(jnp.intaa							)

           SCREAMING_SNAKE_CASE 		=jnp.mod(snake_case     ,1.0							)

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

           SCREAMING_SNAKE_CASE 		=timesteps.astype(jnp.intaa							)

           # initial running values
           SCREAMING_SNAKE_CASE 		=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 			_lowerCAmelCase	( self	:				List[str]     ,snake_case	:				LMSDiscreteSchedulerState     ,snake_case	:				jnp.ndarray     ,snake_case	:				int     ,snake_case	:				jnp.ndarray     ,snake_case	:				int = 4     ,snake_case	:				bool = True     ,):
           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'							)

           SCREAMING_SNAKE_CASE 		=state.sigmas[timestep]

           # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
           if self.config.prediction_type == "epsilon":
                SCREAMING_SNAKE_CASE 		=sample - sigma * model_output
           elif self.config.prediction_type == "v_prediction":
                # * c_out + input * c_skip
                SCREAMING_SNAKE_CASE 		=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
           SCREAMING_SNAKE_CASE 		=(sample - pred_original_sample) / sigma
           SCREAMING_SNAKE_CASE 		=state.replace(derivatives=jnp.append(state.derivatives     ,snake_case							)							)
           if len(state.derivatives							) > order:
                SCREAMING_SNAKE_CASE 		=state.replace(derivatives=jnp.delete(state.derivatives     ,0							)							)

           # 3. Compute linear multistep coefficients
           SCREAMING_SNAKE_CASE 		=min(timestep + 1     ,snake_case							)
           SCREAMING_SNAKE_CASE 		=[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
           SCREAMING_SNAKE_CASE 		=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 			_lowerCAmelCase	( self	:				Tuple     ,snake_case	:				LMSDiscreteSchedulerState     ,snake_case	:				jnp.ndarray     ,snake_case	:				jnp.ndarray     ,snake_case	:				jnp.ndarray     ,):
           SCREAMING_SNAKE_CASE 		=state.sigmas[timesteps].flatten()
           SCREAMING_SNAKE_CASE 		=broadcast_to_shape_from_left(snake_case     ,noise.shape							)

           SCREAMING_SNAKE_CASE 		=original_samples + noise * sigma

           return noisy_samples


      def __len__( self	:				List[str]							):
           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) = }')

