




'''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 			SCREAMING_SNAKE_CASE:
       snake_case_					:	CommonSchedulerState

       # setable values
       snake_case_					:	jnp.ndarray
       snake_case_					:	jnp.ndarray
       snake_case_					:	jnp.ndarray
       snake_case_					:	Optional[int]       =   None

       # running values
       snake_case_					:	Optional[jnp.ndarray]       =   None

       @classmethod
       def        snake_case__     (       cls   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__	)       ->   Optional[Any]:

           """simple docstring"""



           return cls(common=__UpperCAmelCase   ,						init_noise_sigma=__UpperCAmelCase   ,						timesteps=__UpperCAmelCase   ,						sigmas=__UpperCAmelCase	)






@dataclass
class 			SCREAMING_SNAKE_CASE(							__A	):
       snake_case_					:	LMSDiscreteSchedulerState






class 			SCREAMING_SNAKE_CASE(							__A  , __A	):
       snake_case_					:	List[str]       =   [e.name for e in FlaxKarrasDiffusionSchedulers]

       snake_case_					:	jnp.dtype

       @property
       def        snake_case__     (       self	)       ->   Union[str, Any]:

           """simple docstring"""



           return True

       @register_to_config
       def __init__(       self   ,						lowerCamelCase__ = 1000   ,						lowerCamelCase__ = 0.00_01   ,						lowerCamelCase__ = 0.02   ,						lowerCamelCase__ = "linear"   ,						lowerCamelCase__ = None   ,						lowerCamelCase__ = "epsilon"   ,						lowerCamelCase__ = jnp.floataa   ,						)       ->   str:

           """simple docstring"""



           __lowercase     							=		dtype

       def        snake_case__     (       self   ,						lowerCamelCase__ = None	)       ->   LMSDiscreteSchedulerState:

           """simple docstring"""



           if common is None:
               __lowercase     							=		CommonSchedulerState.create(self	)

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

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

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

       def        snake_case__     (       self   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__	)       ->   jnp.ndarray:

           """simple docstring"""



           ((__lowercase	)							,	)     							=		jnp.where(state.timesteps == timestep   ,						size=1	)
           __lowercase     							=		step_index[0]

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

       def        snake_case__     (       self   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__	)       ->   Optional[int]:

           """simple docstring"""



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

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

           return integrated_coeff

       def        snake_case__     (       self   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__ = ()	)       ->   LMSDiscreteSchedulerState:

           """simple docstring"""



           __lowercase     							=		jnp.linspace(self.config.num_train_timesteps - 1   ,						0   ,						__UpperCAmelCase   ,						dtype=self.dtype	)

           __lowercase     							=		jnp.floor(__UpperCAmelCase	).astype(jnp.intaa	)
           __lowercase     							=		jnp.ceil(__UpperCAmelCase	).astype(jnp.intaa	)

           __lowercase     							=		jnp.mod(__UpperCAmelCase   ,						1.0	)

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

           __lowercase     							=		timesteps.astype(jnp.intaa	)

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

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

       def        snake_case__     (       self   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__ = 4   ,						lowerCamelCase__ = True   ,						)       ->   Union[FlaxLMSSchedulerOutput, Tuple]:

           """simple docstring"""



           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"""	)

           __lowercase     							=		state.sigmas[timestep]

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

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

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

           if not return_dict:
               return (prev_sample, state)

           return FlaxLMSSchedulerOutput(prev_sample=__UpperCAmelCase   ,						state=__UpperCAmelCase	)

       def        snake_case__     (       self   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						)       ->   jnp.ndarray:

           """simple docstring"""



           __lowercase     							=		state.sigmas[timesteps].flatten()
           __lowercase     							=		broadcast_to_shape_from_left(__UpperCAmelCase   ,						noise.shape	)

           __lowercase     							=		original_samples + noise * sigma

           return noisy_samples




       def __len__(       self	)       ->   Optional[Any]:

           """simple docstring"""



           return self.config.num_train_timesteps





"""simple docstring"""




def 	UpperCAmelCase       (						UpperCamelCase__ = 100							,     UpperCamelCase__ = 100					):






							"""simple docstring"""





							return max(
							    sum(int(UpperCamelCase__					) for x in str(base**power					)					)
							    for base in range(UpperCamelCase__					)
							    for power in range(UpperCamelCase__					)					)


# Tests
if __name__ == "__main__":
				import doctest

				doctest.testmod()





