

"""simple docstring"""



from __future__ import annotations

import math
import random





def 			_snake_case  (     UpperCAmelCase_	:       int       , UpperCAmelCase_	:       int       , UpperCAmelCase_	:       str      ):
     A__				      =	d * e - 1
     A__				      =	0
     A__				      =	0
     while p == 0:
          A__				      =	random.randint(2       , n - 1      )
          A__				      =	k
          while True:
               if t % 2 == 0:
                    A__				      =	t // 2
                    A__				      =	(g**t) % n
                    A__				      =	math.gcd(x - 1       , lowercase_      )
                    if x > 1 and y > 1:
                         A__				      =	y
                         A__				      =	n // y
                         break  # find the correct factors
               else:
                    break  # t is not divisible by 2, break and choose another g
     return sorted([p, q]      )


if __name__ == "__main__":
 import doctest

 doctest.testmod()









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							:
      lowerCamelCase_      : CommonSchedulerState

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

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







      @classmethod
      def       lowerCAmelCase_       (	cls				,    lowerCamelCase				,    lowerCamelCase				,    lowerCamelCase				,    lowerCamelCase  )		->			Union[str, Any]:
        return cls(common=lowerCamelCase				,    init_noise_sigma=lowerCamelCase				,    timesteps=lowerCamelCase				,    sigmas=lowerCamelCase  )







@dataclass
class 					__lowerCamelCase							(      __snake_case      ):
      lowerCamelCase_      : LMSDiscreteSchedulerState







class 					__lowerCamelCase							(      __snake_case    ,				__snake_case      ):
      lowerCamelCase_      : str  			=   [e.name for e in FlaxKarrasDiffusionSchedulers]

      lowerCamelCase_      : jnp.dtype







      @property
      def       lowerCAmelCase_       (	self  )		->			List[str]:
        return True







      @register_to_config
      def __init__(	self				,    lowerCamelCase = 1000				,    lowerCamelCase = 0.0001				,    lowerCamelCase = 0.02				,    lowerCamelCase = "linear"				,    lowerCamelCase = None				,    lowerCamelCase = "epsilon"				,    lowerCamelCase = jnp.floataa				,    )		->			Optional[Any]:
        snake_case_					= dtype







      def       lowerCAmelCase_       (	self				,    lowerCamelCase = None  )		->			LMSDiscreteSchedulerState:
        if common is None:
          snake_case_					= CommonSchedulerState.create(self  )

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

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

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







      def       lowerCAmelCase_       (	self				,    lowerCamelCase				,    lowerCamelCase				,    lowerCamelCase  )		->			jnp.ndarray:
        ((snake_case_)		,							)					= jnp.where(state.timesteps == timestep				,    size=1  )
        snake_case_					= step_index[0]

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







      def       lowerCAmelCase_       (	self				,    lowerCamelCase				,    lowerCamelCase				,    lowerCamelCase				,    lowerCamelCase  )		->			Any:

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

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

        return integrated_coeff







      def       lowerCAmelCase_       (	self				,    lowerCamelCase				,    lowerCamelCase				,    lowerCamelCase = ()  )		->			LMSDiscreteSchedulerState:
        snake_case_					= jnp.linspace(self.config.num_train_timesteps - 1				,    0				,    lowerCamelCase				,    dtype=self.dtype  )

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

        snake_case_					= jnp.mod(lowerCamelCase				,    1.0  )

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

        snake_case_					= timesteps.astype(jnp.intaa  )

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

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







      def       lowerCAmelCase_       (	self				,    lowerCamelCase				,    lowerCamelCase				,    lowerCamelCase				,    lowerCamelCase				,    lowerCamelCase = 4				,    lowerCamelCase = True				,    )		->			Union[FlaxLMSSchedulerOutput, Tuple]:
        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"""  )

        snake_case_					= state.sigmas[timestep]

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

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

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

        if not return_dict:
          return (prev_sample, state)

        return FlaxLMSSchedulerOutput(prev_sample=lowerCamelCase				,    state=lowerCamelCase  )







      def       lowerCAmelCase_       (	self				,    lowerCamelCase				,    lowerCamelCase				,    lowerCamelCase				,    lowerCamelCase				,    )		->			jnp.ndarray:
        snake_case_					= state.sigmas[timesteps].flatten()
        snake_case_					= broadcast_to_shape_from_left(lowerCamelCase				,    noise.shape  )

        snake_case_					= original_samples + noise * sigma

        return noisy_samples







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