



'''simple docstring'''





import math
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import SchedulerMixin, SchedulerOutput






class    lowerCamelCase_       (							SCREAMING_SNAKE_CASE_  ,  SCREAMING_SNAKE_CASE_	):
  """simple docstring"""




  a_				   =1




  @register_to_config
  def __init__(					self :      Union[str, Any]     ,      _a :      int = 1000     ,      _a :      Optional[Union[np.ndarray, List[float]]] = None  )   ->   Optional[int]:
    # set `betas`, `alphas`, `timesteps`
    self.set_timesteps(_a  )

    # standard deviation of the initial noise distribution
    __lowerCamelCase			:			Union[str, Any]       			=					1.0

    # For now we only support F-PNDM, i.e. the runge-kutta method
    # For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf
    # mainly at formula (9), (12), (13) and the Algorithm 2.
    __lowerCamelCase			:			Optional[int]       			=					4

    # running values
    __lowerCamelCase			:			int       			=					[]




  def 		_lowercase	(					self :      List[Any]     ,      _a :      int     ,      _a :      Union[str, torch.device] = None  )   ->   str:
    __lowerCamelCase			:			Any       			=					num_inference_steps
    __lowerCamelCase			:			Dict       			=					torch.linspace(1     ,      0     ,      num_inference_steps + 1  )[:-1]
    __lowerCamelCase			:			Tuple       			=					torch.cat([steps, torch.tensor([0.0]  )]  )

    if self.config.trained_betas is not None:
      __lowerCamelCase			:			Union[str, Any]       			=					torch.tensor(self.config.trained_betas     ,      dtype=torch.floataa  )
    else:
      __lowerCamelCase			:			List[str]       			=					torch.sin(steps * math.pi / 2  ) ** 2

    __lowerCamelCase			:			str       			=					(1.0 - self.betas**2) ** 0.5

    __lowerCamelCase			:			Optional[Any]       			=					(torch.atana(self.betas     ,      self.alphas  ) / math.pi * 2)[:-1]
    __lowerCamelCase			:			List[Any]       			=					timesteps.to(_a  )

    __lowerCamelCase			:			str       			=					[]




  def 		_lowercase	(					self :      Optional[Any]     ,      _a :      torch.FloatTensor     ,      _a :      int     ,      _a :      torch.FloatTensor     ,      _a :      bool = True     ,      )   ->   Union[SchedulerOutput, Tuple]:
    if self.num_inference_steps is None:
      raise ValueError(
          'Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'  )

    __lowerCamelCase			:			List[str]       			=					(self.timesteps == timestep).nonzero().item()
    __lowerCamelCase			:			Union[str, Any]       			=					timestep_index + 1

    __lowerCamelCase			:			Any       			=					sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
    self.ets.append(_a  )

    if len(self.ets  ) == 1:
      __lowerCamelCase			:			int       			=					self.ets[-1]
    elif len(self.ets  ) == 2:
      __lowerCamelCase			:			Tuple       			=					(3 * self.ets[-1] - self.ets[-2]) / 2
    elif len(self.ets  ) == 3:
      __lowerCamelCase			:			List[str]       			=					(23 * self.ets[-1] - 16 * self.ets[-2] + 5 * self.ets[-3]) / 12
    else:
      __lowerCamelCase			:			Optional[Any]       			=					(1 / 24) * (55 * self.ets[-1] - 59 * self.ets[-2] + 37 * self.ets[-3] - 9 * self.ets[-4])

    __lowerCamelCase			:			Optional[Any]       			=					self._get_prev_sample(_a     ,      _a     ,      _a     ,      _a  )

    if not return_dict:
      return (prev_sample,)

    return SchedulerOutput(prev_sample=_a  )




  def 		_lowercase	(					self :      int     ,      _a :      torch.FloatTensor     ,      *_a :      Union[str, Any]     ,      **_a :      Tuple  )   ->   torch.FloatTensor:
    return sample




  def 		_lowercase	(					self :      Union[str, Any]     ,      _a :      List[str]     ,      _a :      Dict     ,      _a :      List[str]     ,      _a :      Optional[Any]  )   ->   int:
    __lowerCamelCase			:			Optional[int]       			=					self.alphas[timestep_index]
    __lowerCamelCase			:			Dict       			=					self.betas[timestep_index]

    __lowerCamelCase			:			Optional[int]       			=					self.alphas[prev_timestep_index]
    __lowerCamelCase			:			Optional[Any]       			=					self.betas[prev_timestep_index]

    __lowerCamelCase			:			Dict       			=					(sample - sigma * ets) / max(_a     ,      1e-8  )
    __lowerCamelCase			:			Dict       			=					next_alpha * pred + ets * next_sigma

    return prev_sample




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











'''simple docstring'''





def 			a_	(				_lowerCAmelCase			,_lowerCAmelCase			) -> tuple[float, float]:

  # Check if the input is valid
  if not len(_lowerCAmelCase			) == len(_lowerCAmelCase			) == 3:
    raise ValueError('Please enter a valid equation.'			)
  if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
    raise ValueError('Both a & b of two equations can\'t be zero.'			)

  # Extract the coefficients
  __lowerCamelCase			,__lowerCamelCase			,__lowerCamelCase			:			Union[str, Any]       			=					equationa
  __lowerCamelCase			,__lowerCamelCase			,__lowerCamelCase			:			Any       			=					equationa

  # Calculate the determinants of the matrices
  __lowerCamelCase			:			Union[str, Any]       			=					aa * ba - aa * ba
  __lowerCamelCase			:			Dict       			=					ca * ba - ca * ba
  __lowerCamelCase			:			List[str]       			=					aa * ca - aa * ca

  # Check if the system of linear equations has a solution (using Cramer's rule)
  if determinant == 0:
    if determinant_x == determinant_y == 0:
      raise ValueError('Infinite solutions. (Consistent system)'			)
    else:
      raise ValueError('No solution. (Inconsistent system)'			)
  else:
    if determinant_x == determinant_y == 0:
      # Trivial solution (Inconsistent system)
      return (0.0, 0.0)
    else:
      __lowerCamelCase			:			Tuple       			=					determinant_x / determinant
      __lowerCamelCase			:			Union[str, Any]       			=					determinant_y / determinant
      # Non-Trivial Solution (Consistent system)
      return (x, y)






