

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 _UpperCamelCase							(							__A							,		__A      ):
			'''simple docstring'''







			lowerCamelCase__							=1
			@register_to_config
			def __init__(	self							:       Dict					,					a							:       int = 1000					,					a							:       Optional[Union[np.ndarray, List[float]]] = None		)							->				Any:

				"""simple docstring"""

				self.set_timesteps(a		)

				# standard deviation of the initial noise distribution
				SCREAMING_SNAKE_CASE      :					int    =				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.
				SCREAMING_SNAKE_CASE      :					str    =				4

				# running values
				SCREAMING_SNAKE_CASE      :					Optional[int]    =				[]
			def 							__UpperCamelCase       (	self							:       Tuple					,					a							:       int					,					a							:       Union[str, torch.device] = None		)							->				Optional[int]:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE      :					Union[str, Any]    =				num_inference_steps
				SCREAMING_SNAKE_CASE      :					Tuple    =				torch.linspace(1					,					0					,					num_inference_steps + 1		)[:-1]
				SCREAMING_SNAKE_CASE      :					Dict    =				torch.cat([steps, torch.tensor([0.0]		)]		)

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

				SCREAMING_SNAKE_CASE      :					Any    =				(1.0 - self.betas**2) ** 0.5

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

				SCREAMING_SNAKE_CASE      :					str    =				[]
			def 							__UpperCamelCase       (	self							:       int					,					a							:       torch.FloatTensor					,					a							:       int					,					a							:       torch.FloatTensor					,					a							:       bool = True					,					)							->				Union[SchedulerOutput, Tuple]:

				"""simple docstring"""

				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"		)

				SCREAMING_SNAKE_CASE      :					Dict    =				(self.timesteps == timestep).nonzero().item()
				SCREAMING_SNAKE_CASE      :					Tuple    =				timestep_index + 1

				SCREAMING_SNAKE_CASE      :					Union[str, Any]    =				sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
				self.ets.append(a		)

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

				SCREAMING_SNAKE_CASE      :					List[str]    =				self._get_prev_sample(a					,					a					,					a					,					a		)

				if not return_dict:
					return (prev_sample,)

				return SchedulerOutput(prev_sample=a		)
			def 							__UpperCamelCase       (	self							:       Optional[int]					,					a							:       torch.FloatTensor					,					*a							:       Union[str, Any]					,					**a							:       Union[str, Any]		)							->				torch.FloatTensor:

				"""simple docstring"""

				return sample
			def 							__UpperCamelCase       (	self							:       List[Any]					,					a							:       str					,					a							:       Tuple					,					a							:       Any					,					a							:       Union[str, Any]		)							->				Any:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE      :					Dict    =				self.alphas[timestep_index]
				SCREAMING_SNAKE_CASE      :					Any    =				self.betas[timestep_index]

				SCREAMING_SNAKE_CASE      :					str    =				self.alphas[prev_timestep_index]
				SCREAMING_SNAKE_CASE      :					str    =				self.betas[prev_timestep_index]

				SCREAMING_SNAKE_CASE      :					List[Any]    =				(sample - sigma * ets) / max(a					,					1e-8		)
				SCREAMING_SNAKE_CASE      :					Optional[int]    =				next_alpha * pred + ets * next_sigma

				return prev_sample






			def __len__(	self							:       Optional[int]		)							->				Union[str, Any]:

				"""simple docstring"""

				return self.config.num_train_timesteps





"""simple docstring"""


from __future__ import annotations

from collections.abc import Sequence
from typing import Literal


def 					UpperCAmelCase__       (snake_case__							:					str		,   snake_case__							:					str    ):
  """simple docstring"""

  _snake_case							:		Optional[Any]								=  list(snake_case__    )
  _snake_case							:		List[Any]								=  list(snake_case__    )
  _snake_case							:		List[Any]								=  0
  for i in range(len(snake_case__    )    ):
    if lista[i] != lista[i]:
      count += 1
      _snake_case							:		Any								=  """_"""
  if count > 1:
    return False
  else:
    return "".join(snake_case__    )


def 					UpperCAmelCase__       (snake_case__							:					list[str]    ):
  """simple docstring"""

  _snake_case							:		int								=  []
  while True:
    _snake_case							:		Union[str, Any]								=  ["""$"""] * len(snake_case__    )
    _snake_case							:		int								=  []
    for i in range(len(snake_case__    )    ):
      for j in range(i + 1		,   len(snake_case__    )    ):
        _snake_case							:		List[Any]								=  compare_string(binary[i]		,   binary[j]    )
        if k is False:
          _snake_case							:		Dict								=  """*"""
          _snake_case							:		List[Any]								=  """*"""
          temp.append("""X"""    )
    for i in range(len(snake_case__    )    ):
      if checka[i] == "$":
        pi.append(binary[i]    )
    if len(snake_case__    ) == 0:
      return pi
    _snake_case							:		Optional[int]								=  list(set(snake_case__    )    )


def 					UpperCAmelCase__       (snake_case__							:					int		,   snake_case__							:					Sequence[float]    ):
  """simple docstring"""

  _snake_case							:		Optional[int]								=  []
  for minterm in minterms:
    _snake_case							:		Any								=  """"""
    for _ in range(snake_case__    ):
      _snake_case							:		Optional[Any]								=  str(minterm % 2    ) + string
      minterm //= 2
    temp.append(snake_case__    )
  return temp


def 					UpperCAmelCase__       (snake_case__							:					str		,   snake_case__							:					str		,   snake_case__							:					int    ):
  """simple docstring"""

  _snake_case							:		Dict								=  list(snake_case__    )
  _snake_case							:		List[str]								=  list(snake_case__    )
  _snake_case							:		Tuple								=  0
  for i in range(len(snake_case__    )    ):
    if lista[i] != lista[i]:
      count_n += 1
  return count_n == count


def 					UpperCAmelCase__       (snake_case__							:					list[list[int]]		,   snake_case__							:					list[str]    ):
  """simple docstring"""

  _snake_case							:		Any								=  []
  _snake_case							:		Union[str, Any]								=  [0] * len(snake_case__    )
  for i in range(len(chart[0]    )    ):
    _snake_case							:		Tuple								=  0
    _snake_case							:		str								=  -1
    for j in range(len(snake_case__    )    ):
      if chart[j][i] == 1:
        count += 1
        _snake_case							:		Union[str, Any]								=  j
    if count == 1:
      _snake_case							:		Union[str, Any]								=  1
  for i in range(len(snake_case__    )    ):
    if select[i] == 1:
      for j in range(len(chart[0]    )    ):
        if chart[i][j] == 1:
          for k in range(len(snake_case__    )    ):
            _snake_case							:		List[Any]								=  0
      temp.append(prime_implicants[i]    )
  while True:
    _snake_case							:		Optional[int]								=  0
    _snake_case							:		str								=  -1
    _snake_case							:		Any								=  0
    for i in range(len(snake_case__    )    ):
      _snake_case							:		Union[str, Any]								=  chart[i].count(1    )
      if count_n > max_n:
        _snake_case							:		Dict								=  count_n
        _snake_case							:		Dict								=  i

    if max_n == 0:
      return temp

    temp.append(prime_implicants[rem]    )

    for i in range(len(chart[0]    )    ):
      if chart[rem][i] == 1:
        for j in range(len(snake_case__    )    ):
          _snake_case							:		Optional[Any]								=  0


def 					UpperCAmelCase__       (snake_case__							:					list[str]		,   snake_case__							:					list[str]    ):
  """simple docstring"""

  _snake_case							:		int								=  [[0 for x in range(len(snake_case__    )    )] for x in range(len(snake_case__    )    )]
  for i in range(len(snake_case__    )    ):
    _snake_case							:		Any								=  prime_implicants[i].count("""_"""    )
    for j in range(len(snake_case__    )    ):
      if is_for_table(prime_implicants[i]		,   binary[j]		,   snake_case__    ):
        _snake_case							:		Tuple								=  1

  return chart


def 					UpperCAmelCase__       ():
  """simple docstring"""

  _snake_case							:		int								=  int(input("""Enter the no. of variables\n"""    )    )
  _snake_case							:		List[str]								=  [
      float(snake_case__    )
      for x in input(
          """Enter the decimal representation of Minterms 'Spaces Separated'\n"""    ).split()
  ]
  _snake_case							:		List[str]								=  decimal_to_binary(snake_case__		,   snake_case__    )

  _snake_case							:		str								=  check(snake_case__    )
  print("""Prime Implicants are:"""    )
  print(snake_case__    )
  _snake_case							:		int								=  prime_implicant_chart(snake_case__		,   snake_case__    )

  _snake_case							:		str								=  selection(snake_case__		,   snake_case__    )
  print("""Essential Prime Implicants are:"""    )
  print(snake_case__    )


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     main()


