



'''simple docstring'''

from __future__ import annotations

import time
from collections.abc import Sequence
from random import randint

from matplotlib import pyplot as plt



def      __lowerCamelCase     (      lowerCAmelCase_						,			lowerCAmelCase_						,			lowerCAmelCase_  )			->      tuple[int | None, int | None, float]:
		if not arr:
				return None, None, 0
		if low == high:
				return low, high, arr[low]

		_a     :      Any        =							(low + high) // 2
		_a       ,					_a       ,					_a     :      Tuple        =							max_subarray(lowerCAmelCase_						,			lowerCAmelCase_						,			lowerCAmelCase_  )
		_a       ,					_a       ,					_a     :      List[Any]        =							max_subarray(lowerCAmelCase_						,			mid + 1						,			lowerCAmelCase_  )
		_a       ,					_a       ,					_a     :      Optional[int]        =							max_cross_sum(lowerCAmelCase_						,			lowerCAmelCase_						,			lowerCAmelCase_						,			lowerCAmelCase_  )
		if left_sum >= right_sum and left_sum >= cross_sum:
				return left_low, left_high, left_sum
		elif right_sum >= left_sum and right_sum >= cross_sum:
				return right_low, right_high, right_sum
		return cross_left, cross_right, cross_sum



def      __lowerCamelCase     (      lowerCAmelCase_						,			lowerCAmelCase_						,			lowerCAmelCase_						,			lowerCAmelCase_  )			->      tuple[int, int, float]:
		_a       ,					_a     :      List[Any]        =							float('-inf'  ), -1
		_a       ,					_a     :      List[str]        =							float('-inf'  ), -1

		_a     :      int | float        =							0
		for i in range(lowerCAmelCase_						,			low - 1						,			-1  ):
				summ += arr[i]
				if summ > left_sum:
						_a     :      int        =							summ
						_a     :      List[str]        =							i

		_a     :      List[str]        =							0
		for i in range(mid + 1						,			high + 1  ):
				summ += arr[i]
				if summ > right_sum:
						_a     :      List[Any]        =							summ
						_a     :      Optional[Any]        =							i

		return max_left, max_right, (left_sum + right_sum)



def      __lowerCamelCase     (      lowerCAmelCase_  )			->      float:
		_a     :      List[Any]        =							[randint(1						,			lowerCAmelCase_  ) for _ in range(lowerCAmelCase_  )]
		_a     :      str        =							time.time()
		max_subarray(lowerCAmelCase_						,			0						,			input_size - 1  )
		_a     :      Optional[Any]        =							time.time()
		return end - start



def      __lowerCamelCase     (      )			->      None:
		_a     :      Tuple        =							[10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
		_a     :      Union[str, Any]        =							[time_max_subarray(lowerCAmelCase_  ) for input_size in input_sizes]
		print('No of Inputs\t\tTime Taken'  )
		for input_size, runtime in zip(lowerCAmelCase_						,			lowerCAmelCase_  ):
				print(lowerCAmelCase_						,			'\t\t'						,			lowerCAmelCase_  )
		plt.plot(lowerCAmelCase_						,			lowerCAmelCase_  )
		plt.xlabel('Number of Inputs'  )
		plt.ylabel('Time taken in seconds'  )
		plt.show()


if __name__ == "__main__":
							from doctest import testmod

							testmod()





'''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_	(snake_case__							, snake_case__    ):
      '''simple docstring'''

      __UpperCamelCase:  Optional[Any]						=						1




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

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

             # running values
             _UpperCAmelCase     :  Dict							      =    []




      def      _A	(       self						:				Optional[int]						,					A						:				int						,					A						:				Union[str, torch.device] = None       ):
             _UpperCAmelCase     :  int							      =    num_inference_steps
             _UpperCAmelCase     :  Union[str, Any]							      =    torch.linspace(1						,					0						,					num_inference_steps + 1       )[:-1]
             _UpperCAmelCase     :  Any							      =    torch.cat([steps, torch.tensor([0.0]       )]       )

             if self.config.trained_betas is not None:
                    _UpperCAmelCase     :  str							      =    torch.tensor(self.config.trained_betas						,					dtype=torch.floataa       )
             else:
                    _UpperCAmelCase     :  Dict							      =    torch.sin(steps * math.pi / 2       ) ** 2

             _UpperCAmelCase     :  List[Any]							      =    (1.0 - self.betas**2) ** 0.5

             _UpperCAmelCase     :  List[str]							      =    (torch.atana(self.betas						,					self.alphas       ) / math.pi * 2)[:-1]
             _UpperCAmelCase     :  Dict							      =    timesteps.to(A       )

             _UpperCAmelCase     :  Dict							      =    []




      def      _A	(       self						:				Optional[int]						,					A						:				torch.FloatTensor						,					A						:				int						,					A						:				torch.FloatTensor						,					A						:				bool = True						,					):
             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"       )

             _UpperCAmelCase     :  Tuple							      =    (self.timesteps == timestep).nonzero().item()
             _UpperCAmelCase     :  Optional[Any]							      =    timestep_index + 1

             _UpperCAmelCase     :  int							      =    sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
             self.ets.append(A       )

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

             _UpperCAmelCase     :  Union[str, Any]							      =    self._get_prev_sample(A						,					A						,					A						,					A       )

             if not return_dict:
                    return (prev_sample,)

             return SchedulerOutput(prev_sample=A       )




      def      _A	(       self						:				Union[str, Any]						,					A						:				torch.FloatTensor						,					*A						:				Union[str, Any]						,					**A						:				Dict       ):
             return sample




      def      _A	(       self						:				Optional[Any]						,					A						:				Optional[int]						,					A						:				int						,					A						:				Optional[Any]						,					A						:				List[str]       ):
             _UpperCAmelCase     :  List[str]							      =    self.alphas[timestep_index]
             _UpperCAmelCase     :  List[Any]							      =    self.betas[timestep_index]

             _UpperCAmelCase     :  Optional[Any]							      =    self.alphas[prev_timestep_index]
             _UpperCAmelCase     :  Dict							      =    self.betas[prev_timestep_index]

             _UpperCAmelCase     :  Tuple							      =    (sample - sigma * ets) / max(A						,					1E-8       )
             _UpperCAmelCase     :  List[str]							      =    next_alpha * pred + ets * next_sigma

             return prev_sample





      def __len__(       self						:				Union[str, Any]       ):
             return self.config.num_train_timesteps

