





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 A_					(			_lowerCamelCase ,      _lowerCamelCase   ):
   lowerCAmelCase__        = 1




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

         # standard deviation of the initial noise distribution
         __A          =				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.
         __A          =				4

         # running values
         __A          =				[]




   def _lowerCAmelCase      (self	:str    ,   _UpperCamelCase	:int    ,   _UpperCamelCase	:Union[str, torch.device] = None )->					Any:
         __A          =				num_inference_steps
         __A          =				torch.linspace(1    ,   0    ,   num_inference_steps + 1 )[:-1]
         __A          =				torch.cat([steps, torch.tensor([0.0] )] )

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

         __A          =				(1.0 - self.betas**2) ** 0.5

         __A          =				(torch.atana(self.betas    ,   self.alphas ) / math.pi * 2)[:-1]
         __A          =				timesteps.to(_UpperCamelCase )

         __A          =				[]




   def _lowerCAmelCase      (self	:int    ,   _UpperCamelCase	:torch.FloatTensor    ,   _UpperCamelCase	:int    ,   _UpperCamelCase	:torch.FloatTensor    ,   _UpperCamelCase	: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''' )

         __A          =				(self.timesteps == timestep).nonzero().item()
         __A          =				timestep_index + 1

         __A          =				sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
         self.ets.append(_UpperCamelCase )

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

         __A          =				self._get_prev_sample(_UpperCamelCase    ,   _UpperCamelCase    ,   _UpperCamelCase    ,   _UpperCamelCase )

         if not return_dict:
               return (prev_sample,)

         return SchedulerOutput(prev_sample=_UpperCamelCase )




   def _lowerCAmelCase      (self	:str    ,   _UpperCamelCase	:torch.FloatTensor    ,   *_UpperCamelCase	:Optional[Any]    ,   **_UpperCamelCase	:Optional[int] )->					torch.FloatTensor:
         return sample




   def _lowerCAmelCase      (self	:Tuple    ,   _UpperCamelCase	:Tuple    ,   _UpperCamelCase	:List[str]    ,   _UpperCamelCase	:Union[str, Any]    ,   _UpperCamelCase	:Any )->					Any:
         __A          =				self.alphas[timestep_index]
         __A          =				self.betas[timestep_index]

         __A          =				self.alphas[prev_timestep_index]
         __A          =				self.betas[prev_timestep_index]

         __A          =				(sample - sigma * ets) / max(_UpperCamelCase    ,   1e-8 )
         __A          =				next_alpha * pred + ets * next_sigma

         return prev_sample






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












import numpy as np
from PIL import Image



def _a				(	lowerCamelCase:   np.ndarray					,				lowerCamelCase:   int					,				lowerCamelCase:   int )	->						np.ndarray:







      '''simple docstring'''






      __A          =				np.array(lowerCamelCase )
      if arr.shape[0] != arr.shape[1]:
            raise ValueError('''The input array is not a square matrix''' )
      __A          =				0
      __A          =				0
      __A          =				0
      __A          =				0

      # compute the shape of the output matrix
      __A          =				(arr.shape[0] - size) // stride + 1
      # initialize the output matrix with zeros of shape maxpool_shape
      __A          =				np.zeros((maxpool_shape, maxpool_shape) )

      while i < arr.shape[0]:
            if i + size > arr.shape[0]:
                  # if the end of the matrix is reached, break
                  break
            while j < arr.shape[1]:
                  # if the end of the matrix is reached, break
                  if j + size > arr.shape[1]:
                        break
                  # compute the maximum of the pooling matrix
                  __A          =				np.max(arr[i : i + size, j : j + size] )
                  # shift the pooling matrix by stride of column pixels
                  j += stride
                  mat_j += 1

            # shift the pooling matrix by stride of row pixels
            i += stride
            mat_i += 1

            # reset the column index to 0
            __A          =				0
            __A          =				0

      return updated_arr



def _a				(	lowerCamelCase:   np.ndarray					,				lowerCamelCase:   int					,				lowerCamelCase:   int )	->						np.ndarray:







      '''simple docstring'''






      __A          =				np.array(lowerCamelCase )
      if arr.shape[0] != arr.shape[1]:
            raise ValueError('''The input array is not a square matrix''' )
      __A          =				0
      __A          =				0
      __A          =				0
      __A          =				0

      # compute the shape of the output matrix
      __A          =				(arr.shape[0] - size) // stride + 1
      # initialize the output matrix with zeros of shape avgpool_shape
      __A          =				np.zeros((avgpool_shape, avgpool_shape) )

      while i < arr.shape[0]:
            # if the end of the matrix is reached, break
            if i + size > arr.shape[0]:
                  break
            while j < arr.shape[1]:
                  # if the end of the matrix is reached, break
                  if j + size > arr.shape[1]:
                        break
                  # compute the average of the pooling matrix
                  __A          =				int(np.average(arr[i : i + size, j : j + size] ) )
                  # shift the pooling matrix by stride of column pixels
                  j += stride
                  mat_j += 1

            # shift the pooling matrix by stride of row pixels
            i += stride
            mat_i += 1
            # reset the column index to 0
            __A          =				0
            __A          =				0

      return updated_arr


# Main Function
if __name__ == "__main__":
       from doctest import testmod

       testmod(name='avgpooling', verbose=True)

       # Loading the image
       snake_case__					:							Optional[Any]													=     Image.open('path_to_image')

       # Converting the image to numpy array and maxpooling, displaying the result
       # Ensure that the image is a square matrix

       Image.fromarray(maxpooling(np.array(image), size=3, stride=2)).show()

       # Converting the image to numpy array and averagepooling, displaying the result
       # Ensure that the image is a square matrix

       Image.fromarray(avgpooling(np.array(image), size=3, stride=2)).show()





