






"""simple docstring"""


from typing import Any

import numpy as np






class 						snake_case  :





    def __init__(							self	:					Tuple				,		A	:					np.ndarray				,		A	:					int			):


      '''simple docstring'''




      if np.any(tableau[:, -1]				,		where=tableau[:, -1] < 0			):
        raise ValueError('RHS must be > 0'			)

      a     :			Dict				=   tableau
      a,     a     :			List[str]				=   tableau.shape

      # Number of decision variables x1, x2, x3...
      a     :			int				=   n_vars

      # Number of artificial variables to be minimised
      a     :			int				=   len(np.where(tableau[self.n_vars : -1] == -1			)[0]			)

      # 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
      a     :			List[Any]				=   (self.n_art_vars > 0) + 1

      # Number of slack variables added to make inequalities into equalities
      a     :			Tuple				=   self.n_rows - self.n_stages

      # Objectives for each stage
      a     :			Union[str, Any]				=   ['max']

      # In two stage simplex, first minimise then maximise
      if self.n_art_vars:
        self.objectives.append('min'			)

      a     :			Optional[int]				=   ['']

      # Index of current pivot row and column
      a     :			Optional[Any]				=   None
      a     :			List[Any]				=   None

      # Does objective row only contain (non)-negative values?
      a     :			Tuple				=   False





    @staticmethod
    def 				lowerCamelCase__      (							*A	:					int			):


      '''simple docstring'''




      if len(A			) != 3:
        raise ValueError('Must provide n_vars, n_slack, and n_art_vars'			)

      if not all(x >= 0 and isinstance(A				,		A			) for x in args			):
        raise ValueError('All arguments must be non-negative integers'			)

      # decision | slack | artificial
      a     :			Optional[Any]				=   ['x', 's', 'a']
      a     :			List[str]				=   []
      for i in range(3			):
        for j in range(args[i]			):
          titles.append(string_starts[i] + str(j + 1			)			)
      titles.append('RHS'			)
      return titles





    def 				lowerCamelCase__      (							self	:					Any				,		A	:					np.ndarray			):


      '''simple docstring'''




      a     :			Optional[Any]				=   self.objectives[-1]

      # Find entries of highest magnitude in objective rows
      a     :			List[Any]				=   (objective == 'min') - (objective == 'max')
      a     :			Tuple				=   np.argmax(sign * tableau[0, : self.n_vars]			)

      # Choice is only valid if below 0 for maximise, and above for minimise
      if sign * self.tableau[0, col_idx] <= 0:
        a     :			Optional[Any]				=   True
        return 0, 0

      # Pivot row is chosen as having the lowest quotient when elements of
      # the pivot column divide the right-hand side

      # Slice excluding the objective rows
      a     :			Any				=   slice(self.n_stages				,		self.n_rows			)

      # RHS
      a     :			Any				=   tableau[s, -1]

      # Elements of pivot column within slice
      a     :			Tuple				=   tableau[s, col_idx]

      # Array filled with nans
      a     :			Dict				=   np.full(self.n_rows - self.n_stages				,		np.nan			)

      # If element in pivot column is greater than zeron_stages, return
      # quotient or nan otherwise
      a     :			List[Any]				=   np.divide(A				,		A				,		out=A				,		where=divisor > 0			)

      # Arg of minimum quotient excluding the nan values. n_stages is added
      # to compensate for earlier exclusion of objective columns
      a     :			Union[str, Any]				=   np.nanargmin(A			) + self.n_stages
      return row_idx, col_idx





    def 				lowerCamelCase__      (							self	:					List[Any]				,		A	:					np.ndarray				,		A	:					int				,		A	:					int			):


      '''simple docstring'''




      a     :			List[str]				=   tableau[row_idx].copy()

      a     :			Any				=   piv_row[col_idx]

      # Entry becomes 1
      piv_row *= 1 / piv_val

      # Variable in pivot column becomes basic, ie the only non-zero entry
      for idx, coeff in enumerate(tableau[:, col_idx]			):
        tableau[idx] += -coeff * piv_row
      a     :			List[str]				=   piv_row
      return tableau





    def 				lowerCamelCase__      (							self	:					Optional[int]				,		A	:					np.ndarray			):


      '''simple docstring'''




      self.objectives.pop()

      if not self.objectives:
        return tableau

      # Slice containing ids for artificial columns
      a     :			Union[str, Any]				=   slice(-self.n_art_vars - 1				,		-1			)

      # Delete the artificial variable columns
      a     :			Dict				=   np.delete(A				,		A				,		axis=1			)

      # Delete the objective row of the first stage
      a     :			List[str]				=   np.delete(A				,		0				,		axis=0			)

      a     :			Optional[Any]				=   1
      self.n_rows -= 1
      a     :			List[Any]				=   0
      a     :			Any				=   False
      return tableau





    def 				lowerCamelCase__      (							self	:					Union[str, Any]			):


      '''simple docstring'''




      for _ in range(1_0_0			):
        # Completion of each stage removes an objective. If both stages
        # are complete, then no objectives are left
        if not self.objectives:
          a     :			List[str]				=   self.generate_col_titles(
              self.n_vars				,		self.n_slack				,		self.n_art_vars			)

          # Find the values of each variable at optimal solution
          return self.interpret_tableau(self.tableau				,		self.col_titles			)

        a,     a     :			str				=   self.find_pivot(self.tableau			)

        # If there are no more negative values in objective row
        if self.stop_iter:
          # Delete artificial variable columns and rows. Update attributes
          a     :			int				=   self.change_stage(self.tableau			)
        else:
          a     :			Dict				=   self.pivot(self.tableau				,		A				,		A			)
      return {}





    def 				lowerCamelCase__      (							self	:					Optional[Any]				,		A	:					np.ndarray				,		A	:					list[str]			):


      '''simple docstring'''




      a     :			Optional[Any]				=   {'P': abs(tableau[0, -1]			)}

      for i in range(self.n_vars			):
        # Gives ids of nonzero entries in the ith column
        a     :			Tuple				=   np.nonzero(tableau[:, i]			)
        a     :			Dict				=   len(nonzero[0]			)

        # First entry in the nonzero ids
        a     :			List[Any]				=   nonzero[0][0]
        a     :			List[Any]				=   tableau[nonzero_rowidx, i]

        # If there is only one nonzero value in column, which is one
        if n_nonzero == nonzero_val == 1:
          a     :			Union[str, Any]				=   tableau[nonzero_rowidx, -1]
          a     :			List[Any]				=   rhs_val

        # Check for basic variables
      for title in col_titles:
        # Don't add RHS or slack variables to output dict
        if title[0] not in "R-s-a":
          output_dict.setdefault(A				,		0			)
      return output_dict


if __name__ == "__main__":
   import doctest

   doctest.testmod()








# limitations under the License.


from typing import Optional, Tuple, Union

import torch

from diffusers.pipeline_utils import DiffusionPipeline, ImagePipelineOutput

class   A__							(						UpperCamelCase__     ):




						def __init__(				self    :					Any ,			_a    :					Optional[Any] ,			_a    :					List[str]     )							->   Tuple:


										"""simple docstring"""





										super().__init__()
										self.register_modules(unet=_a ,			scheduler=_a     )




						@torch.no_grad()
						def __call__(				self    :					Any ,			_a    :					int = 1 ,			_a    :					Optional[torch.Generator] = None ,			_a    :					int = 50 ,			_a    :					Optional[str] = "pil" ,			_a    :					bool = True ,			**_a    :					Dict ,			)							->   Union[ImagePipelineOutput, Tuple]:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE	     =torch.randn(
										    (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size) ,			generator=_a ,			)
										_SCREAMING_SNAKE_CASE	     =image.to(self.device     )

										# set step values
										self.scheduler.set_timesteps(_a     )

										for t in self.progress_bar(self.scheduler.timesteps     ):
														# 1. predict noise model_output
														_SCREAMING_SNAKE_CASE	     =self.unet(_a ,			_a     ).sample

														# 2. predict previous mean of image x_t-1 and add variance depending on eta
														# eta corresponds to η in paper and should be between [0, 1]
														# do x_t -> x_t-1
														_SCREAMING_SNAKE_CASE	     =self.scheduler.step(_a ,			_a ,			_a     ).prev_sample

										_SCREAMING_SNAKE_CASE	     =(image / 2 + 0.5).clamp(0 ,			1     )
										_SCREAMING_SNAKE_CASE	     =image.cpu().permute(0 ,			2 ,			3 ,			1     ).numpy()
										if output_type == "pil":
														_SCREAMING_SNAKE_CASE	     =self.numpy_to_pil(_a     )

										if not return_dict:
														return (image,), "This is a local test"

										return ImagePipelineOutput(images=_a     ), "This is a local test"