

'''simple docstring'''



from typing import Any

import numpy as np

class 			SCREAMING_SNAKE_CASE					:






      '''simple docstring'''






      def __init__(					self :		Dict     ,					snake_case :		np.ndarray     ,					snake_case :		int   ):



          """simple docstring"""





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

          _snake_case : str												=		tableau
          _snake_case					,							_snake_case : int												=		tableau.shape

          # Number of decision variables x1, x2, x3...
          _snake_case : Any												=		n_vars

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

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

          # Number of slack variables added to make inequalities into equalities
          _snake_case : Optional[Any]												=		self.n_rows - self.n_stages

          # Objectives for each stage
          _snake_case : Optional[int]												=		['max']

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

          _snake_case : List[str]												=		['']

          # Index of current pivot row and column
          _snake_case : Optional[Any]												=		None
          _snake_case : Tuple												=		None

          # Does objective row only contain (non)-negative values?
          _snake_case : Optional[Any]												=		False




      @staticmethod
      def 	__UpperCAmelCase			(					*snake_case :		int   ):



          """simple docstring"""





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

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

          # decision | slack | artificial
          _snake_case : Union[str, Any]												=		['x', 's', 'a']
          _snake_case : List[Any]												=		[]
          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 	__UpperCAmelCase			(					self :		Optional[Any]     ,					snake_case :		np.ndarray   ):



          """simple docstring"""





          _snake_case : Union[str, Any]												=		self.objectives[-1]

          # Find entries of highest magnitude in objective rows
          _snake_case : List[str]												=		(objective == 'min') - (objective == 'max')
          _snake_case : str												=		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:
              _snake_case : 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
          _snake_case : List[str]												=		slice(self.n_stages     ,					self.n_rows   )

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

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

          # Array filled with nans
          _snake_case : Union[str, Any]												=		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
          _snake_case : Tuple												=		np.divide(snake_case     ,					snake_case     ,					out=snake_case     ,					where=divisor > 0   )

          # Arg of minimum quotient excluding the nan values. n_stages is added
          # to compensate for earlier exclusion of objective columns
          _snake_case : Tuple												=		np.nanargmin(snake_case   ) + self.n_stages
          return row_idx, col_idx




      def 	__UpperCAmelCase			(					self :		Tuple     ,					snake_case :		np.ndarray     ,					snake_case :		int     ,					snake_case :		int   ):



          """simple docstring"""





          _snake_case : Optional[Any]												=		tableau[row_idx].copy()

          _snake_case : 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
          _snake_case : int												=		piv_row
          return tableau




      def 	__UpperCAmelCase			(					self :		Dict     ,					snake_case :		np.ndarray   ):



          """simple docstring"""





          self.objectives.pop()

          if not self.objectives:
              return tableau

          # Slice containing ids for artificial columns
          _snake_case : Tuple												=		slice(-self.n_art_vars - 1     ,					-1   )

          # Delete the artificial variable columns
          _snake_case : Tuple												=		np.delete(snake_case     ,					snake_case     ,					axis=1   )

          # Delete the objective row of the first stage
          _snake_case : str												=		np.delete(snake_case     ,					0     ,					axis=0   )

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




      def 	__UpperCAmelCase			(					self :		Tuple   ):



          """simple docstring"""





          for _ in range(100   ):
              # Completion of each stage removes an objective. If both stages
              # are complete, then no objectives are left
              if not self.objectives:
                  _snake_case : 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   )

              _snake_case					,							_snake_case : int												=		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
                  _snake_case : str												=		self.change_stage(self.tableau   )
              else:
                  _snake_case : Optional[Any]												=		self.pivot(self.tableau     ,					snake_case     ,					snake_case   )
          return {}




      def 	__UpperCAmelCase			(					self :		int     ,					snake_case :		np.ndarray     ,					snake_case :		list[str]   ):



          """simple docstring"""





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

          for i in range(self.n_vars   ):
              # Gives ids of nonzero entries in the ith column
              _snake_case : Optional[int]												=		np.nonzero(tableau[:, i]   )
              _snake_case : str												=		len(nonzero[0]   )

              # First entry in the nonzero ids
              _snake_case : str												=		nonzero[0][0]
              _snake_case : int												=		tableau[nonzero_rowidx, i]

              # If there is only one nonzero value in column, which is one
              if n_nonzero == nonzero_val == 1:
                  _snake_case : str												=		tableau[nonzero_rowidx, -1]
                  _snake_case : List[str]												=		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(snake_case     ,					0   )
          return output_dict


if __name__ == "__main__":
   import doctest

   doctest.testmod()






'''simple docstring'''



from typing import List, Optional, Tuple, Union

from . import logging
from .import_utils import is_torch_available, is_torch_version


if is_torch_available():
   import torch

SCREAMING_SNAKE_CASE_    =   logging.get_logger(__name__)  # pylint: disable=invalid-name

try:
   from torch._dynamo import allow_in_graph as maybe_allow_in_graph
except (ImportError, ModuleNotFoundError):

   def   lowerCamelCase__       (      cls)		->    Optional[Any]:



       """simple docstring"""







       return cls

def   lowerCamelCase__       (      a__			,      a__ = None			,      a__ = None			,      a__ = None			,      a__ = None			,      )		->    Dict:



    """simple docstring"""







    _snake_case : Optional[Any]												=		device
    _snake_case : Any												=		shape[0]

    _snake_case : str												=		layout or torch.strided
    _snake_case : str												=		device or torch.device('cpu')

    if generator is not None:
        _snake_case : Any												=		generator.device.type if not isinstance(a__			,      a__) else generator[0].device.type
        if gen_device_type != device.type and gen_device_type == "cpu":
            _snake_case : Optional[Any]												=		'cpu'
            if device != "mps":
                logger.info(
                    F"""The passed generator was created on 'cpu' even though a tensor on {device} was expected."""
                    F""" Tensors will be created on 'cpu' and then moved to {device}. Note that one can probably"""
                    F""" slighly speed up this function by passing a generator that was created on the {device} device.""")
        elif gen_device_type != device.type and gen_device_type == "cuda":
            raise ValueError(F"""Cannot generate a {device} tensor from a generator of type {gen_device_type}.""")

    if isinstance(a__			,      a__):
        _snake_case : Any												=		(1,) + shape[1:]
        _snake_case : int												=		[
            torch.randn(a__			,      generator=generator[i]			,      device=a__			,      dtype=a__			,      layout=a__)
            for i in range(a__)
        ]
        _snake_case : Optional[int]												=		torch.cat(a__			,      dim=0).to(a__)
    else:
        _snake_case : Optional[Any]												=		torch.randn(a__			,      generator=a__			,      device=a__			,      dtype=a__			,      layout=a__).to(a__)

    return latents




def   lowerCamelCase__       (      a__)		->    Optional[Any]:



    """simple docstring"""







    if is_torch_version('<'			,      '2.0.0') or not hasattr(a__			,      '_dynamo'):
        return False
    return isinstance(a__			,      torch._dynamo.eval_frame.OptimizedModule)



