
from typing import Any

import numpy as np






class UpperCAmelCase     :





   '''simple docstring'''


   def __init__(      self  :							Any    ,    lowerCAmelCase_  :							Union[str, Any]    ,    lowerCAmelCase_  :							int  ):

      """simple docstring"""
      # Check if RHS is negative
      if np.any(tableau[:, -1]    ,    where=tableau[:, -1] < 0  ):
         raise ValueError('''RHS must be > 0'''  )

      _A:						Tuple	    = tableau
      _A:						Tuple	    = tableau.shape

      # Number of decision variables x1, x2, x3...
      _A:						Optional[int]	    = n_vars

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

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

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

      # Objectives for each stage
      _A:						str	    = ['''max''']

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

      _A:						Dict	    = ['''''']

      # Index of current pivot row and column
      _A:						str	    = None
      _A:						Optional[Any]	    = None

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


   @staticmethod
   def 				__magic_name__       (      *lowerCAmelCase_  :							Dict  ):

      """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
      _A:						Any	    = ['''x''', '''s''', '''a''']
      _A:						int	    = []
      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 				__magic_name__       (      self  :							Tuple    ,    lowerCAmelCase_  :							List[str]  ):

      """simple docstring"""
      _A:						Optional[int]	    = self.objectives[-1]

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

      # RHS
      _A:						Dict	    = tableau[s, -1]

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

      # Array filled with nans
      _A:						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
      _A:						Optional[Any]	    = 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
      _A:						List[Any]	    = np.nanargmin(snake_case_  ) + self.n_stages
      return row_idx, col_idx


   def 				__magic_name__       (      self  :							str    ,    lowerCAmelCase_  :							str    ,    lowerCAmelCase_  :							Any    ,    lowerCAmelCase_  :							Optional[Any]  ):

      """simple docstring"""
      _A:						Tuple	    = tableau[row_idx].copy()

      _A:						Optional[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:						Dict	    = piv_row
      return tableau


   def 				__magic_name__       (      self  :							Optional[int]    ,    lowerCAmelCase_  :							Dict  ):

      """simple docstring"""
      self.objectives.pop()

      if not self.objectives:
         return tableau

      # Slice containing ids for artificial columns
      _A:						Optional[int]	    = slice(-self.n_art_vars - 1    ,    -1  )

      # Delete the artificial variable columns
      _A:						Optional[int]	    = np.delete(snake_case_    ,    snake_case_    ,    axis=1  )

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

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


   def 				__magic_name__       (      self  :							List[Any]  ):

      """simple docstring"""
      # Stop simplex algorithm from cycling.
      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:						int	    = 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:						Any	    = 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:						Optional[int]	    = self.change_stage(self.tableau  )
         else:
            _A:						Dict	    = self.pivot(self.tableau    ,    snake_case_    ,    snake_case_  )
      return {}


   def 				__magic_name__       (      self  :							int    ,    lowerCAmelCase_  :							Tuple    ,    lowerCAmelCase_  :							Union[str, Any]  ):

      """simple docstring"""
      _A:						Any	    = {'''P''': abs(tableau[0, -1]  )}

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

         # First entry in the nonzero ids
         _A:						List[str]	    = nonzero[0][0]
         _A:						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:						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(snake_case_    ,    0  )
      return output_dict


if __name__ == "__main__":
   import doctest

   doctest.testmod()






import pytest

from datasets.utils.version import Version






@pytest.mark.parametrize(
    '''other, expected_equality'''	,	[
        (Version('''1.0.0'''   ), True),
        ('''1.0.0''', True),
        (Version('''2.0.0'''   ), False),
        ('''2.0.0''', False),
        ('''1''', False),
        ('''a''', False),
        (1, False),
        (None, False),
    ]	,	)
def 						lowerCamelCase__							(      a	,	a   )   ->     str:
   _A:						Tuple	    = Version('''1.0.0'''   )
   assert (version == other) is expected_equality
   assert (version != other) is not expected_equality
   assert (hash(a   ) == hash(a   )) is expected_equality



