


'''simple docstring'''







from typing import Any

import numpy as np


class  __lowerCamelCase :
    """simple docstring"""


    def __init__(  self			:							str      ,							SCREAMING_SNAKE_CASE			:							np.ndarray      ,							SCREAMING_SNAKE_CASE			:							int):
           # Check if RHS is negative
           if np.any(tableau[:, -1]      ,							where=tableau[:, -1] < 0):
                  raise ValueError('RHS must be > 0')

           _A     :	Dict      =					tableau
           _A  , _A     :	Optional[int]      =					tableau.shape

           # Number of decision variables x1, x2, x3...
           _A     :	Union[str, Any]      =					n_vars

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

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

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

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

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

           _A     :	List[Any]      =					['']

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

           # Does objective row only contain (non)-negative values?
           _A     :	List[str]      =					False


    @staticmethod
    def    A    (  *SCREAMING_SNAKE_CASE			:							int):
           if len(SCREAMING_SNAKE_CASE) != 3:
                  raise ValueError('Must provide n_vars, n_slack, and n_art_vars')

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

           # decision | slack | artificial
           _A     :	Optional[Any]      =					['x', 's', 'a']
           _A     :	Optional[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    A    (  self			:							Union[str, Any]      ,							SCREAMING_SNAKE_CASE			:							np.ndarray):
           _A     :	List[Any]      =					self.objectives[-1]

           # Find entries of highest magnitude in objective rows
           _A     :	Optional[Any]      =					(objective == 'min') - (objective == 'max')
           _A     :	int      =					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     :	Dict      =					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     :	Dict      =					slice(self.n_stages      ,							self.n_rows)

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

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

           # Array filled with nans
           _A     :	List[str]      =					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     :	str      =					np.divide(SCREAMING_SNAKE_CASE      ,							SCREAMING_SNAKE_CASE      ,							out=SCREAMING_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     :	int      =					np.nanargmin(SCREAMING_SNAKE_CASE) + self.n_stages
           return row_idx, col_idx


    def    A    (  self			:							List[Any]      ,							SCREAMING_SNAKE_CASE			:							np.ndarray      ,							SCREAMING_SNAKE_CASE			:							int      ,							SCREAMING_SNAKE_CASE			:							int):
           _A     :	Tuple      =					tableau[row_idx].copy()

           _A     :	int      =					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     :	Union[str, Any]      =					piv_row
           return tableau


    def    A    (  self			:							List[str]      ,							SCREAMING_SNAKE_CASE			:							np.ndarray):
           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(SCREAMING_SNAKE_CASE      ,							SCREAMING_SNAKE_CASE      ,							axis=1)

           # Delete the objective row of the first stage
           _A     :	Optional[int]      =					np.delete(SCREAMING_SNAKE_CASE      ,							0      ,							axis=0)

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


    def    A    (  self			:							Optional[Any]):
           # Stop simplex algorithm from cycling.
           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:
                         _A     :	Union[str, Any]      =					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     :	Dict      =					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     :	Dict      =					self.change_stage(self.tableau)
                  else:
                         _A     :	List[Any]      =					self.pivot(self.tableau      ,							SCREAMING_SNAKE_CASE      ,							SCREAMING_SNAKE_CASE)
           return {}


    def    A    (  self			:							Any      ,							SCREAMING_SNAKE_CASE			:							np.ndarray      ,							SCREAMING_SNAKE_CASE			:							list[str]):
           _A     :	List[str]      =					{'P': abs(tableau[0, -1])}

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

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

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


if __name__ == "__main__":
   import doctest

   doctest.testmod()










'''simple docstring'''







from __future__ import annotations






def       lowerCAmelCase__       (				lowerCamelCase     :			list   ):
       _A     :	Union[str, Any]      =					sorted(lowerCamelCase   )
       _A     :	Tuple      =					len(lowerCamelCase   )
       _A     :	int      =					length >> 1
       return (
           (sorted_list[mid_index] + sorted_list[mid_index - 1]) / 2
           if length % 2 == 0
           else sorted_list[mid_index]
       )






def       lowerCAmelCase__       (				):
       import doctest

       doctest.testmod()


if __name__ == "__main__":
   main()






