





"""simple docstring"""




from typing import Any

import numpy as np




class 				_a		:






				def __init__(				self	:					Tuple,				lowerCAmelCase__	:					np.ndarray,				lowerCAmelCase__	:					int							)			->   None:




										'''simple docstring'''



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

										_UpperCamelCase    :      List[Any]						     =					tableau
										_UpperCamelCase     ,							_UpperCamelCase    :      Tuple						     =					tableau.shape

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

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

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

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

										# Objectives for each stage
										_UpperCamelCase    :      Any						     =					['''max''']

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

										_UpperCamelCase    :      int						     =					['''''']

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

										# Does objective row only contain (non)-negative values?
										_UpperCamelCase    :      Union[str, Any]						     =					False






				@staticmethod
				def        snake_case			(				*lowerCAmelCase__	:					int							)			->   list[str]:




										'''simple docstring'''



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

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

										# decision | slack | artificial
										_UpperCamelCase    :      Optional[int]						     =					['''x''', '''s''', '''a''']
										_UpperCamelCase    :      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        snake_case			(				self	:					Union[str, Any],				lowerCAmelCase__	:					np.ndarray							)			->   tuple[Any, Any]:




										'''simple docstring'''



										_UpperCamelCase    :      Tuple						     =					self.objectives[-1]

										# Find entries of highest magnitude in objective rows
										_UpperCamelCase    :      Tuple						     =					(objective == '''min''') - (objective == '''max''')
										_UpperCamelCase    :      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:
																_UpperCamelCase    :      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
										_UpperCamelCase    :      Any						     =					slice(self.n_stages,				self.n_rows							)

										# RHS
										_UpperCamelCase    :      List[str]						     =					tableau[s, -1]

										# Elements of pivot column within slice
										_UpperCamelCase    :      List[str]						     =					tableau[s, col_idx]

										# Array filled with nans
										_UpperCamelCase    :      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
										_UpperCamelCase    :      Optional[int]						     =					np.divide(lowerCAmelCase__,				lowerCAmelCase__,				out=lowerCAmelCase__,				where=divisor > 0							)

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






				def        snake_case			(				self	:					Union[str, Any],				lowerCAmelCase__	:					np.ndarray,				lowerCAmelCase__	:					int,				lowerCAmelCase__	:					int							)			->   np.ndarray:




										'''simple docstring'''



										_UpperCamelCase    :      Tuple						     =					tableau[row_idx].copy()

										_UpperCamelCase    :      List[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
										_UpperCamelCase    :      Any						     =					piv_row
										return tableau






				def        snake_case			(				self	:					Optional[int],				lowerCAmelCase__	:					np.ndarray							)			->   np.ndarray:




										'''simple docstring'''



										self.objectives.pop()

										if not self.objectives:
																return tableau

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

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

										# Delete the objective row of the first stage
										_UpperCamelCase    :      Tuple						     =					np.delete(lowerCAmelCase__,				0,				axis=0							)

										_UpperCamelCase    :      Tuple						     =					1
										self.n_rows -= 1
										_UpperCamelCase    :      Any						     =					0
										_UpperCamelCase    :      Optional[Any]						     =					False
										return tableau






				def        snake_case			(				self	:					Union[str, Any]							)			->   dict[Any, 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:
																						_UpperCamelCase    :      Dict						     =					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							)

																_UpperCamelCase     ,							_UpperCamelCase    :      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
																						_UpperCamelCase    :      Optional[Any]						     =					self.change_stage(self.tableau							)
																else:
																						_UpperCamelCase    :      Optional[Any]						     =					self.pivot(self.tableau,				lowerCAmelCase__,				lowerCAmelCase__							)
										return {}






				def        snake_case			(				self	:					Optional[int],				lowerCAmelCase__	:					np.ndarray,				lowerCAmelCase__	:					list[str]							)			->   dict[str, float]:




										'''simple docstring'''



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

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

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

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


if __name__ == "__main__":
						import doctest

						doctest.testmod()










"""simple docstring"""




def  a_       (							_lowercase     ):
						if len(_lowercase     ) > 1:
												_UpperCamelCase    :      List[str]						     =					len(_lowercase     ) // 2  # Finds the middle of the array
												_UpperCamelCase    :      Dict						     =					arr[
												    :middle_length
												]  # Creates an array of the elements in the first half.
												_UpperCamelCase    :      Union[str, Any]						     =					arr[
												    middle_length:
												]  # Creates an array of the elements in the second half.
												_UpperCamelCase    :      str						     =					len(_lowercase     )
												_UpperCamelCase    :      List[str]						     =					len(_lowercase     )
												merge(_lowercase     )  # Starts sorting the left.
												merge(_lowercase     )  # Starts sorting the right
												_UpperCamelCase    :      Dict						     =					0  # Left Counter
												_UpperCamelCase    :      Union[str, Any]						     =					0  # Right Counter
												_UpperCamelCase    :      Optional[int]						     =					0  # Position Counter
												while (
												    left_index < left_size and right_index < right_size
												):  # Runs until the lowers size of the left and right are sorted.
																		if left_array[left_index] < right_array[right_index]:
																								_UpperCamelCase    :      Dict						     =					left_array[left_index]
																								left_index += 1
																		else:
																								_UpperCamelCase    :      Tuple						     =					right_array[right_index]
																								right_index += 1
																		index += 1
												while (
												    left_index < left_size
												):  # Adds the left over elements in the left half of the array
																		_UpperCamelCase    :      int						     =					left_array[left_index]
																		left_index += 1
																		index += 1
												while (
												    right_index < right_size
												):  # Adds the left over elements in the right half of the array
																		_UpperCamelCase    :      Any						     =					right_array[right_index]
																		right_index += 1
																		index += 1
						return arr


if __name__ == "__main__":
						import doctest

						doctest.testmod()



