




from typing import Any

import numpy as np






class        __lowerCAmelCase					:







			def __init__(			self       :     Any       ,       snake_case__       :     np.ndarray       ,       snake_case__       :     int ):




									"""simple docstring"""


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

									_UpperCAmelCase						=	tableau
									_UpperCAmelCase				,					_UpperCAmelCase						=	tableau.shape

									# Number of decision variables x1, x2, x3...
									_UpperCAmelCase						=	n_vars

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

									# 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
									_UpperCAmelCase						=	(self.n_art_vars > 0) + 1

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

									# Objectives for each stage
									_UpperCAmelCase						=	["max"]

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

									_UpperCAmelCase						=	[""]

									# Index of current pivot row and column
									_UpperCAmelCase						=	None
									_UpperCAmelCase						=	None

									# Does objective row only contain (non)-negative values?
									_UpperCAmelCase						=	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
									_UpperCAmelCase						=	["x", "s", "a"]
									_UpperCAmelCase						=	[]
									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"""


									_UpperCAmelCase						=	self.objectives[-1]

									# Find entries of highest magnitude in objective rows
									_UpperCAmelCase						=	(objective == "min") - (objective == "max")
									_UpperCAmelCase						=	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						=	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						=	slice(self.n_stages       ,       self.n_rows )

									# RHS
									_UpperCAmelCase						=	tableau[s, -1]

									# Elements of pivot column within slice
									_UpperCAmelCase						=	tableau[s, col_idx]

									# Array filled with nans
									_UpperCAmelCase						=	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						=	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
									_UpperCAmelCase						=	np.nanargmin(snake_case__ ) + self.n_stages
									return row_idx, col_idx







			def UpperCamelCase     (			self       :     Optional[Any]       ,       snake_case__       :     np.ndarray       ,       snake_case__       :     int       ,       snake_case__       :     int ):




									"""simple docstring"""


									_UpperCAmelCase						=	tableau[row_idx].copy()

									_UpperCAmelCase						=	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						=	piv_row
									return tableau







			def UpperCamelCase     (			self       :     List[str]       ,       snake_case__       :     np.ndarray ):




									"""simple docstring"""


									self.objectives.pop()

									if not self.objectives:
															return tableau

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

									# Delete the artificial variable columns
									_UpperCAmelCase						=	np.delete(snake_case__       ,       snake_case__       ,       axis=1 )

									# Delete the objective row of the first stage
									_UpperCAmelCase						=	np.delete(snake_case__       ,       0       ,       axis=0 )

									_UpperCAmelCase						=	1
									self.n_rows -= 1
									_UpperCAmelCase						=	0
									_UpperCAmelCase						=	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:
																					_UpperCAmelCase						=	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						=	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						=	self.change_stage(self.tableau )
															else:
																					_UpperCAmelCase						=	self.pivot(self.tableau       ,       snake_case__       ,       snake_case__ )
									return {}







			def UpperCamelCase     (			self       :     Dict       ,       snake_case__       :     np.ndarray       ,       snake_case__       :     list[str] ):




									"""simple docstring"""


									_UpperCAmelCase						=	{"P": abs(tableau[0, -1] )}

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

															# First entry in the nonzero ids
															_UpperCAmelCase						=	nonzero[0][0]
															_UpperCAmelCase						=	tableau[nonzero_rowidx, i]

															# If there is only one nonzero value in column, which is one
															if n_nonzero == nonzero_val == 1:
																					_UpperCAmelCase						=	tableau[nonzero_rowidx, -1]
																					_UpperCAmelCase						=	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()










def 				__SCREAMING_SNAKE_CASE    (     snake_case_		):

						'''simple docstring'''


						return int(snake_case_		) if x - int(snake_case_		) >= 0 else int(snake_case_		) - 1


if __name__ == "__main__":
				import doctest

				doctest.testmod()




