






"""simple docstring"""







from typing import Any

import numpy as np


class     __UpperCAmelCase:




						"""simple docstring"""




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

												lowercase__				:      Dict=       tableau
												lowercase__,	lowercase__				:      Optional[Any]=       tableau.shape

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

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

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

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

												# Objectives for each stage
												lowercase__				:      Optional[Any]=       ["max"]

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

												lowercase__				:      Union[str, Any]=       [""]

												# Index of current pivot row and column
												lowercase__				:      Tuple=       None
												lowercase__				:      List[Any]=       None

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




						@staticmethod
						def 		UpperCAmelCase_       (   *snake_case__			):
												'''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
												lowercase__				:      Optional[Any]=       ["x", "s", "a"]
												lowercase__				:      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       ,  snake_case__			):
												'''simple docstring'''
												lowercase__				:      str=       self.objectives[-1]

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

												# RHS
												lowercase__				:      Tuple=       tableau[s, -1]

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

												# Array filled with nans
												lowercase__				:      Tuple=       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
												lowercase__				:      int=       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
												lowercase__				:      List[str]=       np.nanargmin(snake_case__			) + self.n_stages
												return row_idx, col_idx




						def 		UpperCAmelCase_       (   self       ,  snake_case__       ,  snake_case__       ,  snake_case__			):
												'''simple docstring'''
												lowercase__				:      Optional[Any]=       tableau[row_idx].copy()

												lowercase__				:      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
												lowercase__				:      Dict=       piv_row
												return tableau




						def 		UpperCAmelCase_       (   self       ,  snake_case__			):
												'''simple docstring'''
												self.objectives.pop()

												if not self.objectives:
																		return tableau

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

												# Delete the artificial variable columns
												lowercase__				:      List[Any]=       np.delete(snake_case__       ,  snake_case__       ,  axis=1			)

												# Delete the objective row of the first stage
												lowercase__				:      List[str]=       np.delete(snake_case__       ,  0       ,  axis=0			)

												lowercase__				:      Any=       1
												self.n_rows -= 1
												lowercase__				:      str=       0
												lowercase__				:      Dict=       False
												return tableau




						def 		UpperCAmelCase_       (   self			):
												'''simple docstring'''
												# 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:
																								lowercase__				:      List[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			)

																		lowercase__,	lowercase__				:      Optional[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
																								lowercase__				:      List[Any]=       self.change_stage(self.tableau			)
																		else:
																								lowercase__				:      Dict=       self.pivot(self.tableau       ,  snake_case__       ,  snake_case__			)
												return {}




						def 		UpperCAmelCase_       (   self       ,  snake_case__       ,  snake_case__			):
												'''simple docstring'''
												lowercase__				:      List[Any]=       {"P": abs(tableau[0, -1]			)}

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

																		# First entry in the nonzero ids
																		lowercase__				:      Dict=       nonzero[0][0]
																		lowercase__				:      Optional[int]=       tableau[nonzero_rowidx, i]

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














"""simple docstring"""







import importlib.metadata
import subprocess
import sys





def 						lowercase__(A = False						)				->List[str]:




						"""simple docstring"""



						lowercase__				:      Any=       False
						if "IPython" in sys.modules:
												lowercase__				:      Tuple=       "google.colab" in str(sys.modules["IPython"].get_ipython()						)

						if in_colab:
												if upgrade:
																		lowercase__				:      Optional[int]=       ["pip", "install", "-U", "torch"]
																		subprocess.run(A					,		check=A						)
												# get the current version of torch
												lowercase__				:      Tuple=       importlib.metadata.version("torch"						)
												lowercase__				:      Dict=       torch_version[: torch_version.rindex("."						)]
												lowercase__				:      Dict=       f'''https://storage.googleapis.com/tpu-pytorch/wheels/colab/torch_xla-{torch_version_trunc}-cp37-cp37m-linux_x86_64.whl'''
												lowercase__				:      Union[str, Any]=       ["pip", "install", xla_wheel]
												subprocess.run(A					,		check=A						)
						else:
												raise RuntimeError("`install_xla` utility works only on google colab."						)






