



'''simple docstring'''






from typing import Any

import numpy as np

class 	_lowerCAmelCase     :






		'''simple docstring'''
		def __init__(						self							:       Tuple      ,		UpperCamelCase_							:       np.ndarray      ,		UpperCamelCase_							:       int		)      ->			None:







									'''simple docstring'''





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

									_lowercase							:		List[Any]				=   tableau
									_lowercase			, _lowercase							:		int				=   tableau.shape

									# Number of decision variables x1, x2, x3...
									_lowercase							:		str				=   n_vars

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

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

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

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

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

									_lowercase							:		Optional[Any]				=   ['''''']

									# Index of current pivot row and column
									_lowercase							:		Any				=   None
									_lowercase							:		int				=   None

									# Does objective row only contain (non)-negative values?
									_lowercase							:		Union[str, Any]				=   False
		@staticmethod
		def 						__lowercase      (						*UpperCamelCase_							:       int		)      ->			list[str]:







									'''simple docstring'''





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

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

									# decision | slack | artificial
									_lowercase							:		List[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 						__lowercase      (						self							:       Union[str, Any]      ,		UpperCamelCase_							:       np.ndarray		)      ->			tuple[Any, Any]:







									'''simple docstring'''





									_lowercase							:		int				=   self.objectives[-1]

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

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

									# Elements of pivot column within slice
									_lowercase							:		Optional[Any]				=   tableau[s, col_idx]

									# Array filled with nans
									_lowercase							:		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
									_lowercase							:		Dict				=   np.divide(UpperCamelCase_      ,		UpperCamelCase_      ,		out=UpperCamelCase_      ,		where=divisor > 0		)

									# Arg of minimum quotient excluding the nan values. n_stages is added
									# to compensate for earlier exclusion of objective columns
									_lowercase							:		Tuple				=   np.nanargmin(UpperCamelCase_		) + self.n_stages
									return row_idx, col_idx
		def 						__lowercase      (						self							:       Tuple      ,		UpperCamelCase_							:       np.ndarray      ,		UpperCamelCase_							:       int      ,		UpperCamelCase_							:       int		)      ->			np.ndarray:







									'''simple docstring'''





									_lowercase							:		Optional[Any]				=   tableau[row_idx].copy()

									_lowercase							:		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							:		Union[str, Any]				=   piv_row
									return tableau
		def 						__lowercase      (						self							:       List[str]      ,		UpperCamelCase_							:       np.ndarray		)      ->			np.ndarray:







									'''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[str]				=   np.delete(UpperCamelCase_      ,		UpperCamelCase_      ,		axis=1		)

									# Delete the objective row of the first stage
									_lowercase							:		int				=   np.delete(UpperCamelCase_      ,		0      ,		axis=0		)

									_lowercase							:		List[Any]				=   1
									self.n_rows -= 1
									_lowercase							:		Union[str, Any]				=   0
									_lowercase							:		Tuple				=   False
									return tableau
		def 						__lowercase      (						self							:       Union[str, Any]		)      ->			dict[Any, Any]:







									'''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:
																							_lowercase							:		List[str]				=   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[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
																							_lowercase							:		Tuple				=   self.change_stage(self.tableau		)
																else:
																							_lowercase							:		str				=   self.pivot(self.tableau      ,		UpperCamelCase_      ,		UpperCamelCase_		)
									return {}





		def 						__lowercase      (						self							:       str      ,		UpperCamelCase_							:       np.ndarray      ,		UpperCamelCase_							:       list[str]		)      ->			dict[str, float]:







									'''simple docstring'''





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

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

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

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


if __name__ == "__main__":
						import doctest

						doctest.testmod()








'''simple docstring'''






import warnings

from .generation import FlaxGenerationMixin

class 	_lowerCAmelCase     (    __A       ):






		'''simple docstring'''
		# warning at import time
		warnings.warn(
		    'Importing `FlaxGenerationMixin` from `src/transformers/generation_flax_utils.py` is deprecated and will '
		    'be removed in Transformers v5. Import as `from transformers import FlaxGenerationMixin` instead.'     ,		__A     ,		)



