



'''simple docstring'''



from typing import Any

import numpy as np






class 			_SCREAMING_SNAKE_CASE				:



			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'''			)

							snake_case__      :   List[Any]      =    tableau
							snake_case__      :   int      =    tableau.shape

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

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

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

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

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

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

							snake_case__      :   Optional[Any]      =    ['''''']

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

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



			@staticmethod
			def 				lowerCAmelCase (     *__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
							snake_case__      :   List[Any]      =    ['''x''', '''s''', '''a''']
							snake_case__      :   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 				lowerCAmelCase (     self		:						Union[str, Any]    ,			__UpperCamelCase		:						np.ndarray			)      ->      tuple[Any, Any]:
							"""simple docstring"""





							snake_case__      :   int      =    self.objectives[-1]

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

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

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

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



			def 				lowerCAmelCase (     self		:						Tuple    ,			__UpperCamelCase		:						np.ndarray    ,			__UpperCamelCase		:						int    ,			__UpperCamelCase		:						int			)      ->      np.ndarray:
							"""simple docstring"""





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

							snake_case__      :   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
							snake_case__      :   Union[str, Any]      =    piv_row
							return tableau



			def 				lowerCAmelCase (     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
							snake_case__      :   str      =    slice(-self.n_art_vars - 1    ,			-1			)

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

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

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



			def 				lowerCAmelCase (     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:
															snake_case__      :   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			)

											snake_case__      :   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
															snake_case__      :   Tuple      =    self.change_stage(self.tableau			)
											else:
															snake_case__      :   str      =    self.pivot(self.tableau    ,			UpperCamelCase_    ,			UpperCamelCase_			)
							return {}







			def 				lowerCAmelCase (     self		:						str    ,			__UpperCamelCase		:						np.ndarray    ,			__UpperCamelCase		:						list[str]			)      ->      dict[str, float]:
							"""simple docstring"""





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

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

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

											# If there is only one nonzero value in column, which is one
											if n_nonzero == nonzero_val == 1:
															snake_case__      :   Optional[Any]      =    tableau[nonzero_rowidx, -1]
															snake_case__      :   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 abc
import copy
import dataclasses
from dataclasses import dataclass
from typing import ClassVar, Dict, Type, TypeVar

from ..features import Features


lowerCamelCase__	  =		TypeVar('T', bound='TaskTemplate')

@dataclass(frozen=__A       )
class 	_lowerCAmelCase     (    abc.ABC       ):






		'''simple docstring'''
		# `task` is not a ClassVar since we want it to be part of the `asdict` output for JSON serialization
		snake_case_							= 42
		snake_case_							= 42
		snake_case_							= 42
		def 						__lowercase      (						self							:       T      ,		UpperCamelCase_							:       Features		)      ->			T:







									'''simple docstring'''





									return copy.deepcopy(self		)
		@property
		def 						__lowercase      (						self							:       int		)      ->			Features:







									'''simple docstring'''





									return Features(**self.input_schema      ,		**self.label_schema		)
		@property
		@abc.abstractmethod
		def 						__lowercase      (						self							:       List[str]		)      ->			Dict[str, str]:







									'''simple docstring'''





									raise NotImplementedError





		@classmethod
		def 						__lowercase      (						cls							:       Type[T]      ,		UpperCamelCase_							:       dict		)      ->			T:







									'''simple docstring'''





									_lowercase							:		List[str]				=   {f.name for f in dataclasses.fields(cls		)}
									return cls(**{k: v for k, v in template_dict.items() if k in field_names}		)



