
'''simple docstring'''





from typing import Any

import numpy as np

class     a :




				def __init__(				self						:					Dict,     SCREAMING_SNAKE_CASE_						:					str,     SCREAMING_SNAKE_CASE_						:					Union[str, Any]   ):







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

										snake_case							:  str			=     tableau
										snake_case,       snake_case							:  int			=     tableau.shape

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

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

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

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

										# Objectives for each stage
										snake_case							:  str			=     ['''max''']

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

										snake_case							:  str			=     ['''''']

										# Index of current pivot row and column
										snake_case							:  List[Any]			=     None
										snake_case							:  str			=     None

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




				@staticmethod
				def 						__snake_case				(				*SCREAMING_SNAKE_CASE_						:					Tuple   ):







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

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

										# decision | slack | artificial
										snake_case							:  Union[str, Any]			=     ['''x''', '''s''', '''a''']
										snake_case							:  int			=     []
										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						:					Tuple,     SCREAMING_SNAKE_CASE_						:					Optional[int]   ):
										snake_case							:  Union[str, Any]			=     self.objectives[-1]

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

										# RHS
										snake_case							:  Dict			=     tableau[s, -1]

										# Elements of pivot column within slice
										snake_case							:  int			=     tableau[s, col_idx]

										# Array filled with nans
										snake_case							:  Union[str, Any]			=     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							:  Any			=     np.divide(lowercase__,     lowercase__,     out=lowercase__,     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							:  Any			=     np.nanargmin(lowercase__   ) + self.n_stages
										return row_idx, col_idx




				def 						__snake_case				(				self						:					Optional[Any],     SCREAMING_SNAKE_CASE_						:					int,     SCREAMING_SNAKE_CASE_						:					Dict,     SCREAMING_SNAKE_CASE_						:					int   ):
										snake_case							:  List[Any]			=     tableau[row_idx].copy()

										snake_case							:  List[str]			=     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 						__snake_case				(				self						:					Any,     SCREAMING_SNAKE_CASE_						:					Tuple   ):
										self.objectives.pop()

										if not self.objectives:
																return tableau

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

										# Delete the artificial variable columns
										snake_case							:  Tuple			=     np.delete(lowercase__,     lowercase__,     axis=1   )

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

										snake_case							:  Optional[Any]			=     1
										self.n_rows -= 1
										snake_case							:  int			=     0
										snake_case							:  List[Any]			=     False
										return tableau




				def 						__snake_case				(				self						:					Tuple   ):







										for _ in range(1_00   ):
																# Completion of each stage removes an objective. If both stages
																# are complete, then no objectives are left
																if not self.objectives:
																						snake_case							:  Optional[int]			=     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,       snake_case							:  str			=     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							:  Dict			=     self.change_stage(self.tableau   )
																else:
																						snake_case							:  Union[str, Any]			=     self.pivot(self.tableau,     lowercase__,     lowercase__   )
										return {}




				def 						__snake_case				(				self						:					Union[str, Any],     SCREAMING_SNAKE_CASE_						:					Dict,     SCREAMING_SNAKE_CASE_						:					Optional[int]   ):
										snake_case							:  Optional[Any]			=     {'''P''': abs(tableau[0, -1]   )}

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

																# First entry in the nonzero ids
																snake_case							:  int			=     nonzero[0][0]
																snake_case							:  List[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							:  str			=     tableau[nonzero_rowidx, -1]
																						snake_case							:  Tuple			=     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(lowercase__,     0   )
										return output_dict


if __name__ == "__main__":
						import doctest

						doctest.testmod()



"""simple docstring"""




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


snake_case					  =						{'configuration_qdqbert': ['QDQBERT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'QDQBertConfig']}

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	snake_case					  =						[
	    'QDQBERT_PRETRAINED_MODEL_ARCHIVE_LIST',
	    'QDQBertForMaskedLM',
	    'QDQBertForMultipleChoice',
	    'QDQBertForNextSentencePrediction',
	    'QDQBertForQuestionAnswering',
	    'QDQBertForSequenceClassification',
	    'QDQBertForTokenClassification',
	    'QDQBertLayer',
	    'QDQBertLMHeadModel',
	    'QDQBertModel',
	    'QDQBertPreTrainedModel',
	    'load_tf_weights_in_qdqbert',
	]


if TYPE_CHECKING:
	from .configuration_qdqbert import QDQBERT_PRETRAINED_CONFIG_ARCHIVE_MAP, QDQBertConfig

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_qdqbert import (
		    QDQBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
		    QDQBertForMaskedLM,
		    QDQBertForMultipleChoice,
		    QDQBertForNextSentencePrediction,
		    QDQBertForQuestionAnswering,
		    QDQBertForSequenceClassification,
		    QDQBertForTokenClassification,
		    QDQBertLayer,
		    QDQBertLMHeadModel,
		    QDQBertModel,
		    QDQBertPreTrainedModel,
		    load_tf_weights_in_qdqbert,
		)


else:
	import sys

	snake_case					  =						_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
