






"""simple docstring"""
from typing import Any

import numpy as np



class 		a_      :







      '''simple docstring'''

      def __init__(self,     lowerCamelCase_,     lowerCamelCase_					):

       '''simple docstring'''



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

       lowerCamelCase__     :			Dict     				=						tableau
       lowerCamelCase__				,     lowerCamelCase__     :			Dict     				=						tableau.shape

       # Number of decision variables x1, x2, x3...
       lowerCamelCase__     :			Any     				=						n_vars

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

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

       # Number of slack variables added to make inequalities into equalities
       lowerCamelCase__     :			List[str]     				=						self.n_rows - self.n_stages

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

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

       lowerCamelCase__     :			Optional[int]     				=						['']

       # Index of current pivot row and column
       lowerCamelCase__     :			Optional[int]     				=						None
       lowerCamelCase__     :			int     				=						None

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




      @staticmethod
      def 			a__							(*lowerCamelCase_					):

       '''simple docstring'''



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

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

       # decision | slack | artificial
       lowerCamelCase__     :			Optional[Any]     				=						['x', 's', 'a']
       lowerCamelCase__     :			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 			a__							(self,     lowerCamelCase_					):

       '''simple docstring'''



       lowerCamelCase__     :			str     				=						self.objectives[-1]

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

       # RHS
       lowerCamelCase__     :			int     				=						tableau[s, -1]

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

       # Array filled with nans
       lowerCamelCase__     :			List[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
       lowerCamelCase__     :			List[Any]     				=						np.divide(lowerCamelCase_,     lowerCamelCase_,     out=lowerCamelCase_,     where=divisor > 0					)

       # Arg of minimum quotient excluding the nan values. n_stages is added
       # to compensate for earlier exclusion of objective columns
       lowerCamelCase__     :			Optional[Any]     				=						np.nanargmin(lowerCamelCase_					) + self.n_stages
       return row_idx, col_idx




      def 			a__							(self,     lowerCamelCase_,     lowerCamelCase_,     lowerCamelCase_					):

       '''simple docstring'''



       lowerCamelCase__     :			Union[str, Any]     				=						tableau[row_idx].copy()

       lowerCamelCase__     :			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
       lowerCamelCase__     :			Any     				=						piv_row
       return tableau




      def 			a__							(self,     lowerCamelCase_					):

       '''simple docstring'''



       self.objectives.pop()

       if not self.objectives:
        return tableau

       # Slice containing ids for artificial columns
       lowerCamelCase__     :			List[str]     				=						slice(-self.n_art_vars - 1,     -1					)

       # Delete the artificial variable columns
       lowerCamelCase__     :			int     				=						np.delete(lowerCamelCase_,     lowerCamelCase_,     axis=1					)

       # Delete the objective row of the first stage
       lowerCamelCase__     :			str     				=						np.delete(lowerCamelCase_,     0,     axis=0					)

       lowerCamelCase__     :			Union[str, Any]     				=						1
       self.n_rows -= 1
       lowerCamelCase__     :			Optional[int]     				=						0
       lowerCamelCase__     :			Optional[int]     				=						False
       return tableau




      def 			a__							(self					):

       '''simple docstring'''



       for _ in range(1_0_0					):
        # Completion of each stage removes an objective. If both stages
        # are complete, then no objectives are left
        if not self.objectives:
         lowerCamelCase__     :			Optional[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					)

        lowerCamelCase__				,     lowerCamelCase__     :			Dict     				=						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
         lowerCamelCase__     :			Any     				=						self.change_stage(self.tableau					)
        else:
         lowerCamelCase__     :			Optional[Any]     				=						self.pivot(self.tableau,     lowerCamelCase_,     lowerCamelCase_					)
       return {}





      def 			a__							(self,     lowerCamelCase_,     lowerCamelCase_					):

       '''simple docstring'''



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

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

        # First entry in the nonzero ids
        lowerCamelCase__     :			List[str]     				=						nonzero[0][0]
        lowerCamelCase__     :			Optional[Any]     				=						tableau[nonzero_rowidx, i]

        # If there is only one nonzero value in column, which is one
        if n_nonzero == nonzero_val == 1:
         lowerCamelCase__     :			Union[str, Any]     				=						tableau[nonzero_rowidx, -1]
         lowerCamelCase__     :			int     				=						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(lowerCamelCase_,     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


A_			: Dict				=			{"configuration_qdqbert": ["QDQBERT_PRETRAINED_CONFIG_ARCHIVE_MAP", "QDQBertConfig"]}

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      A_			: Tuple				=			[
          "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

      A_			: Tuple				=			_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)

