


from typing import Any

import numpy as np







class 				lowerCamelCase__       :





     def __init__(self		,					UpperCAmelCase		,					UpperCAmelCase	)					->       None:




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

      _lowercase											=tableau
      _lowercase											=tableau.shape

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

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

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

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

      # Objectives for each stage
      _lowercase											=['max']

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

      _lowercase											=['']

      # Index of current pivot row and column
      _lowercase											=None
      _lowercase											=None

      # Does objective row only contain (non)-negative values?
      _lowercase											=False





     @staticmethod
     def 					__A (*UpperCAmelCase	)					->       list[str]:




      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
      _lowercase											=['x', 's', 'a']
      _lowercase											=[]
      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		,					UpperCAmelCase	)					->       tuple[Any, Any]:
      _lowercase											=self.objectives[-1]

      # Find entries of highest magnitude in objective rows
      _lowercase											=(objective == 'min') - (objective == 'max')
      _lowercase											=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											=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											=slice(self.n_stages		,					self.n_rows	)

      # RHS
      _lowercase											=tableau[s, -1]

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

      # Array filled with nans
      _lowercase											=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											=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
      _lowercase											=np.nanargmin(lowercase_	) + self.n_stages
      return row_idx, col_idx





     def 					__A (self		,					UpperCAmelCase		,					UpperCAmelCase		,					UpperCAmelCase	)					->       np.ndarray:
      _lowercase											=tableau[row_idx].copy()

      _lowercase											=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											=piv_row
      return tableau





     def 					__A (self		,					UpperCAmelCase	)					->       np.ndarray:
      self.objectives.pop()

      if not self.objectives:
       return tableau

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

      # Delete the artificial variable columns
      _lowercase											=np.delete(lowercase_		,					lowercase_		,					axis=1	)

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

      _lowercase											=1
      self.n_rows -= 1
      _lowercase											=0
      _lowercase											=False
      return tableau





     def 					__A (self	)					->       dict[Any, Any]:




      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:
        _lowercase											=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											=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											=self.change_stage(self.tableau	)
       else:
        _lowercase											=self.pivot(self.tableau		,					lowercase_		,					lowercase_	)
      return {}





     def 					__A (self		,					UpperCAmelCase		,					UpperCAmelCase	)					->       dict[str, float]:
      _lowercase											={'P': abs(tableau[0, -1]	)}

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

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

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








from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


UpperCAmelCase__            =							{'''configuration_visual_bert''': ['''VISUAL_BERT_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''VisualBertConfig''']}

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase__            =							[
      '''VISUAL_BERT_PRETRAINED_MODEL_ARCHIVE_LIST''',
      '''VisualBertForMultipleChoice''',
      '''VisualBertForPreTraining''',
      '''VisualBertForQuestionAnswering''',
      '''VisualBertForRegionToPhraseAlignment''',
      '''VisualBertForVisualReasoning''',
      '''VisualBertLayer''',
      '''VisualBertModel''',
      '''VisualBertPreTrainedModel''',
  ]


if TYPE_CHECKING:
  from .configuration_visual_bert import VISUAL_BERT_PRETRAINED_CONFIG_ARCHIVE_MAP, VisualBertConfig

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_visual_bert import (
        VISUAL_BERT_PRETRAINED_MODEL_ARCHIVE_LIST,
        VisualBertForMultipleChoice,
        VisualBertForPreTraining,
        VisualBertForQuestionAnswering,
        VisualBertForRegionToPhraseAlignment,
        VisualBertForVisualReasoning,
        VisualBertLayer,
        VisualBertModel,
        VisualBertPreTrainedModel,
    )


else:
  import sys

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

