

from typing import Any

import numpy as np






class 							A_				:


     def __init__(							self    :	Any    ,						UpperCAmelCase    :	np.ndarray    ,						UpperCAmelCase    :	int      )							->			None:
      # Check if RHS is negative
      if np.any(tableau[:, -1]    ,						where=tableau[:, -1] < 0      ):
       raise ValueError('RHS must be > 0'      )

      __lowerCAmelCase:     List[str]     			=   tableau
      __lowerCAmelCase:     int     			=   tableau.shape

      # Number of decision variables x1, x2, x3...
      __lowerCAmelCase:     Tuple     			=   n_vars

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

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

      # Number of slack variables added to make inequalities into equalities
      __lowerCAmelCase:     Union[str, Any]     			=   self.n_rows - self.n_stages

      # Objectives for each stage
      __lowerCAmelCase:     Optional[Any]     			=   ['max']

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

      __lowerCAmelCase:     Any     			=   ['']

      # Index of current pivot row and column
      __lowerCAmelCase:     List[Any]     			=   None
      __lowerCAmelCase:     int     			=   None

      # Does objective row only contain (non)-negative values?
      __lowerCAmelCase:     List[str]     			=   False


     @staticmethod
     def 						UpperCAmelCase						(							*UpperCAmelCase    :	int      )							->			list[str]:
      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
      __lowerCAmelCase:     Tuple     			=   ['x', 's', 'a']
      __lowerCAmelCase:     Union[str, 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 						UpperCAmelCase						(							self    :	Union[str, Any]    ,						UpperCAmelCase    :	np.ndarray      )							->			tuple[Any, Any]:
      __lowerCAmelCase:     int     			=   self.objectives[-1]

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

      # RHS
      __lowerCAmelCase:     List[str]     			=   tableau[s, -1]

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

      # Array filled with nans
      __lowerCAmelCase:     Optional[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[str]     			=   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
      __lowerCAmelCase:     List[Any]     			=   np.nanargmin(UpperCAmelCase      ) + self.n_stages
      return row_idx, col_idx


     def 						UpperCAmelCase						(							self    :	Optional[int]    ,						UpperCAmelCase    :	np.ndarray    ,						UpperCAmelCase    :	int    ,						UpperCAmelCase    :	int      )							->			np.ndarray:
      __lowerCAmelCase:     Union[str, Any]     			=   tableau[row_idx].copy()

      __lowerCAmelCase:     Tuple     			=   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:     Optional[int]     			=   piv_row
      return tableau


     def 						UpperCAmelCase						(							self    :	Union[str, Any]    ,						UpperCAmelCase    :	np.ndarray      )							->			np.ndarray:
      self.objectives.pop()

      if not self.objectives:
       return tableau

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

      # Delete the artificial variable columns
      __lowerCAmelCase:     List[Any]     			=   np.delete(UpperCAmelCase    ,						UpperCAmelCase    ,						axis=1      )

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

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


     def 						UpperCAmelCase						(							self    :	Optional[int]      )							->			dict[Any, Any]:
      # Stop simplex algorithm from cycling.
      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:     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:     Optional[int]     			=   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:     Optional[int]     			=   self.change_stage(self.tableau      )
       else:
        __lowerCAmelCase:     List[str]     			=   self.pivot(self.tableau    ,						UpperCAmelCase    ,						UpperCAmelCase      )
      return {}


     def 						UpperCAmelCase						(							self    :	Dict    ,						UpperCAmelCase    :	np.ndarray    ,						UpperCAmelCase    :	list[str]      )							->			dict[str, float]:
      __lowerCAmelCase:     Optional[int]     			=   {'P': abs(tableau[0, -1]      )}

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

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

       # If there is only one nonzero value in column, which is one
       if n_nonzero == nonzero_val == 1:
        __lowerCAmelCase:     Optional[int]     			=   tableau[nonzero_rowidx, -1]
        __lowerCAmelCase:     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(UpperCAmelCase    ,						0      )
      return output_dict


if __name__ == "__main__":
  import doctest

  doctest.testmod()








from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_keras_nlp_available,
    is_tensorflow_text_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


_a	 =     {
    '''configuration_gpt2''': ['''GPT2_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''GPT2Config''', '''GPT2OnnxConfig'''],
    '''tokenization_gpt2''': ['''GPT2Tokenizer'''],
}

try:
  if not is_tokenizers_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _a	 =     ['''GPT2TokenizerFast''']

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _a	 =     [
      '''GPT2_PRETRAINED_MODEL_ARCHIVE_LIST''',
      '''GPT2DoubleHeadsModel''',
      '''GPT2ForQuestionAnswering''',
      '''GPT2ForSequenceClassification''',
      '''GPT2ForTokenClassification''',
      '''GPT2LMHeadModel''',
      '''GPT2Model''',
      '''GPT2PreTrainedModel''',
      '''load_tf_weights_in_gpt2''',
  ]

try:
  if not is_tf_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _a	 =     [
      '''TF_GPT2_PRETRAINED_MODEL_ARCHIVE_LIST''',
      '''TFGPT2DoubleHeadsModel''',
      '''TFGPT2ForSequenceClassification''',
      '''TFGPT2LMHeadModel''',
      '''TFGPT2MainLayer''',
      '''TFGPT2Model''',
      '''TFGPT2PreTrainedModel''',
  ]

try:
  if not is_keras_nlp_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _a	 =     ['''TFGPT2Tokenizer''']

try:
  if not is_flax_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _a	 =     ['''FlaxGPT2LMHeadModel''', '''FlaxGPT2Model''', '''FlaxGPT2PreTrainedModel''']

if TYPE_CHECKING:
  from .configuration_gpta import GPT2_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTaConfig, GPTaOnnxConfig
  from .tokenization_gpta import GPTaTokenizer

  try:
    if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_gpta_fast import GPTaTokenizerFast

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_gpta import (
        GPT2_PRETRAINED_MODEL_ARCHIVE_LIST,
        GPTaDoubleHeadsModel,
        GPTaForQuestionAnswering,
        GPTaForSequenceClassification,
        GPTaForTokenClassification,
        GPTaLMHeadModel,
        GPTaModel,
        GPTaPreTrainedModel,
        load_tf_weights_in_gpta,
    )

  try:
    if not is_tf_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_tf_gpta import (
        TF_GPT2_PRETRAINED_MODEL_ARCHIVE_LIST,
        TFGPTaDoubleHeadsModel,
        TFGPTaForSequenceClassification,
        TFGPTaLMHeadModel,
        TFGPTaMainLayer,
        TFGPTaModel,
        TFGPTaPreTrainedModel,
    )

  try:
    if not is_keras_nlp_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_gpta_tf import TFGPTaTokenizer

  try:
    if not is_flax_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_flax_gpta import FlaxGPTaLMHeadModel, FlaxGPTaModel, FlaxGPTaPreTrainedModel

else:
  import sys

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





