code: 
  
  
  '''simple docstring'''
  
  from typing import Any
  
  import numpy as np
  
  
  
  
  
  
  
  class  UpperCAmelCase :
  
   def __init__( self :	Optional[Any],					a_ :	np.ndarray,					a_ :	int					):
  
  
  
  
  
      """simple docstring"""
  
  
  
      if np.any(tableau[:, -1],					where=tableau[:, -1] < 0					):
         raise ValueError("RHS must be > 0"					)
  
      UpperCamelCase__ 						=						tableau
      UpperCamelCase__						,		UpperCamelCase__ 						=						tableau.shape
  
      # Number of decision variables x1, x2, x3...
      UpperCamelCase__ 						=						n_vars
  
      # Number of artificial variables to be minimised
      UpperCamelCase__ 						=						len(np.where(tableau[self.n_vars : -1] == -1					)[0]					)
  
      # 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
      UpperCamelCase__ 						=						(self.n_art_vars > 0) + 1
  
      # Number of slack variables added to make inequalities into equalities
      UpperCamelCase__ 						=						self.n_rows - self.n_stages
  
      # Objectives for each stage
      UpperCamelCase__ 						=						["max"]
  
      # In two stage simplex, first minimise then maximise
      if self.n_art_vars:
         self.objectives.append("min"					)
  
      UpperCamelCase__ 						=						[""]
  
      # Index of current pivot row and column
      UpperCamelCase__ 						=						None
      UpperCamelCase__ 						=						None
  
      # Does objective row only contain (non)-negative values?
      UpperCamelCase__ 						=						False
  
   @staticmethod
   def 		lowercase_						( *a_ :	int					):
  
  
  
  
  
      """simple docstring"""
  
  
  
      if len(a_					) != 3:
         raise ValueError("Must provide n_vars, n_slack, and n_art_vars"					)
  
      if not all(x >= 0 and isinstance(a_,					a_					) for x in args					):
         raise ValueError("All arguments must be non-negative integers"					)
  
      # decision | slack | artificial
      UpperCamelCase__ 						=						["x", "s", "a"]
      UpperCamelCase__ 						=						[]
      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 		lowercase_						( self :	int,					a_ :	np.ndarray					):
  
  
  
  
  
      """simple docstring"""
  
  
  
      UpperCamelCase__ 						=						self.objectives[-1]
  
      # Find entries of highest magnitude in objective rows
      UpperCamelCase__ 						=						(objective == "min") - (objective == "max")
      UpperCamelCase__ 						=						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:
         UpperCamelCase__ 						=						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
      UpperCamelCase__ 						=						slice(self.n_stages,					self.n_rows					)
  
      # RHS
      UpperCamelCase__ 						=						tableau[s, -1]
  
      # Elements of pivot column within slice
      UpperCamelCase__ 						=						tableau[s, col_idx]
  
      # Array filled with nans
      UpperCamelCase__ 						=						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
      UpperCamelCase__ 						=						np.divide(a_,					a_,					out=a_,					where=divisor > 0					)
  
      # Arg of minimum quotient excluding the nan values. n_stages is added
      # to compensate for earlier exclusion of objective columns
      UpperCamelCase__ 						=						np.nanargmin(a_					) + self.n_stages
      return row_idx, col_idx
  
   def 		lowercase_						( self :	List[Any],					a_ :	np.ndarray,					a_ :	int,					a_ :	int					):
  
  
  
  
  
      """simple docstring"""
  
  
  
      UpperCamelCase__ 						=						tableau[row_idx].copy()
  
      UpperCamelCase__ 						=						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
      UpperCamelCase__ 						=						piv_row
      return tableau
  
   def 		lowercase_						( self :	Dict,					a_ :	np.ndarray					):
  
  
  
  
  
      """simple docstring"""
  
  
  
      self.objectives.pop()
  
      if not self.objectives:
         return tableau
  
      # Slice containing ids for artificial columns
      UpperCamelCase__ 						=						slice(-self.n_art_vars - 1,					-1					)
  
      # Delete the artificial variable columns
      UpperCamelCase__ 						=						np.delete(a_,					a_,					axis=1					)
  
      # Delete the objective row of the first stage
      UpperCamelCase__ 						=						np.delete(a_,					0,					axis=0					)
  
      UpperCamelCase__ 						=						1
      self.n_rows -= 1
      UpperCamelCase__ 						=						0
      UpperCamelCase__ 						=						False
      return tableau
  
   def 		lowercase_						( self :	Optional[int]					):
  
  
  
  
  
      """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:
            UpperCamelCase__ 						=						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					)
  
         UpperCamelCase__						,		UpperCamelCase__ 						=						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
            UpperCamelCase__ 						=						self.change_stage(self.tableau					)
         else:
            UpperCamelCase__ 						=						self.pivot(self.tableau,					a_,					a_					)
      return {}
  
   def 		lowercase_						( self :	List[Any],					a_ :	np.ndarray,					a_ :	list[str]					):
  
  
  
  
  
      """simple docstring"""
  
  
  
      UpperCamelCase__ 						=						{"P": abs(tableau[0, -1]					)}
  
      for i in range(self.n_vars					):
         # Gives ids of nonzero entries in the ith column
         UpperCamelCase__ 						=						np.nonzero(tableau[:, i]					)
         UpperCamelCase__ 						=						len(nonzero[0]					)
  
         # First entry in the nonzero ids
         UpperCamelCase__ 						=						nonzero[0][0]
         UpperCamelCase__ 						=						tableau[nonzero_rowidx, i]
  
         # If there is only one nonzero value in column, which is one
         if n_nonzero == nonzero_val == 1:
            UpperCamelCase__ 						=						tableau[nonzero_rowidx, -1]
            UpperCamelCase__ 						=						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(a_,					0					)
      return output_dict
  
  
  if __name__ == "__main__":
         import doctest
  
         doctest.testmod()
style_context: 
  
  
  '''simple docstring'''
  
  from typing import TYPE_CHECKING
  
  from ...utils import (
      OptionalDependencyNotAvailable,
      _LazyModule,
      is_sentencepiece_available,
      is_tokenizers_available,
      is_torch_available,
  )
  
  
  __lowercase:		int							=     {
      "configuration_open_llama": ["OPEN_LLAMA_PRETRAINED_CONFIG_ARCHIVE_MAP", "OpenLlamaConfig"],
  }
  
  try:
         if not is_sentencepiece_available():
                raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
         pass
  else:
         __lowercase:		str							=     ["LlamaTokenizer"]
  
  try:
         if not is_tokenizers_available():
                raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
         pass
  else:
         __lowercase:		List[Any]							=     ["LlamaTokenizerFast"]
  
  try:
         if not is_torch_available():
                raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
         pass
  else:
         __lowercase:		Union[str, Any]							=     [
             "OpenLlamaForCausalLM",
             "OpenLlamaModel",
             "OpenLlamaPreTrainedModel",
             "OpenLlamaForSequenceClassification",
         ]
  
  
  if TYPE_CHECKING:
         from .configuration_open_llama import OPEN_LLAMA_PRETRAINED_CONFIG_ARCHIVE_MAP, OpenLlamaConfig
  
         try:
                if not is_sentencepiece_available():
                       raise OptionalDependencyNotAvailable()
         except OptionalDependencyNotAvailable:
                pass
         else:
                from transformers import LlamaTokenizer
  
         try:
                if not is_tokenizers_available():
                       raise OptionalDependencyNotAvailable()
         except OptionalDependencyNotAvailable:
                pass
         else:
                from transformers import LlamaTokenizerFast
  
         try:
                if not is_torch_available():
                       raise OptionalDependencyNotAvailable()
         except OptionalDependencyNotAvailable:
                pass
         else:
                from .modeling_open_llama import (
                    OpenLlamaForCausalLM,
                    OpenLlamaForSequenceClassification,
                    OpenLlamaModel,
                    OpenLlamaPreTrainedModel,
                )
  
  
  else:
         import sys
  
         __lowercase:		Tuple							=     _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)