
def 						lowercase_			(   A__		)							->							int:
    """simple docstring"""

    if num < 0:
        return -1
    return 1 if num else 0



def 						lowercase_			(   )							->							None:
    """simple docstring"""

    assert signum(5		) == 1
    assert signum(-5		) == -1
    assert signum(0		) == 0


if __name__ == "__main__":
   print(signum(12))
   print(signum(-12))
   print(signum(0))



from typing import Any

import numpy as np







class      lowerCamelCase		:





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

         snake_case      =					tableau
         snake_case     ,							snake_case      =					tableau.shape

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

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

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

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

         # Objectives for each stage
         snake_case      =					["max"]

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

         snake_case      =					[""]

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

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





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

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

         # RHS
         snake_case      =					tableau[s, -1]

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

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





     def 		UpperCAmelCase(self      :    int				,    _A      :    np.ndarray				,    _A      :    int				,    _A      :    int   )						->						np.ndarray:
         snake_case      =					tableau[row_idx].copy()

         snake_case      =					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      =					piv_row
         return tableau





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

         if not self.objectives:
             return tableau

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

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

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

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





     def 		UpperCAmelCase(self      :    Optional[Any]   )						->						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:
                 snake_case      =					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      =					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      =					self.change_stage(self.tableau   )
             else:
                 snake_case      =					self.pivot(self.tableau				,    _A				,    _A   )
         return {}





     def 		UpperCAmelCase(self      :    Optional[Any]				,    _A      :    np.ndarray				,    _A      :    list[str]   )						->						dict[str, float]:
         snake_case      =					{"P": abs(tableau[0, -1]   )}

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

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

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

