



"""simple docstring"""






from typing import Any

import numpy as np

class 	__lowerCAmelCase							:


     '''simple docstring'''


     def __init__(      self    ,       a    ,       a   ):




          """simple docstring"""





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

          snake_case_						:List[Any]								=						tableau
          snake_case_						:Dict								=						tableau.shape

          # Number of decision variables x1, x2, x3...
          snake_case_						:Union[str, Any]								=						n_vars

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

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

          # Number of slack variables added to make inequalities into equalities
          snake_case_						:Optional[int]								=						self.n_rows - self.n_stages

          # Objectives for each stage
          snake_case_						:Union[str, Any]								=						["max"]

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

          snake_case_						:Dict								=						[""]

          # Index of current pivot row and column
          snake_case_						:List[str]								=						None
          snake_case_						:List[Any]								=						None

          # Does objective row only contain (non)-negative values?
          snake_case_						:Union[str, Any]								=						False







     @staticmethod
     def 		_a (      *a   ):




          """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
          snake_case_						:Tuple								=						["x", "s", "a"]
          snake_case_						:Dict								=						[]
          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    ,       a   ):




          """simple docstring"""





          snake_case_						:str								=						self.objectives[-1]

          # Find entries of highest magnitude in objective rows
          snake_case_						:Dict								=						(objective == "min") - (objective == "max")
          snake_case_						:Optional[Any]								=						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_						:Dict								=						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_						:str								=						slice(self.n_stages    ,       self.n_rows   )

          # RHS
          snake_case_						:Optional[Any]								=						tableau[s, -1]

          # Elements of pivot column within slice
          snake_case_						:Union[str, Any]								=						tableau[s, col_idx]

          # Array filled with nans
          snake_case_						: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
          snake_case_						:Dict								=						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_						:List[Any]								=						np.nanargmin(a   ) + self.n_stages
          return row_idx, col_idx







     def 		_a (      self    ,       a    ,       a    ,       a   ):




          """simple docstring"""





          snake_case_						:Tuple								=						tableau[row_idx].copy()

          snake_case_						: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
          snake_case_						:str								=						piv_row
          return tableau







     def 		_a (      self    ,       a   ):




          """simple docstring"""





          self.objectives.pop()

          if not self.objectives:
               return tableau

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

          # Delete the artificial variable columns
          snake_case_						:Optional[int]								=						np.delete(a    ,       a    ,       axis=1   )

          # Delete the objective row of the first stage
          snake_case_						:List[str]								=						np.delete(a    ,       0    ,       axis=0   )

          snake_case_						:Optional[Any]								=						1
          self.n_rows -= 1
          snake_case_						:List[Any]								=						0
          snake_case_						:Dict								=						False
          return tableau







     def 		_a (      self   ):




          """simple docstring"""





          for _ in range(1_00   ):
               # Completion of each stage removes an objective. If both stages
               # are complete, then no objectives are left
               if not self.objectives:
                    snake_case_						:str								=						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_						:Union[str, Any]								=						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_						:str								=						self.change_stage(self.tableau   )
               else:
                    snake_case_						:str								=						self.pivot(self.tableau    ,       a    ,       a   )
          return {}







     def 		_a (      self    ,       a    ,       a   ):




          """simple docstring"""





          snake_case_						:Any								=						{"P": abs(tableau[0, -1]   )}

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

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

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


if __name__ == "__main__":
    import doctest

    doctest.testmod()






"""simple docstring"""






def      A      (			_A,     _A = 1_000							):




					"""simple docstring"""
					if (not isinstance(_A,     _A							)) or (digit_position <= 0):
										raise ValueError("Digit position must be a positive integer"							)
					elif (not isinstance(_A,     _A							)) or (precision < 0):
										raise ValueError("Precision must be a nonnegative integer"							)

					# compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
					# accurate
					snake_case_						:List[Any]								=						(
					    4 * _subsum(_A,     1,     _A							)
					    - 2 * _subsum(_A,     4,     _A							)
					    - _subsum(_A,     5,     _A							)
					    - _subsum(_A,     6,     _A							)
					)

					# return the first hex digit of the fractional part of the result
					return hex(int((sum_result % 1) * 16							)							)[2:]
def      A      (			_A,     _A,     _A							):




					"""simple docstring"""
					snake_case_						:int								=						0.0
					for sum_index in range(digit_pos_to_extract + precision							):
										snake_case_						:Optional[Any]								=						8 * sum_index + denominator_addend
										if sum_index < digit_pos_to_extract:
															# if the exponential term is an integer and we mod it by the denominator
															# before dividing, only the integer part of the sum will change;
															# the fractional part will not
															snake_case_						:List[Any]								=						pow(
															    16,     digit_pos_to_extract - 1 - sum_index,     _A							)
										else:
															snake_case_						:Optional[Any]								=						pow(16,     digit_pos_to_extract - 1 - sum_index							)
										total += exponential_term / denominator
					return total


if __name__ == "__main__":
				import doctest

				doctest.testmod()

