

from typing import Any

import numpy as np



class 						a_			:



      """simple docstring"""







      def __init__( self	:				Dict     ,snake_case	:				np.ndarray     ,snake_case	:				int							):
           # Check if RHS is negative
           if np.any(tableau[:, -1]     ,where=tableau[:, -1] < 0							):
                raise ValueError('RHS must be > 0'							)

           SCREAMING_SNAKE_CASE 		=tableau
           SCREAMING_SNAKE_CASE		,    SCREAMING_SNAKE_CASE 		=tableau.shape

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

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

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

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

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

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

           SCREAMING_SNAKE_CASE 		=['']

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

           # Does objective row only contain (non)-negative values?
           SCREAMING_SNAKE_CASE 		=False
      @staticmethod
      def 			_lowerCAmelCase	( *snake_case	:				int							):
           if len(snake_case							) != 3:
                raise ValueError('Must provide n_vars, n_slack, and n_art_vars'							)

           if not all(x >= 0 and isinstance(snake_case     ,snake_case							) for x in args							):
                raise ValueError('All arguments must be non-negative integers'							)

           # decision | slack | artificial
           SCREAMING_SNAKE_CASE 		=['x', 's', 'a']
           SCREAMING_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 			_lowerCAmelCase	( self	:				str     ,snake_case	:				np.ndarray							):
           SCREAMING_SNAKE_CASE 		=self.objectives[-1]

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

           # RHS
           SCREAMING_SNAKE_CASE 		=tableau[s, -1]

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

           # Array filled with nans
           SCREAMING_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
           SCREAMING_SNAKE_CASE 		=np.divide(snake_case     ,snake_case     ,out=snake_case     ,where=divisor > 0							)

           # Arg of minimum quotient excluding the nan values. n_stages is added
           # to compensate for earlier exclusion of objective columns
           SCREAMING_SNAKE_CASE 		=np.nanargmin(snake_case							) + self.n_stages
           return row_idx, col_idx
      def 			_lowerCAmelCase	( self	:				Optional[int]     ,snake_case	:				np.ndarray     ,snake_case	:				int     ,snake_case	:				int							):
           SCREAMING_SNAKE_CASE 		=tableau[row_idx].copy()

           SCREAMING_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
           SCREAMING_SNAKE_CASE 		=piv_row
           return tableau
      def 			_lowerCAmelCase	( self	:				Any     ,snake_case	:				np.ndarray							):
           self.objectives.pop()

           if not self.objectives:
                return tableau

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

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

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

           SCREAMING_SNAKE_CASE 		=1
           self.n_rows -= 1
           SCREAMING_SNAKE_CASE 		=0
           SCREAMING_SNAKE_CASE 		=False
           return tableau
      def 			_lowerCAmelCase	( self	:				Union[str, Any]							):
           # Stop simplex algorithm from cycling.
           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:
                     SCREAMING_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							)

                SCREAMING_SNAKE_CASE		,    SCREAMING_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
                     SCREAMING_SNAKE_CASE 		=self.change_stage(self.tableau							)
                else:
                     SCREAMING_SNAKE_CASE 		=self.pivot(self.tableau     ,snake_case     ,snake_case							)
           return {}


      def 			_lowerCAmelCase	( self	:				Optional[int]     ,snake_case	:				np.ndarray     ,snake_case	:				list[str]							):
           SCREAMING_SNAKE_CASE 		={'P': abs(tableau[0, -1]							)}

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

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

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


if __name__ == "__main__":
 import doctest

 doctest.testmod()




import math



class 						a_			:



      """simple docstring"""







      def __init__( self	:				str     ,snake_case	:				List[Any]     ,snake_case	:				Union[str, Any]     ,snake_case	:				Optional[int]							):
           SCREAMING_SNAKE_CASE 		=x
           SCREAMING_SNAKE_CASE 		=y
           SCREAMING_SNAKE_CASE 		=z


      def __repr__( self	:				Any							):
           return f'Point({self.x}, {self.y}, {self.z})'







def      snake_case__							(  lowerCAmelCase_,       lowerCAmelCase_     ):





     """simple docstring"""







     return math.sqrt(abs((b.x - a.x) ** 2 + (b.y - a.y) ** 2 + (b.z - a.z) ** 2     )     )


if __name__ == "__main__":
 import doctest

 doctest.testmod()

