




'''simple docstring'''





from typing import Any

import numpy as np






class     lowercase  :






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

         SCREAMING_SNAKE_CASE__      :					List[str]							    =			tableau
         SCREAMING_SNAKE_CASE__    ,					SCREAMING_SNAKE_CASE__      :					int							    =			tableau.shape

         # Number of decision variables x1, x2, x3...
         SCREAMING_SNAKE_CASE__      :					str							    =			n_vars

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

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

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

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

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

         SCREAMING_SNAKE_CASE__      :					Dict							    =			['''''']

         # Index of current pivot row and column
         SCREAMING_SNAKE_CASE__      :					Any							    =			None
         SCREAMING_SNAKE_CASE__      :					Optional[Any]							    =			None

         # Does objective row only contain (non)-negative values?
         SCREAMING_SNAKE_CASE__      :					Tuple							    =			False






      @staticmethod
      def  A__(*a__       )							-> 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
         SCREAMING_SNAKE_CASE__      :					str							    =			['''x''', '''s''', '''a''']
         SCREAMING_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__       )							-> tuple[Any, Any]:
         SCREAMING_SNAKE_CASE__      :					str							    =			self.objectives[-1]

         # Find entries of highest magnitude in objective rows
         SCREAMING_SNAKE_CASE__      :					Dict							    =			(objective == '''min''') - (objective == '''max''')
         SCREAMING_SNAKE_CASE__      :					Optional[int]							    =			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__      :					Optional[Any]							    =			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__      :					Optional[int]							    =			slice(self.n_stages			,	self.n_rows       )

         # RHS
         SCREAMING_SNAKE_CASE__      :					Tuple							    =			tableau[s, -1]

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

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






      def  A__(self			,	a__			,	a__			,	a__       )							-> np.ndarray:
         SCREAMING_SNAKE_CASE__      :					Optional[Any]							    =			tableau[row_idx].copy()

         SCREAMING_SNAKE_CASE__      :					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
         SCREAMING_SNAKE_CASE__      :					Union[str, Any]							    =			piv_row
         return tableau






      def  A__(self			,	a__       )							-> np.ndarray:
         self.objectives.pop()

         if not self.objectives:
            return tableau

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

         # Delete the artificial variable columns
         SCREAMING_SNAKE_CASE__      :					Tuple							    =			np.delete(a__			,	a__			,	axis=1       )

         # Delete the objective row of the first stage
         SCREAMING_SNAKE_CASE__      :					str							    =			np.delete(a__			,	0			,	axis=0       )

         SCREAMING_SNAKE_CASE__      :					Optional[int]							    =			1
         self.n_rows -= 1
         SCREAMING_SNAKE_CASE__      :					Tuple							    =			0
         SCREAMING_SNAKE_CASE__      :					List[str]							    =			False
         return tableau






      def  A__(self       )							-> 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:
               SCREAMING_SNAKE_CASE__      :					Optional[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       )

            SCREAMING_SNAKE_CASE__    ,					SCREAMING_SNAKE_CASE__      :					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
               SCREAMING_SNAKE_CASE__      :					List[str]							    =			self.change_stage(self.tableau       )
            else:
               SCREAMING_SNAKE_CASE__      :					List[str]							    =			self.pivot(self.tableau			,	a__			,	a__       )
         return {}






      def  A__(self			,	a__			,	a__       )							-> dict[str, float]:
         SCREAMING_SNAKE_CASE__      :					Tuple							    =			{'''P''': abs(tableau[0, -1]       )}

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

            # First entry in the nonzero ids
            SCREAMING_SNAKE_CASE__      :					List[str]							    =			nonzero[0][0]
            SCREAMING_SNAKE_CASE__      :					Dict							    =			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__      :					List[Any]							    =			tableau[nonzero_rowidx, -1]
               SCREAMING_SNAKE_CASE__      :					Dict							    =			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'''





lowercase__								=						[[0, 1, 1], [0, 0, 1], [1, 0, 0]]






class     lowercase  :






      def __init__(self			,	a__       )							-> List[Any]:
         SCREAMING_SNAKE_CASE__      :					int							    =			name
         SCREAMING_SNAKE_CASE__      :					Tuple							    =			[]
         SCREAMING_SNAKE_CASE__      :					Any							    =			[]






      def  A__(self			,	a__       )							-> Dict:
         self.inbound.append(a__       )






      def  A__(self			,	a__       )							-> Any:
         self.outbound.append(a__       )






      def __repr__(self       )							-> List[str]:
         return f"""<node={self.name} inbound={self.inbound} outbound={self.outbound}>"""


def 					UpperCamelCase						(	snake_case						,  snake_case=3						,  snake_case=0.85 ):




   '''simple docstring'''

   SCREAMING_SNAKE_CASE__      :					Union[str, Any]							    =			{}
   for node in nodes:
      SCREAMING_SNAKE_CASE__      :					List[Any]							    =			1

   SCREAMING_SNAKE_CASE__      :					int							    =			{}
   for node in nodes:
      SCREAMING_SNAKE_CASE__      :					Union[str, Any]							    =			len(node.outbound )

   for i in range(snake_case ):
      print(f"""======= Iteration {i + 1} =======""" )
      for _, node in enumerate(snake_case ):
         SCREAMING_SNAKE_CASE__      :					Union[str, Any]							    =			(1 - d) + d * sum(
             ranks[ib] / outbounds[ib] for ib in node.inbound )
      print(snake_case )


def 					UpperCamelCase						(	):




   '''simple docstring'''

   SCREAMING_SNAKE_CASE__      :					Any							    =			list(input('''Enter Names of the Nodes: ''' ).split() )

   SCREAMING_SNAKE_CASE__      :					str							    =			[Node(snake_case ) for name in names]

   for ri, row in enumerate(snake_case ):
      for ci, col in enumerate(snake_case ):
         if col == 1:
            nodes[ci].add_inbound(names[ri] )
            nodes[ri].add_outbound(names[ci] )

   print('''======= Nodes =======''' )
   for node in nodes:
      print(snake_case )

   page_rank(snake_case )


if __name__ == "__main__":
       main()

