





from typing import Any

import numpy as np
class 							snake_case_		:







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

				lowerCamelCase :			List[Any]    		=tableau
				lowerCamelCase		, lowerCamelCase :			List[Any]    		=tableau.shape

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

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

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

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

				# Objectives for each stage
				lowerCamelCase :			Union[str, Any]    		=['''max''']

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

				lowerCamelCase :			Dict    		=['''''']

				# Index of current pivot row and column
				lowerCamelCase :			List[Any]    		=None
				lowerCamelCase :			Optional[int]    		=None

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







		@staticmethod
		def       __lowercase (		*__lowercase )					-> list[str]:
				if len(__lowercase ) != 3:
						raise ValueError('''Must provide n_vars, n_slack, and n_art_vars''' )

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

				# decision | slack | artificial
				lowerCamelCase :			Union[str, Any]    		=['''x''', '''s''', '''a''']
				lowerCamelCase :			List[Any]    		=[]
				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      ,  __lowercase )					-> tuple[Any, Any]:
				lowerCamelCase :			Optional[Any]    		=self.objectives[-1]

				# Find entries of highest magnitude in objective rows
				lowerCamelCase :			Dict    		=(objective == '''min''') - (objective == '''max''')
				lowerCamelCase :			Union[str, 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:
						lowerCamelCase :			List[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
				lowerCamelCase :			Tuple    		=slice(self.n_stages      ,  self.n_rows )

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

				# Elements of pivot column within slice
				lowerCamelCase :			int    		=tableau[s, col_idx]

				# Array filled with nans
				lowerCamelCase :			List[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
				lowerCamelCase :			Any    		=np.divide(__lowercase      ,  __lowercase      ,  out=__lowercase      ,  where=divisor > 0 )

				# Arg of minimum quotient excluding the nan values. n_stages is added
				# to compensate for earlier exclusion of objective columns
				lowerCamelCase :			List[str]    		=np.nanargmin(__lowercase ) + self.n_stages
				return row_idx, col_idx







		def       __lowercase (		self      ,  __lowercase      ,  __lowercase      ,  __lowercase )					-> np.ndarray:
				lowerCamelCase :			List[str]    		=tableau[row_idx].copy()

				lowerCamelCase :			Optional[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
				lowerCamelCase :			int    		=piv_row
				return tableau







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

				if not self.objectives:
						return tableau

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

				# Delete the artificial variable columns
				lowerCamelCase :			Any    		=np.delete(__lowercase      ,  __lowercase      ,  axis=1 )

				# Delete the objective row of the first stage
				lowerCamelCase :			Optional[int]    		=np.delete(__lowercase      ,  0      ,  axis=0 )

				lowerCamelCase :			int    		=1
				self.n_rows -= 1
				lowerCamelCase :			Tuple    		=0
				lowerCamelCase :			int    		=False
				return tableau







		def       __lowercase (		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:
								lowerCamelCase :			Union[str, 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 )

						lowerCamelCase		, lowerCamelCase :			str    		=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
								lowerCamelCase :			Optional[int]    		=self.change_stage(self.tableau )
						else:
								lowerCamelCase :			Optional[int]    		=self.pivot(self.tableau      ,  __lowercase      ,  __lowercase )
				return {}







		def       __lowercase (		self      ,  __lowercase      ,  __lowercase )					-> dict[str, float]:
				lowerCamelCase :			Any    		={'''P''': abs(tableau[0, -1] )}

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

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

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


if __name__ == "__main__":
				import doctest

				doctest.testmod()








import pytest

from datasets.utils.version import Version


@pytest.mark.parametrize(
    '''other, expected_equality'''				,							[
        (Version('''1.0.0'''		), True),
        ('''1.0.0''', True),
        (Version('''2.0.0'''		), False),
        ('''2.0.0''', False),
        ('''1''', False),
        ('''a''', False),
        (1, False),
        (None, False),
    ]				,							)
def        A__						(							SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_		) ->  Optional[int]:
		lowerCamelCase :			str    		=Version('''1.0.0'''		)
		assert (version == other) is expected_equality
		assert (version != other) is not expected_equality
		assert (hash(SCREAMING_SNAKE_CASE_		) == hash(SCREAMING_SNAKE_CASE_		)) is expected_equality

