


"""simple docstring"""



from typing import Any

import numpy as np







class       __a	:







				def __init__(   self			,  UpperCAmelCase			,  UpperCAmelCase      ):

					'''simple docstring'''






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

					lowerCAmelCase_			       = tableau
					lowerCAmelCase_       ,  lowerCAmelCase_			       = tableau.shape

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

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

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

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

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

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

					lowerCAmelCase_			       = ['''''']

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

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







				@staticmethod
				def     lowerCamelCase_    (   *UpperCAmelCase      ):

					'''simple docstring'''






					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_			       = ['''x''', '''s''', '''a''']
					lowerCAmelCase_			       = []
					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			,  UpperCAmelCase      ):

					'''simple docstring'''






					lowerCAmelCase_			       = self.objectives[-1]

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

					# RHS
					lowerCAmelCase_			       = tableau[s, -1]

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

					# Array filled with nans
					lowerCAmelCase_			       = 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_			       = 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_			       = np.nanargmin(lowercase_      ) + self.n_stages
					return row_idx, col_idx







				def     lowerCamelCase_    (   self			,  UpperCAmelCase			,  UpperCAmelCase			,  UpperCAmelCase      ):

					'''simple docstring'''






					lowerCAmelCase_			       = tableau[row_idx].copy()

					lowerCAmelCase_			       = 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_			       = piv_row
					return tableau







				def     lowerCamelCase_    (   self			,  UpperCAmelCase      ):

					'''simple docstring'''






					self.objectives.pop()

					if not self.objectives:
						return tableau

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

					# Delete the artificial variable columns
					lowerCAmelCase_			       = np.delete(lowercase_			,  lowercase_			,  axis=1      )

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

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







				def     lowerCamelCase_    (   self      ):

					'''simple docstring'''






					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:
							lowerCAmelCase_			       = 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_			       = 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_			       = self.change_stage(self.tableau      )
						else:
							lowerCAmelCase_			       = self.pivot(self.tableau			,  lowercase_			,  lowercase_      )
					return {}







				def     lowerCamelCase_    (   self			,  UpperCAmelCase			,  UpperCAmelCase      ):

					'''simple docstring'''






					lowerCAmelCase_			       = {'''P''': abs(tableau[0, -1]      )}

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

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

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



"""simple docstring"""



lowercase_							 =       [0.485, 0.456, 0.406]
lowercase_							 =       [0.229, 0.224, 0.225]
lowercase_							 =       [0.5, 0.5, 0.5]
lowercase_							 =       [0.5, 0.5, 0.5]
lowercase_							 =       [0.4814_5466, 0.457_8275, 0.4082_1073]
lowercase_							 =       [0.2686_2954, 0.2613_0258, 0.2757_7711]