




'''simple docstring'''







from typing import Any

import numpy as np





class 					lowerCamelCase_							:




					'''simple docstring'''






					def __init__(   self,  __UpperCamelCase,  __UpperCamelCase			):



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

							_snake_case     	=	tableau
							_snake_case	,   _snake_case     	=	tableau.shape

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

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

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

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

							# Objectives for each stage
							_snake_case     	=	["max"]

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

							_snake_case     	=	[""]

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

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






					@staticmethod
					def     __SCREAMING_SNAKE_CASE     (   *__UpperCamelCase			):



							if len(lowerCamelCase__			) != 3:
									raise ValueError("Must provide n_vars, n_slack, and n_art_vars"			)

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

							# decision | slack | artificial
							_snake_case     	=	["x", "s", "a"]
							_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     __SCREAMING_SNAKE_CASE     (   self,  __UpperCamelCase			):
							_snake_case     	=	self.objectives[-1]

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

							# RHS
							_snake_case     	=	tableau[s, -1]

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

							# Array filled with nans
							_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
							_snake_case     	=	np.divide(lowerCamelCase__,  lowerCamelCase__,  out=lowerCamelCase__,  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     	=	np.nanargmin(lowerCamelCase__			) + self.n_stages
							return row_idx, col_idx






					def     __SCREAMING_SNAKE_CASE     (   self,  __UpperCamelCase,  __UpperCamelCase,  __UpperCamelCase			):
							_snake_case     	=	tableau[row_idx].copy()

							_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
							_snake_case     	=	piv_row
							return tableau






					def     __SCREAMING_SNAKE_CASE     (   self,  __UpperCamelCase			):
							self.objectives.pop()

							if not self.objectives:
									return tableau

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

							# Delete the artificial variable columns
							_snake_case     	=	np.delete(lowerCamelCase__,  lowerCamelCase__,  axis=1			)

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

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






					def     __SCREAMING_SNAKE_CASE     (   self			):



							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:
											_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			)

									_snake_case	,   _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
											_snake_case     	=	self.change_stage(self.tableau			)
									else:
											_snake_case     	=	self.pivot(self.tableau,  lowerCamelCase__,  lowerCamelCase__			)
							return {}






					def     __SCREAMING_SNAKE_CASE     (   self,  __UpperCamelCase,  __UpperCamelCase			):
							_snake_case     	=	{"P": abs(tableau[0, -1]			)}

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

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

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


if __name__ == "__main__":
						import doctest

						doctest.testmod()











'''simple docstring'''







def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) * 9 / 5) + 32						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round(float(lowercase_  ) + 273.15						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) * 9 / 5) + 491.67						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) - 32) * 5 / 9						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round(((float(lowercase_  ) - 32) * 5 / 9) + 273.15						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round(float(lowercase_  ) + 459.67						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round(float(lowercase_  ) - 273.15						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round(((float(lowercase_  ) - 273.15) * 9 / 5) + 32						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) * 9 / 5)						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) - 491.67) * 5 / 9						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round(float(lowercase_  ) - 459.67						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) * 5 / 9)						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) * 1.25 + 273.15)						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) * 2.25 + 32)						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) * 1.25)						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) * 2.25 + 32 + 459.67)						,							lowercase_  )


if __name__ == "__main__":
						import doctest

						doctest.testmod()





