





'''simple docstring'''







from typing import Any

import numpy as np





class     _UpperCAmelCase							:
		def __init__(  self,__SCREAMING_SNAKE_CASE,__SCREAMING_SNAKE_CASE			):



					'''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__			(  *__SCREAMING_SNAKE_CASE			):



					'''simple docstring'''

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

					if not all(x >= 0 and isinstance(__SCREAMING_SNAKE_CASE,__SCREAMING_SNAKE_CASE			) 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,__SCREAMING_SNAKE_CASE			):



					'''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(__SCREAMING_SNAKE_CASE,__SCREAMING_SNAKE_CASE,out=__SCREAMING_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
					__lowerCAmelCase											=				np.nanargmin(__SCREAMING_SNAKE_CASE			) + self.n_stages
					return row_idx, col_idx
		def   lowerCamelCase__			(  self,__SCREAMING_SNAKE_CASE,__SCREAMING_SNAKE_CASE,__SCREAMING_SNAKE_CASE			):



					'''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,__SCREAMING_SNAKE_CASE			):



					'''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(__SCREAMING_SNAKE_CASE,__SCREAMING_SNAKE_CASE,axis=1			)

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

					__lowerCAmelCase											=				1
					self.n_rows -= 1
					__lowerCAmelCase											=				0
					__lowerCAmelCase											=				False
					return tableau
		def   lowerCamelCase__			(  self			):



					'''simple docstring'''

					for _ in range(1_00			):
								# 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,__SCREAMING_SNAKE_CASE,__SCREAMING_SNAKE_CASE			)
					return {}







		def   lowerCamelCase__			(  self,__SCREAMING_SNAKE_CASE,__SCREAMING_SNAKE_CASE			):



					'''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(__SCREAMING_SNAKE_CASE,0			)
					return output_dict


if __name__ == "__main__":
	import doctest

	doctest.testmod()








'''simple docstring'''







import importlib
import sys
from argparse import REMAINDER, ArgumentParser
from pathlib import Path

import torch_xla.distributed.xla_multiprocessing as xmp





def    _lowerCAmelCase						(						)					->					List[str]:
			__lowerCAmelCase											=				ArgumentParser(
			    description=(
			        """PyTorch TPU distributed training launch helper utility that will spawn up multiple distributed processes"""
			    )	)

			# Optional arguments for the launch helper
			parser.add_argument("""--num_cores"""					,	type=lowercase					,	default=1					,	help="""Number of TPU cores to use (1 or 8)."""	)

			# positional
			parser.add_argument(
			    """training_script"""					,	type=lowercase					,	help=(
			        """The full path to the single TPU training """
			        """program/script to be launched in parallel, """
			        """followed by all the arguments for the """
			        """training script"""
			    )					,	)

			# rest from the training program
			parser.add_argument("""training_script_args"""					,	nargs=lowercase	)

			return parser.parse_args()





def    _lowerCAmelCase						(						)					->					Any:
			__lowerCAmelCase											=				parse_args()

			# Import training_script as a module.
			__lowerCAmelCase											=				Path(args.training_script	)
			sys.path.append(str(script_fpath.parent.resolve()	)	)
			__lowerCAmelCase											=				script_fpath.stem
			__lowerCAmelCase											=				importlib.import_module(lowercase	)

			# Patch sys.argv
			__lowerCAmelCase											=				[args.training_script] + args.training_script_args + ["""--tpu_num_cores""", str(args.num_cores	)]

			xmp.spawn(mod._mp_fn					,	args=()					,	nprocs=args.num_cores	)


if __name__ == "__main__":
	main()

