code: 
  
  
  import importlib
  import sys
  from argparse import REMAINDER, ArgumentParser
  from pathlib import Path
  
  import torch_xla.distributed.xla_multiprocessing as xmp
  
  
  
  
  def   lowerCamelCase_       (					):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						a_					=		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=UpperCAmelCase__       ,    default=1       ,    help="""Number of TPU cores to use (1 or 8)."""      )
  
  						# positional
  						parser.add_argument(
  						    """training_script"""       ,    type=UpperCAmelCase__       ,    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=UpperCAmelCase__      )
  
  						return parser.parse_args()
  
  
  
  
  def   lowerCamelCase_       (					):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						a_					=		parse_args()
  
  						# Import training_script as a module.
  						a_					=		Path(args.training_script      )
  						sys.path.append(str(script_fpath.parent.resolve()      )      )
  						a_					=		script_fpath.stem
  						a_					=		importlib.import_module(UpperCAmelCase__      )
  
  						# Patch sys.argv
  						a_					=		[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()
style_context: 
  
  
  from collections.abc import Callable
  from math import log
  from os import name, system
  from random import gauss, seed
  from typing import TypeVar
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						seed(1      )
  						return [gauss(UpperCAmelCase__       ,    UpperCAmelCase__      ) for _ in range(UpperCAmelCase__      )]
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						return [k for k in range(UpperCAmelCase__      ) for _ in range(instance_count[k]      )]
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						return sum(UpperCAmelCase__      ) / instance_count
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						return instance_count / total_count
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						a_					=		[]  # An empty list to store all squared differences
  						# iterate over number of elements in items
  						for i in range(len(UpperCAmelCase__      )      ):
  												# for loop iterates over number of elements in inner layer of items
  												for j in range(len(items[i]      )      ):
  																		# appending squared differences to 'squared_diff' list
  																		squared_diff.append((items[i][j] - means[i]) ** 2      )
  
      # one divided by (the number of all instances - number of classes) multiplied by
      # sum of all squared differences
  						a_					=		len(UpperCAmelCase__      )  # Number of classes in dataset
  						return 1 / (total_count - n_classes) * sum(UpperCAmelCase__      )
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						a_					=		[]
  						# for loop iterates over number of elements in list
  						for i in range(len(UpperCAmelCase__      )      ):
  												# for loop iterates over number of inner items of each element
  												for j in range(len(x_items[i]      )      ):
  																		a_					=		[]  # to store all discriminant values of each item as a list
  																		# for loop iterates over number of classes we have in our dataset
  																		for k in range(len(UpperCAmelCase__      )      ):
  																								# appending values of discriminants for each class to 'temp' list
  																								temp.append(
  																								    x_items[i][j] * (means[k] / variance)
  																								    - (means[k] ** 2 / (2 * variance))
  																								    + log(probabilities[k]      )      )
  																		# appending discriminant values of each item to 'results' list
  																		results.append(UpperCAmelCase__      )
  
  						return [result.index(max(UpperCAmelCase__      )      ) for result in results]
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						a_					=		sum(1 for i, j in zip(UpperCAmelCase__       ,    UpperCAmelCase__      ) if i == j      )
  						# percentage of accuracy equals to number of correct predictions divided by number
  						# of all data and multiplied by 100
  						return (correct / len(UpperCAmelCase__      )) * 100
  
  
  A_    :					Dict             =TypeVar("""num""")
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__ = lambda UpperCAmelCase__      : True       ,    UpperCAmelCase__ = None       ,    ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						while True:
  												try:
  																		a_					=		input_type(input(UpperCAmelCase__      ).strip() or default      )
  																		if condition(UpperCAmelCase__      ):
  																								return user_input
  																		else:
  																								print(F"{user_input}: {err_msg}"      )
  																								continue
  												except ValueError:
  																		print(
  																		    F"{user_input}: Incorrect input type, expected {input_type.__name__!r}"      )
  
  
  
  
  def   lowerCamelCase_       (					):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						while True:
  												print(""" Linear Discriminant Analysis """.center(50       ,    """*"""      )      )
  												print("""*""" * 50       ,    """\n"""      )
  												print("""First of all we should specify the number of classes that"""      )
  												print("""we want to generate as training dataset"""      )
  												# Trying to get number of classes
  												a_					=		valid_input(
  												    input_type=UpperCAmelCase__       ,    condition=lambda UpperCAmelCase__      : x > 0       ,    input_msg="""Enter the number of classes (Data Groupings): """       ,    err_msg="""Number of classes should be positive!"""       ,    )
  
  												print("""-""" * 100      )
  
  												# Trying to get the value of standard deviation
  												a_					=		valid_input(
  												    input_type=UpperCAmelCase__       ,    condition=lambda UpperCAmelCase__      : x >= 0       ,    input_msg=(
  												        """Enter the value of standard deviation"""
  												        """(Default value is 1.0 for all classes): """
  												    )       ,    err_msg="""Standard deviation should not be negative!"""       ,    default="""1.0"""       ,    )
  
  												print("""-""" * 100      )
  
  												# Trying to get number of instances in classes and theirs means to generate
  												# dataset
  												a_					=		[]  # An empty list to store instance counts of classes in dataset
  												for i in range(UpperCAmelCase__      ):
  																		a_					=		valid_input(
  																		    input_type=UpperCAmelCase__       ,    condition=lambda UpperCAmelCase__      : x > 0       ,    input_msg=(F"Enter The number of instances for class_{i+1}: ")       ,    err_msg="""Number of instances should be positive!"""       ,    )
  																		counts.append(UpperCAmelCase__      )
  												print("""-""" * 100      )
  
  												# An empty list to store values of user-entered means of classes
  												a_					=		[]
  												for a in range(UpperCAmelCase__      ):
  																		a_					=		valid_input(
  																		    input_type=UpperCAmelCase__       ,    input_msg=(F"Enter the value of mean for class_{a+1}: ")       ,    err_msg="""This is an invalid value."""       ,    )
  																		user_means.append(UpperCAmelCase__      )
  												print("""-""" * 100      )
  
  												print("""Standard deviation: """       ,    UpperCAmelCase__      )
  												# print out the number of instances in classes in separated line
  												for i, count in enumerate(UpperCAmelCase__       ,    1      ):
  																		print(F"Number of instances in class_{i} is: {count}"      )
  												print("""-""" * 100      )
  
  												# print out mean values of classes separated line
  												for i, user_mean in enumerate(UpperCAmelCase__       ,    1      ):
  																		print(F"Mean of class_{i} is: {user_mean}"      )
  												print("""-""" * 100      )
  
  												# Generating training dataset drawn from gaussian distribution
  												a_					=		[
  												    gaussian_distribution(user_means[j]       ,    UpperCAmelCase__       ,    counts[j]      )
  												    for j in range(UpperCAmelCase__      )
  												]
  												print("""Generated Normal Distribution: \n"""       ,    UpperCAmelCase__      )
  												print("""-""" * 100      )
  
  												# Generating Ys to detecting corresponding classes
  												a_					=		y_generator(UpperCAmelCase__       ,    UpperCAmelCase__      )
  												print("""Generated Corresponding Ys: \n"""       ,    UpperCAmelCase__      )
  												print("""-""" * 100      )
  
  												# Calculating the value of actual mean for each class
  												a_					=		[calculate_mean(counts[k]       ,    x[k]      ) for k in range(UpperCAmelCase__      )]
  												# for loop iterates over number of elements in 'actual_means' list and print
  												# out them in separated line
  												for i, actual_mean in enumerate(UpperCAmelCase__       ,    1      ):
  																		print(F"Actual(Real) mean of class_{i} is: {actual_mean}"      )
  												print("""-""" * 100      )
  
  												# Calculating the value of probabilities for each class
  												a_					=		[
  												    calculate_probabilities(counts[i]       ,    sum(UpperCAmelCase__      )      ) for i in range(UpperCAmelCase__      )
  												]
  
  												# for loop iterates over number of elements in 'probabilities' list and print
  												# out them in separated line
  												for i, probability in enumerate(UpperCAmelCase__       ,    1      ):
  																		print(F"Probability of class_{i} is: {probability}"      )
  												print("""-""" * 100      )
  
  												# Calculating the values of variance for each class
  												a_					=		calculate_variance(UpperCAmelCase__       ,    UpperCAmelCase__       ,    sum(UpperCAmelCase__      )      )
  												print("""Variance: """       ,    UpperCAmelCase__      )
  												print("""-""" * 100      )
  
  												# Predicting Y values
  												# storing predicted Y values in 'pre_indexes' variable
  												a_					=		predict_y_values(UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__      )
  												print("""-""" * 100      )
  
  												# Calculating Accuracy of the model
  												print(F"Accuracy: {accuracy(UpperCAmelCase__       ,    UpperCAmelCase__      )}"      )
  												print("""-""" * 100      )
  												print(""" DONE """.center(100       ,    """+"""      )      )
  
  												if input("""Press any key to restart or 'q' for quit: """      ).strip().lower() == "q":
  																		print("""\n""" + """GoodBye!""".center(100       ,    """-"""      ) + """\n"""      )
  																		break
  												system("""cls""" if name == """nt""" else """clear"""      )  # noqa: S605
  
  
  if __name__ == "__main__":
  	main()