code: 
  
  
  '''simple docstring'''
  
  
  
  
  from collections.abc import Callable
  from math import log
  from os import name, system
  from random import gauss, seed
  from typing import TypeVar
  
  
  
  
  
  def 							a_       (						lowercase							,						lowercase							,						lowercase    )			->list:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				seed(1    )
  				return [gauss(lowercase							,						lowercase    ) for _ in range(lowercase    )]
  
  
  
  
  
  def 							a_       (						lowercase							,						lowercase    )			->list:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				return [k for k in range(lowercase    ) for _ in range(instance_count[k]    )]
  
  
  
  
  
  def 							a_       (						lowercase							,						lowercase    )			->float:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				return sum(lowercase    ) / instance_count
  
  
  
  
  
  def 							a_       (						lowercase							,						lowercase    )			->float:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				return instance_count / total_count
  
  
  
  
  
  def 							a_       (						lowercase							,						lowercase							,						lowercase    )			->float:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				__lowerCamelCase		:      Any											=					[]  # An empty list to store all squared differences
  				# iterate over number of elements in items
  				for i in range(len(lowercase    )    ):
  								# 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
  				__lowerCamelCase		:      Optional[int]											=					len(lowercase    )  # Number of classes in dataset
  				return 1 / (total_count - n_classes) * sum(lowercase    )
  
  
  
  
  
  def 							a_       (						lowercase							,						lowercase							,						lowercase							,						lowercase    )			->list:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				__lowerCamelCase		:      Optional[Any]											=					[]
  				# for loop iterates over number of elements in list
  				for i in range(len(lowercase    )    ):
  								# for loop iterates over number of inner items of each element
  								for j in range(len(x_items[i]    )    ):
  												__lowerCamelCase		:      int											=					[]  # 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(lowercase    )    ):
  																# 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(lowercase    )
  
  				return [result.index(max(lowercase    )    ) for result in results]
  
  
  
  
  
  def 							a_       (						lowercase							,						lowercase    )			->float:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				__lowerCamelCase		:      Tuple											=					sum(1 for i, j in zip(lowercase							,						lowercase    ) 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(lowercase    )) * 100
  
  
  __lowercase  :      Dict      		=				TypeVar("""num""")
  
  
  
  
  
  def 							a_       (						lowercase							,						lowercase							,						lowercase							,						lowercase = lambda lowercase    : True							,						lowercase = None							,						)			->num:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				while True:
  								try:
  												__lowerCamelCase		:      Optional[int]											=					input_type(input(lowercase    ).strip() or default    )
  												if condition(lowercase    ):
  																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 							a_       (						)			->Tuple:
  
  
  
  
  
  
  				'''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
  								__lowerCamelCase		:      Optional[int]											=					valid_input(
  								    input_type=lowercase							,						condition=lambda lowercase    : 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
  								__lowerCamelCase		:      Union[str, Any]											=					valid_input(
  								    input_type=lowercase							,						condition=lambda lowercase    : 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
  								__lowerCamelCase		:      Optional[int]											=					[]  # An empty list to store instance counts of classes in dataset
  								for i in range(lowercase    ):
  												__lowerCamelCase		:      Optional[int]											=					valid_input(
  												    input_type=lowercase							,						condition=lambda lowercase    : x > 0							,						input_msg=(F'Enter The number of instances for class_{i+1}: ')							,						err_msg="Number of instances should be positive!"							,						)
  												counts.append(lowercase    )
  								print("-" * 100    )
  
  								# An empty list to store values of user-entered means of classes
  								__lowerCamelCase		:      List[str]											=					[]
  								for a in range(lowercase    ):
  												__lowerCamelCase		:      Union[str, Any]											=					valid_input(
  												    input_type=lowercase							,						input_msg=(F'Enter the value of mean for class_{a+1}: ')							,						err_msg="This is an invalid value."							,						)
  												user_means.append(lowercase    )
  								print("-" * 100    )
  
  								print("Standard deviation: "							,						lowercase    )
  								# print out the number of instances in classes in separated line
  								for i, count in enumerate(lowercase							,						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(lowercase							,						1    ):
  												print(F'Mean of class_{i} is: {user_mean}'    )
  								print("-" * 100    )
  
  								# Generating training dataset drawn from gaussian distribution
  								__lowerCamelCase		:      Tuple											=					[
  								    gaussian_distribution(user_means[j]							,						lowercase							,						counts[j]    )
  								    for j in range(lowercase    )
  								]
  								print("Generated Normal Distribution: \n"							,						lowercase    )
  								print("-" * 100    )
  
  								# Generating Ys to detecting corresponding classes
  								__lowerCamelCase		:      Any											=					y_generator(lowercase							,						lowercase    )
  								print("Generated Corresponding Ys: \n"							,						lowercase    )
  								print("-" * 100    )
  
  								# Calculating the value of actual mean for each class
  								__lowerCamelCase		:      Tuple											=					[calculate_mean(counts[k]							,						x[k]    ) for k in range(lowercase    )]
  								# for loop iterates over number of elements in 'actual_means' list and print
  								# out them in separated line
  								for i, actual_mean in enumerate(lowercase							,						1    ):
  												print(F'Actual(Real) mean of class_{i} is: {actual_mean}'    )
  								print("-" * 100    )
  
  								# Calculating the value of probabilities for each class
  								__lowerCamelCase		:      List[str]											=					[
  								    calculate_probabilities(counts[i]							,						sum(lowercase    )    ) for i in range(lowercase    )
  								]
  
  								# for loop iterates over number of elements in 'probabilities' list and print
  								# out them in separated line
  								for i, probability in enumerate(lowercase							,						1    ):
  												print(F'Probability of class_{i} is: {probability}'    )
  								print("-" * 100    )
  
  								# Calculating the values of variance for each class
  								__lowerCamelCase		:      List[str]											=					calculate_variance(lowercase							,						lowercase							,						sum(lowercase    )    )
  								print("Variance: "							,						lowercase    )
  								print("-" * 100    )
  
  								# Predicting Y values
  								# storing predicted Y values in 'pre_indexes' variable
  								__lowerCamelCase		:      Optional[Any]											=					predict_y_values(lowercase							,						lowercase							,						lowercase							,						lowercase    )
  								print("-" * 100    )
  
  								# Calculating Accuracy of the model
  								print(F'Accuracy: {accuracy(lowercase							,						lowercase    )}'    )
  								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()
  
  
  
  
  
  
style_context: 
  
  
  '''simple docstring'''
  
  
  
  
  import unittest
  from functools import partial
  
  import torch
  
  from accelerate import Accelerator, debug_launcher
  from accelerate.state import AcceleratorState, GradientState
  from accelerate.test_utils import require_cpu, require_huggingface_suite
  from accelerate.utils import GradientAccumulationPlugin
  
  
  
  
  
  def 							a_       (						lowercase=2							,						lowercase=True							,						lowercase=False    )			->Optional[Any]:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				__lowerCamelCase		:      List[str]											=					Accelerator(step_scheduler_with_optimizer=lowercase							,						split_batches=lowercase    )
  				__lowerCamelCase		:      Union[str, Any]											=					torch.nn.Linear(2							,						4    )
  				__lowerCamelCase		:      str											=					torch.optim.AdamW(model.parameters()							,						lr=1.0    )
  				__lowerCamelCase		:      List[str]											=					torch.optim.lr_scheduler.OneCycleLR(lowercase							,						max_lr=0.0_1							,						steps_per_epoch=2							,						epochs=1    )
  				__lowerCamelCase						,					__lowerCamelCase						,					__lowerCamelCase		:      List[Any]											=					accelerator.prepare(lowercase							,						lowercase							,						lowercase    )
  
  				# Optimizer has stepped
  				scheduler.step()
  				if step_scheduler_with_optimizer or (num_processes == 1):
  								assert (
  								    scheduler.scheduler.last_epoch == num_processes
  								), F'Last Epoch ({scheduler.scheduler.last_epoch}) != Num Processes ({num_processes})'
  				else:
  								assert (
  								    scheduler.scheduler.last_epoch != num_processes
  								), F'Last Epoch ({scheduler.scheduler.last_epoch}) == Num Processes ({num_processes})'
  
  
  
  
  
  def 							a_       (						lowercase=2							,						lowercase=True							,						lowercase=False    )			->Dict:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				__lowerCamelCase		:      Dict											=					Accelerator(step_scheduler_with_optimizer=lowercase							,						split_batches=lowercase    )
  				__lowerCamelCase		:      Tuple											=					torch.nn.Linear(2							,						4    )
  				__lowerCamelCase		:      Optional[Any]											=					torch.optim.AdamW(model.parameters()							,						lr=1.0    )
  				__lowerCamelCase		:      Optional[Any]											=					torch.optim.lr_scheduler.LambdaLR(lowercase							,						lr_lambda=lambda lowercase    : 1 - n / 10    )
  				__lowerCamelCase						,					__lowerCamelCase						,					__lowerCamelCase		:      Optional[int]											=					accelerator.prepare(lowercase							,						lowercase							,						lowercase    )
  
  				# Optimizer has stepped
  				__lowerCamelCase		:      List[Any]											=					False
  				scheduler.step()
  				__lowerCamelCase		:      List[Any]											=					1 - (num_processes if (step_scheduler_with_optimizer and not split_batches) else 1) / 10
  				assert (
  				    scheduler.get_last_lr()[0] == expected_lr
  				), F'Wrong lr found at first step, expected {expected_lr}, got {scheduler.get_last_lr()[0]}'
  
  				# Optimizer has not stepped
  				__lowerCamelCase		:      Any											=					True
  				scheduler.step()
  				if not step_scheduler_with_optimizer:
  								__lowerCamelCase		:      int											=					1 - 2 / 10
  				assert (
  				    scheduler.get_last_lr()[0] == expected_lr
  				), F'Wrong lr found at second step, expected {expected_lr}, got {scheduler.get_last_lr()[0]}'
  
  
  
  
  
  def 							a_       (						lowercase = 2    )			->Dict:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				from transformers import get_linear_schedule_with_warmup
  
  				__lowerCamelCase		:      str											=					[1, 2, 4]
  				for num_steps in steps:
  								__lowerCamelCase		:      List[Any]											=					GradientAccumulationPlugin(num_steps=lowercase							,						adjust_scheduler=num_steps > 1    )
  								__lowerCamelCase		:      Dict											=					Accelerator(gradient_accumulation_plugin=lowercase    )
  								__lowerCamelCase		:      Any											=					torch.nn.Linear(2							,						4    )
  								__lowerCamelCase		:      List[Any]											=					torch.optim.AdamW(model.parameters()							,						lr=1_0.0    )
  								__lowerCamelCase		:      Optional[Any]											=					get_linear_schedule_with_warmup(optimizer=lowercase							,						num_warmup_steps=0							,						num_training_steps=20    )
  
  								__lowerCamelCase						,					__lowerCamelCase						,					__lowerCamelCase		:      Optional[int]											=					accelerator.prepare(lowercase							,						lowercase							,						lowercase    )
  
  								for i in range(10 * num_steps    ):
  												with accelerator.accumulate(lowercase    ):
  																optimizer.step()
  																scheduler.step()
  
  												if i == (10 * num_steps - 2):
  																assert (
  																    scheduler.get_last_lr()[0] != 0
  																), F'Wrong lr found at second-to-last step, expected non-zero, got {scheduler.get_last_lr()[0]}. num_steps: {num_steps}'
  								assert (
  								    scheduler.get_last_lr()[0] == 0
  								), F'Wrong lr found at last step, expected 0, got {scheduler.get_last_lr()[0]}'
  								GradientState._reset_state()
  
  
  
  
  
  @require_cpu
  class _snake_case   ( unittest.TestCase   ):
  							"""simple docstring"""
  
  
  
  
  
  							def 		__SCREAMING_SNAKE_CASE(   self	)     ->Tuple:
  
  
  
  											"""simple docstring"""
  
  
  
  
  
  
  
  											debug_launcher(partial(__A			,				num_processes=1	)			,				num_processes=1	)
  											debug_launcher(partial(__A			,				num_processes=1			,				split_batches=__A	)			,				num_processes=1	)
  
  
  
  
  
  
  
  							def 		__SCREAMING_SNAKE_CASE(   self	)     ->Tuple:
  
  
  
  											"""simple docstring"""
  
  
  
  
  
  
  
  											debug_launcher(partial(__A			,				num_processes=1	)			,				num_processes=1	)
  											debug_launcher(partial(__A			,				num_processes=1			,				split_batches=__A	)			,				num_processes=1	)
  
  
  
  
  
  
  
  							def 		__SCREAMING_SNAKE_CASE(   self	)     ->Optional[Any]:
  
  
  
  											"""simple docstring"""
  
  
  
  
  
  
  
  											debug_launcher(partial(__A			,				num_processes=1			,				step_scheduler_with_optimizer=__A	)			,				num_processes=1	)
  
  
  
  
  
  
  
  							def 		__SCREAMING_SNAKE_CASE(   self	)     ->Dict:
  
  
  
  											"""simple docstring"""
  
  
  
  
  
  
  
  											debug_launcher(partial(__A			,				num_processes=1			,				step_scheduler_with_optimizer=__A	)			,				num_processes=1	)
  
  
  
  
  
  
  
  							def 		__SCREAMING_SNAKE_CASE(   self	)     ->Optional[int]:
  
  
  
  											"""simple docstring"""
  
  
  
  
  
  
  
  											AcceleratorState._reset_state(__A	)
  											debug_launcher(__A	)
  											debug_launcher(partial(__A			,				num_processes=1			,				split_batches=__A	)			,				num_processes=1	)
  
  
  
  
  
  
  
  							def 		__SCREAMING_SNAKE_CASE(   self	)     ->Union[str, Any]:
  
  
  
  											"""simple docstring"""
  
  
  
  
  
  
  
  											AcceleratorState._reset_state(__A	)
  											debug_launcher(__A	)
  											debug_launcher(partial(__A			,				num_processes=1			,				split_batches=__A	)			,				num_processes=1	)
  
  
  
  
  
  
  
  							def 		__SCREAMING_SNAKE_CASE(   self	)     ->Any:
  
  
  
  											"""simple docstring"""
  
  
  
  
  
  
  
  											AcceleratorState._reset_state(__A	)
  											debug_launcher(partial(__A			,				step_scheduler_with_optimizer=__A	)	)
  
  
  
  
  
  
  
  							def 		__SCREAMING_SNAKE_CASE(   self	)     ->List[Any]:
  
  
  
  											"""simple docstring"""
  
  
  
  
  
  
  
  											AcceleratorState._reset_state(__A	)
  											debug_launcher(partial(__A			,				step_scheduler_with_optimizer=__A	)	)
  
  
  
  
  
  
  
  							@require_huggingface_suite
  							def 		__SCREAMING_SNAKE_CASE(   self	)     ->Dict:
  
  
  
  											"""simple docstring"""
  
  
  
  
  
  
  
  											AcceleratorState._reset_state(__A	)
  											debug_launcher(partial(__A			,				num_processes=1	)	)
  											debug_launcher(__A	)
  
  
  
  
  
  