






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__						(  A		,				A		,				A					):
   seed(1					)
   return [gauss(A		,				A					) for _ in range(A					)]
def       a__						(  A		,				A					):
   return [k for k in range(A					) for _ in range(instance_count[k]					)]
def       a__						(  A		,				A					):
   return sum(A					) / instance_count
def       a__						(  A		,				A					):
   return instance_count / total_count
def       a__						(  A		,				A		,				A					):
   lowercase__						:	Union[str, Any]         = []  # An empty list to store all squared differences
   # iterate over number of elements in items
   for i in range(len(A					)					):
      # 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
   lowercase__						:	Optional[int]         = len(A					)  # Number of classes in dataset
   return 1 / (total_count - n_classes) * sum(A					)
def       a__						(  A		,				A		,				A		,				A					):
   lowercase__						:	List[str]         = []
   # for loop iterates over number of elements in list
   for i in range(len(A					)					):
      # for loop iterates over number of inner items of each element
      for j in range(len(x_items[i]					)					):
         lowercase__						:	List[str]         = []  # 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(A					)					):
            # 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(A					)

   return [result.index(max(A					)					) for result in results]
def       a__						(  A		,				A					):
   lowercase__						:	Optional[Any]         = sum(1 for i, j in zip(A		,				A					) 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(A					)) * 100


a    =       TypeVar('num')
def       a__						(  A		,				A		,				A		,				A = lambda A					: True		,				A = None		,				):
   while True:
      try:
         lowercase__						:	Any         = input_type(input(A					).strip() or default					)
         if condition(A					):
            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__						(  ):
   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
      lowercase__						:	List[str]         = valid_input(
          input_type=A		,				condition=lambda A					: 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
      lowercase__						:	List[str]         = valid_input(
          input_type=A		,				condition=lambda A					: 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
      lowercase__						:	Optional[Any]         = []  # An empty list to store instance counts of classes in dataset
      for i in range(A					):
         lowercase__						:	Any         = valid_input(
             input_type=A		,				condition=lambda A					: x > 0		,				input_msg=(F'''Enter The number of instances for class_{i+1}: ''')		,				err_msg="""Number of instances should be positive!"""		,				)
         counts.append(A					)
      print("""-""" * 100					)

      # An empty list to store values of user-entered means of classes
      lowercase__						:	Optional[int]         = []
      for a in range(A					):
         lowercase__						:	str         = valid_input(
             input_type=A		,				input_msg=(F'''Enter the value of mean for class_{a+1}: ''')		,				err_msg="""This is an invalid value."""		,				)
         user_means.append(A					)
      print("""-""" * 100					)

      print("""Standard deviation: """		,				A					)
      # print out the number of instances in classes in separated line
      for i, count in enumerate(A		,				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(A		,				1					):
         print(F'''Mean of class_{i} is: {user_mean}'''					)
      print("""-""" * 100					)

      # Generating training dataset drawn from gaussian distribution
      lowercase__						:	Optional[int]         = [
          gaussian_distribution(user_means[j]		,				A		,				counts[j]					)
          for j in range(A					)
      ]
      print("""Generated Normal Distribution: \n"""		,				A					)
      print("""-""" * 100					)

      # Generating Ys to detecting corresponding classes
      lowercase__						:	Dict         = y_generator(A		,				A					)
      print("""Generated Corresponding Ys: \n"""		,				A					)
      print("""-""" * 100					)

      # Calculating the value of actual mean for each class
      lowercase__						:	str         = [calculate_mean(counts[k]		,				x[k]					) for k in range(A					)]
      # for loop iterates over number of elements in 'actual_means' list and print
      # out them in separated line
      for i, actual_mean in enumerate(A		,				1					):
         print(F'''Actual(Real) mean of class_{i} is: {actual_mean}'''					)
      print("""-""" * 100					)

      # Calculating the value of probabilities for each class
      lowercase__						:	str         = [
          calculate_probabilities(counts[i]		,				sum(A					)					) for i in range(A					)
      ]

      # for loop iterates over number of elements in 'probabilities' list and print
      # out them in separated line
      for i, probability in enumerate(A		,				1					):
         print(F'''Probability of class_{i} is: {probability}'''					)
      print("""-""" * 100					)

      # Calculating the values of variance for each class
      lowercase__						:	str         = calculate_variance(A		,				A		,				sum(A					)					)
      print("""Variance: """		,				A					)
      print("""-""" * 100					)

      # Predicting Y values
      # storing predicted Y values in 'pre_indexes' variable
      lowercase__						:	Dict         = predict_y_values(A		,				A		,				A		,				A					)
      print("""-""" * 100					)

      # Calculating Accuracy of the model
      print(F'''Accuracy: {accuracy(A		,				A					)}'''					)
      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()










from __future__ import annotations

from collections.abc import Iterator
from typing import Any
class        __snake_case:



 def __init__(	self   :   Union[str, Any] ,		UpperCAmelCase__   :   Any	):

    """simple docstring"""






    lowercase__						:	Any         = data
    lowercase__						:	Node | None         = None







 def __str__(	self   :   Dict	):

    """simple docstring"""






    return f'''{self.data}'''
class        __snake_case:



 def __init__(	self   :   Optional[Any]	):

    """simple docstring"""






    lowercase__						:	Node | None         = None
    lowercase__						:	Node | None         = None



 def __iter__(	self   :   Any	):

    """simple docstring"""






    lowercase__						:	Any         = self.front
    while node:
       yield node.data
       lowercase__						:	List[str]         = node.next



 def __len__(	self   :   Union[str, Any]	):

    """simple docstring"""






    return len(tuple(iter(self	)	)	)



 def __str__(	self   :   Optional[Any]	):

    """simple docstring"""






    return " <- ".join(str(UpperCAmelCase__	) for item in self	)



 def 						UpperCAmelCase    (	self   :   List[str]	):

    """simple docstring"""






    return len(self	) == 0



 def 						UpperCAmelCase    (	self   :   Optional[int] ,		UpperCAmelCase__   :   Any	):

    """simple docstring"""






    lowercase__						:	List[str]         = Node(UpperCAmelCase__	)
    if self.is_empty():
       lowercase__						:	List[Any]         = node
    else:
       assert isinstance(self.rear ,		UpperCAmelCase__	)
       lowercase__						:	Any         = node
       lowercase__						:	Union[str, Any]         = node



 def 						UpperCAmelCase    (	self   :   List[Any]	):

    """simple docstring"""






    if self.is_empty():
       raise IndexError("""dequeue from empty queue"""	)
    assert isinstance(self.front ,		UpperCAmelCase__	)
    lowercase__						:	Tuple         = self.front
    lowercase__						:	Any         = self.front.next
    if self.front is None:
       lowercase__						:	List[Any]         = None
    return node.data







 def 						UpperCAmelCase    (	self   :   Optional[Any]	):

    """simple docstring"""






    lowercase__						:	List[Any]         = None


if __name__ == "__main__":
 from doctest import testmod

 testmod()


