



"""simple docstring"""
class    a		:



  def __init__(  self	:   Union[str, Any]    ,						lowerCAmelCase	:   Optional[int]						)       ->   List[str]:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_:	Optional[int]            =data
     SCREAMING_SNAKE_CASE_:	Dict            =None
     SCREAMING_SNAKE_CASE_:	Union[str, Any]            =None





  def __str__(  self	:   Dict						)       ->   List[str]:


     '''simple docstring'''




     return f'''{self.data}'''







class    a		:



  def __init__(  self	:   List[str]						)       ->   str:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_:	str            =None
     SCREAMING_SNAKE_CASE_:	Dict            =None



  def __iter__(  self	:   Optional[int]						)       ->   Dict:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_:	int            =self.head
     while node:
        yield node.data
        SCREAMING_SNAKE_CASE_:	List[Any]            =node.next



  def __str__(  self	:   List[Any]						)       ->   Optional[int]:


     '''simple docstring'''




     return "->".join([str(lowerCAmelCase						) for item in self]						)



  def __len__(  self	:   List[Any]						)       ->   List[str]:


     '''simple docstring'''




     return sum(1 for _ in self						)



  def 		lowerCamelCase__    (  self	:   int    ,						lowerCAmelCase	:   Union[str, Any]						)       ->   Any:


     '''simple docstring'''




     self.insert_at_nth(0    ,						lowerCAmelCase						)



  def 		lowerCamelCase__    (  self	:   Union[str, Any]    ,						lowerCAmelCase	:   Any						)       ->   Optional[Any]:


     '''simple docstring'''




     self.insert_at_nth(len(self						)    ,						lowerCAmelCase						)



  def 		lowerCamelCase__    (  self	:   str    ,						lowerCAmelCase	:   int    ,						lowerCAmelCase	:   str						)       ->   int:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_:	str            =len(self						)

     if not 0 <= index <= length:
        raise IndexError("""list index out of range"""						)
     SCREAMING_SNAKE_CASE_:	Optional[Any]            =Node(lowerCAmelCase						)
     if self.head is None:
        SCREAMING_SNAKE_CASE_:	Tuple            =new_node
     elif index == 0:
        SCREAMING_SNAKE_CASE_:	List[str]            =new_node
        SCREAMING_SNAKE_CASE_:	str            =self.head
        SCREAMING_SNAKE_CASE_:	Any            =new_node
     elif index == length:
        SCREAMING_SNAKE_CASE_:	List[Any]            =new_node
        SCREAMING_SNAKE_CASE_:	Optional[Any]            =self.tail
        SCREAMING_SNAKE_CASE_:	Dict            =new_node
     else:
        SCREAMING_SNAKE_CASE_:	Union[str, Any]            =self.head
        for _ in range(0    ,						lowerCAmelCase						):
           SCREAMING_SNAKE_CASE_:	Union[str, Any]            =temp.next
        SCREAMING_SNAKE_CASE_:	Union[str, Any]            =new_node
        SCREAMING_SNAKE_CASE_:	Union[str, Any]            =temp.previous
        SCREAMING_SNAKE_CASE_:	int            =temp
        SCREAMING_SNAKE_CASE_:	Dict            =new_node



  def 		lowerCamelCase__    (  self	:   str						)       ->   int:


     '''simple docstring'''




     return self.delete_at_nth(0						)



  def 		lowerCamelCase__    (  self	:   Tuple						)       ->   Optional[Any]:


     '''simple docstring'''




     return self.delete_at_nth(len(self						) - 1						)



  def 		lowerCamelCase__    (  self	:   Any    ,						lowerCAmelCase	:   int						)       ->   int:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_:	List[str]            =len(self						)

     if not 0 <= index <= length - 1:
        raise IndexError("""list index out of range"""						)
     SCREAMING_SNAKE_CASE_:	Union[str, Any]            =self.head  # default first node
     if length == 1:
        SCREAMING_SNAKE_CASE_:	Optional[Any]            =None
     elif index == 0:
        SCREAMING_SNAKE_CASE_:	Optional[int]            =self.head.next
        SCREAMING_SNAKE_CASE_:	List[Any]            =None
     elif index == length - 1:
        SCREAMING_SNAKE_CASE_:	Union[str, Any]            =self.tail
        SCREAMING_SNAKE_CASE_:	Any            =self.tail.previous
        SCREAMING_SNAKE_CASE_:	Optional[Any]            =None
     else:
        SCREAMING_SNAKE_CASE_:	List[str]            =self.head
        for _ in range(0    ,						lowerCAmelCase						):
           SCREAMING_SNAKE_CASE_:	int            =temp.next
        SCREAMING_SNAKE_CASE_:	Tuple            =temp
        SCREAMING_SNAKE_CASE_:	List[Any]            =temp.previous
        SCREAMING_SNAKE_CASE_:	List[Any]            =temp.next
     return delete_node.data



  def 		lowerCamelCase__    (  self	:   Dict    ,						lowerCAmelCase	:   Optional[Any]						)       ->   str:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_:	Tuple            =self.head

     while current.data != data:  # Find the position to delete
        if current.next:
           SCREAMING_SNAKE_CASE_:	List[Any]            =current.next
        else:  # We have reached the end an no value matches
           raise ValueError("""No data matching given value"""						)

     if current == self.head:
        self.delete_head()

     elif current == self.tail:
        self.delete_tail()

     else:  # Before: 1 <--> 2(current) <--> 3
        SCREAMING_SNAKE_CASE_:	Any            =current.next  # 1 --> 3
        SCREAMING_SNAKE_CASE_:	List[Any]            =current.previous  # 1 <--> 3
     return data





  def 		lowerCamelCase__    (  self	:   Optional[Any]						)       ->   Union[str, Any]:


     '''simple docstring'''




     return len(self						) == 0







def        __magic_name__			(							):
   SCREAMING_SNAKE_CASE_:	List[str]            =DoublyLinkedList()
   assert linked_list.is_empty() is True
   assert str(lowercase	) == ""

   try:
      linked_list.delete_head()
      raise AssertionError  # This should not happen.
   except IndexError:
      assert True  # This should happen.

   try:
      linked_list.delete_tail()
      raise AssertionError  # This should not happen.
   except IndexError:
      assert True  # This should happen.

   for i in range(10	):
      assert len(lowercase	) == i
      linked_list.insert_at_nth(lowercase							,     i + 1	)
   assert str(lowercase	) == "->".join(str(lowercase	) for i in range(1							,     11	)	)

   linked_list.insert_at_head(0	)
   linked_list.insert_at_tail(11	)
   assert str(lowercase	) == "->".join(str(lowercase	) for i in range(0							,     12	)	)

   assert linked_list.delete_head() == 0
   assert linked_list.delete_at_nth(9	) == 10
   assert linked_list.delete_tail() == 11
   assert len(lowercase	) == 9
   assert str(lowercase	) == "->".join(str(lowercase	) for i in range(1							,     10	)	)


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

   testmod()








"""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        __magic_name__			(							lowercase							,     lowercase							,     lowercase	):
   seed(1	)
   return [gauss(lowercase							,     lowercase	) for _ in range(lowercase	)]





def        __magic_name__			(							lowercase							,     lowercase	):
   return [k for k in range(lowercase	) for _ in range(instance_count[k]	)]





def        __magic_name__			(							lowercase							,     lowercase	):
   return sum(lowercase	) / instance_count





def        __magic_name__			(							lowercase							,     lowercase	):
   return instance_count / total_count





def        __magic_name__			(							lowercase							,     lowercase							,     lowercase	):
   SCREAMING_SNAKE_CASE_:	Optional[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
   SCREAMING_SNAKE_CASE_:	Union[str, Any]            =len(lowercase	)  # Number of classes in dataset
   return 1 / (total_count - n_classes) * sum(lowercase	)





def        __magic_name__			(							lowercase							,     lowercase							,     lowercase							,     lowercase	):
   SCREAMING_SNAKE_CASE_:	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]	)	):
         SCREAMING_SNAKE_CASE_:	Optional[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        __magic_name__			(							lowercase							,     lowercase	):
   SCREAMING_SNAKE_CASE_:	Dict            =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


_UpperCAmelCase       =     TypeVar("""num""")





def        __magic_name__			(							lowercase							,     lowercase							,     lowercase							,     lowercase = lambda lowercase	: True							,     lowercase = None							,     ):
   while True:
      try:
         SCREAMING_SNAKE_CASE_:	List[Any]            =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        __magic_name__			(							):
   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
      SCREAMING_SNAKE_CASE_:	List[Any]            =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
      SCREAMING_SNAKE_CASE_:	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
      SCREAMING_SNAKE_CASE_:	Optional[Any]            =[]  # An empty list to store instance counts of classes in dataset
      for i in range(lowercase	):
         SCREAMING_SNAKE_CASE_:	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
      SCREAMING_SNAKE_CASE_:	Optional[Any]            =[]
      for a in range(lowercase	):
         SCREAMING_SNAKE_CASE_:	Tuple            =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
      SCREAMING_SNAKE_CASE_:	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
      SCREAMING_SNAKE_CASE_:	int            =y_generator(lowercase							,     lowercase	)
      print("""Generated Corresponding Ys: \n"""							,     lowercase	)
      print("""-""" * 100	)

      # Calculating the value of actual mean for each class
      SCREAMING_SNAKE_CASE_:	str            =[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
      SCREAMING_SNAKE_CASE_:	List[Any]            =[
          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
      SCREAMING_SNAKE_CASE_:	str            =calculate_variance(lowercase							,     lowercase							,     sum(lowercase	)	)
      print("""Variance: """							,     lowercase	)
      print("""-""" * 100	)

      # Predicting Y values
      # storing predicted Y values in 'pre_indexes' variable
      SCREAMING_SNAKE_CASE_:	Dict            =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()



