
'''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 snake_case_    (				lowercase__      ,					lowercase__      ,					lowercase__		):
  seed(1		)
  return [gauss(lowercase__      ,					lowercase__		) for _ in range(lowercase__		)]







def snake_case_    (				lowercase__      ,					lowercase__		):
  return [k for k in range(lowercase__		) for _ in range(instance_count[k]		)]







def snake_case_    (				lowercase__      ,					lowercase__		):
  return sum(lowercase__		) / instance_count







def snake_case_    (				lowercase__      ,					lowercase__		):
  return instance_count / total_count







def snake_case_    (				lowercase__      ,					lowercase__      ,					lowercase__		):
  UpperCAmelCase__			:				Optional[int]												=       []  # 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
  UpperCAmelCase__			:				Tuple												=       len(lowercase__		)  # Number of classes in dataset
  return 1 / (total_count - n_classes) * sum(lowercase__		)







def snake_case_    (				lowercase__      ,					lowercase__      ,					lowercase__      ,					lowercase__		):
  UpperCAmelCase__			:				List[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]		)		):
      UpperCAmelCase__			:				Tuple												=       []  # 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 snake_case_    (				lowercase__      ,					lowercase__		):
  UpperCAmelCase__			:				Optional[int]												=       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__		)) * 1_0_0


SCREAMING_SNAKE_CASE    =					TypeVar("""num""")







def snake_case_    (				lowercase__      ,					lowercase__      ,					lowercase__      ,					lowercase__ = lambda lowercase__		: True      ,					lowercase__ = None      ,					):
  while True:
    try:
      UpperCAmelCase__			:				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 snake_case_    (				):
  while True:
    print(" Linear Discriminant Analysis ".center(5_0      ,					"*"		)		)
    print("*" * 5_0      ,					"\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
    UpperCAmelCase__			:				List[str]												=       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("-" * 1_0_0		)

    # Trying to get the value of standard deviation
    UpperCAmelCase__			:				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("-" * 1_0_0		)

    # Trying to get number of instances in classes and theirs means to generate
    # dataset
    UpperCAmelCase__			:				List[str]												=       []  # An empty list to store instance counts of classes in dataset
    for i in range(lowercase__		):
      UpperCAmelCase__			:				List[Any]												=       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("-" * 1_0_0		)

    # An empty list to store values of user-entered means of classes
    UpperCAmelCase__			:				int												=       []
    for a in range(lowercase__		):
      UpperCAmelCase__			:				Optional[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("-" * 1_0_0		)

    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("-" * 1_0_0		)

    # 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("-" * 1_0_0		)

    # Generating training dataset drawn from gaussian distribution
    UpperCAmelCase__			:				int												=       [
        gaussian_distribution(user_means[j]      ,					lowercase__      ,					counts[j]		)
        for j in range(lowercase__		)
    ]
    print("Generated Normal Distribution: \n"      ,					lowercase__		)
    print("-" * 1_0_0		)

    # Generating Ys to detecting corresponding classes
    UpperCAmelCase__			:				Tuple												=       y_generator(lowercase__      ,					lowercase__		)
    print("Generated Corresponding Ys: \n"      ,					lowercase__		)
    print("-" * 1_0_0		)

    # Calculating the value of actual mean for each class
    UpperCAmelCase__			:				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("-" * 1_0_0		)

    # Calculating the value of probabilities for each class
    UpperCAmelCase__			:				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("-" * 1_0_0		)

    # Calculating the values of variance for each class
    UpperCAmelCase__			:				Any												=       calculate_variance(lowercase__      ,					lowercase__      ,					sum(lowercase__		)		)
    print("Variance: "      ,					lowercase__		)
    print("-" * 1_0_0		)

    # Predicting Y values
    # storing predicted Y values in 'pre_indexes' variable
    UpperCAmelCase__			:				str												=       predict_y_values(lowercase__      ,					lowercase__      ,					lowercase__      ,					lowercase__		)
    print("-" * 1_0_0		)

    # Calculating Accuracy of the model
    print(F"""Accuracy: {accuracy(lowercase__      ,					lowercase__		)}"""		)
    print("-" * 1_0_0		)
    print(" DONE ".center(1_0_0      ,					"+"		)		)

    if input("Press any key to restart or 'q' for quit: "		).strip().lower() == "q":
      print("\n" + "GoodBye!".center(1_0_0      ,					"-"		) + "\n"		)
      break
    system("cls" if name == "nt" else "clear"		)  # noqa: S605


if __name__ == "__main__":
      main()





'''simple docstring'''





def snake_case_    (				lowercase__      ,					lowercase__ = 1_3		):
  UpperCAmelCase__			:				Optional[Any]												=       ""
  for c in s:
    if "A" <= c <= "Z":
      out += chr(ord("A"		) + (ord(lowercase__		) - ord("A"		) + n) % 2_6		)
    elif "a" <= c <= "z":
      out += chr(ord("a"		) + (ord(lowercase__		) - ord("a"		) + n) % 2_6		)
    else:
      out += c
  return out







def snake_case_    (				):
  UpperCAmelCase__			:				Dict												=       input("Enter message: "		)

  UpperCAmelCase__			:				Optional[int]												=       dencrypt(lowercase__      ,					1_3		)
  print("Encryption:"      ,					lowercase__		)

  UpperCAmelCase__			:				Union[str, Any]												=       dencrypt(lowercase__      ,					1_3		)
  print("Decryption: "      ,					lowercase__		)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()



