






import numpy as np


def 						_A     (       SCREAMING_SNAKE_CASE__						:			List[str] ):
    UpperCamelCase :Dict										=     np.exp(SCREAMING_SNAKE_CASE__ )

    # Add up the all the exponentials
    UpperCamelCase :Any										=     np.sum(SCREAMING_SNAKE_CASE__ )

    # Divide every exponent by the sum of all exponents
    UpperCamelCase :Optional[int]										=     exponent_vector / sum_of_exponents

    return softmax_vector


if __name__ == "__main__":
 print(softmax((0,)))













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     (       SCREAMING_SNAKE_CASE__						:			float  ,						SCREAMING_SNAKE_CASE__						:			float  ,						SCREAMING_SNAKE_CASE__						:			int ):
    seed(1 )
    return [gauss(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ ) for _ in range(SCREAMING_SNAKE_CASE__ )]


def 						_A     (       SCREAMING_SNAKE_CASE__						:			int  ,						SCREAMING_SNAKE_CASE__						:			list ):
    return [k for k in range(SCREAMING_SNAKE_CASE__ ) for _ in range(instance_count[k] )]


def 						_A     (       SCREAMING_SNAKE_CASE__						:			int  ,						SCREAMING_SNAKE_CASE__						:			list ):
    return sum(SCREAMING_SNAKE_CASE__ ) / instance_count


def 						_A     (       SCREAMING_SNAKE_CASE__						:			int  ,						SCREAMING_SNAKE_CASE__						:			int ):
    return instance_count / total_count


def 						_A     (       SCREAMING_SNAKE_CASE__						:			list  ,						SCREAMING_SNAKE_CASE__						:			list  ,						SCREAMING_SNAKE_CASE__						:			int ):
    UpperCamelCase :Optional[Any]										=     []  # An empty list to store all squared differences
    # iterate over number of elements in items
    for i in range(len(SCREAMING_SNAKE_CASE__ ) ):
        # 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(SCREAMING_SNAKE_CASE__ )  # Number of classes in dataset
    return 1 / (total_count - n_classes) * sum(SCREAMING_SNAKE_CASE__ )


def 						_A     (       SCREAMING_SNAKE_CASE__						:			list  ,						SCREAMING_SNAKE_CASE__						:			list  ,						SCREAMING_SNAKE_CASE__						:			float  ,						SCREAMING_SNAKE_CASE__						:			list ):
    UpperCamelCase :Dict										=     []
    # for loop iterates over number of elements in list
    for i in range(len(SCREAMING_SNAKE_CASE__ ) ):
        # for loop iterates over number of inner items of each element
        for j in range(len(x_items[i] ) ):
            UpperCamelCase :List[Any]										=     []  # 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(SCREAMING_SNAKE_CASE__ ) ):
                # 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(SCREAMING_SNAKE_CASE__ )

    return [result.index(max(SCREAMING_SNAKE_CASE__ ) ) for result in results]


def 						_A     (       SCREAMING_SNAKE_CASE__						:			list  ,						SCREAMING_SNAKE_CASE__						:			list ):
    UpperCamelCase :List[Any]										=     sum(1 for i, j in zip(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ ) 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(SCREAMING_SNAKE_CASE__ )) * 100


__snake_case							      =						TypeVar("""num""")


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

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

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

        # Generating training dataset drawn from gaussian distribution
        UpperCamelCase :Tuple										=     [
            gaussian_distribution(user_means[j]  ,						SCREAMING_SNAKE_CASE__  ,						counts[j] )
            for j in range(SCREAMING_SNAKE_CASE__ )
        ]
        print('''Generated Normal Distribution: \n'''  ,						SCREAMING_SNAKE_CASE__ )
        print('''-''' * 100 )

        # Generating Ys to detecting corresponding classes
        UpperCamelCase :int										=     y_generator(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ )
        print('''Generated Corresponding Ys: \n'''  ,						SCREAMING_SNAKE_CASE__ )
        print('''-''' * 100 )

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

        # Calculating the value of probabilities for each class
        UpperCamelCase :Dict										=     [
            calculate_probabilities(counts[i]  ,						sum(SCREAMING_SNAKE_CASE__ ) ) for i in range(SCREAMING_SNAKE_CASE__ )
        ]

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

        # Calculating the values of variance for each class
        UpperCamelCase :int										=     calculate_variance(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__  ,						sum(SCREAMING_SNAKE_CASE__ ) )
        print('''Variance: '''  ,						SCREAMING_SNAKE_CASE__ )
        print('''-''' * 100 )

        # Predicting Y values
        # storing predicted Y values in 'pre_indexes' variable
        UpperCamelCase :Any										=     predict_y_values(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ )
        print('''-''' * 100 )

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





