
# Logistic Regression from scratch

# In[62]:

# In[63]:

# importing all the required libraries

import numpy as np
from matplotlib import pyplot as plt
from sklearn import datasets



def 						lowercase_      (       A__		)							->							List[str]:
				"""simple docstring"""

				return 1 / (1 + np.exp(-z		))



def 						lowercase_      (       A__			,		A__		)							->							int:
				"""simple docstring"""

				return (-y * np.log(A__		) - (1 - y) * np.log(1 - h		)).mean()



def 						lowercase_      (       A__			,		A__			,		A__		)							->							Dict:
				"""simple docstring"""

				snake_case								= np.dot(A__			,		A__		)
				return np.sum(y * scores - np.log(1 + np.exp(A__		)		)		)



def 						lowercase_      (       A__			,		A__			,		A__			,		A__=7_0000		)							->							List[Any]:
				"""simple docstring"""

				snake_case								= np.zeros(x.shape[1]		)

				for iterations in range(A__		):
								snake_case								= np.dot(A__			,		A__		)
								snake_case								= sigmoid_function(A__		)
								snake_case								= np.dot(x.T			,		h - y		) / y.size
								snake_case								= theta - alpha * gradient  # updating the weights
								snake_case								= np.dot(A__			,		A__		)
								snake_case								= sigmoid_function(A__		)
								snake_case								= cost_function(A__			,		A__		)
								if iterations % 100 == 0:
												print(F'loss: {j} \t'		)  # printing the loss after every 100 iterations
				return theta


# In[68]:

if __name__ == "__main__":
			_A   =			datasets.load_iris()
			_A   =			iris.data[:, :2]
			_A   =			(iris.target != 0) * 1

			_A   =			0.1
			_A   =			logistic_reg(alpha, x, y, max_iterations=7_00_00)
			print("theta: ", theta)  # printing the theta i.e our weights vector



			def 						lowercase_      (       A__		)							->							Union[str, Any]:
							"""simple docstring"""

							return sigmoid_function(
							    np.dot(A__			,		A__		)		)  # predicting the value of probability from the logistic regression algorithm

			plt.figure(figsize=(10, 6))
			plt.scatter(x[y == 0][:, 0], x[y == 0][:, 1], color="b", label="0")
			plt.scatter(x[y == 1][:, 0], x[y == 1][:, 1], color="r", label="1")
			((_A) ,  (_A))   =			(x[:, 0].min(), x[:, 0].max())
			((_A) ,  (_A))   =			(x[:, 1].min(), x[:, 1].max())
			((_A) ,  (_A))   =			np.meshgrid(np.linspace(xa_min, xa_max), np.linspace(xa_min, xa_max))
			_A   =			np.c_[xxa.ravel(), xxa.ravel()]
			_A   =			predict_prob(grid).reshape(xxa.shape)
			plt.contour(xxa, xxa, probs, [0.5], linewidths=1, colors="black")

			plt.legend()





			plt.show()



from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt



def 						lowercase_      (       A__		)							->							bool:
    """simple docstring"""

    snake_case								= int(number**0.5		)
    return number == sq * sq



def 						lowercase_      (       A__			,		A__			,		A__			,		A__			,		A__			,		A__		)							->							tuple[int, int]:
    """simple docstring"""

    snake_case								= x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
    snake_case								= x_den * y_den * z_den
    snake_case								= gcd(A__			,		A__		)
    top //= hcf
    bottom //= hcf
    return top, bottom



def 						lowercase_      (       A__ = 35		)							->							int:
    """simple docstring"""

    snake_case								= set()
    snake_case								= 42
    snake_case								= Fraction(0		)
    snake_case								= 42

    for x_num in range(1			,		order + 1		):
        for x_den in range(x_num + 1			,		order + 1		):
            for y_num in range(1			,		order + 1		):
                for y_den in range(y_num + 1			,		order + 1		):
                    # n=1
                    snake_case								= x_num * y_den + x_den * y_num
                    snake_case								= x_den * y_den
                    snake_case								= gcd(A__			,		A__		)
                    z_num //= hcf
                    z_den //= hcf
                    if 0 < z_num < z_den <= order:
                        snake_case								= add_three(
                            A__			,		A__			,		A__			,		A__			,		A__			,		A__		)
                        unique_s.add(A__		)

                    # n=2
                    snake_case								= (
                        x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
                    )
                    snake_case								= x_den * x_den * y_den * y_den
                    if is_sq(A__		) and is_sq(A__		):
                        snake_case								= int(sqrt(A__		)		)
                        snake_case								= int(sqrt(A__		)		)
                        snake_case								= gcd(A__			,		A__		)
                        z_num //= hcf
                        z_den //= hcf
                        if 0 < z_num < z_den <= order:
                            snake_case								= add_three(
                                A__			,		A__			,		A__			,		A__			,		A__			,		A__		)
                            unique_s.add(A__		)

                    # n=-1
                    snake_case								= x_num * y_num
                    snake_case								= x_den * y_num + x_num * y_den
                    snake_case								= gcd(A__			,		A__		)
                    z_num //= hcf
                    z_den //= hcf
                    if 0 < z_num < z_den <= order:
                        snake_case								= add_three(
                            A__			,		A__			,		A__			,		A__			,		A__			,		A__		)
                        unique_s.add(A__		)

                    # n=2
                    snake_case								= x_num * x_num * y_num * y_num
                    snake_case								= (
                        x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
                    )
                    if is_sq(A__		) and is_sq(A__		):
                        snake_case								= int(sqrt(A__		)		)
                        snake_case								= int(sqrt(A__		)		)
                        snake_case								= gcd(A__			,		A__		)
                        z_num //= hcf
                        z_den //= hcf
                        if 0 < z_num < z_den <= order:
                            snake_case								= add_three(
                                A__			,		A__			,		A__			,		A__			,		A__			,		A__		)
                            unique_s.add(A__		)

    for num, den in unique_s:
        total += Fraction(A__			,		A__		)

    return total.denominator + total.numerator


if __name__ == "__main__":
   print(f"{solution() = }")

