





'''simple docstring'''





# 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 	lowerCAmelCase_					(						__UpperCAmelCase:    List[Any]   )   ->			List[Any]:
    return 1 / (1 + np.exp(-z   ))




def 	lowerCAmelCase_					(						__UpperCAmelCase:    Any	,     __UpperCAmelCase:    Optional[Any]   )   ->			Any:
    return (-y * np.log(lowerCAmelCase__   ) - (1 - y) * np.log(1 - h   )).mean()




def 	lowerCAmelCase_					(						__UpperCAmelCase:    Any	,     __UpperCAmelCase:    List[str]	,     __UpperCAmelCase:    Union[str, Any]   )   ->			List[str]:
    UpperCamelCase__							:       Union[str, Any]      =   np.dot(lowerCAmelCase__	,     lowerCAmelCase__   )
    return np.sum(y * scores - np.log(1 + np.exp(lowerCAmelCase__   )   )   )




def 	lowerCAmelCase_					(						__UpperCAmelCase:    str	,     __UpperCAmelCase:    List[str]	,     __UpperCAmelCase:    List[str]	,     __UpperCAmelCase:    Dict=7_0000   )   ->			List[Any]:
    UpperCamelCase__							:       Union[str, Any]      =   np.zeros(x.shape[1]   )

    for iterations in range(lowerCAmelCase__   ):
        UpperCamelCase__							:       List[str]      =   np.dot(lowerCAmelCase__	,     lowerCAmelCase__   )
        UpperCamelCase__							:       Dict      =   sigmoid_function(lowerCAmelCase__   )
        UpperCamelCase__							:       Any      =   np.dot(x.T	,     h - y   ) / y.size
        UpperCamelCase__							:       Optional[Any]      =   theta - alpha * gradient  # updating the weights
        UpperCamelCase__							:       Optional[int]      =   np.dot(lowerCAmelCase__	,     lowerCAmelCase__   )
        UpperCamelCase__							:       Dict      =   sigmoid_function(lowerCAmelCase__   )
        UpperCamelCase__							:       Optional[Any]      =   cost_function(lowerCAmelCase__	,     lowerCAmelCase__   )
        if iterations % 100 == 0:
            print(f"loss: {j} \t"   )  # printing the loss after every 100 iterations
    return theta


# In[68]:

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

  UpperCAmelCase_  							=				0.1
  UpperCAmelCase_  							=				logistic_reg(alpha, x, y, max_iterations=7_0000)
  print('theta: ', theta)  # printing the theta i.e our weights vector




  def 	lowerCAmelCase_					(						__UpperCAmelCase:    int   )   ->			Optional[int]:
      return sigmoid_function(
          np.dot(lowerCAmelCase__	,     lowerCAmelCase__   )   )  # 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')
  ((UpperCAmelCase_)							,     (UpperCAmelCase_))  							=				(x[:, 0].min(), x[:, 0].max())
  ((UpperCAmelCase_)							,     (UpperCAmelCase_))  							=				(x[:, 1].min(), x[:, 1].max())
  ((UpperCAmelCase_)							,     (UpperCAmelCase_))  							=				np.meshgrid(np.linspace(xa_min, xa_max), np.linspace(xa_min, xa_max))
  UpperCAmelCase_  							=				np.c_[xxa.ravel(), xxa.ravel()]
  UpperCAmelCase_  							=				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 math import gcd




def 	lowerCAmelCase_					(						__UpperCAmelCase:    int	,     __UpperCAmelCase:    int = 2	,     __UpperCAmelCase:    int = 1	,     __UpperCAmelCase:    int = 3	,     )   ->			int | None:
    # A value less than 2 can cause an infinite loop in the algorithm.
    if num < 2:
        raise ValueError('''The input value cannot be less than 2'''   )

    # Because of the relationship between ``f(f(x))`` and ``f(x)``, this
    # algorithm struggles to find factors that are divisible by two.
    # As a workaround, we specifically check for two and even inputs.
    #   See: https://math.stackexchange.com/a/2856214/165820
    if num > 2 and num % 2 == 0:
        return 2

    # Pollard's Rho algorithm requires a function that returns pseudorandom
    # values between 0 <= X < ``num``.  It doesn't need to be random in the
    # sense that the output value is cryptographically secure or difficult
    # to calculate, it only needs to be random in the sense that all output
    # values should be equally likely to appear.
    # For this reason, Pollard suggested using ``f(x) = (x**2 - 1) % num``
    # However, the success of Pollard's algorithm isn't guaranteed and is
    # determined in part by the initial seed and the chosen random function.
    # To make retries easier, we will instead use ``f(x) = (x**2 + C) % num``
    # where ``C`` is a value that we can modify between each attempt.
    def rand_fn(__UpperCAmelCase:    int	,     __UpperCAmelCase:    int	,     __UpperCAmelCase:    int   ) -> int:
        return (pow(__UpperCAmelCase	,     2   ) + step) % modulus

    for _ in range(__UpperCAmelCase   ):
        # These track the position within the cycle detection logic.
        UpperCamelCase__							:       List[Any]      =   seed
        UpperCamelCase__							:       List[str]      =   seed

        while True:
            # At each iteration, the tortoise moves one step and the hare moves two.
            UpperCamelCase__							:       Optional[int]      =   rand_fn(__UpperCAmelCase	,     __UpperCAmelCase	,     __UpperCAmelCase   )
            UpperCamelCase__							:       List[str]      =   rand_fn(__UpperCAmelCase	,     __UpperCAmelCase	,     __UpperCAmelCase   )
            UpperCamelCase__							:       Optional[int]      =   rand_fn(__UpperCAmelCase	,     __UpperCAmelCase	,     __UpperCAmelCase   )

            # At some point both the tortoise and the hare will enter a cycle whose
            # length ``p`` is a divisor of ``num``.  Once in that cycle, at some point
            # the tortoise and hare will end up on the same value modulo ``p``.
            # We can detect when this happens because the position difference between
            # the tortoise and the hare will share a common divisor with ``num``.
            UpperCamelCase__							:       Optional[int]      =   gcd(hare - tortoise	,     __UpperCAmelCase   )

            if divisor == 1:
                # No common divisor yet, just keep searching.
                continue
            else:
                # We found a common divisor!
                if divisor == num:
                    # Unfortunately, the divisor is ``num`` itself and is useless.
                    break
                else:
                    # The divisor is a nontrivial factor of ``num``!
                    return divisor

        # If we made it here, then this attempt failed.
        # We need to pick a new starting seed for the tortoise and hare
        # in addition to a new step value for the random function.
        # To keep this example implementation deterministic, the
        # new values will be generated based on currently available
        # values instead of using something like ``random.randint``.

        # We can use the hare's position as the new seed.
        # This is actually what Richard Brent's the "optimized" variant does.
        UpperCamelCase__							:       List[str]      =   hare

        # The new step value for the random function can just be incremented.
        # At first the results will be similar to what the old function would
        # have produced, but the value will quickly diverge after a bit.
        step += 1

    # We haven't found a divisor within the requested number of attempts.
    # We were unlucky or ``num`` itself is actually prime.
    return None


if __name__ == "__main__":
  import argparse

  UpperCAmelCase_  							=				argparse.ArgumentParser()
  parser.add_argument(
      'num',
      type=int,
      help='The value to find a divisor of',
  )
  parser.add_argument(
      '--attempts',
      type=int,
      default=3,
      help='The number of attempts before giving up',
  )
  UpperCAmelCase_  							=				parser.parse_args()

  UpperCAmelCase_  							=				pollard_rho(args.num, attempts=args.attempts)
  if divisor is None:
    print(F'''{args.num} is probably prime''')
  else:
    UpperCAmelCase_  							=				args.num // divisor
    print(F'''{args.num} = {divisor} * {quotient}''')

