import numpy as np
from numpy import ndarray
from scipy.optimize import Bounds, LinearConstraint, minimize



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: ndarray			)							->      float:







  """simple docstring"""





  return np.dot(__UpperCamelCase				,  __UpperCamelCase			)







class __snake_case       :




   def __init__(					self    :       int ,			*,
       _lowercase    :       float = np.inf ,			_lowercase    :       str = "linear" ,			_lowercase    :       float = 0.0 ,			):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__    							=   regularization
     SCREAMING_SNAKE_CASE__    							=   gamma
     if kernel == "linear":
       SCREAMING_SNAKE_CASE__    							=   self.__linear
     elif kernel == "rbf":
       if self.gamma == 0:
         raise ValueError("""rbf kernel requires gamma"""   )
       if not isinstance(self.gamma ,			(float, int)   ):
         raise ValueError("""gamma must be float or int"""   )
       if not self.gamma > 0:
         raise ValueError("""gamma must be > 0"""   )
       SCREAMING_SNAKE_CASE__    							=   self.__rbf
       # in the future, there could be a default value like in sklearn
       # sklear: def_gamma = 1/(n_features * X.var()) (wiki)
       # previously it was 1/(n_features)
     else:
       SCREAMING_SNAKE_CASE__    							=   f"""Unknown kernel: {kernel}"""
       raise ValueError(_lowercase   )




   def 			__a		(					self    :       int ,			_lowercase    :       ndarray ,			_lowercase    :       ndarray   ):



     """simple docstring"""






     return np.dot(_lowercase ,			_lowercase   )




   def 			__a		(					self    :       List[str] ,			_lowercase    :       ndarray ,			_lowercase    :       ndarray   ):



     """simple docstring"""






     return np.exp(-(self.gamma * norm_squared(vectora - vectora   ))   )




   def 			__a		(					self    :       List[str] ,			_lowercase    :       list[ndarray] ,			_lowercase    :       ndarray   ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__    							=   observations
     SCREAMING_SNAKE_CASE__    							=   classes

     # using Wolfe's Dual to calculate w.
     # Primal problem: minimize 1/2*norm_squared(w)
     #   constraint: yn(w . xn + b) >= 1
     #
     # With l a vector
     # Dual problem: maximize sum_n(ln) -
     #       1/2 * sum_n(sum_m(ln*lm*yn*ym*xn . xm))
     #   constraint: self.C >= ln >= 0
     #           and sum_n(ln*yn) = 0
     # Then we get w using w = sum_n(ln*yn*xn)
     # At the end we can get b ~= mean(yn - w . xn)
     #
     # Since we use kernels, we only need l_star to calculate b
     # and to classify observations

     ((SCREAMING_SNAKE_CASE__)							,  )    							=   np.shape(_lowercase   )

     def to_minimize(_lowercase    :       ndarray   ) -> float:
       SCREAMING_SNAKE_CASE__    							=   0
       ((SCREAMING_SNAKE_CASE__)							,  )    							=   np.shape(_lowercase   )
       for i in range(_lowercase   ):
         for j in range(_lowercase   ):
           s += (
               candidate[i]
               * candidate[j]
               * classes[i]
               * classes[j]
               * self.kernel(observations[i] ,			observations[j]   )
           )
       return 1 / 2 * s - sum(_lowercase   )

     SCREAMING_SNAKE_CASE__    							=   LinearConstraint(_lowercase ,			0 ,			0   )
     SCREAMING_SNAKE_CASE__    							=   Bounds(0 ,			self.regularization   )

     SCREAMING_SNAKE_CASE__    							=   minimize(
         _lowercase ,			np.ones(_lowercase   ) ,			bounds=_lowercase ,			constraints=[ly_contraint]   ).x
     SCREAMING_SNAKE_CASE__    							=   l_star

     # calculating mean offset of separation plane to points
     SCREAMING_SNAKE_CASE__    							=   0
     for i in range(_lowercase   ):
       for j in range(_lowercase   ):
         s += classes[i] - classes[i] * self.optimum[i] * self.kernel(
             observations[i] ,			observations[j]   )
     SCREAMING_SNAKE_CASE__    							=   s / n




   def 			__a		(					self    :       Optional[int] ,			_lowercase    :       ndarray   ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__    							=   sum(
         self.optimum[n]
         * self.classes[n]
         * self.kernel(self.observations[n] ,			_lowercase   )
         for n in range(len(self.classes   )   )   )
     return 1 if s + self.offset >= 0 else -1


if __name__ == "__main__":
   import doctest

   doctest.testmod()

# 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 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: Tuple			)							->      int:







  """simple docstring"""





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



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: List[Any]				,  __UpperCamelCase					: Union[str, Any]			)							->      Optional[Any]:







  """simple docstring"""





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



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: List[Any]				,  __UpperCamelCase					: List[Any]				,  __UpperCamelCase					: Union[str, Any]			)							->      int:







  """simple docstring"""





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



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: Tuple				,  __UpperCamelCase					: Optional[int]				,  __UpperCamelCase					: Tuple				,  __UpperCamelCase					: Any=7_00_00			)							->      Optional[int]:







  """simple docstring"""





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

  for iterations in range(__UpperCamelCase			):
    SCREAMING_SNAKE_CASE__    							=   np.dot(__UpperCamelCase				,  __UpperCamelCase			)
    SCREAMING_SNAKE_CASE__    							=   sigmoid_function(__UpperCamelCase			)
    SCREAMING_SNAKE_CASE__    							=   np.dot(x.T				,  h - y			) / y.size
    SCREAMING_SNAKE_CASE__    							=   theta - alpha * gradient  # updating the weights
    SCREAMING_SNAKE_CASE__    							=   np.dot(__UpperCamelCase				,  __UpperCamelCase			)
    SCREAMING_SNAKE_CASE__    							=   sigmoid_function(__UpperCamelCase			)
    SCREAMING_SNAKE_CASE__    							=   cost_function(__UpperCamelCase				,  __UpperCamelCase			)
    if iterations % 1_00 == 0:
      print(f"""loss: {j} \t"""			)  # printing the loss after every 100 iterations
  return theta


# In[68]:

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

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



   def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: List[str]			)							->      Tuple:







     """simple docstring"""





     return sigmoid_function(
         np.dot(__UpperCamelCase				,  __UpperCamelCase			)			)  # 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''')
   ((__lowerCamelCase)     ,		(__lowerCamelCase))    :				int							     =	(x[:, 0].min(), x[:, 0].max())
   ((__lowerCamelCase)     ,		(__lowerCamelCase))    :				List[Any]							     =	(x[:, 1].min(), x[:, 1].max())
   ((__lowerCamelCase)     ,		(__lowerCamelCase))    :				List[Any]							     =	np.meshgrid(np.linspace(xa_min, xa_max), np.linspace(xa_min, xa_max))
   __lowerCamelCase    :				Optional[int]							     =	np.c_[xxa.ravel(), xxa.ravel()]
   __lowerCamelCase    :				Optional[int]							     =	predict_prob(grid).reshape(xxa.shape)
   plt.contour(xxa, xxa, probs, [0.5], linewidths=1, colors='''black''')

   plt.legend()






   plt.show()
