



"""simple docstring"""







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



def      __UpperCAmelCase      (    __lowerCamelCase	)							->      float:
		return np.dot(__lowerCamelCase						,     __lowerCamelCase	)
class        __A       :







		'''simple docstring'''





		def __init__(	self						:  Optional[int]			,*,
		    _snake_case						:  float = np.inf			,_snake_case						:  str = "linear"			,_snake_case						:  float = 0.0			,)					->		None:






				"""simple docstring"""



				lowercase__   :    str				=			regularization
				lowercase__   :    List[str]				=			gamma
				if kernel == "linear":
						lowercase__   :    Any				=			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'''						)
						lowercase__   :    Optional[int]				=			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:
						lowercase__   :    int				=			f"""Unknown kernel: {kernel}"""
						raise ValueError(_snake_case						)







		def 					UpperCAmelCase    (	self						:  str			,_snake_case						:  ndarray			,_snake_case						:  ndarray						)					->		float:






				"""simple docstring"""



				return np.dot(_snake_case			,_snake_case						)







		def 					UpperCAmelCase    (	self						:  Dict			,_snake_case						:  ndarray			,_snake_case						:  ndarray						)					->		float:






				"""simple docstring"""



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







		def 					UpperCAmelCase    (	self						:  Optional[Any]			,_snake_case						:  list[ndarray]			,_snake_case						:  ndarray						)					->		None:






				"""simple docstring"""



				lowercase__   :    Union[str, Any]				=			observations
				lowercase__   :    Tuple				=			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

				((lowercase__)		,			)   :    Optional[int]				=			np.shape(_snake_case						)

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

				lowercase__   :    Optional[int]				=			LinearConstraint(_snake_case			,0			,0						)
				lowercase__   :    Any				=			Bounds(0			,self.regularization						)

				lowercase__   :    Optional[int]				=			minimize(
				    _snake_case			,np.ones(_snake_case						)			,bounds=_snake_case			,constraints=[ly_contraint]						).x
				lowercase__   :    Union[str, Any]				=			l_star

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







		def 					UpperCAmelCase    (	self						:  Optional[Any]			,_snake_case						:  ndarray						)					->		int:






				"""simple docstring"""



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


if __name__ == "__main__":
							import doctest

							doctest.testmod()




"""simple docstring"""







def 					a__			(				SCREAMING_SNAKE_CASE    :    float				,      SCREAMING_SNAKE_CASE    :    float				,      SCREAMING_SNAKE_CASE    :    int				):


  '''simple docstring'''







  if principal <= 0:
    raise Exception("Principal borrowed must be > 0"				)
  if rate_per_annum < 0:
    raise Exception("Rate of interest must be >= 0"				)
  if years_to_repay <= 0 or not isinstance(SCREAMING_SNAKE_CASE				,      SCREAMING_SNAKE_CASE				):
    raise Exception("Years to repay must be an integer > 0"				)

  # Yearly rate is divided by 12 to get monthly rate
  lowerCAmelCase     :     Tuple								=							rate_per_annum / 1_2

  # Years to repay is multiplied by 12 to get number of payments as payment is monthly
  lowerCAmelCase     :     List[Any]								=							years_to_repay * 1_2

  return (
      principal
      * rate_per_month
      * (1 + rate_per_month) ** number_of_payments
      / ((1 + rate_per_month) ** number_of_payments - 1)
  )


if __name__ == "__main__":
     import doctest

     doctest.testmod()





