



"""simple docstring"""

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




def __lowercase    (							_a					):
    return np.dot(_a	,    _a					)




class  _UpperCAmelCase :

 def __init__(  self	: int						,  *,
     lowercase_	: float = np.inf						,  lowercase_	: str = "linear"						,  lowercase_	: float = 0.0						,  ):
     snake_case_				:  Optional[Any]       =			regularization
     snake_case_				:  Tuple       =			gamma
     if kernel == "linear":
         snake_case_				:  int       =			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'''       )
         snake_case_				:  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:
         snake_case_				:  List[Any]       =			f"Unknown kernel: {kernel}"
         raise ValueError(lowercase_       )

 def 		_snake_case      (  self	: int						,  lowercase_	: ndarray						,  lowercase_	: ndarray       ):
     return np.dot(lowercase_						,  lowercase_       )

 def 		_snake_case      (  self	: int						,  lowercase_	: ndarray						,  lowercase_	: ndarray       ):
     return np.exp(-(self.gamma * norm_squared(vectora - vectora       ))       )

 def 		_snake_case      (  self	: Any						,  lowercase_	: list[ndarray]						,  lowercase_	: ndarray       ):
     snake_case_				:  Union[str, Any]       =			observations
     snake_case_				:  int       =			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

     ((snake_case_),			)				:  List[str]       =			np.shape(lowercase_       )

     def to_minimize(lowercase_	: ndarray       ) -> float:
         snake_case_				:  Tuple       =			0
         ((snake_case_),			)				:  Optional[Any]       =			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_       )

     snake_case_				:  Optional[Any]       =			LinearConstraint(lowercase_						,  0						,  0       )
     snake_case_				:  str       =			Bounds(0						,  self.regularization       )

     snake_case_				:  int       =			minimize(
         lowercase_						,  np.ones(lowercase_       )						,  bounds=lowercase_						,  constraints=[ly_contraint]       ).x
     snake_case_				:  Optional[Any]       =			l_star

     # calculating mean offset of separation plane to points
     snake_case_				:  List[Any]       =			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]       )
     snake_case_				:  Union[str, Any]       =			s / n






 def 		_snake_case      (  self	: List[str]						,  lowercase_	: ndarray       ):
     snake_case_				:  int       =			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()










"""simple docstring"""

import math
import sys

import cva
import numpy as np




def __lowercase    (							_a	,    _a					):
    # For applying gaussian function for each element in matrix.
    snake_case_				:  Dict       =			math.sqrt(_a					)
    snake_case_				:  Tuple       =			1 / (sigma * math.sqrt(2 * math.pi					))
    return cons * np.exp(-((img / sigma) ** 2) * 0.5					)




def __lowercase    (							_a	,    _a	,    _a	,    _a					):
    snake_case_				:  Optional[int]       =			kernel_size // 2
    return img[x - half : x + half + 1, y - half : y + half + 1]




def __lowercase    (							_a	,    _a					):
    # Creates a gaussian kernel of given dimension.
    snake_case_				:  Union[str, Any]       =			np.zeros((kernel_size, kernel_size)					)
    for i in range(0	,    _a					):
        for j in range(0	,    _a					):
            snake_case_				:  Union[str, Any]       =			math.sqrt(
                abs(i - kernel_size // 2					) ** 2 + abs(j - kernel_size // 2					) ** 2					)
    return vec_gaussian(_a	,    _a					)




def __lowercase    (							_a	,    _a	,    _a	,    _a	,    ):
    snake_case_				:  int       =			np.zeros(img.shape					)
    snake_case_				:  str       =			get_gauss_kernel(_a	,    _a					)
    snake_case_,			snake_case_				:  Any       =			img.shape
    for i in range(kernel_size // 2	,    size_x - kernel_size // 2					):
        for j in range(kernel_size // 2	,    size_y - kernel_size // 2					):
            snake_case_				:  List[Any]       =			get_slice(_a	,    _a	,    _a	,    _a					)
            snake_case_				:  Union[str, Any]       =			img_s - img_s[kernel_size // 2, kernel_size // 2]
            snake_case_				:  Optional[Any]       =			vec_gaussian(_a	,    _a					)
            snake_case_				:  Dict       =			np.multiply(_a	,    _a					)
            snake_case_				:  Dict       =			np.multiply(_a	,    _a					)
            snake_case_				:  List[Any]       =			np.sum(_a					) / np.sum(_a					)
            snake_case_				:  Dict       =			val
    return imga




def __lowercase    (							_a					):
    snake_case_				:  Optional[int]       =			args[1] if args[1:] else '''../image_data/lena.jpg'''
    snake_case_				:  int       =			float(args[2]					) if args[2:] else 1.0
    snake_case_				:  Dict       =			float(args[3]					) if args[3:] else 1.0
    if args[4:]:
        snake_case_				:  Optional[Any]       =			int(args[4]					)
        snake_case_				:  Union[str, Any]       =			kernel_size + abs(kernel_size % 2 - 1					)
    else:
        snake_case_				:  Union[str, Any]       =			5
    return filename, spatial_variance, intensity_variance, kernel_size


if __name__ == "__main__":
     lowercase__					,lowercase__					,lowercase__					,lowercase__					:						Tuple												=			parse_args(sys.argv)
     lowercase__					:						str												=			cva.imread(filename, 0)
     cva.imshow('''input image''', img)

     lowercase__					:						Tuple												=			img / 2_55
     lowercase__					:						Optional[int]												=			out.astype('''float32''')
     lowercase__					:						Union[str, Any]												=			bilateral_filter(out, spatial_variance, intensity_variance, kernel_size)
     lowercase__					:						List[str]												=			out * 2_55
     lowercase__					:						List[str]												=			np.uinta(out)
     cva.imshow('''output image''', out)
     cva.waitKey(0)
     cva.destroyAllWindows()





