


'''simple docstring'''



from __future__ import annotations

import math
import random
from collections.abc import Collection
from typing import overload






class 	UpperCamelCase__:




				def __init__(		self      :			int				,   lowerCAmelCase      :			Collection[float] | None = None				)->					None:

										"""simple docstring"""




										if components is None:
																UpperCAmelCase					    =     []
										UpperCAmelCase					    =     list(lowerCAmelCase				)




				def __len__(		self      :			List[Any]				)->					int:

										"""simple docstring"""




										return len(self.__components				)




				def __str__(		self      :			int				)->					str:

										"""simple docstring"""




										return "(" + ",".join(map(lowerCAmelCase				,   self.__components				)				) + ")"




				def __add__(		self      :			Tuple				,   lowerCAmelCase      :			Vector				)->					Vector:

										"""simple docstring"""




										UpperCAmelCase					    =     len(self				)
										if size == len(lowerCAmelCase				):
																UpperCAmelCase					    =     [self.__components[i] + other.component(lowerCAmelCase				) for i in range(lowerCAmelCase				)]
																return Vector(lowerCAmelCase				)
										else:
																raise Exception('''must have the same size'''				)




				def __sub__(		self      :			int				,   lowerCAmelCase      :			Vector				)->					Vector:

										"""simple docstring"""




										UpperCAmelCase					    =     len(self				)
										if size == len(lowerCAmelCase				):
																UpperCAmelCase					    =     [self.__components[i] - other.component(lowerCAmelCase				) for i in range(lowerCAmelCase				)]
																return Vector(lowerCAmelCase				)
										else:  # error case
																raise Exception('''must have the same size'''				)




				@overload
				def __mul__(		self      :			int				,   lowerCAmelCase      :			float				)->					Vector:

										"""simple docstring"""




										...




				@overload
				def __mul__(		self      :			Tuple				,   lowerCAmelCase      :			Vector				)->					float:

										"""simple docstring"""




										...




				def __mul__(		self      :			Optional[int]				,   lowerCAmelCase      :			float | Vector				)->					float | Vector:

										"""simple docstring"""




										if isinstance(lowerCAmelCase				,   (float, int)				):
																UpperCAmelCase					    =     [c * other for c in self.__components]
																return Vector(lowerCAmelCase				)
										elif isinstance(lowerCAmelCase				,   lowerCAmelCase				) and len(self				) == len(lowerCAmelCase				):
																UpperCAmelCase					    =     len(self				)
																UpperCAmelCase					    =     [self.__components[i] * other.component(lowerCAmelCase				) for i in range(lowerCAmelCase				)]
																return sum(lowerCAmelCase				)
										else:  # error case
																raise Exception('''invalid operand!'''				)




				def 					a__(		self      :			Union[str, Any]				)->					Vector:

										"""simple docstring"""




										return Vector(self.__components				)




				def 					a__(		self      :			List[Any]				,   lowerCAmelCase      :			int				)->					float:

										"""simple docstring"""




										if isinstance(lowerCAmelCase				,   lowerCAmelCase				) and -len(self.__components				) <= i < len(self.__components				):
																return self.__components[i]
										else:
																raise Exception('''index out of range'''				)




				def 					a__(		self      :			Any				,   lowerCAmelCase      :			int				,   lowerCAmelCase      :			float				)->					None:

										"""simple docstring"""




										assert -len(self.__components				) <= pos < len(self.__components				)
										UpperCAmelCase					    =     value




				def 					a__(		self      :			int				)->					float:

										"""simple docstring"""




										if len(self.__components				) == 0:
																raise Exception('''Vector is empty'''				)
										UpperCAmelCase					    =     [c**2 for c in self.__components]
										return math.sqrt(sum(lowerCAmelCase				)				)





				def 					a__(		self      :			Optional[int]				,   lowerCAmelCase      :			Vector				,   lowerCAmelCase      :			bool = False				)->					float:

										"""simple docstring"""




										UpperCAmelCase					    =     self * other
										UpperCAmelCase					    =     self.euclidean_length() * other.euclidean_length()
										if deg:
																return math.degrees(math.acos(num / den				)				)
										else:
																return math.acos(num / den				)







def 				lowerCamelCase__				(	A       :      int					):




						'''simple docstring'''






						assert isinstance(A				,       A					)
						return Vector([0] * dimension					)


def 				lowerCamelCase__				(	A       :      int				,       A       :      int					):




						'''simple docstring'''






						assert isinstance(A				,       A					) and (isinstance(A				,       A					))
						UpperCAmelCase					    =     [0] * dimension
						UpperCAmelCase					    =     1
						return Vector(A					)


def 				lowerCamelCase__				(	A       :      float				,       A       :      Vector				,       A       :      Vector					):




						'''simple docstring'''






						assert (
						    isinstance(A				,       A					)
						    and isinstance(A				,       A					)
						    and (isinstance(A				,       (int, float)					))
						)
						return x * scalar + y


def 				lowerCamelCase__				(	A       :      int				,       A       :      int				,       A       :      int					):




						'''simple docstring'''






						random.seed(A					)
						UpperCAmelCase					    =     [random.randint(A				,       A					) for _ in range(A					)]
						return Vector(A					)






class 	UpperCamelCase__:




				def __init__(		self      :			Tuple				,   lowerCAmelCase      :			list[list[float]]				,   lowerCAmelCase      :			int				,   lowerCAmelCase      :			int				)->					None:

										"""simple docstring"""




										UpperCAmelCase					    =     matrix
										UpperCAmelCase					    =     w
										UpperCAmelCase					    =     h




				def __str__(		self      :			int				)->					str:

										"""simple docstring"""




										UpperCAmelCase					    =     ''''''
										for i in range(self.__height				):
																ans += "|"
																for j in range(self.__width				):
																						if j < self.__width - 1:
																												ans += str(self.__matrix[i][j]				) + ","
																						else:
																												ans += str(self.__matrix[i][j]				) + "|\n"
										return ans




				def __add__(		self      :			Any				,   lowerCAmelCase      :			Matrix				)->					Matrix:

										"""simple docstring"""




										if self.__width == other.width() and self.__height == other.height():
																UpperCAmelCase					    =     []
																for i in range(self.__height				):
																						UpperCAmelCase					    =     [
																						    self.__matrix[i][j] + other.component(lowerCAmelCase				,   lowerCAmelCase				)
																						    for j in range(self.__width				)
																						]
																						matrix.append(lowerCAmelCase				)
																return Matrix(lowerCAmelCase				,   self.__width				,   self.__height				)
										else:
																raise Exception('''matrix must have the same dimension!'''				)




				def __sub__(		self      :			int				,   lowerCAmelCase      :			Matrix				)->					Matrix:

										"""simple docstring"""




										if self.__width == other.width() and self.__height == other.height():
																UpperCAmelCase					    =     []
																for i in range(self.__height				):
																						UpperCAmelCase					    =     [
																						    self.__matrix[i][j] - other.component(lowerCAmelCase				,   lowerCAmelCase				)
																						    for j in range(self.__width				)
																						]
																						matrix.append(lowerCAmelCase				)
																return Matrix(lowerCAmelCase				,   self.__width				,   self.__height				)
										else:
																raise Exception('''matrices must have the same dimension!'''				)




				@overload
				def __mul__(		self      :			Tuple				,   lowerCAmelCase      :			float				)->					Matrix:

										"""simple docstring"""




										...




				@overload
				def __mul__(		self      :			List[str]				,   lowerCAmelCase      :			Vector				)->					Vector:

										"""simple docstring"""




										...




				def __mul__(		self      :			List[str]				,   lowerCAmelCase      :			float | Vector				)->					Vector | Matrix:

										"""simple docstring"""




										if isinstance(lowerCAmelCase				,   lowerCAmelCase				):  # matrix-vector
																if len(lowerCAmelCase				) == self.__width:
																						UpperCAmelCase					    =     zero_vector(self.__height				)
																						for i in range(self.__height				):
																												UpperCAmelCase					    =     [
																												    self.__matrix[i][j] * other.component(lowerCAmelCase				)
																												    for j in range(self.__width				)
																												]
																												ans.change_component(lowerCAmelCase				,   sum(lowerCAmelCase				)				)
																						return ans
																else:
																						raise Exception(
																						    '''vector must have the same size as the '''
																						    '''number of columns of the matrix!'''				)
										elif isinstance(lowerCAmelCase				,   (int, float)				):  # matrix-scalar
																UpperCAmelCase					    =     [
																    [self.__matrix[i][j] * other for j in range(self.__width				)]
																    for i in range(self.__height				)
																]
																return Matrix(lowerCAmelCase				,   self.__width				,   self.__height				)
										return None




				def 					a__(		self      :			Dict				)->					int:

										"""simple docstring"""




										return self.__height




				def 					a__(		self      :			Optional[int]				)->					int:

										"""simple docstring"""




										return self.__width




				def 					a__(		self      :			List[Any]				,   lowerCAmelCase      :			int				,   lowerCAmelCase      :			int				)->					float:

										"""simple docstring"""




										if 0 <= x < self.__height and 0 <= y < self.__width:
																return self.__matrix[x][y]
										else:
																raise Exception('''change_component: indices out of bounds'''				)




				def 					a__(		self      :			Any				,   lowerCAmelCase      :			int				,   lowerCAmelCase      :			int				,   lowerCAmelCase      :			float				)->					None:

										"""simple docstring"""




										if 0 <= x < self.__height and 0 <= y < self.__width:
																UpperCAmelCase					    =     value
										else:
																raise Exception('''change_component: indices out of bounds'''				)




				def 					a__(		self      :			Optional[Any]				,   lowerCAmelCase      :			int				,   lowerCAmelCase      :			int				)->					float:

										"""simple docstring"""




										if self.__height != self.__width:
																raise Exception('''Matrix is not square'''				)
										UpperCAmelCase					    =     self.__matrix[:x] + self.__matrix[x + 1 :]
										for i in range(len(lowerCAmelCase				)				):
																UpperCAmelCase					    =     minor[i][:y] + minor[i][y + 1 :]
										return Matrix(lowerCAmelCase				,   self.__width - 1				,   self.__height - 1				).determinant()




				def 					a__(		self      :			Union[str, Any]				,   lowerCAmelCase      :			int				,   lowerCAmelCase      :			int				)->					float:

										"""simple docstring"""




										if self.__height != self.__width:
																raise Exception('''Matrix is not square'''				)
										if 0 <= x < self.__height and 0 <= y < self.__width:
																return (-1) ** (x + y) * self.minor(lowerCAmelCase				,   lowerCAmelCase				)
										else:
																raise Exception('''Indices out of bounds'''				)





				def 					a__(		self      :			Optional[Any]				)->					float:

										"""simple docstring"""




										if self.__height != self.__width:
																raise Exception('''Matrix is not square'''				)
										if self.__height < 1:
																raise Exception('''Matrix has no element'''				)
										elif self.__height == 1:
																return self.__matrix[0][0]
										elif self.__height == 2:
																return (
																    self.__matrix[0][0] * self.__matrix[1][1]
																    - self.__matrix[0][1] * self.__matrix[1][0]
																)
										else:
																UpperCAmelCase					    =     [
																    self.__matrix[0][y] * self.cofactor(0				,   lowerCAmelCase				) for y in range(self.__width				)
																]
																return sum(lowerCAmelCase				)







def 				lowerCamelCase__				(	A       :      int					):




						'''simple docstring'''






						UpperCAmelCase					    =     [[0] * n for _ in range(A					)]
						return Matrix(A				,       A				,       A					)




def 				lowerCamelCase__				(	A       :      int				,       A       :      int				,       A       :      int				,       A       :      int					):




						'''simple docstring'''






						random.seed(A					)
						UpperCAmelCase					    =     [
						    [random.randint(A				,       A					) for _ in range(A					)] for _ in range(A					)
						]
						return Matrix(A				,       A				,       A					)









'''simple docstring'''



import numpy as np
from cva import COLOR_BGR2GRAY, CV_8UC3, cvtColor, filteraD, imread, imshow, waitKey


def 				lowerCamelCase__				(	A       :      int				,       A       :      int				,       A       :      int				,       A       :      int				,       A       :      int				,       A       :      int					):




						'''simple docstring'''






						if (ksize % 2) == 0:
												UpperCAmelCase					    =     ksize + 1
						UpperCAmelCase					    =     np.zeros((ksize, ksize)				,       dtype=np.floataa					)

						# each value
						for y in range(A					):
												for x in range(A					):
																		# distance from center
																		UpperCAmelCase					    =     x - ksize // 2
																		UpperCAmelCase					    =     y - ksize // 2

																		# degree to radiant
																		UpperCAmelCase					    =     theta / 1_80 * np.pi
																		UpperCAmelCase					    =     np.cos(_theta					)
																		UpperCAmelCase					    =     np.sin(_theta					)

																		# get kernel x
																		UpperCAmelCase					    =     cos_theta * px + sin_theta * py

																		# get kernel y
																		UpperCAmelCase					    =     -sin_theta * px + cos_theta * py

																		# fill kernel
																		UpperCAmelCase					    =     np.exp(
																		    -(_x**2 + gamma**2 * _y**2) / (2 * sigma**2)					) * np.cos(2 * np.pi * _x / lambd + psi					)

						return gabor


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	# read original image
	_lowercase      :      Tuple            =					imread("""../image_data/lena.jpg""")
	# turn image in gray scale value
	_lowercase      :      int            =					cvtColor(img, COLOR_BGR2GRAY)

	# Apply multiple Kernel to detect edges
	_lowercase      :      List[str]            =					np.zeros(gray.shape[:2])
	for theta in [0, 30, 60, 90, 120, 150]:
		_lowercase      :      List[Any]            =					gabor_filter_kernel(10, 8, theta, 10, 0, 0)
		out += filteraD(gray, CV_8UC3, kernel_aa)
	_lowercase      :      Optional[int]            =					out / out.max() * 255
	_lowercase      :      Optional[int]            =					out.astype(np.uinta)

	imshow("""Original""", gray)
	imshow("""Gabor filter with 20x20 mask and 6 directions""", out)

	waitKey(0)





