





"""simple docstring"""






from __future__ import annotations

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




class  __lowercase	:







					'''simple docstring'''




					def __init__(  self		,	_UpperCAmelCase = None   ):
									if components is None:
													__a       :  List[str]					=     []
									__a       :  str					=     list(a__   )







					def __len__(  self   ):
									return len(self.__components   )







					def __str__(  self   ):
									return "(" + ",".join(map(a__		,	self.__components   )   ) + ")"







					def __add__(  self		,	_UpperCAmelCase   ):
									__a       :  List[str]					=     len(self   )
									if size == len(a__   ):
													__a       :  str					=     [self.__components[i] + other.component(a__   ) for i in range(a__   )]
													return Vector(a__   )
									else:
													raise Exception('''must have the same size'''   )







					def __sub__(  self		,	_UpperCAmelCase   ):
									__a       :  int					=     len(self   )
									if size == len(a__   ):
													__a       :  Optional[Any]					=     [self.__components[i] - other.component(a__   ) for i in range(a__   )]
													return Vector(a__   )
									else:  # error case
													raise Exception('''must have the same size'''   )







					@overload
					def __mul__(  self		,	_UpperCAmelCase   ):
									...







					@overload
					def __mul__(  self		,	_UpperCAmelCase   ):
									...







					def __mul__(  self		,	_UpperCAmelCase   ):
									if isinstance(a__		,	(float, int)   ):
													__a       :  List[Any]					=     [c * other for c in self.__components]
													return Vector(a__   )
									elif isinstance(a__		,	a__   ) and len(self   ) == len(a__   ):
													__a       :  List[Any]					=     len(self   )
													__a       :  List[str]					=     [self.__components[i] * other.component(a__   ) for i in range(a__   )]
													return sum(a__   )
									else:  # error case
													raise Exception('''invalid operand!'''   )







					def        _lowerCamelCase						(  self   ):
									return Vector(self.__components   )







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







					def        _lowerCamelCase						(  self		,	_UpperCAmelCase		,	_UpperCAmelCase   ):
									assert -len(self.__components   ) <= pos < len(self.__components   )
									__a       :  int					=     value







					def        _lowerCamelCase						(  self   ):
									if len(self.__components   ) == 0:
													raise Exception('''Vector is empty'''   )
									__a       :  int					=     [c**2 for c in self.__components]
									return math.sqrt(sum(a__   )   )







					def        _lowerCamelCase						(  self		,	_UpperCAmelCase		,	_UpperCAmelCase = False   ):
									__a       :  List[Any]					=     self * other
									__a       :  int					=     self.euclidean_length() * other.euclidean_length()
									if deg:
													return math.degrees(math.acos(num / den   )   )
									else:
													return math.acos(num / den   )






def 			__A					(	a_  :int)						->						Vector:
				assert isinstance(_lowerCamelCase      ,				_lowerCamelCase)
				return Vector([0] * dimension)

def 			__A					(	a_  :int      ,				a_  :int)						->						Vector:
				assert isinstance(_lowerCamelCase      ,				_lowerCamelCase) and (isinstance(_lowerCamelCase      ,				_lowerCamelCase))
				__a       :  Union[str, Any]					=     [0] * dimension
				__a       :  List[Any]					=     1
				return Vector(_lowerCamelCase)

def 			__A					(	a_  :float      ,				a_  :Vector      ,				a_  :Vector)						->						Vector:
				assert (
				    isinstance(_lowerCamelCase      ,				_lowerCamelCase)
				    and isinstance(_lowerCamelCase      ,				_lowerCamelCase)
				    and (isinstance(_lowerCamelCase      ,				(int, float)))
				)
				return x * scalar + y

def 			__A					(	a_  :int      ,				a_  :int      ,				a_  :int)						->						Vector:
				random.seed(_lowerCamelCase)
				__a       :  Union[str, Any]					=     [random.randint(_lowerCamelCase      ,				_lowerCamelCase) for _ in range(_lowerCamelCase)]
				return Vector(_lowerCamelCase)




class  __lowercase	:







					'''simple docstring'''




					def __init__(  self		,	_UpperCAmelCase		,	_UpperCAmelCase		,	_UpperCAmelCase   ):
									__a       :  List[Any]					=     matrix
									__a       :  Dict					=     w
									__a       :  Optional[int]					=     h







					def __str__(  self   ):
									__a       :  Tuple					=     """"""
									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		,	_UpperCAmelCase   ):
									if self.__width == other.width() and self.__height == other.height():
													__a       :  str					=     []
													for i in range(self.__height   ):
																	__a       :  List[Any]					=     [
																	    self.__matrix[i][j] + other.component(a__		,	a__   )
																	    for j in range(self.__width   )
																	]
																	matrix.append(a__   )
													return Matrix(a__		,	self.__width		,	self.__height   )
									else:
													raise Exception('''matrix must have the same dimension!'''   )







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







					@overload
					def __mul__(  self		,	_UpperCAmelCase   ):
									...







					@overload
					def __mul__(  self		,	_UpperCAmelCase   ):
									...







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







					def        _lowerCamelCase						(  self   ):
									return self.__height







					def        _lowerCamelCase						(  self   ):
									return self.__width







					def        _lowerCamelCase						(  self		,	_UpperCAmelCase		,	_UpperCAmelCase   ):
									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        _lowerCamelCase						(  self		,	_UpperCAmelCase		,	_UpperCAmelCase		,	_UpperCAmelCase   ):
									if 0 <= x < self.__height and 0 <= y < self.__width:
													__a       :  List[str]					=     value
									else:
													raise Exception('''change_component: indices out of bounds'''   )







					def        _lowerCamelCase						(  self		,	_UpperCAmelCase		,	_UpperCAmelCase   ):
									if self.__height != self.__width:
													raise Exception('''Matrix is not square'''   )
									__a       :  Optional[Any]					=     self.__matrix[:x] + self.__matrix[x + 1 :]
									for i in range(len(a__   )   ):
													__a       :  Any					=     minor[i][:y] + minor[i][y + 1 :]
									return Matrix(a__		,	self.__width - 1		,	self.__height - 1   ).determinant()







					def        _lowerCamelCase						(  self		,	_UpperCAmelCase		,	_UpperCAmelCase   ):
									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(a__		,	a__   )
									else:
													raise Exception('''Indices out of bounds'''   )







					def        _lowerCamelCase						(  self   ):
									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:
													__a       :  Dict					=     [
													    self.__matrix[0][y] * self.cofactor(0		,	a__   ) for y in range(self.__width   )
													]
													return sum(a__   )






def 			__A					(	a_  :int)						->						Matrix:
				__a       :  list[list[float]]					=     [[0] * n for _ in range(_lowerCamelCase)]
				return Matrix(_lowerCamelCase      ,				_lowerCamelCase      ,				_lowerCamelCase)






def 			__A					(	a_  :int      ,				a_  :int      ,				a_  :int      ,				a_  :int)						->						Matrix:
				random.seed(_lowerCamelCase)
				__a       :  list[list[float]]					=     [
				    [random.randint(_lowerCamelCase      ,				_lowerCamelCase) for _ in range(_lowerCamelCase)] for _ in range(_lowerCamelCase)
				]
				return Matrix(_lowerCamelCase      ,				_lowerCamelCase      ,				_lowerCamelCase)
"""simple docstring"""




from itertools import product

from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
from numpy import dot, exp, mgrid, pi, ravel, square, uinta, zeros





def 							SCREAMING_SNAKE_CASE     (			_lowerCamelCase						:       Optional[Any]			,_lowerCamelCase						:       int	)       ->      List[str]:
  _lowerCAmelCase						:       Tuple  			=     k_size // 2
  _lowerCAmelCase			,	_lowerCAmelCase						:       List[str]  			=     mgrid[0 - center : k_size - center, 0 - center : k_size - center]
  _lowerCAmelCase						:       Union[str, Any]  			=     1 / (2 * pi * sigma) * exp(-(square(_lowerCamelCase	) + square(_lowerCamelCase	)) / (2 * square(_lowerCamelCase	))	)
  return g





def 							SCREAMING_SNAKE_CASE     (			_lowerCamelCase						:       Dict			,_lowerCamelCase						:       int			,_lowerCamelCase						:       int	)       ->      Dict:
  _lowerCAmelCase			,	_lowerCAmelCase						:       str  			=     image.shape[0], image.shape[1]
  # dst image height and width
  _lowerCAmelCase						:       Optional[int]  			=     height - k_size + 1
  _lowerCAmelCase						:       Dict  			=     width - k_size + 1

  # im2col, turn the k_size*k_size pixels into a row and np.vstack all rows
  _lowerCAmelCase						:       Tuple  			=     zeros((dst_height * dst_width, k_size * k_size)	)
  _lowerCAmelCase						:       int  			=     0
  for i, j in product(range(_lowerCamelCase	)			,range(_lowerCamelCase	)	):
    _lowerCAmelCase						:       Any  			=     ravel(image[i : i + k_size, j : j + k_size]	)
    _lowerCAmelCase						:       Union[str, Any]  			=     window
    row += 1

  #  turn the kernel into shape(k*k, 1)
  _lowerCAmelCase						:       List[Any]  			=     gen_gaussian_kernel(_lowerCamelCase			,_lowerCamelCase	)
  _lowerCAmelCase						:       str  			=     ravel(_lowerCamelCase	)

  # reshape and get the dst image
  _lowerCAmelCase						:       int  			=     dot(_lowerCamelCase			,_lowerCamelCase	).reshape(_lowerCamelCase			,_lowerCamelCase	).astype(_lowerCamelCase	)

  return dst


if __name__ == "__main__":
     # read original image
     _a      :		Optional[Any]           =   imread(r'../image_data/lena.jpg')
     # turn image in gray scale value
     _a      :		Dict           =   cvtColor(img, COLOR_BGR2GRAY)

     # get values with two different mask size
     _a      :		Union[str, Any]           =   gaussian_filter(gray, 3, sigma=1)
     _a      :		List[Any]           =   gaussian_filter(gray, 5, sigma=0.8)

     # show result images
     imshow('gaussian filter with 3x3 mask', gaussianaxa)
     imshow('gaussian filter with 5x5 mask', gaussianaxa)
     waitKey()




