





'''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  a__    (    lowercase :					List[str], lowercase :					Any				)		->		List[str]:





     """simple docstring"""

     _UpperCamelCase       =	k_size // 2
     _UpperCamelCase   ,    _UpperCamelCase       =	mgrid[0 - center : k_size - center, 0 - center : k_size - center]
     _UpperCamelCase       =	1 / (2 * pi * sigma) * exp(-(square(lowercase				) + square(lowercase				)) / (2 * square(lowercase				))				)
     return g







def  a__    (    lowercase :					str, lowercase :					Union[str, Any], lowercase :					List[str]				)		->		int:





     """simple docstring"""

     _UpperCamelCase   ,    _UpperCamelCase       =	image.shape[0], image.shape[1]
     # dst image height and width
     _UpperCamelCase       =	height - k_size + 1
     _UpperCamelCase       =	width - k_size + 1

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

     #  turn the kernel into shape(k*k, 1)
     _UpperCamelCase       =	gen_gaussian_kernel(lowercase, lowercase				)
     _UpperCamelCase       =	ravel(lowercase				)

     # reshape and get the dst image
     _UpperCamelCase       =	dot(lowercase, lowercase				).reshape(lowercase, lowercase				).astype(lowercase				)

     return dst


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

   # get values with two different mask size
   lowercase__						:      int	=    gaussian_filter(gray, 3, sigma=1)
   lowercase__						:      Union[str, 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()









'''simple docstring'''

from math import isclose, sqrt







def  a__    (    lowercase :					float, lowercase :					float, lowercase :					float				)		->		tuple[float, float, float]:





     """simple docstring"""

     _UpperCamelCase       =	point_y / 4 / point_x
     _UpperCamelCase       =	2 * normal_gradient / (1 + normal_gradient * normal_gradient)
     _UpperCamelCase       =	(1 - normal_gradient * normal_gradient) / (
         1 + normal_gradient * normal_gradient
     )
     _UpperCamelCase       =	(sa - ca * incoming_gradient) / (ca + sa * incoming_gradient)

     # to find the next point, solve the simultaeneous equations:
     # y^2 + 4x^2 = 100
     # y - b = m * (x - a)
     # ==> A x^2 + B x + C = 0
     _UpperCamelCase       =	outgoing_gradient**2 + 4
     _UpperCamelCase       =	2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
     _UpperCamelCase       =	(point_y - outgoing_gradient * point_x) ** 2 - 100

     _UpperCamelCase       =	(
         -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term				)
     ) / (2 * quadratic_term)
     _UpperCamelCase       =	(
         -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term				)
     ) / (2 * quadratic_term)

     # two solutions, one of which is our input point
     _UpperCamelCase       =	x_minus if isclose(lowercase, lowercase				) else x_plus
     _UpperCamelCase       =	point_y + outgoing_gradient * (next_x - point_x)

     return next_x, next_y, outgoing_gradient







def  a__    (    lowercase :					float = 1.4, lowercase :					float = -9.6				)		->		int:





     """simple docstring"""

     _UpperCamelCase       =	0
     _UpperCamelCase       =	first_x_coord
     _UpperCamelCase       =	first_y_coord
     _UpperCamelCase       =	(1_0.1 - point_y) / (0.0 - point_x)

     while not (-0.0_1 <= point_x <= 0.0_1 and point_y > 0):
          _UpperCamelCase   ,    _UpperCamelCase   ,    _UpperCamelCase       =	next_point(lowercase, lowercase, lowercase				)
          num_reflections += 1

     return num_reflections


if __name__ == "__main__":
   print(F"""{solution() = }""")



