





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        __lowerCamelCase (							__a       :Optional[int]   ,					__a       :str   )		->    Optional[Any]:






		"""simple docstring"""

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







def        __lowerCamelCase (							__a       :Optional[int]   ,					__a       :Dict   ,					__a       :List[str]   )		->    Any:






		"""simple docstring"""

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

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

		#  turn the kernel into shape(k*k, 1)
		A__  				=       gen_gaussian_kernel(_a   ,					_a   )
		A__  				=       ravel(_a   )

		# reshape and get the dst image
		A__  				=       dot(_a   ,					_a   ).reshape(_a   ,					_a   ).astype(_a   )

		return dst


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

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










def        __lowerCamelCase (							__a       :float   ,					__a       :list[float]   )		->    float:






		"""simple docstring"""

		if discount_rate < 0:
				raise ValueError("""Discount rate cannot be negative"""   )
		if not cash_flows:
				raise ValueError("""Cash flows list cannot be empty"""   )
		A__  				=       sum(
		    cash_flow / ((1 + discount_rate) ** i) for i, cash_flow in enumerate(__a   )   )
		return round(__a   ,					ndigits=2   )


if __name__ == "__main__":
					import doctest

					doctest.testmod()



