




"""simple docstring"""







import math
import sys

import cva
import numpy as np

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->np.ndarray:






		"""simple docstring"""


		__lowercase				:		Union[str, Any]												=				math.sqrt(__lowerCAmelCase				)
		__lowercase				:		Optional[Any]												=				1 / (sigma * math.sqrt(2 * math.pi				))
		return cons * np.exp(-((img / sigma) ** 2) * 0.5				)

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase,  _lowerCamelCase,  _lowerCamelCase				)			->np.ndarray:






		"""simple docstring"""


		__lowercase				:		str												=				kernel_size // 2
		return img[x - half : x + half + 1, y - half : y + half + 1]

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->np.ndarray:






		"""simple docstring"""


		__lowercase				:		int												=				np.zeros((kernel_size, kernel_size)				)
		for i in range(0,  __lowerCAmelCase				):
				for j in range(0,  __lowerCAmelCase				):
						__lowercase				:		Tuple												=				math.sqrt(
						    abs(i - kernel_size // 2				) ** 2 + abs(j - kernel_size // 2				) ** 2				)
		return vec_gaussian(__lowerCAmelCase,  __lowerCAmelCase				)

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase,  _lowerCamelCase,  _lowerCamelCase,  )			->np.ndarray:






		"""simple docstring"""


		__lowercase				:		Optional[Any]												=				np.zeros(img.shape				)
		__lowercase				:		Any												=				get_gauss_kernel(__lowerCAmelCase,  __lowerCAmelCase				)
		__lowercase				:		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				):
						__lowercase				:		str												=				get_slice(__lowerCAmelCase,  __lowerCAmelCase,  __lowerCAmelCase,  __lowerCAmelCase				)
						__lowercase				:		int												=				img_s - img_s[kernel_size // 2, kernel_size // 2]
						__lowercase				:		Optional[int]												=				vec_gaussian(__lowerCAmelCase,  __lowerCAmelCase				)
						__lowercase				:		Optional[Any]												=				np.multiply(__lowerCAmelCase,  __lowerCAmelCase				)
						__lowercase				:		List[str]												=				np.multiply(__lowerCAmelCase,  __lowerCAmelCase				)
						__lowercase				:		Dict												=				np.sum(__lowerCAmelCase				) / np.sum(__lowerCAmelCase				)
						__lowercase				:		Optional[Any]												=				val
		return imga

def 						snake_case__       (					_lowerCamelCase				)			->tuple:






		"""simple docstring"""


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


if __name__ == "__main__":
						__A   :  int					=      parse_args(sys.argv)
						__A   :  List[Any]					=      cva.imread(filename, 0)
						cva.imshow('input image', img)

						__A   :  int					=      img / 2_5_5
						__A   :  Tuple					=      out.astype('float32')
						__A   :  Dict					=      bilateral_filter(out, spatial_variance, intensity_variance, kernel_size)
						__A   :  Any					=      out * 2_5_5
						__A   :  Any					=      np.uinta(out)
						cva.imshow('output image', out)
						cva.waitKey(0)
						cva.destroyAllWindows()






"""simple docstring"""







from __future__ import annotations

import math

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->list:






		"""simple docstring"""


		if len(_lowerCamelCase				) != 2 or len(a[0]				) != 2 or len(_lowerCamelCase				) != 2 or len(b[0]				) != 2:
				raise Exception("Matrices are not 2x2"				)
		__lowercase				:		Tuple												=				[
		    [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
		    [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
		]
		return new_matrix

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->Dict:






		"""simple docstring"""


		return [
		    [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]				)				)]
		    for row in range(len(_lowerCamelCase				)				)
		]

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->Tuple:






		"""simple docstring"""


		return [
		    [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]				)				)]
		    for row in range(len(_lowerCamelCase				)				)
		]

def 						snake_case__       (					_lowerCamelCase				)			->tuple[list, list, list, list]:






		"""simple docstring"""


		if len(_lowerCamelCase				) % 2 != 0 or len(a[0]				) % 2 != 0:
				raise Exception("Odd matrices are not supported!"				)

		__lowercase				:		Tuple												=				len(_lowerCamelCase				)
		__lowercase				:		Any												=				matrix_length // 2

		__lowercase				:		Dict												=				[[a[i][j] for j in range(_lowerCamelCase,  _lowerCamelCase				)] for i in range(_lowerCamelCase				)]
		__lowercase				:		List[str]												=				[
		    [a[i][j] for j in range(_lowerCamelCase,  _lowerCamelCase				)] for i in range(_lowerCamelCase,  _lowerCamelCase				)
		]

		__lowercase				:		Union[str, Any]												=				[[a[i][j] for j in range(_lowerCamelCase				)] for i in range(_lowerCamelCase				)]
		__lowercase				:		List[str]												=				[[a[i][j] for j in range(_lowerCamelCase				)] for i in range(_lowerCamelCase,  _lowerCamelCase				)]

		return top_left, top_right, bot_left, bot_right

def 						snake_case__       (					_lowerCamelCase				)			->tuple[int, int]:






		"""simple docstring"""


		return len(_lowerCamelCase				), len(matrix[0]				)

def 						snake_case__       (					_lowerCamelCase				)			->None:






		"""simple docstring"""


		print("\n".join(str(_lowerCamelCase				) for line in matrix				)				)

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->list:






		"""simple docstring"""


		if matrix_dimensions(_lowerCamelCase				) == (2, 2):
				return default_matrix_multiplication(_lowerCamelCase,  _lowerCamelCase				)

		__lowercase						,__lowercase						,__lowercase						,__lowercase				:		Optional[Any]												=				split_matrix(_lowerCamelCase				)
		__lowercase						,__lowercase						,__lowercase						,__lowercase				:		Any												=				split_matrix(_lowerCamelCase				)

		__lowercase				:		str												=				actual_strassen(_lowerCamelCase,  matrix_subtraction(_lowerCamelCase,  _lowerCamelCase				)				)
		__lowercase				:		Dict												=				actual_strassen(matrix_addition(_lowerCamelCase,  _lowerCamelCase				),  _lowerCamelCase				)
		__lowercase				:		Union[str, Any]												=				actual_strassen(matrix_addition(_lowerCamelCase,  _lowerCamelCase				),  _lowerCamelCase				)
		__lowercase				:		Any												=				actual_strassen(_lowerCamelCase,  matrix_subtraction(_lowerCamelCase,  _lowerCamelCase				)				)
		__lowercase				:		List[Any]												=				actual_strassen(matrix_addition(_lowerCamelCase,  _lowerCamelCase				),  matrix_addition(_lowerCamelCase,  _lowerCamelCase				)				)
		__lowercase				:		Optional[int]												=				actual_strassen(matrix_subtraction(_lowerCamelCase,  _lowerCamelCase				),  matrix_addition(_lowerCamelCase,  _lowerCamelCase				)				)
		__lowercase				:		Optional[Any]												=				actual_strassen(matrix_subtraction(_lowerCamelCase,  _lowerCamelCase				),  matrix_addition(_lowerCamelCase,  _lowerCamelCase				)				)

		__lowercase				:		str												=				matrix_addition(matrix_subtraction(matrix_addition(_lowerCamelCase,  _lowerCamelCase				),  _lowerCamelCase				),  _lowerCamelCase				)
		__lowercase				:		Dict												=				matrix_addition(_lowerCamelCase,  _lowerCamelCase				)
		__lowercase				:		int												=				matrix_addition(_lowerCamelCase,  _lowerCamelCase				)
		__lowercase				:		Union[str, Any]												=				matrix_subtraction(matrix_subtraction(matrix_addition(_lowerCamelCase,  _lowerCamelCase				),  _lowerCamelCase				),  _lowerCamelCase				)

		# construct the new matrix from our 4 quadrants
		__lowercase				:		Optional[int]												=				[]
		for i in range(len(_lowerCamelCase				)				):
				new_matrix.append(top_left[i] + top_right[i]				)
		for i in range(len(_lowerCamelCase				)				):
				new_matrix.append(bot_left[i] + bot_right[i]				)
		return new_matrix

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->list:






		"""simple docstring"""


		if matrix_dimensions(_lowerCamelCase				)[1] != matrix_dimensions(_lowerCamelCase				)[0]:
				__lowercase				:		int												=				(
				    "Unable to multiply these matrices, please check the dimensions.\n"
				    F'Matrix A: {matrixa}\n'
				    F'Matrix B: {matrixa}'
				)
				raise Exception(_lowerCamelCase				)
		__lowercase				:		List[Any]												=				matrix_dimensions(_lowerCamelCase				)
		__lowercase				:		Tuple												=				matrix_dimensions(_lowerCamelCase				)

		if dimensiona[0] == dimensiona[1] and dimensiona[0] == dimensiona[1]:
				return [matrixa, matrixa]

		__lowercase				:		int												=				max(*_lowerCamelCase,  *_lowerCamelCase				)
		__lowercase				:		Any												=				int(math.pow(2,  math.ceil(math.loga(_lowerCamelCase				)				)				)				)
		__lowercase				:		Dict												=				matrixa
		__lowercase				:		str												=				matrixa

		# Adding zeros to the matrices so that the arrays dimensions are the same and also
		# power of 2
		for i in range(0,  _lowerCamelCase				):
				if i < dimensiona[0]:
						for _ in range(dimensiona[1],  _lowerCamelCase				):
								new_matrixa[i].append(0				)
				else:
						new_matrixa.append([0] * maxim				)
				if i < dimensiona[0]:
						for _ in range(dimensiona[1],  _lowerCamelCase				):
								new_matrixa[i].append(0				)
				else:
						new_matrixa.append([0] * maxim				)

		__lowercase				:		Dict												=				actual_strassen(_lowerCamelCase,  _lowerCamelCase				)

		# Removing the additional zeros
		for i in range(0,  _lowerCamelCase				):
				if i < dimensiona[0]:
						for _ in range(dimensiona[1],  _lowerCamelCase				):
								final_matrix[i].pop()
				else:
						final_matrix.pop()
		return final_matrix


if __name__ == "__main__":
						__A   :  int					=      [
						    [2, 3, 4, 5],
						    [6, 4, 3, 1],
						    [2, 3, 6, 7],
						    [3, 1, 2, 4],
						    [2, 3, 4, 5],
						    [6, 4, 3, 1],
						    [2, 3, 6, 7],
						    [3, 1, 2, 4],
						    [2, 3, 4, 5],
						    [6, 2, 3, 1],
						]
						__A   :  Union[str, Any]					=      [[0, 2, 1, 1], [1_6, 2, 3, 3], [2, 2, 7, 7], [1_3, 1_1, 2_2, 4]]
						print(strassen(matrixa, matrixa))
