"""simple docstring"""




def 				_UpperCAmelCase		(							lowerCamelCase__  ):





		"""simple docstring"""




		lowerCAmelCase__   = current_set.copy()
		for row_index, row in enumerate(lowerCamelCase__  ):
				lowerCAmelCase__   = row[0]
				for column_index, column in enumerate(lowerCamelCase__  ):
						if magnitude == 0:
								lowerCAmelCase__   = column
								continue
						lowerCAmelCase__   = column / magnitude
    # Subtract to cancel term
		lowerCAmelCase__   = current_set[0]
		lowerCAmelCase__   = [first_row]
		lowerCAmelCase__   = current_set[1::]
		for row in current_set:
				lowerCAmelCase__   = []
				# If first term is 0, it is already in form we want, so we preserve it
				if row[0] == 0:
						final_set.append(lowerCamelCase__  )
						continue
				for column_index in range(len(lowerCamelCase__  )  ):
						temp_row.append(first_row[column_index] - row[column_index]  )
				final_set.append(lowerCamelCase__  )
		# Create next recursion iteration set
		if len(final_set[0]  ) != 3:
				lowerCAmelCase__   = final_set[0]
				lowerCAmelCase__   = []
				lowerCAmelCase__   = []
				for row in final_set[1::]:
						current_first_column.append(row[0]  )
						next_iteration.append(row[1::]  )
				lowerCAmelCase__   = simplify(lowerCamelCase__  )
				for i in range(len(lowerCamelCase__  )  ):
						resultant[i].insert(0      ,	current_first_column[i]  )
				resultant.insert(0      ,	lowerCamelCase__  )
				lowerCAmelCase__   = resultant
		return final_set







def 				_UpperCAmelCase		(							lowerCamelCase__  ):





		"""simple docstring"""




		if len(lowerCamelCase__  ) == 0:
				raise IndexError("""solve_simultaneous() requires n lists of length n+1"""  )
		lowerCAmelCase__   = len(lowerCamelCase__  ) + 1
		if any(len(lowerCamelCase__  ) != _length for item in equations  ):
				raise IndexError("""solve_simultaneous() requires n lists of length n+1"""  )
		for row in equations:
				if any(not isinstance(lowerCamelCase__      ,	(int, float)  ) for column in row  ):
						raise ValueError("""solve_simultaneous() requires lists of integers"""  )
		if len(lowerCamelCase__  ) == 1:
				return [equations[0][-1] / equations[0][0]]
		lowerCAmelCase__   = equations.copy()
		if any(0 in row for row in data_set  ):
				lowerCAmelCase__   = data_set.copy()
				lowerCAmelCase__   = []
				for row_index, row in enumerate(lowerCamelCase__  ):
						if 0 not in row:
								lowerCAmelCase__   = data_set.pop(lowerCamelCase__  )
								break
				if not full_row:
						raise ValueError("""solve_simultaneous() requires at least 1 full equation"""  )
				data_set.insert(0      ,	lowerCamelCase__  )
		lowerCAmelCase__   = data_set.copy()
		lowerCAmelCase__   = simplify(lowerCamelCase__  )
		lowerCAmelCase__   = simplified[::-1]
		lowerCAmelCase__   = []
		for row in simplified:
				lowerCAmelCase__   = row[-1]
				if not solutions:
						if row[-2] == 0:
								solutions.append(0  )
								continue
						solutions.append(current_solution / row[-2]  )
						continue
				lowerCAmelCase__   = row.copy()[: len(lowerCamelCase__  ) - 1 :]
				while temp_row[0] == 0:
						temp_row.pop(0  )
				if len(lowerCamelCase__  ) == 0:
						solutions.append(0  )
						continue
				lowerCAmelCase__   = temp_row[1::]
				lowerCAmelCase__   = temp_row[::-1]
				for column_index, column in enumerate(lowerCamelCase__  ):
						current_solution -= column * solutions[column_index]
				solutions.append(lowerCamelCase__  )
		lowerCAmelCase__   = []
		for item in solutions:
				final.append(float(round(lowerCamelCase__      ,	5  )  )  )
		return final[::-1]


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			__lowerCAmelCase     :				Optional[Any]    				=    [
			    [2, 1, 1, 1, 1, 4],
			    [1, 2, 1, 1, 1, 5],
			    [1, 1, 2, 1, 1, 6],
			    [1, 1, 1, 2, 1, 7],
			    [1, 1, 1, 1, 2, 8],
			]
			print(solve_simultaneous(eq))
			print(solve_simultaneous([[4, 2]]))





"""simple docstring"""




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







def 				_UpperCAmelCase		(							lowerCamelCase__      ,	lowerCamelCase__      ,	lowerCamelCase__      ,	lowerCamelCase__      ,	lowerCamelCase__      ,	lowerCamelCase__  ):





		"""simple docstring"""




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

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

						# degree to radiant
						lowerCAmelCase__   = theta / 180 * np.pi
						lowerCAmelCase__   = np.cos(_theta  )
						lowerCAmelCase__   = np.sin(_theta  )

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

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

						# fill kernel
						lowerCAmelCase__   = 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
			__lowerCAmelCase     :				Tuple    				=    imread("../image_data/lena.jpg")
			# turn image in gray scale value
			__lowerCAmelCase     :				List[str]    				=    cvtColor(img, COLOR_BGR2GRAY)

			# Apply multiple Kernel to detect edges
			__lowerCAmelCase     :				Union[str, Any]    				=    np.zeros(gray.shape[:2])
			for theta in [0, 30, 60, 90, 1_20, 1_50]:
						__lowerCAmelCase     :				Union[str, Any]    				=    gabor_filter_kernel(10, 8, theta, 10, 0, 0)
						out += filteraD(gray, CV_8UC3, kernel_aa)
			__lowerCAmelCase     :				Optional[int]    				=    out / out.max() * 2_55
			__lowerCAmelCase     :				Tuple    				=    out.astype(np.uinta)

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

			waitKey(0)




