



import cva
import numpy as np

from digital_image_processing.filters.convolve import img_convolve
from digital_image_processing.filters.sobel_filter import sobel_filter

_lowercase				:					str     					=1_80




def    UpperCAmelCase					(  lowercase__						:					List[str]				,					lowercase__						:					str	):



			'''simple docstring'''





			a__					=  k_size // 2
			a__				,       a__					=  np.mgrid[0 - center : k_size - center, 0 - center : k_size - center]
			a__					=  (
			    1
			    / (2 * np.pi * sigma)
			    * np.exp(-(np.square(lowercase__	) + np.square(lowercase__	)) / (2 * np.square(lowercase__	))	)
			)
			return g




def    UpperCAmelCase					(  lowercase__						:					Optional[int]				,					lowercase__						:					Any				,					lowercase__						:					Union[str, Any]	):



			'''simple docstring'''





			a__					=  np.zeros(lowercase__	)

			for row in range(1				,					image_shape[0] - 1	):
						for col in range(1				,					image_shape[1] - 1	):
									a__					=  gradient_direction[row, col]

									if (
									    0 <= direction < PI / 8
									    or 15 * PI / 8 <= direction <= 2 * PI
									    or 7 * PI / 8 <= direction <= 9 * PI / 8
									):
												a__					=  sobel_grad[row, col - 1]
												a__					=  sobel_grad[row, col + 1]
												if sobel_grad[row, col] >= w and sobel_grad[row, col] >= e:
															a__					=  sobel_grad[row, col]

									elif (
									    PI / 8 <= direction < 3 * PI / 8
									    or 9 * PI / 8 <= direction < 11 * PI / 8
									):
												a__					=  sobel_grad[row + 1, col - 1]
												a__					=  sobel_grad[row - 1, col + 1]
												if sobel_grad[row, col] >= sw and sobel_grad[row, col] >= ne:
															a__					=  sobel_grad[row, col]

									elif (
									    3 * PI / 8 <= direction < 5 * PI / 8
									    or 11 * PI / 8 <= direction < 13 * PI / 8
									):
												a__					=  sobel_grad[row - 1, col]
												a__					=  sobel_grad[row + 1, col]
												if sobel_grad[row, col] >= n and sobel_grad[row, col] >= s:
															a__					=  sobel_grad[row, col]

									elif (
									    5 * PI / 8 <= direction < 7 * PI / 8
									    or 13 * PI / 8 <= direction < 15 * PI / 8
									):
												a__					=  sobel_grad[row - 1, col - 1]
												a__					=  sobel_grad[row + 1, col + 1]
												if sobel_grad[row, col] >= nw and sobel_grad[row, col] >= se:
															a__					=  sobel_grad[row, col]

			return destination




def    UpperCAmelCase					(  lowercase__						:					Dict				,					lowercase__						:					Dict				,					lowercase__						:					List[str]				,					lowercase__						:					Optional[int]				,					lowercase__						:					List[str]				,					lowercase__						:					Optional[Any]	):



			'''simple docstring'''





			for row in range(1				,					image_shape[0] - 1	):
						for col in range(1				,					image_shape[1] - 1	):
									if destination[row, col] >= threshold_high:
												a__					=  strong
									elif destination[row, col] <= threshold_low:
												a__					=  0
									else:
												a__					=  weak




def    UpperCAmelCase					(  lowercase__						:					Dict				,					lowercase__						:					Dict				,					lowercase__						:					Optional[Any]				,					lowercase__						:					str	):



			'''simple docstring'''





			for row in range(1				,					image_shape[0]	):
						for col in range(1				,					image_shape[1]	):
									if destination[row, col] == weak:
												if 255 in (
												    destination[row, col + 1],
												    destination[row, col - 1],
												    destination[row - 1, col],
												    destination[row + 1, col],
												    destination[row - 1, col - 1],
												    destination[row + 1, col - 1],
												    destination[row - 1, col + 1],
												    destination[row + 1, col + 1],
												):
															a__					=  strong
												else:
															a__					=  0




def    UpperCAmelCase					(  lowercase__						:					List[str]				,					lowercase__						:					Any=15				,					lowercase__						:					Dict=30				,					lowercase__						:					List[Any]=128				,					lowercase__						:					Any=255	):



			'''simple docstring'''





			a__					=  img_convolve(lowercase__				,					gen_gaussian_kernel(9				,					sigma=1.4	)	)
			# get the gradient and degree by sobel_filter
			a__				,       a__					=  sobel_filter(lowercase__	)
			a__					=  PI + np.radadeg(lowercase__	)

			a__					=  suppress_non_maximum(image.shape				,					lowercase__				,					lowercase__	)

			detect_high_low_threshold(
			    image.shape				,					lowercase__				,					lowercase__				,					lowercase__				,					lowercase__				,					lowercase__	)

			track_edge(image.shape				,					lowercase__				,					lowercase__				,					lowercase__	)

			return destination


if __name__ == "__main__":
	# read original image in gray mode
	_lowercase				:					List[str]     					=cva.imread(R"""../image_data/lena.jpg""", 0)
	# canny edge detection
	_lowercase				:					str     					=canny(lena)
	cva.imshow("""canny""", canny_destination)
	cva.waitKey(0)






from typing import Any

import numpy as np




def    UpperCAmelCase					(  lowercase__						:					np.ndarray	):



			'''simple docstring'''





			assert np.shape(lowercase__	)[0] == np.shape(lowercase__	)[1]

			# If matrix not symmetric, exit right away.
			if np.allclose(lowercase__				,					matrix.T	) is False:
						return False

			# Get eigenvalues and eignevectors for a symmetric matrix.
			a__				,       a__					=  np.linalg.eigh(lowercase__	)

			# Check sign of all eigenvalues.
			# np.all returns a value of type np.bool_
			return bool(np.all(eigen_values > 0	)	)




def    UpperCAmelCase					(  lowercase__						:					int	):



			'''simple docstring'''





			a__					=  np.random.randn(lowercase__				,					lowercase__	)
			a__					=  np.dot(lowercase__				,					random_matrix.T	)
			assert _is_matrix_spd(lowercase__	)
			return spd_matrix




def    UpperCAmelCase					(  lowercase__						:					np.ndarray				,					lowercase__						:					np.ndarray				,					lowercase__						:					int = 1000				,					lowercase__						:					float = 1e-8				,					):



			'''simple docstring'''





			assert np.shape(lowercase__	)[0] == np.shape(lowercase__	)[1]
			assert np.shape(lowercase__	)[0] == np.shape(lowercase__	)[0]
			assert _is_matrix_spd(lowercase__	)

			# Initialize solution guess, residual, search direction.
			a__					=  np.zeros((np.shape(lowercase__	)[0], 1)	)
			a__					=  np.copy(lowercase__	)
			a__					=  np.copy(lowercase__	)

			# Set initial errors in solution guess and residual.
			a__					=  1e9
			a__					=  1e9
			a__					=  1e9

			# Set iteration counter to threshold number of iterations.
			a__					=  0

			while error > tol:
						# Save this value so we only calculate the matrix-vector product once.
						a__					=  np.dot(lowercase__				,					lowercase__	)

						# The main algorithm.

						# Update search direction magnitude.
						a__					=  np.dot(ra.T				,					lowercase__	) / np.dot(pa.T				,					lowercase__	)
						# Update solution guess.
						a__					=  xa + alpha * pa
						# Calculate new residual.
						a__					=  ra - alpha * w
						# Calculate new Krylov subspace scale.
						a__					=  np.dot(r.T				,					lowercase__	) / np.dot(ra.T				,					lowercase__	)
						# Calculate new A conjuage search direction.
						a__					=  r + beta * pa

						# Calculate errors.
						a__					=  np.linalg.norm(r - ra	)
						a__					=  np.linalg.norm(x - xa	)
						a__					=  np.maximum(lowercase__				,					lowercase__	)

						# Update variables.
						a__					=  np.copy(lowercase__	)
						a__					=  np.copy(lowercase__	)
						a__					=  np.copy(lowercase__	)

						# Update number of iterations.
						iterations += 1
						if iterations > max_iterations:
									break

			return x




def    UpperCAmelCase					(  ):



			'''simple docstring'''





			a__					=  3
			a__					=  _create_spd_matrix(lowercase__	)
			a__					=  np.random.randn(lowercase__				,					1	)
			a__					=  np.dot(lowercase__				,					lowercase__	)

			# Numpy solution.
			a__					=  np.linalg.solve(lowercase__				,					lowercase__	)

			# Our implementation.
			a__					=  conjugate_gradient(lowercase__				,					lowercase__	)

			# Ensure both solutions are close to x_true (and therefore one another).
			assert np.linalg.norm(x_numpy - x_true	) <= 1e-6
			assert np.linalg.norm(x_conjugate_gradient - x_true	) <= 1e-6


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	test_conjugate_gradient()

