






import logging

import numpy as np
import pytest
from scipy.linalg import eigh

logging.basicConfig(level=logging.INFO, format="""%(message)s""")





def 				snake_case  (     lowerCamelCase					):




	'''simple docstring'''







	return input_array.reshape((input_array.size, 1)					)





def 				snake_case  (     lowerCamelCase				,  lowerCamelCase				,  lowerCamelCase					):




	'''simple docstring'''







	__lowercase             =  np.nan
	for i in range(lowerCamelCase					):
		__lowercase             =  features[:, labels == i]
		__lowercase             =  data.mean(1					)
		# Centralize the data of class i
		__lowercase             =  data - column_reshape(lowerCamelCase					)
		if i > 0:
			# If covariance_sum is not None
			covariance_sum += np.dot(lowerCamelCase				,  centered_data.T					)
		else:
			# If covariance_sum is np.nan (i.e. first loop)
			__lowercase             =  np.dot(lowerCamelCase				,  centered_data.T					)

	return covariance_sum / features.shape[1]





def 				snake_case  (     lowerCamelCase				,  lowerCamelCase				,  lowerCamelCase					):




	'''simple docstring'''







	__lowercase             =  features.mean(1					)
	__lowercase             =  np.nan
	for i in range(lowerCamelCase					):
		__lowercase             =  features[:, labels == i]
		__lowercase             =  data.shape[1]
		__lowercase             =  data.mean(1					)
		if i > 0:
			# If covariance_sum is not None
			covariance_sum += device_data * np.dot(
			    column_reshape(lowerCamelCase					) - column_reshape(lowerCamelCase					)				,  (column_reshape(lowerCamelCase					) - column_reshape(lowerCamelCase					)).T				,  )
		else:
			# If covariance_sum is np.nan (i.e. first loop)
			__lowercase             =  device_data * np.dot(
			    column_reshape(lowerCamelCase					) - column_reshape(lowerCamelCase					)				,  (column_reshape(lowerCamelCase					) - column_reshape(lowerCamelCase					)).T				,  )

	return covariance_sum / features.shape[1]





def 				snake_case  (     lowerCamelCase				,  lowerCamelCase					):




	'''simple docstring'''







	if features.any():
		__lowercase             =  features.mean(1					)
		# Center the dataset
		__lowercase             =  features - np.reshape(lowerCamelCase				,  (data_mean.size, 1)					)
		__lowercase             =  np.dot(lowerCamelCase				,  centered_data.T					) / features.shape[1]
		__lowercase       ,						__lowercase             =  np.linalg.eigh(lowerCamelCase					)
		# Take all the columns in the reverse order (-1), and then takes only the first
		__lowercase             =  eigenvectors[:, ::-1][:, 0:dimensions]
		# Project the database on the new space
		__lowercase             =  np.dot(filtered_eigenvectors.T				,  lowerCamelCase					)
		logging.info("""Principal Component Analysis computed"""					)

		return projected_data
	else:
		logging.basicConfig(level=logging.ERROR				,  format="""%(message)s"""				,  force=lowerCamelCase					)
		logging.error("""Dataset empty"""					)
		raise AssertionError





def 				snake_case  (     lowerCamelCase				,  lowerCamelCase				,  lowerCamelCase				,  lowerCamelCase					):




	'''simple docstring'''







	assert classes > dimensions

	# Check if features have been already loaded
	if features.any:
		__lowercase       ,						__lowercase             =  eigh(
		    covariance_between_classes(lowerCamelCase				,  lowerCamelCase				,  lowerCamelCase					)				,  covariance_within_classes(lowerCamelCase				,  lowerCamelCase				,  lowerCamelCase					)				,  )
		__lowercase             =  eigenvectors[:, ::-1][:, :dimensions]
		__lowercase       ,						__lowercase       ,						__lowercase             =  np.linalg.svd(lowerCamelCase					)
		__lowercase             =  svd_matrix[:, 0:dimensions]
		__lowercase             =  np.dot(filtered_svd_matrix.T				,  lowerCamelCase					)
		logging.info("""Linear Discriminant Analysis computed"""					)

		return projected_data
	else:
		logging.basicConfig(level=logging.ERROR				,  format="""%(message)s"""				,  force=lowerCamelCase					)
		logging.error("""Dataset empty"""					)
		raise AssertionError





def 				snake_case  (     ):




	'''simple docstring'''







	__lowercase             =  np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]					)
	__lowercase             =  np.array([0, 0, 0, 1, 1]					)
	__lowercase             =  2
	__lowercase             =  2

	# Assert that the function raises an AssertionError if dimensions > classes
	with pytest.raises(lowerCamelCase					) as error_info:
		__lowercase             =  linear_discriminant_analysis(
		    lowerCamelCase				,  lowerCamelCase				,  lowerCamelCase				,  lowerCamelCase					)
		if isinstance(lowerCamelCase				,  np.ndarray					):
			raise AssertionError(
			    """Did not raise AssertionError for dimensions > classes"""					)
		assert error_info.type is AssertionError





def 				snake_case  (     ):




	'''simple docstring'''







	__lowercase             =  np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]					)
	__lowercase             =  2
	__lowercase             =  np.array([[6.92820323, 8.66025404, 10.39230485], [3.0, 3.0, 3.0]]					)

	with pytest.raises(lowerCamelCase					) as error_info:
		__lowercase             =  principal_component_analysis(lowerCamelCase				,  lowerCamelCase					)
		if not np.allclose(lowerCamelCase				,  lowerCamelCase					):
			raise AssertionError
		assert error_info.type is AssertionError


if __name__ == "__main__":
						import doctest

						doctest.testmod()









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





def 				snake_case  (     lowerCamelCase				,  lowerCamelCase				,  lowerCamelCase				,  lowerCamelCase				,  lowerCamelCase				,  lowerCamelCase					):




	'''simple docstring'''







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

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

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

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

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

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

						# Apply multiple Kernel to detect edges
						__UpperCamelCase      :      Union[str, Any]     						=						np.zeros(gray.shape[:2])
						for theta in [0, 30, 60, 90, 120, 150]:
												__UpperCamelCase      :      Tuple     						=						gabor_filter_kernel(10, 8, theta, 10, 0, 0)
												out += filteraD(gray, CV_8UC3, kernel_aa)
						__UpperCamelCase      :      List[str]     						=						out / out.max() * 255
						__UpperCamelCase      :      List[str]     						=						out.astype(np.uinta)

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

						waitKey(0)

