



def      _A				(UpperCamelCase		:      float      ,			UpperCamelCase		:      float      ,			UpperCamelCase		:      float      ,			UpperCamelCase		:      float      ,			UpperCamelCase		:      float      ,			)  ->float:



			'''simple docstring'''







			lowerCamelCase__ :      List[str]								=		[redshift, radiation_density, matter_density, dark_energy]
			if any(p < 0 for p in parameters ):
						raise ValueError("""All input parameters must be positive""" )

			if any(p > 1 for p in parameters[1:4] ):
						raise ValueError("""Relative densities cannot be greater than one""" )
			else:
						lowerCamelCase__ :      Any								=		1 - (matter_density + radiation_density + dark_energy)

						lowerCamelCase__ :      Union[str, Any]								=		(
						    radiation_density * (redshift + 1) ** 4
						    + matter_density * (redshift + 1) ** 3
						    + curvature * (redshift + 1) ** 2
						    + dark_energy
						)

						lowerCamelCase__ :      Optional[Any]								=		hubble_constant * e_a ** (1 / 2)
						return hubble


if __name__ == "__main__":
				import doctest

				# run doctest
				doctest.testmod()

				# demo LCDM approximation
				_lowercase     							=						0.3

				print(
				    hubble_parameter(
				        hubble_constant=68.3,
				        radiation_density=1E-4,
				        matter_density=matter_density,
				        dark_energy=1 - matter_density,
				        redshift=0,
				    )
				)








from pathlib import Path

import cva
import numpy as np
from matplotlib import pyplot as plt






def      _A				(UpperCamelCase		:      np.ndarray      ,			UpperCamelCase		:      np.ndarray      ,			UpperCamelCase		:      np.ndarray      ,			UpperCamelCase		:      int      ,			UpperCamelCase		:      int )  ->np.ndarray:



			'''simple docstring'''







			lowerCamelCase__ :      Union[str, Any]								=		cva.getAffineTransform(UpperCamelCase      ,			UpperCamelCase )
			return cva.warpAffine(UpperCamelCase      ,			UpperCamelCase      ,			(rows, cols) )


if __name__ == "__main__":
				# read original image
				_lowercase     							=						cva.imread(
				    str(Path(__file__).resolve().parent.parent / '''image_data''' / '''lena.jpg''')
				)
				# turn image in gray scale value
				_lowercase     							=						cva.cvtColor(image, cva.COLOR_BGR2GRAY)
				# get image shape
				_lowercase							,				_lowercase     							=						gray_img.shape

				# set different points to rotate image
				_lowercase     							=						np.array([[50, 50], [2_00, 50], [50, 2_00]], np.floataa)
				_lowercase     							=						np.array([[10, 1_00], [2_00, 50], [1_00, 2_50]], np.floataa)
				_lowercase     							=						np.array([[50, 50], [1_50, 50], [1_20, 2_00]], np.floataa)
				_lowercase     							=						np.array([[10, 1_00], [80, 50], [1_80, 2_50]], np.floataa)

				# add all rotated images in a list
				_lowercase     							=						[
				    gray_img,
				    get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
				    get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
				    get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
				]

				# plot different image rotations
				_lowercase     							=						plt.figure(1)
				_lowercase     							=						['''Original''', '''Rotation 1''', '''Rotation 2''', '''Rotation 3''']
				for i, image in enumerate(images):
								plt.subplot(2, 2, i + 1), plt.imshow(image, '''gray''')
								plt.title(titles[i])
								plt.axis('''off''')
								plt.subplots_adjust(left=0.0, bottom=0.05, right=1.0, top=0.95)
				plt.show()



