
'''simple docstring'''







from math import pi, sqrt, tan







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			float:
	if side_length < 0:
		raise ValueError('surface_area_cube() only accepts non-negative values'			)
	return 6 * side_length**2







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A    ,       __A			) ->			float:
	if length < 0 or breadth < 0 or height < 0:
		raise ValueError('surface_area_cuboid() only accepts non-negative values'			)
	return 2 * ((length * breadth) + (breadth * height) + (length * height))







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			float:
	if radius < 0:
		raise ValueError('surface_area_sphere() only accepts non-negative values'			)
	return 4 * pi * radius**2







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			float:
	if radius < 0:
		raise ValueError('surface_area_hemisphere() only accepts non-negative values'			)
	return 3 * pi * radius**2







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			float:
	if radius < 0 or height < 0:
		raise ValueError('surface_area_cone() only accepts non-negative values'			)
	return pi * radius * (radius + (height**2 + radius**2) ** 0.5)







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A    ,       __A			) ->			float:
	if radius_a < 0 or radius_a < 0 or height < 0:
		raise ValueError(
		    'surface_area_conical_frustum() only accepts non-negative values'			)
	_snake_case     		=	(height**2 + (radius_a - radius_a) ** 2) ** 0.5
	return pi * ((slant_height * (radius_a + radius_a)) + radius_a**2 + radius_a**2)







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			float:
	if radius < 0 or height < 0:
		raise ValueError('surface_area_cylinder() only accepts non-negative values'			)
	return 2 * pi * radius * (height + radius)







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			float:
	if torus_radius < 0 or tube_radius < 0:
		raise ValueError('surface_area_torus() only accepts non-negative values'			)
	if torus_radius < tube_radius:
		raise ValueError(
		    'surface_area_torus() does not support spindle or self intersecting tori'			)
	return 4 * pow(__A    ,       2			) * torus_radius * tube_radius







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			float:
	if length < 0 or width < 0:
		raise ValueError('area_rectangle() only accepts non-negative values'			)
	return length * width







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			float:
	if side_length < 0:
		raise ValueError('area_square() only accepts non-negative values'			)
	return side_length**2







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			float:
	if base < 0 or height < 0:
		raise ValueError('area_triangle() only accepts non-negative values'			)
	return (base * height) / 2







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A    ,       __A			) ->			float:
	if sidea < 0 or sidea < 0 or sidea < 0:
		raise ValueError('area_triangle_three_sides() only accepts non-negative values'			)
	elif sidea + sidea < sidea or sidea + sidea < sidea or sidea + sidea < sidea:
		raise ValueError('Given three sides do not form a triangle'			)
	_snake_case     		=	(sidea + sidea + sidea) / 2
	_snake_case     		=	sqrt(
	    semi_perimeter
	    * (semi_perimeter - sidea)
	    * (semi_perimeter - sidea)
	    * (semi_perimeter - sidea)			)
	return area







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			float:
	if base < 0 or height < 0:
		raise ValueError('area_parallelogram() only accepts non-negative values'			)
	return base * height







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A    ,       __A			) ->			float:
	if basea < 0 or basea < 0 or height < 0:
		raise ValueError('area_trapezium() only accepts non-negative values'			)
	return 1 / 2 * (basea + basea) * height







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			float:
	if radius < 0:
		raise ValueError('area_circle() only accepts non-negative values'			)
	return pi * radius**2







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			float:
	if radius_x < 0 or radius_y < 0:
		raise ValueError('area_ellipse() only accepts non-negative values'			)
	return pi * radius_x * radius_y







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			float:
	if diagonal_a < 0 or diagonal_a < 0:
		raise ValueError('area_rhombus() only accepts non-negative values'			)
	return 1 / 2 * diagonal_a * diagonal_a







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			float:
	if not isinstance(__A    ,       __A			) or sides < 3:
		raise ValueError(
		    'area_reg_polygon() only accepts integers greater than or \
equal to three as number of sides'			)
	elif length < 0:
		raise ValueError(
		    'area_reg_polygon() only accepts non-negative values as \
length of a side'			)
	return (sides * length**2) / (4 * tan(pi / sides			))
	return (sides * length**2) / (4 * tan(pi / sides			))


if __name__ == "__main__":
					import doctest

					doctest.testmod(verbose=True)  # verbose so we can see methods missing tests

					print("[DEMO] Areas of various geometric shapes: \n")
					print(F'''Rectangle: {area_rectangle(10, 20) = }''')
					print(F'''Square: {area_square(10) = }''')
					print(F'''Triangle: {area_triangle(10, 10) = }''')
					print(F'''Triangle: {area_triangle_three_sides(5, 12, 13) = }''')
					print(F'''Parallelogram: {area_parallelogram(10, 20) = }''')
					print(F'''Rhombus: {area_rhombus(10, 20) = }''')
					print(F'''Trapezium: {area_trapezium(10, 20, 30) = }''')
					print(F'''Circle: {area_circle(20) = }''')
					print(F'''Ellipse: {area_ellipse(10, 20) = }''')
					print("\nSurface Areas of various geometric shapes: \n")
					print(F'''Cube: {surface_area_cube(20) = }''')
					print(F'''Cuboid: {surface_area_cuboid(10, 20, 30) = }''')
					print(F'''Sphere: {surface_area_sphere(20) = }''')
					print(F'''Hemisphere: {surface_area_hemisphere(20) = }''')
					print(F'''Cone: {surface_area_cone(10, 20) = }''')
					print(F'''Conical Frustum: {surface_area_conical_frustum(10, 20, 30) = }''')
					print(F'''Cylinder: {surface_area_cylinder(10, 20) = }''')
					print(F'''Torus: {surface_area_torus(20, 10) = }''')
					print(F'''Equilateral Triangle: {area_reg_polygon(3, 10) = }''')
					print(F'''Square: {area_reg_polygon(4, 10) = }''')
					print(F'''Reqular Pentagon: {area_reg_polygon(5, 10) = }''')



'''simple docstring'''







from typing import Any

import numpy as np







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			bool:
	return np.array_equal(__A    ,       matrix.conjugate().T			)







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			Any:
	_snake_case     		=	v.conjugate().T
	_snake_case     		=	v_star.dot(__A			)
	assert isinstance(__A    ,       np.ndarray			)
	return (v_star_dot.dot(__A			)) / (v_star.dot(__A			))







def        SCREAMING_SNAKE_CASE__			(     ) ->			None:
	_snake_case     		=	np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]			)
	_snake_case     		=	np.array([[1], [2], [3]]			)
	assert is_hermitian(__A			), F'{a} is not hermitian.'
	print(rayleigh_quotient(__A    ,       __A			)			)

	_snake_case     		=	np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]			)
	assert is_hermitian(__A			), F'{a} is not hermitian.'
	assert rayleigh_quotient(__A    ,       __A			) == float(3			)


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					tests()

