


'''simple docstring'''







from __future__ import annotations

from math import pi, pow





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     int | float				)	->		float:
						if side_length < 0:
												raise ValueError('''vol_cube() only accepts non-negative values'''				)
						return pow(SCREAMING_SNAKE_CASE__,     3				)





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     float,     SCREAMING_SNAKE_CASE__ :     float				)	->		float:
						if height < 0 or radius < 0:
												raise ValueError('''vol_spherical_cap() only accepts non-negative values'''				)
						# Volume is 1/3 pi * height squared * (3 * radius - height)
						return 1 / 3 * pi * pow(SCREAMING_SNAKE_CASE__,     2				) * (3 * radius - height)





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     float,     SCREAMING_SNAKE_CASE__ :     float,     SCREAMING_SNAKE_CASE__ :     float				)	->		float:
						if radius_a < 0 or radius_a < 0 or centers_distance < 0:
												raise ValueError('''vol_spheres_intersect() only accepts non-negative values'''				)
						if centers_distance == 0:
												return vol_sphere(min(SCREAMING_SNAKE_CASE__,     SCREAMING_SNAKE_CASE__				)				)

						UpperCAmelCase_     : Dict         =					(
						    (radius_a - radius_a + centers_distance)
						    * (radius_a + radius_a - centers_distance)
						    / (2 * centers_distance)
						)
						UpperCAmelCase_     : Optional[Any]         =					(
						    (radius_a - radius_a + centers_distance)
						    * (radius_a + radius_a - centers_distance)
						    / (2 * centers_distance)
						)

						return vol_spherical_cap(SCREAMING_SNAKE_CASE__,     SCREAMING_SNAKE_CASE__				) + vol_spherical_cap(SCREAMING_SNAKE_CASE__,     SCREAMING_SNAKE_CASE__				)





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     float,     SCREAMING_SNAKE_CASE__ :     float,     SCREAMING_SNAKE_CASE__ :     float				)	->		float:

						if radius_a <= 0 or radius_a <= 0 or centers_distance < 0:
												raise ValueError(
												    '''vol_spheres_union() only accepts non-negative values, non-zero radius'''				)

						if centers_distance == 0:
												return vol_sphere(max(SCREAMING_SNAKE_CASE__,     SCREAMING_SNAKE_CASE__				)				)

						return (
						    vol_sphere(SCREAMING_SNAKE_CASE__				)
						    + vol_sphere(SCREAMING_SNAKE_CASE__				)
						    - vol_spheres_intersect(SCREAMING_SNAKE_CASE__,     SCREAMING_SNAKE_CASE__,     SCREAMING_SNAKE_CASE__				)
						)





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





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     float,     SCREAMING_SNAKE_CASE__ :     float				)	->		float:
						if height < 0 or area_of_base < 0:
												raise ValueError('''vol_cone() only accepts non-negative values'''				)
						return area_of_base * height / 3.0





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     float,     SCREAMING_SNAKE_CASE__ :     float				)	->		float:
						if height < 0 or radius < 0:
												raise ValueError('''vol_right_circ_cone() only accepts non-negative values'''				)
						return pi * pow(SCREAMING_SNAKE_CASE__,     2				) * height / 3.0





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





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     float,     SCREAMING_SNAKE_CASE__ :     float				)	->		float:
						if height < 0 or area_of_base < 0:
												raise ValueError('''vol_pyramid() only accepts non-negative values'''				)
						return area_of_base * height / 3.0





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     float				)	->		float:
						if radius < 0:
												raise ValueError('''vol_sphere() only accepts non-negative values'''				)
						# Volume is 4/3 * pi * radius cubed
						return 4 / 3 * pi * pow(SCREAMING_SNAKE_CASE__,     3				)





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     float				)	->		float:
						if radius < 0:
												raise ValueError('''vol_hemisphere() only accepts non-negative values'''				)
						# Volume is radius cubed * pi * 2/3
						return pow(SCREAMING_SNAKE_CASE__,     3				) * pi * 2 / 3





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     float,     SCREAMING_SNAKE_CASE__ :     float				)	->		float:
						if height < 0 or radius < 0:
												raise ValueError('''vol_circular_cylinder() only accepts non-negative values'''				)
						# Volume is radius squared * height * pi
						return pow(SCREAMING_SNAKE_CASE__,     2				) * height * pi





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     float,     SCREAMING_SNAKE_CASE__ :     float,     SCREAMING_SNAKE_CASE__ :     float				)	->		float:
						# Volume - (outer_radius squared - inner_radius squared) * pi * height
						if inner_radius < 0 or outer_radius < 0 or height < 0:
												raise ValueError(
												    '''vol_hollow_circular_cylinder() only accepts non-negative values'''				)
						if outer_radius <= inner_radius:
												raise ValueError('''outer_radius must be greater than inner_radius'''				)
						return pi * (pow(SCREAMING_SNAKE_CASE__,     2				) - pow(SCREAMING_SNAKE_CASE__,     2				)) * height





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     float,     SCREAMING_SNAKE_CASE__ :     float,     SCREAMING_SNAKE_CASE__ :     float				)	->		float:
						# Volume is 1/3 * pi * height *
						#           (radius_1 squared + radius_2 squared + radius_1 * radius_2)
						if radius_a < 0 or radius_a < 0 or height < 0:
												raise ValueError('''vol_conical_frustum() only accepts non-negative values'''				)
						return (
						    1
						    / 3
						    * pi
						    * height
						    * (pow(SCREAMING_SNAKE_CASE__,     2				) + pow(SCREAMING_SNAKE_CASE__,     2				) + radius_a * radius_a)
						)





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     float,     SCREAMING_SNAKE_CASE__ :     float				)	->		float:
						if torus_radius < 0 or tube_radius < 0:
												raise ValueError('''vol_torus() only accepts non-negative values'''				)
						return 2 * pow(SCREAMING_SNAKE_CASE__,     2				) * torus_radius * pow(SCREAMING_SNAKE_CASE__,     2				)





def     lowerCamelCase_ (					)	->		Any:
						print('''Volumes:'''				)
						print(F"""Cube: {vol_cube(2				) = }"""				)  # = 8
						print(F"""Cuboid: {vol_cuboid(2,     2,     2				) = }"""				)  # = 8
						print(F"""Cone: {vol_cone(2,     2				) = }"""				)  # ~= 1.33
						print(F"""Right Circular Cone: {vol_right_circ_cone(2,     2				) = }"""				)  # ~= 8.38
						print(F"""Prism: {vol_prism(2,     2				) = }"""				)  # = 4
						print(F"""Pyramid: {vol_pyramid(2,     2				) = }"""				)  # ~= 1.33
						print(F"""Sphere: {vol_sphere(2				) = }"""				)  # ~= 33.5
						print(F"""Hemisphere: {vol_hemisphere(2				) = }"""				)  # ~= 16.75
						print(F"""Circular Cylinder: {vol_circular_cylinder(2,     2				) = }"""				)  # ~= 25.1
						print(F"""Torus: {vol_torus(2,     2				) = }"""				)  # ~= 157.9
						print(F"""Conical Frustum: {vol_conical_frustum(2,     2,     4				) = }"""				)  # ~= 58.6
						print(F"""Spherical cap: {vol_spherical_cap(1,     2				) = }"""				)  # ~= 5.24
						print(F"""Spheres intersetion: {vol_spheres_intersect(2,     2,     1				) = }"""				)  # ~= 21.21
						print(F"""Spheres union: {vol_spheres_union(2,     2,     1				) = }"""				)  # ~= 45.81
						print(
						    F"""Hollow Circular Cylinder: {vol_hollow_circular_cylinder(1,     2,     3				) = }"""				)  # ~= 28.3


if __name__ == "__main__":
					main()












'''simple docstring'''







from typing import List, Optional, Tuple, Union

import torch

from ...models import UNetaDModel
from ...schedulers import PNDMScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput


class    __a (lowerCamelCase       ):
							__a   :				UNetaDModel
							__a   :				PNDMScheduler

							def __init__(							self							:       Optional[Any]    ,       __magic_name__							:       UNetaDModel    ,       __magic_name__							:       PNDMScheduler				)   ->    Tuple:







													"""simple docstring"""
													super().__init__()

													UpperCAmelCase_     : Optional[int]         =					PNDMScheduler.from_config(scheduler.config				)

													self.register_modules(unet=__magic_name__    ,       scheduler=__magic_name__				)



							@torch.no_grad()
							def __call__(							self							:       Union[str, Any]    ,       __magic_name__							:       int = 1    ,       __magic_name__							:       int = 50    ,       __magic_name__							:       Optional[Union[torch.Generator, List[torch.Generator]]] = None    ,       __magic_name__							:       Optional[str] = "pil"    ,       __magic_name__							:       bool = True    ,       **__magic_name__							:       Dict    ,       )   ->    Union[ImagePipelineOutput, Tuple]:







													"""simple docstring"""
													UpperCAmelCase_     : Dict         =					randn_tensor(
													    (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)    ,       generator=__magic_name__    ,       device=self.device    ,       )

													self.scheduler.set_timesteps(__magic_name__				)
													for t in self.progress_bar(self.scheduler.timesteps				):
																			UpperCAmelCase_     : Optional[int]         =					self.unet(__magic_name__    ,       __magic_name__				).sample

																			UpperCAmelCase_     : str         =					self.scheduler.step(__magic_name__    ,       __magic_name__    ,       __magic_name__				).prev_sample

													UpperCAmelCase_     : int         =					(image / 2 + 0.5).clamp(0    ,       1				)
													UpperCAmelCase_     : Any         =					image.cpu().permute(0    ,       2    ,       3    ,       1				).numpy()
													if output_type == "pil":
																			UpperCAmelCase_     : Optional[int]         =					self.numpy_to_pil(__magic_name__				)

													if not return_dict:
																			return (image,)

													return ImagePipelineOutput(images=__magic_name__				)





