


from __future__ import annotations

from math import pi, pow



def 			_lowerCAmelCase						(							lowerCAmelCase_							:int | float							)->float:
   '''simple docstring'''






   if side_length < 0:
      raise ValueError("vol_cube() only accepts non-negative values"							)
   return pow(lowerCAmelCase_		,						3							)



def 			_lowerCAmelCase						(							lowerCAmelCase_							:float		,						lowerCAmelCase_							:float							)->float:
   '''simple docstring'''






   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(lowerCAmelCase_		,						2							) * (3 * radius - height)



def 			_lowerCAmelCase						(							lowerCAmelCase_							:float		,						lowerCAmelCase_							:float		,						lowerCAmelCase_							:float							)->float:
   '''simple docstring'''






   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(lowerCAmelCase_		,						lowerCAmelCase_							)							)

   snake_case_					    =					(
       (radius_a - radius_a + centers_distance)
       * (radius_a + radius_a - centers_distance)
       / (2 * centers_distance)
   )
   snake_case_					    =					(
       (radius_a - radius_a + centers_distance)
       * (radius_a + radius_a - centers_distance)
       / (2 * centers_distance)
   )

   return vol_spherical_cap(lowerCAmelCase_		,						lowerCAmelCase_							) + vol_spherical_cap(lowerCAmelCase_		,						lowerCAmelCase_							)



def 			_lowerCAmelCase						(							lowerCAmelCase_							:float		,						lowerCAmelCase_							:float		,						lowerCAmelCase_							:float							)->float:
   '''simple docstring'''






   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(lowerCAmelCase_		,						lowerCAmelCase_							)							)

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



def 			_lowerCAmelCase						(							lowerCAmelCase_							:float		,						lowerCAmelCase_							:float		,						lowerCAmelCase_							:float							)->float:
   '''simple docstring'''






   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						(							lowerCAmelCase_							:float		,						lowerCAmelCase_							:float							)->float:
   '''simple docstring'''






   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						(							lowerCAmelCase_							:float		,						lowerCAmelCase_							:float							)->float:
   '''simple docstring'''






   if height < 0 or radius < 0:
      raise ValueError("vol_right_circ_cone() only accepts non-negative values"							)
   return pi * pow(lowerCAmelCase_		,						2							) * height / 3.0



def 			_lowerCAmelCase						(							lowerCAmelCase_							:float		,						lowerCAmelCase_							:float							)->float:
   '''simple docstring'''






   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						(							lowerCAmelCase_							:float		,						lowerCAmelCase_							:float							)->float:
   '''simple docstring'''






   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						(							lowerCAmelCase_							:float							)->float:
   '''simple docstring'''






   if radius < 0:
      raise ValueError("vol_sphere() only accepts non-negative values"							)
   # Volume is 4/3 * pi * radius cubed
   return 4 / 3 * pi * pow(lowerCAmelCase_		,						3							)



def 			_lowerCAmelCase						(							lowerCAmelCase_							:float							)->float:
   '''simple docstring'''






   if radius < 0:
      raise ValueError("vol_hemisphere() only accepts non-negative values"							)
   # Volume is radius cubed * pi * 2/3
   return pow(lowerCAmelCase_		,						3							) * pi * 2 / 3



def 			_lowerCAmelCase						(							lowerCAmelCase_							:float		,						lowerCAmelCase_							:float							)->float:
   '''simple docstring'''






   if height < 0 or radius < 0:
      raise ValueError("vol_circular_cylinder() only accepts non-negative values"							)
   # Volume is radius squared * height * pi
   return pow(lowerCAmelCase_		,						2							) * height * pi



def 			_lowerCAmelCase						(							lowerCAmelCase_							:float		,						lowerCAmelCase_							:float		,						lowerCAmelCase_							:float							)->float:
   '''simple docstring'''






   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(lowerCAmelCase_		,						2							) - pow(lowerCAmelCase_		,						2							)) * height



def 			_lowerCAmelCase						(							lowerCAmelCase_							:float		,						lowerCAmelCase_							:float		,						lowerCAmelCase_							:float							)->float:
   '''simple docstring'''






   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(lowerCAmelCase_		,						2							) + pow(lowerCAmelCase_		,						2							) + radius_a * radius_a)
   )



def 			_lowerCAmelCase						(							lowerCAmelCase_							:float		,						lowerCAmelCase_							:float							)->float:
   '''simple docstring'''






   if torus_radius < 0 or tube_radius < 0:
      raise ValueError("vol_torus() only accepts non-negative values"							)
   return 2 * pow(lowerCAmelCase_		,						2							) * torus_radius * pow(lowerCAmelCase_		,						2							)



def 			_lowerCAmelCase						(							)->str:
   '''simple docstring'''






   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()








from typing import List, Optional, Tuple, Union

import torch

from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput


class     __lowerCAmelCase     ( a					):






  """simple docstring"""





  def __init__(     self       :       List[str]    ,				_lowerCAmelCase       :       Optional[Any]    ,				_lowerCAmelCase       :       Tuple  )   -> str:




     """simple docstring"""
     super().__init__()
     self.register_modules(unet=_lowerCAmelCase    ,				scheduler=_lowerCAmelCase  )



  @torch.no_grad()
  def __call__(     self       :       Tuple    ,				_lowerCAmelCase       :       int = 1    ,				_lowerCAmelCase       :       Optional[Union[torch.Generator, List[torch.Generator]]] = None    ,				_lowerCAmelCase       :       int = 1_0_0_0    ,				_lowerCAmelCase       :       Optional[str] = "pil"    ,				_lowerCAmelCase       :       bool = True    ,				)   -> Union[ImagePipelineOutput, Tuple]:




     """simple docstring"""
     # Sample gaussian noise to begin loop
     if isinstance(self.unet.config.sample_size    ,				_lowerCAmelCase  ):
        snake_case_					    =					(
            batch_size,
            self.unet.config.in_channels,
            self.unet.config.sample_size,
            self.unet.config.sample_size,
        )
     else:
        snake_case_					    =					(batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)

     if self.device.type == "mps":
        # randn does not work reproducibly on mps
        snake_case_					    =					randn_tensor(_lowerCAmelCase    ,				generator=_lowerCAmelCase  )
        snake_case_					    =					image.to(self.device  )
     else:
        snake_case_					    =					randn_tensor(_lowerCAmelCase    ,				generator=_lowerCAmelCase    ,				device=self.device  )

     # set step values
     self.scheduler.set_timesteps(_lowerCAmelCase  )

     for t in self.progress_bar(self.scheduler.timesteps  ):
        # 1. predict noise model_output
        snake_case_					    =					self.unet(_lowerCAmelCase    ,				_lowerCAmelCase  ).sample

        # 2. compute previous image: x_t -> x_t-1
        snake_case_					    =					self.scheduler.step(_lowerCAmelCase    ,				_lowerCAmelCase    ,				_lowerCAmelCase    ,				generator=_lowerCAmelCase  ).prev_sample

     snake_case_					    =					(image / 2 + 0.5).clamp(0    ,				1  )
     snake_case_					    =					image.cpu().permute(0    ,				2    ,				3    ,				1  ).numpy()
     if output_type == "pil":
        snake_case_					    =					self.numpy_to_pil(_lowerCAmelCase  )

     if not return_dict:
        return (image,)

     return ImagePipelineOutput(images=_lowerCAmelCase  )




