'''simple docstring'''




from __future__ import annotations

from math import pi, pow



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



def 						__snake_case (       lowerCAmelCase       :     float      ,  lowerCAmelCase       :     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(lowerCAmelCase      ,  2			) * (3 * radius - height)



def 						__snake_case (       lowerCAmelCase       :     float      ,  lowerCAmelCase       :     float      ,  lowerCAmelCase       :     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(lowerCAmelCase      ,  lowerCAmelCase			)			)

 __UpperCAmelCase         =					(
     (radius_a - radius_a + centers_distance)
     * (radius_a + radius_a - centers_distance)
     / (2 * centers_distance)
 )
 __UpperCAmelCase         =					(
     (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 						__snake_case (       lowerCAmelCase       :     float      ,  lowerCAmelCase       :     float      ,  lowerCAmelCase       :     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(lowerCAmelCase      ,  lowerCAmelCase			)			)

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



def 						__snake_case (       lowerCAmelCase       :     float      ,  lowerCAmelCase       :     float      ,  lowerCAmelCase       :     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 						__snake_case (       lowerCAmelCase       :     float      ,  lowerCAmelCase       :     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 						__snake_case (       lowerCAmelCase       :     float      ,  lowerCAmelCase       :     float			):
 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 						__snake_case (       lowerCAmelCase       :     float      ,  lowerCAmelCase       :     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 						__snake_case (       lowerCAmelCase       :     float      ,  lowerCAmelCase       :     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 						__snake_case (       lowerCAmelCase       :     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(lowerCAmelCase      ,  3			)



def 						__snake_case (       lowerCAmelCase       :     float			):
 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 						__snake_case (       lowerCAmelCase       :     float      ,  lowerCAmelCase       :     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(lowerCAmelCase      ,  2			) * height * pi



def 						__snake_case (       lowerCAmelCase       :     float      ,  lowerCAmelCase       :     float      ,  lowerCAmelCase       :     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(lowerCAmelCase      ,  2			) - pow(lowerCAmelCase      ,  2			)) * height



def 						__snake_case (       lowerCAmelCase       :     float      ,  lowerCAmelCase       :     float      ,  lowerCAmelCase       :     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(lowerCAmelCase      ,  2			) + pow(lowerCAmelCase      ,  2			) + radius_a * radius_a)
 )



def 						__snake_case (       lowerCAmelCase       :     float      ,  lowerCAmelCase       :     float			):
 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 						__snake_case (       ):
 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 Union

import torch
from PIL import Image
from torchvision import transforms as tfms
from tqdm.auto import tqdm
from transformers import CLIPTextModel, CLIPTokenizer

from diffusers import (
    AutoencoderKL,
    DDIMScheduler,
    DiffusionPipeline,
    LMSDiscreteScheduler,
    PNDMScheduler,
    UNetaDConditionModel,
)

class   _lowercase(     _lowerCamelCase				):



   """simple docstring"""





   def __init__(							self:    List[str]			,a:    AutoencoderKL			,a:    CLIPTextModel			,a:    CLIPTokenizer			,a:    UNetaDConditionModel			,a:    Union[PNDMScheduler, LMSDiscreteScheduler, DDIMScheduler]			,):
    super().__init__()

    self.register_modules(vae=a			,text_encoder=a			,tokenizer=a			,unet=a			,scheduler=a	)





   def 			snake_case	(							self:    Union[str, Any]			,a:    Any	):
    with torch.no_grad():
     __UpperCAmelCase         =					self.vae.encode(tfms.ToTensor()(a	).unsqueeze(0	).to(self.device	) * 2 - 1	)
     __UpperCAmelCase         =					0.18215 * latent.latent_dist.sample()
    return latent





   def 			snake_case	(							self:    Any			,a:    List[str]	):
    __UpperCAmelCase         =					(1 / 0.18215) * latent
    with torch.no_grad():
     __UpperCAmelCase         =					self.vae.decode(a	).sample
    __UpperCAmelCase         =					(img / 2 + 0.5).clamp(0			,1	)
    __UpperCAmelCase         =					img.detach().cpu().permute(0			,2			,3			,1	).numpy()
    __UpperCAmelCase         =					(img * 255).round().astype('uint8'	)
    return Image.fromarray(img[0]	)





   def 			snake_case	(							self:    Any			,a:    str	):
    __UpperCAmelCase         =					self.tokenizer(
        a			,padding='max_length'			,max_length=self.tokenizer.model_max_length			,truncation=a			,return_tensors='pt'			,)

    __UpperCAmelCase         =					self.text_encoder(text_input.input_ids.to(self.device	)	)[0]

    __UpperCAmelCase         =					self.tokenizer(
        ''			,padding='max_length'			,max_length=self.tokenizer.model_max_length			,truncation=a			,return_tensors='pt'			,)

    __UpperCAmelCase         =					self.text_encoder(uncond_input.input_ids.to(self.device	)	)[0]

    return torch.cat([uncond_embedding, text_embedding]	)





   def __call__(							self:    Optional[Any]			,a:    Image.Image			,a:    str			,a:    float = 0.3			,a:    float = 0.6			,a:    float = 0.5			,a:    int = 42			,a:    int = 50			,a:    float = 7.5			,):
    __UpperCAmelCase         =					steps - int(kmin * steps	)
    __UpperCAmelCase         =					steps - int(kmax * steps	)

    __UpperCAmelCase         =					self.prep_text(a	)

    self.scheduler.set_timesteps(a	)

    __UpperCAmelCase  ,			__UpperCAmelCase         =					img.size
    __UpperCAmelCase         =					self.encode(a	)

    torch.manual_seed(a	)
    __UpperCAmelCase         =					torch.randn(
        (1, self.unet.config.in_channels, height // 8, width // 8)			,).to(self.device	)

    __UpperCAmelCase         =					self.scheduler.add_noise(
        a			,a			,timesteps=self.scheduler.timesteps[tmax]			,)

    __UpperCAmelCase         =					torch.cat([latents] * 2	)

    __UpperCAmelCase         =					self.scheduler.scale_model_input(a			,self.scheduler.timesteps[tmax]	)

    with torch.no_grad():
     __UpperCAmelCase         =					self.unet(
         a			,self.scheduler.timesteps[tmax]			,encoder_hidden_states=a			,).sample

    __UpperCAmelCase  ,			__UpperCAmelCase         =					pred.chunk(2	)
    __UpperCAmelCase         =					pred_uncond + guidance_scale * (pred_text - pred_uncond)

    __UpperCAmelCase         =					self.scheduler.step(a			,self.scheduler.timesteps[tmax]			,a	).prev_sample

    for i, t in enumerate(tqdm(self.scheduler.timesteps	)	):
     if i > tmax:
      if i < tmin:  # layout generation phase
       __UpperCAmelCase         =					self.scheduler.add_noise(
           a			,a			,timesteps=a			,)

       __UpperCAmelCase         =					(mix_factor * latents) + (
           1 - mix_factor
       ) * orig_latents  # interpolating between layout noise and conditionally generated noise to preserve layout sematics
       __UpperCAmelCase         =					torch.cat([input] * 2	)

      else:  # content generation phase
       __UpperCAmelCase         =					torch.cat([latents] * 2	)

      __UpperCAmelCase         =					self.scheduler.scale_model_input(a			,a	)

      with torch.no_grad():
       __UpperCAmelCase         =					self.unet(
           a			,a			,encoder_hidden_states=a			,).sample

      __UpperCAmelCase  ,			__UpperCAmelCase         =					pred.chunk(2	)
      __UpperCAmelCase         =					pred_uncond + guidance_scale * (pred_text - pred_uncond)

      __UpperCAmelCase         =					self.scheduler.step(a			,a			,a	).prev_sample

    return self.decode(a	)



