'''simple docstring'''





from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray





def      lowerCAmelCase_    ( snake_case_	:			float ,   snake_case_	:			float ,   snake_case_	:			bool = False      )   ->				list[float]:


     '''simple docstring'''




     if radian_mode:
          return [magnitude * cos(__lowerCamelCase      ), magnitude * sin(__lowerCamelCase      )]
     return [magnitude * cos(radians(__lowerCamelCase      )      ), magnitude * sin(radians(__lowerCamelCase      )      )]





def      lowerCAmelCase_    ( snake_case_	:			NDArray[floataa] ,   snake_case_	:			NDArray[floataa] ,   snake_case_	:			float = 10**-1      )   ->				bool:


     '''simple docstring'''




     UpperCAmelCase_	   =       cross(__lowerCamelCase ,   __lowerCamelCase      )
     UpperCAmelCase_	   =       sum(__lowerCamelCase      )
     return abs(__lowerCamelCase      ) < eps


if __name__ == "__main__":
    # Test to check if it works
    SCREAMING_SNAKE_CASE_:					str  =array(
        [
            polar_force(7_18.4, 1_80 - 30),
            polar_force(8_79.54, 45),
            polar_force(1_00, -90),
        ]
    )

    SCREAMING_SNAKE_CASE_:					int  =array([[0, 0], [0, 0], [0, 0]])

    assert in_static_equilibrium(forces, location)

    # Problem 1 in image_data/2D_problems.jpg
    SCREAMING_SNAKE_CASE_:					List[str]  =array(
        [
            polar_force(30 * 9.81, 15),
            polar_force(2_15, 1_80 - 45),
            polar_force(2_64, 90 - 30),
        ]
    )

    SCREAMING_SNAKE_CASE_:					List[Any]  =array([[0, 0], [0, 0], [0, 0]])

    assert in_static_equilibrium(forces, location)

    # Problem in image_data/2D_problems_1.jpg
    SCREAMING_SNAKE_CASE_:					str  =array([[0, -20_00], [0, -12_00], [0, 1_56_00], [0, -1_24_00]])

    SCREAMING_SNAKE_CASE_:					str  =array([[0, 0], [6, 0], [10, 0], [12, 0]])

    assert in_static_equilibrium(forces, location)

    import doctest

    doctest.testmod()





'''simple docstring'''





import inspect
from typing import List, Optional, Tuple, Union

import torch

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




class 	__A				(			UpperCamelCase__     ):



    def __init__(self   :   Union[str, Any]       ,      __a   :   VQModel       ,      __a   :   UNetaDModel       ,      __a   :   DDIMScheduler			):
         super().__init__()
         self.register_modules(vqvae=__a       ,      unet=__a       ,      scheduler=__a			)






    @torch.no_grad()
    def __call__(self   :   str       ,      __a   :   int = 1       ,      __a   :   Optional[Union[torch.Generator, List[torch.Generator]]] = None       ,      __a   :   float = 0.0       ,      __a   :   int = 50       ,      __a   :   Optional[str] = "pil"       ,      __a   :   bool = True       ,      **__a   :   Optional[int]       ,      ):
         UpperCAmelCase_	   =       randn_tensor(
             (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)       ,      generator=__a       ,      )
         UpperCAmelCase_	   =       latents.to(self.device			)

         # scale the initial noise by the standard deviation required by the scheduler
         UpperCAmelCase_	   =       latents * self.scheduler.init_noise_sigma

         self.scheduler.set_timesteps(__a			)

         # prepare extra kwargs for the scheduler step, since not all schedulers have the same signature
         UpperCAmelCase_	   =       "eta" in set(inspect.signature(self.scheduler.step			).parameters.keys()			)

         UpperCAmelCase_	   =       {}
         if accepts_eta:
              UpperCAmelCase_	   =       eta

         for t in self.progress_bar(self.scheduler.timesteps			):
              UpperCAmelCase_	   =       self.scheduler.scale_model_input(__a       ,      __a			)
              # predict the noise residual
              UpperCAmelCase_	   =       self.unet(__a       ,      __a			).sample
              # compute the previous noisy sample x_t -> x_t-1
              UpperCAmelCase_	   =       self.scheduler.step(__a       ,      __a       ,      __a       ,      **__a			).prev_sample

         # decode the image latents with the VAE
         UpperCAmelCase_	   =       self.vqvae.decode(__a			).sample

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

         if not return_dict:
              return (image,)

         return ImagePipelineOutput(images=__a			)




