


def    snake_case_     (  snake_case			,							snake_case     )  ->				Tuple:
       # "extended trapezoidal rule"
       # int(f) = dx/2 * (f1 + 2f2 + ... + fn)
       lowercase__:   List[Any]  			=   (boundary[1] - boundary[0]) / steps
       lowercase__:   Tuple  			=   boundary[0]
       lowercase__:   int  			=   boundary[1]
       lowercase__:   List[Any]  			=   make_points(snake_case			,							snake_case			,							snake_case     )
       lowercase__:   Union[str, Any]  			=   0.0
       y += (h / 2.0) * f(snake_case     )
       for i in x_i:
              # print(i)
              y += h * f(snake_case     )
       y += (h / 2.0) * f(snake_case     )
       return y




def    snake_case_     (  snake_case			,							snake_case			,							snake_case     )  ->				Dict:
       lowercase__:   int  			=   a + h
       while x < (b - h):
              yield x
              lowercase__:   Any  			=   x + h




def    snake_case_     (  snake_case     )  ->				Dict:  # enter your function here
       lowercase__:   Tuple  			=   (x - 0) * (x - 0)
       return y




def    snake_case_     (  )  ->				Tuple:
       lowercase__:   List[str]  			=   0.0  # Lower bound of integration
       lowercase__:   Any  			=   1.0  # Upper bound of integration
       lowercase__:   Tuple  			=   1_0.0  # define number of steps or resolution
       lowercase__:   Dict  			=   [a, b]  # define boundary of integration
       lowercase__:   Union[str, Any]  			=   method_a(snake_case			,							snake_case     )
       print(f'y = {y}'     )


if __name__ == "__main__":
 main()






from math import acos, sin
from typing import List, Tuple, Union

import numpy as np
import torch
from PIL import Image

from ...models import AutoencoderKL, UNetaDConditionModel
from ...schedulers import DDIMScheduler, DDPMScheduler
from ...utils import randn_tensor
from ..pipeline_utils import AudioPipelineOutput, BaseOutput, DiffusionPipeline, ImagePipelineOutput
from .mel import Mel





class   __a			(    __UpperCamelCase      ):
 __lowercase :							Any        = ['vqvae']
 def __init__(   self				, lowerCAmelCase__				, lowerCAmelCase__				, lowerCAmelCase__				, lowerCAmelCase__				, )					->				Union[str, Any]:




        '''simple docstring'''
        super().__init__()
        self.register_modules(unet=lowerCAmelCase__				, scheduler=lowerCAmelCase__				, mel=lowerCAmelCase__				, vqvae=lowerCAmelCase__ )
 def 		SCREAMING_SNAKE_CASE__   (   self )					->				int:




        '''simple docstring'''
        return 50 if isinstance(self.scheduler				, lowerCAmelCase__ ) else 1_000
 @torch.no_grad()
 def __call__(   self				, lowerCAmelCase__ = 1				, lowerCAmelCase__ = None				, lowerCAmelCase__ = None				, lowerCAmelCase__ = 0				, lowerCAmelCase__ = 0				, lowerCAmelCase__ = None				, lowerCAmelCase__ = None				, lowerCAmelCase__ = 0				, lowerCAmelCase__ = 0				, lowerCAmelCase__ = None				, lowerCAmelCase__ = 0				, lowerCAmelCase__ = None				, lowerCAmelCase__ = None				, lowerCAmelCase__=True				, )					->				Union[
     Union[AudioPipelineOutput, ImagePipelineOutput],
     Tuple[List[Image.Image], Tuple[int, List[np.ndarray]]],
 ]:




        '''simple docstring'''
        lowercase__:   Union[str, Any]  			=   steps or self.get_default_steps()
        self.scheduler.set_timesteps(lowerCAmelCase__ )
        lowercase__:   Optional[int]  			=   step_generator or generator
        # For backwards compatibility
        if type(self.unet.config.sample_size ) == int:
               lowercase__:   Optional[int]  			=   (self.unet.config.sample_size, self.unet.config.sample_size)
        if noise is None:
               lowercase__:   List[str]  			=   randn_tensor(
                   (
                       batch_size,
                       self.unet.config.in_channels,
                       self.unet.config.sample_size[0],
                       self.unet.config.sample_size[1],
                   )				, generator=lowerCAmelCase__				, device=self.device				, )
        lowercase__:   List[Any]  			=   noise
        lowercase__:   int  			=   None

        if audio_file is not None or raw_audio is not None:
               self.mel.load_audio(lowerCAmelCase__				, lowerCAmelCase__ )
               lowercase__:   int  			=   self.mel.audio_slice_to_image(lowerCAmelCase__ )
               lowercase__:   int  			=   np.frombuffer(input_image.tobytes()				, dtype='uint8' ).reshape(
                   (input_image.height, input_image.width) )
               lowercase__:   str  			=   (input_image / 255) * 2 - 1
               lowercase__:   Union[str, Any]  			=   torch.tensor(input_image[np.newaxis, :, :]				, dtype=torch.float ).to(self.device )

               if self.vqvae is not None:
                      lowercase__:   Optional[int]  			=   self.vqvae.encode(torch.unsqueeze(lowerCAmelCase__				, 0 ) ).latent_dist.sample(
                          generator=lowerCAmelCase__ )[0]
                      lowercase__:   Dict  			=   self.vqvae.config.scaling_factor * input_images

               if start_step > 0:
                      lowercase__:   List[Any]  			=   self.scheduler.add_noise(lowerCAmelCase__				, lowerCAmelCase__				, self.scheduler.timesteps[start_step - 1] )

               lowercase__:   str  			=   (
                   self.unet.config.sample_size[1] * self.mel.get_sample_rate() / self.mel.x_res / self.mel.hop_length
               )
               lowercase__:   Dict  			=   int(mask_start_secs * pixels_per_second )
               lowercase__:   Tuple  			=   int(mask_end_secs * pixels_per_second )
               lowercase__:   List[Any]  			=   self.scheduler.add_noise(lowerCAmelCase__				, lowerCAmelCase__				, torch.tensor(self.scheduler.timesteps[start_step:] ) )

        for step, t in enumerate(self.progress_bar(self.scheduler.timesteps[start_step:] ) ):
               if isinstance(self.unet				, lowerCAmelCase__ ):
                      lowercase__:   Union[str, Any]  			=   self.unet(lowerCAmelCase__				, lowerCAmelCase__				, lowerCAmelCase__ )['sample']
               else:
                      lowercase__:   Optional[Any]  			=   self.unet(lowerCAmelCase__				, lowerCAmelCase__ )['sample']

               if isinstance(self.scheduler				, lowerCAmelCase__ ):
                      lowercase__:   List[str]  			=   self.scheduler.step(
                          model_output=lowerCAmelCase__				, timestep=lowerCAmelCase__				, sample=lowerCAmelCase__				, eta=lowerCAmelCase__				, generator=lowerCAmelCase__				, )['prev_sample']
               else:
                      lowercase__:   int  			=   self.scheduler.step(
                          model_output=lowerCAmelCase__				, timestep=lowerCAmelCase__				, sample=lowerCAmelCase__				, generator=lowerCAmelCase__				, )['prev_sample']

               if mask is not None:
                      if mask_start > 0:
                             lowercase__:   List[Any]  			=   mask[:, step, :, :mask_start]
                      if mask_end > 0:
                             lowercase__:   Optional[int]  			=   mask[:, step, :, -mask_end:]

        if self.vqvae is not None:
               # 0.18215 was scaling factor used in training to ensure unit variance
               lowercase__:   Union[str, Any]  			=   1 / self.vqvae.config.scaling_factor * images
               lowercase__:   Optional[Any]  			=   self.vqvae.decode(lowerCAmelCase__ )['sample']

        lowercase__:   Dict  			=   (images / 2 + 0.5).clamp(0				, 1 )
        lowercase__:   List[Any]  			=   images.cpu().permute(0				, 2				, 3				, 1 ).numpy()
        lowercase__:   int  			=   (images * 255).round().astype('uint8' )
        lowercase__:   Optional[Any]  			=   list(
            (Image.fromarray(_[:, :, 0] ) for _ in images)
            if images.shape[3] == 1
            else (Image.fromarray(lowerCAmelCase__				, mode='RGB' ).convert('L' ) for _ in images) )

        lowercase__:   Dict  			=   [self.mel.image_to_audio(lowerCAmelCase__ ) for _ in images]
        if not return_dict:
               return images, (self.mel.get_sample_rate(), audios)

        return BaseOutput(**AudioPipelineOutput(np.array(lowerCAmelCase__ )[:, np.newaxis, :] )				, **ImagePipelineOutput(lowerCAmelCase__ ) )
 @torch.no_grad()
 def 		SCREAMING_SNAKE_CASE__   (   self				, lowerCAmelCase__				, lowerCAmelCase__ = 50 )					->				np.ndarray:




        '''simple docstring'''
        assert isinstance(self.scheduler				, lowerCAmelCase__ )
        self.scheduler.set_timesteps(lowerCAmelCase__ )
        lowercase__:   List[str]  			=   np.array(
            [np.frombuffer(image.tobytes()				, dtype='uint8' ).reshape((1, image.height, image.width) ) for image in images] )
        lowercase__:   str  			=   (sample / 255) * 2 - 1
        lowercase__:   str  			=   torch.Tensor(lowerCAmelCase__ ).to(self.device )

        for t in self.progress_bar(torch.flip(self.scheduler.timesteps				, (0,) ) ):
               lowercase__:   Union[str, Any]  			=   t - self.scheduler.config.num_train_timesteps // self.scheduler.num_inference_steps
               lowercase__:   Optional[Any]  			=   self.scheduler.alphas_cumprod[t]
               lowercase__:   str  			=   (
                   self.scheduler.alphas_cumprod[prev_timestep]
                   if prev_timestep >= 0
                   else self.scheduler.final_alpha_cumprod
               )
               lowercase__:   str  			=   1 - alpha_prod_t
               lowercase__:   int  			=   self.unet(lowerCAmelCase__				, lowerCAmelCase__ )['sample']
               lowercase__:   int  			=   (1 - alpha_prod_t_prev) ** 0.5 * model_output
               lowercase__:   Optional[int]  			=   (sample - pred_sample_direction) * alpha_prod_t_prev ** (-0.5)
               lowercase__:   Any  			=   sample * alpha_prod_t ** 0.5 + beta_prod_t ** 0.5 * model_output

        return sample
 @staticmethod
 def 		SCREAMING_SNAKE_CASE__   (   lowerCAmelCase__				, lowerCAmelCase__				, lowerCAmelCase__ )					->				torch.Tensor:




        '''simple docstring'''
        lowercase__:   Any  			=   acos(torch.dot(torch.flatten(lowerCAmelCase__ )				, torch.flatten(lowerCAmelCase__ ) ) / torch.norm(lowerCAmelCase__ ) / torch.norm(lowerCAmelCase__ ) )
        return sin((1 - alpha) * theta ) * xa / sin(lowerCAmelCase__ ) + sin(alpha * theta ) * xa / sin(lowerCAmelCase__ )


