





from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403






def     lowerCamelCase__			(__lowerCamelCase,       __lowerCamelCase,       __lowerCamelCase = "x",       __lowerCamelCase = 10**-10,       __lowerCamelCase = 1,       ):
     _SCREAMING_SNAKE_CASE       :	Any						    =							symbols(__lowerCamelCase	)
     _SCREAMING_SNAKE_CASE       :	Optional[Any]						    =							lambdify(__lowerCamelCase,       __lowerCamelCase	)
     _SCREAMING_SNAKE_CASE       :	Union[str, Any]						    =							lambdify(__lowerCamelCase,       diff(__lowerCamelCase,       __lowerCamelCase	)	)

     _SCREAMING_SNAKE_CASE       :	Optional[Any]						    =							starting_point

     while True:
          if diff_function(__lowerCamelCase	) != 0:
               _SCREAMING_SNAKE_CASE       :	Tuple						    =							prev_guess - multiplicity * func(__lowerCamelCase	) / diff_function(
                   __lowerCamelCase	)
          else:
               raise ZeroDivisionError("Could not find root"	) from None

          # Precision is checked by comparing the difference of consecutive guesses
          if abs(next_guess - prev_guess	) < precision:
               return next_guess

          _SCREAMING_SNAKE_CASE       :	Any						    =							next_guess


# Let's Execute
if __name__ == "__main__":
     # Find root of trigonometric function
     # Find value of pi
     print(f"The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}")

     # Find root of polynomial
     # Find fourth Root of 5
     print(f"The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5J)}")

     # Find value of e
     print(
         'The root of log(y) - 1 = 0 is ',
         f"{newton_raphson('log(y) - 1', 2, variable='y')}",
     )

     # Exponential Roots
     print(
         'The root of exp(x) - 1 = 0 is',
         f"{newton_raphson('exp(x) - 1', 10, precision=0.005)}",
     )

     # Find root of cos(x)
     print(f"The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}")






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 			lowerCAmelCase__( __lowercase    ):






       '''simple docstring'''


       __snake_case 			=    ['vqvae']




       def __init__(      self    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						)			->     Optional[Any]:
            super().__init__()
            self.register_modules(unet=__lowerCamelCase    ,						scheduler=__lowerCamelCase    ,						mel=__lowerCamelCase    ,						vqvae=__lowerCamelCase							)




       def     UpperCamelCase_			(      self							)			->     int:
            return 5_0 if isinstance(self.scheduler    ,						__lowerCamelCase							) else 1_0_0_0




       @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]]],
       ]:
            _SCREAMING_SNAKE_CASE       :	List[Any]						    =							steps or self.get_default_steps()
            self.scheduler.set_timesteps(__lowerCamelCase							)
            _SCREAMING_SNAKE_CASE       :	List[Any]						    =							step_generator or generator
            # For backwards compatibility
            if type(self.unet.config.sample_size							) == int:
                 _SCREAMING_SNAKE_CASE       :	Dict						    =							(self.unet.config.sample_size, self.unet.config.sample_size)
            if noise is None:
                 _SCREAMING_SNAKE_CASE       :	Tuple						    =							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    ,						)
            _SCREAMING_SNAKE_CASE       :	Any						    =							noise
            _SCREAMING_SNAKE_CASE       :	Optional[Any]						    =							None

            if audio_file is not None or raw_audio is not None:
                 self.mel.load_audio(__lowerCamelCase    ,						__lowerCamelCase							)
                 _SCREAMING_SNAKE_CASE       :	Tuple						    =							self.mel.audio_slice_to_image(__lowerCamelCase							)
                 _SCREAMING_SNAKE_CASE       :	str						    =							np.frombuffer(input_image.tobytes()    ,						dtype="uint8"							).reshape(
                     (input_image.height, input_image.width)							)
                 _SCREAMING_SNAKE_CASE       :	List[Any]						    =							(input_image / 2_5_5) * 2 - 1
                 _SCREAMING_SNAKE_CASE       :	Optional[int]						    =							torch.tensor(input_image[np.newaxis, :, :]    ,						dtype=torch.float							).to(self.device							)

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

                 if start_step > 0:
                      _SCREAMING_SNAKE_CASE       :	List[str]						    =							self.scheduler.add_noise(__lowerCamelCase    ,						__lowerCamelCase    ,						self.scheduler.timesteps[start_step - 1]							)

                 _SCREAMING_SNAKE_CASE       :	Dict						    =							(
                     self.unet.config.sample_size[1] * self.mel.get_sample_rate() / self.mel.x_res / self.mel.hop_length
                 )
                 _SCREAMING_SNAKE_CASE       :	Dict						    =							int(mask_start_secs * pixels_per_second							)
                 _SCREAMING_SNAKE_CASE       :	str						    =							int(mask_end_secs * pixels_per_second							)
                 _SCREAMING_SNAKE_CASE       :	List[str]						    =							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							):
                      _SCREAMING_SNAKE_CASE       :	str						    =							self.unet(__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase							)["sample"]
                 else:
                      _SCREAMING_SNAKE_CASE       :	List[str]						    =							self.unet(__lowerCamelCase    ,						__lowerCamelCase							)["sample"]

                 if isinstance(self.scheduler    ,						__lowerCamelCase							):
                      _SCREAMING_SNAKE_CASE       :	Tuple						    =							self.scheduler.step(
                          model_output=__lowerCamelCase    ,						timestep=__lowerCamelCase    ,						sample=__lowerCamelCase    ,						eta=__lowerCamelCase    ,						generator=__lowerCamelCase    ,						)["prev_sample"]
                 else:
                      _SCREAMING_SNAKE_CASE       :	Tuple						    =							self.scheduler.step(
                          model_output=__lowerCamelCase    ,						timestep=__lowerCamelCase    ,						sample=__lowerCamelCase    ,						generator=__lowerCamelCase    ,						)["prev_sample"]

                 if mask is not None:
                      if mask_start > 0:
                           _SCREAMING_SNAKE_CASE       :	Tuple						    =							mask[:, step, :, :mask_start]
                      if mask_end > 0:
                           _SCREAMING_SNAKE_CASE       :	Optional[Any]						    =							mask[:, step, :, -mask_end:]

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

            _SCREAMING_SNAKE_CASE       :	Tuple						    =							(images / 2 + 0.5).clamp(0    ,						1							)
            _SCREAMING_SNAKE_CASE       :	List[str]						    =							images.cpu().permute(0    ,						2    ,						3    ,						1							).numpy()
            _SCREAMING_SNAKE_CASE       :	int						    =							(images * 2_5_5).round().astype("uint8"							)
            _SCREAMING_SNAKE_CASE       :	Dict						    =							list(
                (Image.fromarray(_[:, :, 0]							) for _ in images)
                if images.shape[3] == 1
                else (Image.fromarray(__lowerCamelCase    ,						mode="RGB"							).convert("L"							) for _ in images)							)

            _SCREAMING_SNAKE_CASE       :	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     UpperCamelCase_			(      self    ,						__lowerCamelCase    ,						__lowerCamelCase = 5_0							)			->     np.ndarray:
            assert isinstance(self.scheduler    ,						__lowerCamelCase							)
            self.scheduler.set_timesteps(__lowerCamelCase							)
            _SCREAMING_SNAKE_CASE       :	Optional[Any]						    =							np.array(
                [np.frombuffer(image.tobytes()    ,						dtype="uint8"							).reshape((1, image.height, image.width)							) for image in images]							)
            _SCREAMING_SNAKE_CASE       :	Optional[Any]						    =							(sample / 2_5_5) * 2 - 1
            _SCREAMING_SNAKE_CASE       :	Optional[int]						    =							torch.Tensor(__lowerCamelCase							).to(self.device							)

            for t in self.progress_bar(torch.flip(self.scheduler.timesteps    ,						(0,)							)							):
                 _SCREAMING_SNAKE_CASE       :	Any						    =							t - self.scheduler.config.num_train_timesteps // self.scheduler.num_inference_steps
                 _SCREAMING_SNAKE_CASE       :	int						    =							self.scheduler.alphas_cumprod[t]
                 _SCREAMING_SNAKE_CASE       :	List[str]						    =							(
                     self.scheduler.alphas_cumprod[prev_timestep]
                     if prev_timestep >= 0
                     else self.scheduler.final_alpha_cumprod
                 )
                 _SCREAMING_SNAKE_CASE       :	Union[str, Any]						    =							1 - alpha_prod_t
                 _SCREAMING_SNAKE_CASE       :	List[Any]						    =							self.unet(__lowerCamelCase    ,						__lowerCamelCase							)["sample"]
                 _SCREAMING_SNAKE_CASE       :	Dict						    =							(1 - alpha_prod_t_prev) ** 0.5 * model_output
                 _SCREAMING_SNAKE_CASE       :	Any						    =							(sample - pred_sample_direction) * alpha_prod_t_prev ** (-0.5)
                 _SCREAMING_SNAKE_CASE       :	Union[str, Any]						    =							sample * alpha_prod_t ** 0.5 + beta_prod_t ** 0.5 * model_output

            return sample







       @staticmethod
       def     UpperCamelCase_			(      __lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase							)			->     torch.Tensor:
            _SCREAMING_SNAKE_CASE       :	Tuple						    =							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							)