






"""simple docstring"""





def     __lowercase					(    a :				list[list] )					->					list[list]:
      __snake_case      :    Dict  			=current_set.copy()
      for row_index, row in enumerate(a ):
            __snake_case      :    Union[str, Any]  			=row[0]
            for column_index, column in enumerate(a ):
                  if magnitude == 0:
                        __snake_case      :    str  			=column
                        continue
                  __snake_case      :    Union[str, Any]  			=column / magnitude
    # Subtract to cancel term
      __snake_case      :    List[Any]  			=current_set[0]
      __snake_case      :    Dict  			=[first_row]
      __snake_case      :    List[Any]  			=current_set[1::]
      for row in current_set:
            __snake_case      :    Any  			=[]
            # If first term is 0, it is already in form we want, so we preserve it
            if row[0] == 0:
                  final_set.append(a )
                  continue
            for column_index in range(len(a ) ):
                  temp_row.append(first_row[column_index] - row[column_index] )
            final_set.append(a )
      # Create next recursion iteration set
      if len(final_set[0] ) != 3:
            __snake_case      :    Dict  			=final_set[0]
            __snake_case      :    Optional[Any]  			=[]
            __snake_case      :    List[str]  			=[]
            for row in final_set[1::]:
                  current_first_column.append(row[0] )
                  next_iteration.append(row[1::] )
            __snake_case      :    str  			=simplify(a )
            for i in range(len(a ) ):
                  resultant[i].insert(0       ,		current_first_column[i] )
            resultant.insert(0       ,		a )
            __snake_case      :    List[str]  			=resultant
      return final_set



def     __lowercase					(    a :				list[list] )					->					list:
      if len(a ) == 0:
            raise IndexError('''solve_simultaneous() requires n lists of length n+1''' )
      __snake_case      :    int  			=len(a ) + 1
      if any(len(a ) != _length for item in equations ):
            raise IndexError('''solve_simultaneous() requires n lists of length n+1''' )
      for row in equations:
            if any(not isinstance(a       ,		(int, float) ) for column in row ):
                  raise ValueError('''solve_simultaneous() requires lists of integers''' )
      if len(a ) == 1:
            return [equations[0][-1] / equations[0][0]]
      __snake_case      :    str  			=equations.copy()
      if any(0 in row for row in data_set ):
            __snake_case      :    int  			=data_set.copy()
            __snake_case      :    Tuple  			=[]
            for row_index, row in enumerate(a ):
                  if 0 not in row:
                        __snake_case      :    Any  			=data_set.pop(a )
                        break
            if not full_row:
                  raise ValueError('''solve_simultaneous() requires at least 1 full equation''' )
            data_set.insert(0       ,		a )
      __snake_case      :    str  			=data_set.copy()
      __snake_case      :    str  			=simplify(a )
      __snake_case      :    Union[str, Any]  			=simplified[::-1]
      __snake_case      :    list  			=[]
      for row in simplified:
            __snake_case      :    List[Any]  			=row[-1]
            if not solutions:
                  if row[-2] == 0:
                        solutions.append(0 )
                        continue
                  solutions.append(current_solution / row[-2] )
                  continue
            __snake_case      :    int  			=row.copy()[: len(a ) - 1 :]
            while temp_row[0] == 0:
                  temp_row.pop(0 )
            if len(a ) == 0:
                  solutions.append(0 )
                  continue
            __snake_case      :    List[Any]  			=temp_row[1::]
            __snake_case      :    int  			=temp_row[::-1]
            for column_index, column in enumerate(a ):
                  current_solution -= column * solutions[column_index]
            solutions.append(a )
      __snake_case      :    Any  			=[]
      for item in solutions:
            final.append(float(round(a       ,		5 ) ) )
      return final[::-1]


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    UpperCamelCase_	:				Union[str, Any]										= [
        [2, 1, 1, 1, 1, 4],
        [1, 2, 1, 1, 1, 5],
        [1, 1, 2, 1, 1, 6],
        [1, 1, 1, 2, 1, 7],
        [1, 1, 1, 1, 2, 8],
    ]
    print(solve_simultaneous(eq))
    print(solve_simultaneous([[4, 2]]))










"""simple docstring"""





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      _lowercase (     lowerCAmelCase						):
      _a   :     Optional[Any]								=   ['''vqvae''']


      def __init__(    self				:	Optional[Any]							,   a				:	AutoencoderKL							,   a				:	UNetaDConditionModel							,   a				:	Mel							,   a				:	Union[DDIMScheduler, DDPMScheduler]							,   ):





            """simple docstring"""







            super().__init__()
            self.register_modules(unet=a							,   scheduler=a							,   mel=a							,   vqvae=a						)


      def _UpperCamelCase						(    self				:	Any						):





            """simple docstring"""







            return 5_0 if isinstance(self.scheduler							,   a						) else 1_0_0_0


      @torch.no_grad()
      def __call__(    self				:	Optional[int]							,   a				:	int = 1							,   a				:	str = None							,   a				:	np.ndarray = None							,   a				:	int = 0							,   a				:	int = 0							,   a				:	int = None							,   a				:	torch.Generator = None							,   a				:	float = 0							,   a				:	float = 0							,   a				:	torch.Generator = None							,   a				:	float = 0							,   a				:	torch.Tensor = None							,   a				:	torch.Tensor = None							,   a				:	Optional[int]=True							,   ):





            """simple docstring"""







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

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

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

                  if start_step > 0:
                        __snake_case      :    str  			=self.scheduler.add_noise(a							,   a							,   self.scheduler.timesteps[start_step - 1]						)

                  __snake_case      :    Optional[Any]  			=(
                      self.unet.config.sample_size[1] * self.mel.get_sample_rate() / self.mel.x_res / self.mel.hop_length
                  )
                  __snake_case      :    int  			=int(mask_start_secs * pixels_per_second						)
                  __snake_case      :    Any  			=int(mask_end_secs * pixels_per_second						)
                  __snake_case      :    Union[str, Any]  			=self.scheduler.add_noise(a							,   a							,   torch.tensor(self.scheduler.timesteps[start_step:]						)						)

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

                  if isinstance(self.scheduler							,   a						):
                        __snake_case      :    List[str]  			=self.scheduler.step(
                            model_output=a							,   timestep=a							,   sample=a							,   eta=a							,   generator=a							,   )['''prev_sample''']
                  else:
                        __snake_case      :    List[Any]  			=self.scheduler.step(
                            model_output=a							,   timestep=a							,   sample=a							,   generator=a							,   )['''prev_sample''']

                  if mask is not None:
                        if mask_start > 0:
                              __snake_case      :    Any  			=mask[:, step, :, :mask_start]
                        if mask_end > 0:
                              __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
                  __snake_case      :    str  			=1 / self.vqvae.config.scaling_factor * images
                  __snake_case      :    Optional[int]  			=self.vqvae.decode(a						)['''sample''']

            __snake_case      :    int  			=(images / 2 + 0.5).clamp(0							,   1						)
            __snake_case      :    Optional[Any]  			=images.cpu().permute(0							,   2							,   3							,   1						).numpy()
            __snake_case      :    Optional[int]  			=(images * 2_5_5).round().astype('''uint8'''						)
            __snake_case      :    Tuple  			=list(
                (Image.fromarray(_[:, :, 0]						) for _ in images)
                if images.shape[3] == 1
                else (Image.fromarray(a							,   mode='''RGB'''						).convert('''L'''						) for _ in images)						)

            __snake_case      :    Union[str, Any]  			=[self.mel.image_to_audio(a						) for _ in images]
            if not return_dict:
                  return images, (self.mel.get_sample_rate(), audios)

            return BaseOutput(**AudioPipelineOutput(np.array(a						)[:, np.newaxis, :]						)							,   **ImagePipelineOutput(a						)						)


      @torch.no_grad()
      def _UpperCamelCase						(    self				:	int							,   a				:	List[Image.Image]							,   a				:	int = 5_0						):





            """simple docstring"""







            assert isinstance(self.scheduler							,   a						)
            self.scheduler.set_timesteps(a						)
            __snake_case      :    Dict  			=np.array(
                [np.frombuffer(image.tobytes()							,   dtype='''uint8'''						).reshape((1, image.height, image.width)						) for image in images]						)
            __snake_case      :    Any  			=(sample / 2_5_5) * 2 - 1
            __snake_case      :    Any  			=torch.Tensor(a						).to(self.device						)

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

            return sample







      @staticmethod
      def _UpperCamelCase						(    a				:	torch.Tensor							,   a				:	torch.Tensor							,   a				:	float						):





            """simple docstring"""







            __snake_case      :    List[Any]  			=acos(torch.dot(torch.flatten(a						)							,   torch.flatten(a						)						) / torch.norm(a						) / torch.norm(a						)						)
            return sin((1 - alpha) * theta						) * xa / sin(a						) + sin(alpha * theta						) * xa / sin(a						)


